All-Normal Dispersion Fiber Supercontinuum: Principles, Design, and Applications of a Unique White Light Source

Abstract

Ultrafast and low-noise supercontinuum (SC) sources based on all-normal dispersion (ANDi) fibers are emerging as key-enabling technology for new applications in spectroscopy, microscopy, and ultrafast photonics. In this chapter we review the fundamental physics, fiber designs, and applications of this unique white light source.

6.1 Introduction

Supercontinuum (SC) generation has become a scientific and commercial success story in the past decade driven by specialty optical fiber technology, in particular the invention of the photonic crystal fiber (PCF). From optical frequency metrology to biophotonic imaging—its unique spectral properties have revolutionized dozens of applications, many of which are described in this book. However, especially noise-sensitive or ultrafast photonics applications such as time-resolved spectroscopy and nonlinear pulse compression, which require not only a broad spectral bandwidth but also a coherent ultrashort pulse in the time domain, have struggled to incorporate fiber-based SC sources.

The reasons behind this initially surprising lack of adoption are the nonlinear dynamics in the most commonly used fiber design for SC generation when laser pulses with sub-picosecond durations are used for pumping. This “conventional” PCF design has a single zero dispersion wavelength (ZDW) closely matched to the central wavelength of the pump pulses, which are injected on the anomalous dispersion side and close to the ZDW. Figure 6.1 shows the group velocity dispersion (GVD) curve of such a fiber with ZDW at 780 nm. PCFs with similar dispersion designs are commercially available (e.g., NKT NL-PM-750) and frequently employed for pumping with Ti-sapphire femtosecond systems around 800 nm central wavelength. This anomalous dispersion pumping leads to rich soliton-driven nonlinear dynamics that maximize the obtainable bandwidth for a given pump source, but also cause the temporal breakup of the injected pump pulse and high sensitivity to noise (Dudley et al., 2006). Consequently, the generated SCs have highly complex temporal and spectral profiles that fluctuate from shot to shot under most pumping conditions, i.e., they have poor temporal coherence properties. This often plays a precision or resolution-limiting role, e.g., in applications that use the coherence as content in the acquired signal, such as coherent anti-Stokes Raman scattering (CARS) microscopy. Fiber-based SC sources using this conventional fiber design have therefore found only very limited use in ultrafast photonics and noise-sensitive applications.

Fig. 6.1

Typical fiber dispersion profiles for two different concepts of SC generation. The “conventional” PCF has a single zero dispersion wavelength (ZDW) at 780 nm and is intended for anomalous dispersion pumping around 800 nm. The ANDi PCF has a minimum dispersion wavelength (MDW) at 1050 nm and is optimized for normal dispersion pumping in the vicinity of this MDW. Both fiber designs can be adapted for a large range of different pump wavelengths and can cover the spectral regions from the UV to the mid-IR

It has long been known that temporal pulse breakup and noise amplification can largely be avoided when pumping occurs entirely in the normal dispersion regime. In fact, the first ever SC generation in 1970 was observed in the normal dispersion region of bulk glasses and crystals, as described by Alfano and Shapiro in their three seminal papers (Alfano & Shapiro, 1970a, b, c). In their pioneering work, they reported the formation of filaments with micrometer diameters and centimeter lengths due to self-focusing of the optical pulse, and could link the spectral broadening to nonlinear electronic cloud distortion in these filaments leading to self-phase modulation and four-wave mixing, which are highly deterministic processes and conserve both coherence and temporal integrity of the input pulse. The filaments work as a short “natural fiber”: they guide the light with extremely high intensity over extended lengths and therefore enhance the nonlinear interaction with the material. A review of SC generation in the normal dispersion region in a variety of condensed matter and gases can be found in Chaps. 1 and 2. After the realization of low-loss optical fibers, high intensity light pulses could be guided over much longer lengths than in bulk materials, which quickly led to the first fiber-based SC demonstrations (Lin & Stolen, 1976; Lin et al., 1978). In these cases pumping occurred also in the normal dispersion region, but long nanosecond pump pulse durations led to the occurrence of noise-seeded Raman scattering and resulted in the formation of incoherent SCs. When sub-picosecond pump pulses are employed, normal dispersion pumping of a fiber generates highly coherent SC pulses with properties very similar to the bulk case, but is associated with significantly reduced spectral bandwidths compared to anomalous dispersion pumping due to the steep slope of the dispersion curve and fast temporal broadening of the pump pulse. Hence, it has attracted only little attention after PCF technology was available.

This situation changed with the introduction of all-normal dispersion (ANDi) PCFs (Heidt, 2010). They are designed to have a flattened convex profile of normal GVD with a distinct point where the dispersion is closest to zero (minimum dispersion wavelength, MDW), but exhibit no ZDW in the region of interest. Figure 6.1 shows the dispersion curve of an ANDi PCF with MDW at 1050 nm. Similar to the ZDW in the conventional SC generation, the MDW should be located in the vicinity of the central pump wavelength to obtain maximum spectral broadening. The design shown here is therefore suited for pumping with ytterbium-doped fiber laser systems around 1 μm, and a commercial PCF with very similar dispersion profile is available, whose properties are discussed in more detail in Sect. 6.6.1. The low and flat dispersion minimizes temporal broadening of the input pulse and enables the generation of SCs with ultrabroad, more than octave-spanning bandwidths previously only known from anomalous dispersion pumping. At the same time, the SCs benefit from the typical characteristics of normal dispersion pumping, such as low-noise sensitivity, preservation of the injected ultrashort pump pulse, smooth and uniform spectral and temporal profiles, and the absence of spectral fine structure. Inspired by earlier work on PCFs with two closely spaced ZDWs (Hilligsøe et al., 2004; Falk et al., 2005) and solid circular fibers (Hori et al., 2004; Nishizawa & Takayanagi, 2007), the design of ANDi PCFs optimized for pumping at the emission wavelengths of the most commonly employed femtosecond pump sources and the first experimental demonstrations of octave-spanning coherent SC generation in these fibers was a breakthrough for the application of fiber-based SC sources in ultrafast photonics and noise-sensitive applications (Heidt, 2010; Heidt et al., 2011a; Hooper et al., 2011).

This chapter is dedicated to this relatively new concept of SC generation in optical fibers. We compare the characteristics of conventional, anomalously pumped SCs and ANDi SCs in detail using the fiber dispersion profiles of Fig. 6.1 as representative examples, explore the nonlinear dynamics of SC generation in the normal dispersion regime, examine the origins of noise in SC generation and how it can be suppressed by appropriate engineering of the fiber, give guidelines for the design of ANDi fibers for SC generation from the deep ultraviolet to the mid-infrared spectral regions, and review the most important experimental results and applications.

6.2 Brief Remarks About Numerical Modeling

The numerical simulations we use in this chapter are based on the generalized nonlinear Schrödinger equation (GNSLE) already introduced in Chap. 3 by Agrawal. In order to solve this equation, we use the Runge–Kutta in the interaction picture (RK4IP) integration method described by Hult (2008). We evaluate the GNLSE entirely in the frequency domain, because this approach was found to be numerically more accurate and efficient than the time-domain formulation (Rieznik et al., 2012). Additionally we employ an adaptive step size algorithm to improve computational speed and ensure sufficient accuracy as the pulse is propagated along the fiber (Heidt, 2009). A version of our simulation code that includes all these features in a MATLAB implementation is freely available for download under http://www.freeopticsproject.org.

In general, such pulse propagation models require the GVD and nonlinear characteristics of the fiber under investigation as input, which have to be obtained from the fiber’s geometry and material properties. Commercial packages are available for this, but in the special case of PCFs with hexagonal lattice geometry, an analytical method has been formulated to obtain dispersion and effective mode field diameter of the fundamental mode (Koshiba & Saitoh, 2004; Saitoh & Koshiba, 2005). This can serve as a good starting point for any researcher wishing to simulate nonlinear pulse propagation in microstructured optical fibers.

We assume propagation in a single transversal mode and a single polarization axis, and exclude any coupling between the fundamental polarization modes. These conditions are usually fulfilled in highly birefringent fibers when the pump pulse polarization is aligned to one of the principle fiber polarization axes. For low-birefringence fibers or for off-axis pumping linear and nonlinear mode coupling, effects can introduce additional nonlinear processes with important consequences for the noise and coherence properties of the generated SC. The origin of noise in SC generation dynamics and its control by appropriate fiber engineering are discussed in Sect. 6.5.

6.3 Supercontinuum Generation: Conventional vs. ANDi PCF

The objective of this section is to give an overview of the most important differences between ANDi and conventional SC generation, using numerical simulations and the two fibers introduced in Sect. 6.1 as representative examples. We focus on the nonlinear dynamics and properties that are most relevant from an applications point of view. For a more detailed discussion of the nonlinear effects responsible for spectral broadening, we refer to Chaps. 3 and 5 by Agrawal and Taylor for conventional fibers and Sect. 6.4 in this chapter for ANDi fibers. Of course, this can only be a qualitative comparison as the exact properties and dynamics of SC generation are sensitively dependent on both fiber and pump source parameters, and the specialized literature and numerical simulations should be consulted to ensure that the SC properties generated from a specific system fulfill the requirements of any particular application of interest.

A good first impression of the major differences between the SCs generated in ANDi and conventional PCF can be obtained from Fig. 6.2, which illustrates the SC development in the spectral and temporal domain in our two example fibers from Fig. 6.1 under realistic pumping conditions. In the conventional case, these simulations correspond to pumping in the anomalous dispersion region with pump pulses of 50 fs duration (FWHM) and 10 kW peak power at 850 nm. For the ANDi fiber, we also consider 50 fs pump pulses, but with higher peak power of 90 kW and centered at 1050 nm, close to the MDW of the fiber.

Fig. 6.2

Spectral and temporal evolution of the SC generation process in the PCFs of Fig. 6.1. (a) Conventional PCF, pumped at 850 nm with a 50 fs, 10 kW pulse. (b) ANDi PCF, pumped at 1050 nm with a 50 fs, 90 kW input pulse. Note the different scales (logarithmic vs. linear) used in these simulations, highlighting the superior flatness and smoothness of the ANDi SC

When the pump pulses are injected into the anomalous dispersion region of the conventional PCF, they form solitons of order N = (L _D/L _NL)^1/2 ≫ 1, where ${L}_D={T}_0^2/\left|{\beta}_2\right|$ and L _NL = (γP ₀)⁻¹ are the dispersive and nonlinear lengths introduced in Chap. 3, respectively, γ and β₂ are nonlinear and second-order dispersive parameter of the fiber, and T ₀ and P ₀ are duration and peak power of the pump pulse. For our specific example, N ≈ 6.6. Consequently, the initial dynamics of spectral broadening and temporal compression are very similar to the well-known high-order soliton evolution (Agrawal, 2007). However, the presence of higher-order dispersion and Raman scattering disturbs their ideal periodic evolution, and after approximately 1.5 cm, the pulses break up (Golovchenko et al., 1985). This process known as soliton fission is a crucial point in the nonlinear dynamics: the integrity of the input pulse is lost, and the temporal profile becomes extremely complex, consisting of a train of individual fundamental solitons and low-level dispersive waves (Herrmann et al., 2002). At the same time, the clean high-order soliton spectrum is transformed into a complex and highly structured SC as the solitons continuously self-frequency shift to longer wavelengths due to the Raman effect and transfer some of their energy to dispersive waves in the normal dispersion regime (Mitschke & Mollenauer, 1986; Gordon, 1986; Akhmediev & Karlsson, 1995; Gu et al., 2002). These dynamics are visualized in Fig. 6.2a, which highlight in particular the point of soliton fission, a spectrally and temporally shifting soliton and the dispersive waves. Of course, if the multi-pulse structure is undesirable in an application, it is possible to optimize the fiber length and interrupt the evolution just before soliton fission occurs. This has been studied in the context of soliton pulse compression, and a characteristic fission length could be determined that can be written approximately as (Chen & Kelley, 2002)

$$ {L}_{\mathrm{fiss}}\simeq {L}_D/N={T}_0{\left(\gamma {P}_0\left|{\beta}_2\right|\right)}^{-1/2} $$

(6.1)

At this point the high-order soliton assumes its maximum spectral bandwidth and shortest pulse duration. However, the necessity of matching the fiber parameters exactly to the pump source and the quickly deteriorating quality of the compressed pulse with increasing N have limited the practical relevance of this technique for ultrafast photonics. Significant parts of spectral bandwidth and power density in the spectral wings are only generated after soliton fission occurs, and hence it is an integral part of the conventional SC generation dynamics.

In contrast, these soliton dynamics are completely suppressed in the ANDi fiber. As shown in Fig. 6.2b, during the SC evolution, a single ultrashort pulse is maintained at all times, which temporally broadens from its original duration of 50 fs to about 1 ps at the end of the investigated 10 cm propagation distance as it experiences normal dispersion along the fiber. After the initial formation of spectral side lobes, which identify SPM as the dominant spectral broadening process (Stolen & Lin, 1978), the spectrum smoothens very quickly and acquires an almost uniform rectangular shape with flat top and steep edges. The broadening is concluded after approximately 5 cm, which can be attributed to the decreasing peak power as the pulse spreads temporally. Both spectral and temporal profiles do not acquire any significant fine structure. In fact, the SC generation process occurs so quickly and smoothly that the logarithmic scale chosen for the conventional case is inadequate here, and even the linear scale used in the plots in Fig. 6.2b reveals very little about the broadening dynamics. We therefore investigate the SC development in more detail in Sect. 6.4 using projected axis spectrograms. Yet it is clear already from this initial comparison that the ANDi fiber delivers much cleaner, less complex, and more uniform SC pulses than would be possible in the conventional case. This is achieved at the cost of requiring higher peak powers than soliton-driven SC generation to achieve comparable, octave-spanning spectral bandwidths. However, the required peak powers are within easy reach of modern femtosecond oscillators and therefore do not limit the applicability of this type of SC.

6.3.1 Spectro-Temporal Characteristics

A more intuitive insight into the SC characteristics can be obtained from Fig. 6.3, which displays the time–wavelength correlations of the SCs investigated in the previous section in a projected axis spectrogram. This is arguably the most complete visualization of any ultrafast optical waveform (Cohen, 1989). These snapshots of the SC pulses are taken after a propagation distance of 15 cm in the conventional PCF and 6 cm in ANDi PCF, when the respective spectral broadening processes are essentially concluded. The pump pulse parameters are identical to the previous section. The figure visually contrasts the relative simplicity of the ANDi SC pulse against the full spectro-temporal complexity of the conventional SC, and can be used to deduct the major advantages of ANDi over conventional SCs.

Fig. 6.3

Characteristic projected axis spectrograms of (a) conventional SC and (b) ANDi SC after the respective spectral broadening processes are concluded. Pump pulse parameters are identical to Fig. 6.2

Pulse Conservation

We have already seen in the previous section that the SC generation process in ANDi fibers conserves a single ultrashort pulse in the time domain. In addition we can now deduce from the spectrogram that it also maintains a well-defined and relatively simple phase distribution. In the purely normal dispersion of the ANDi fiber, the group velocity strictly increases with wavelength, and hence the wavelength distribution within the SC pulse is also strictly increasing: from the slower short wavelengths at the trailing pulse edge to the faster long wavelengths at the front of the pulse. At the center of the pulse near the MDW, where the dispersion is minimal, the pulse has a nearly linear chirp, with increasing nonlinear contributions for wavelengths located in the pulse wings.

This is in sharp contrast to the significantly more complex temporal characteristics of the conventional SC. Here wavelength components at or near the ZDW are the first to arrive at any given position along the fiber. All other radiation experiences a higher group index and hence is delayed with respect to that at the ZDW (Knight & Wadsworth, 2010). Consequently, the spectrogram takes on a “U” shape with a normal (top) and anomalous (bottom) dispersion arm. Radiation in normal and anomalous dispersion arms can therefore temporally overlap and create interference structures and fast oscillations, as shown in the highlighted section between 0.8 and 1.1 ps. The individual solitons originating from the soliton fission process are readily identifiable as compact objects in the spectrogram, while the dispersive waves in the normal dispersion arm can be linked to low-level pedestals traveling in between the solitons and at the trailing edge of the pulse. The spectral phase follows the intrinsic fiber group index profile, but contains significant fine structure as well as distinct flat regions of wavelength-independent spectral phase across the fundamental solitons (Dudley & Coen, 2004).

Spectral Uniformity

A large part of the fine structure in the conventional SC spectrum can be linked to the distinct spectral signatures of the individual solitons. Additionally, the overlapping bandwidths of the temporally separated solitons cause spectral interference fringes in the central part of the spectrum (Gu et al., 2002). In the ANDi SC pulse, each wavelength component is located at a unique temporal position inside the pulse, such that spectral or temporal interference is avoided and both spectrum and temporal profile are free of any significant fine structure.

Compressibility

The enormous bandwidths of supercontinua should allow the generation of very short, few-cycle (sub-5 fs) pulses using appropriate dispersive compression. Although it has been shown that it is indeed theoretically possible to compress the complex temporal structure of an octave-spanning conventional SC back into a single, few-cycle pulse by dispersively compensating its spectral phase (Dudley & Coen, 2004), in practice this could never be demonstrated owing to the significant fine structure present in spectrum and group delay (Schenkel et al., 2005). In contrast, the simple phase profile of the ANDi SC pulse is excellently suited for pulse compression, and in fact has led to the generation of high-quality, Fourier-limited pulses as short as 3.7 fs (Demmler et al., 2011). More details on the application of ANDi fibers in nonlinear pulse compression can be found in Sect. 6.7.1 of this chapter.

Coherence and Stability

So far we have only considered the evolution of a single ultrashort pulse in the fiber. However, since there is always a certain level of quantum or technical noise on the input pulses, the evolution of subsequent pulses inside the fiber is not necessarily identical. The properties of the generated SC might change considerably from shot to shot if the nonlinear effects responsible for the spectral broadening are sensitive to this noise. Driven by the increased demand for ultra-low noise broadband coherent light sources in spectroscopy, microscopy, and ultrafast photonics, ANDi SCs are rapidly gaining popularity in these fields as it becomes increasingly apparent that the fiber design strongly suppresses the gain for noise-amplifying incoherent nonlinear dynamics (Heidt et al., 2017). In Sect. 6.5 we provide further details on the origin of SC noise and how to control it using specialty optical fiber design principles.

6.4 Nonlinear Dynamics in ANDi Fibers

In this section we have a closer look at the nonlinear dynamics in ANDi SC generation and identify the physical effects dominating the broadening process using numerical simulations. We focus on the coherent nonlinear processes that do not introduce any excess noise; pulse-to-pulse fluctuations and noise introduced by incoherent nonlinear processes are further discussed in Sect. 6.5.

6.4.1 Spectrogram Analysis

A very convenient way to display the evolution of the pulse as it propagates along the fiber is the projected-axis spectrogram representation already introduced in Sect. 6.3.1. As representative example we chose again the ANDi PCF of Fig. 6.1, pumped at 1050 nm with a 90 kW peak power input pulse. However, we use a longer pump pulse duration of 200 fs since the nonlinear dynamics are slowed down for longer pulses and the physical effects can easier be identified. Fig. 6.4a shows the spectral and temporal evolution of the SC generation process over a propagation distance of 20 cm. Three distinctive positions along the fiber at 2.0 cm, 3.7 cm, and 20 cm are marked, and the spectrograms of the SC pulse at these positions are displayed in Fig. 6.4b.

Fig. 6.4

(a) Simulated spectral and temporal evolution of the SC generation process in the ANDi PCF of Fig. 6.1, pumped with a 200 fs, 90 kW pulse at 1050 nm. (b) Projected axis spectrograms of the SC pulse at 2.0 cm, 3.7 cm, and 20 cm. Arrows indicate energy transfer process due to optical wave breaking

For our input pulse and fiber parameters, L _D is >20 cm, i.e., much longer than L _NL (<1 mm). The dynamics are therefore initially dominated by nonlinear effects, in particular SPM-induced spectral broadening, which is discussed in more detail in Chaps. 1 and 2 of this book. The spectrogram of the SC pulse at 2.0 cm clearly shows the SPM-characteristic S shape, with spectral broadening toward longer wavelengths occurring at the leading edge of the pulse, while broadening toward shorter wavelengths is introduced at the trailing pulse edge. The spectrum also displays the typical oscillatory structure associated with SPM, which is created by spectral interference of identical spectral components being present at different temporal positions within the pulse.

With further propagation the dispersion profile of the fiber becomes the governing factor of the nonlinear dynamics: since the fiber exhibits normal dispersion at all wavelengths, the group velocity monotonically increases with wavelength. Hence, the pulse tail travels faster than the blue-shifted wavelength components created by SPM in the intermediate section of the pulse (marked in spectrogram (I) in Fig. 6.4b). The faster tail eventually overtakes the slower intermediate section, which leads to the steepening of the trailing pulse edge and the onset of optical wave breaking (OWB) (Anderson et al., 1992). The temporal overlap of the two pulse components with different instantaneous frequencies leads to the nonlinear generation of new frequency components at

$$ {\omega}_{\mathrm{OWB}}=2{\omega}_{\mathrm{SPM}}-{\omega}_0, $$

(6.2)

via a degenerate four-wave mixing (FWM) process (Agrawal, 2007; Finot et al., 2008), where ω_SPM is the angular frequency of the SPM components in the intermediate pulse section and ω₀ is the center frequency of the pulse. The energy transfer process from the center to the wing of the spectrum is clearly visible after 3.7 cm of propagation in spectrogram (II) in Fig. 6.4b and marked with an arrow. The overlap of SPM-generated components around 900 nm with the pulse tail at 1050 nm creates a new wavelength band around 750 nm. After further propagation, OWB also occurs on the leading pulse edge (not shown) and generates new wavelengths extending to >1400 nm. During the remaining part of the propagation, OWB continuously redistributes energy from the central frequency to the spectral wings until the original front and tail of the pulse at ω₀ are completely depleted. The corresponding spectrogram at the end of the 20 cm propagation distance is finally very similar to Fig. 6.3b, except for the longer temporal pulse duration. After OWB is concluded, no interference structures are present in neither temporal nor spectral profile as the OWB process assigns each wavelength to a unique temporal position within the pulse.

In summary, after an initial phase of SPM-dominated broadening OWB occurs on both leading and trailing edges of the pulse and is responsible for the generation of the extreme wavelengths on both sides of the spectrum as well as for the uniform temporal and spectral profiles of the final SC spectrum. As a consequence, a single ultrashort pulse with well-defined phase is available from the fiber after the SC generation process.

6.4.2 Influence of Fiber and Pump Pulse Parameters

The FWM energy transfer from the spectral center to the wings occurs only in the instant of their temporal overlap as they propagate with different group velocities. Hence, the OWB-induced FWM processes, which create the extreme wavelength components of the SC spectrum, are not phase-matched. Therefore, there is no restriction on the achievable bandwidth of the spectrum—it solely depends on the amount of SPM-induced broadening before OWB occurs, according to Eq. (6.2). With this insight we can deduce some general dependencies of the generated SC bandwidth on fiber and input pulse parameters.

Since L_NL ≪ L_D in the first phase of the propagation, we can initially neglect dispersive effects and estimate the spectral broadening due to SPM as

$$ \left|{\omega}_{\mathrm{SPM}}\left(\mathrm{z},\mathrm{t}\right)-{\omega}_0\right|=\gamma {P}_0\frac{\partial U(t)}{\partial t}z, $$

(6.3)

where U(t) is the normalized intensity profile of the input pulse and z the propagation distance (Agrawal, 2007). In order to estimate the maximum broadening at the point of OWB, we estimate the maximum slope of the pump pulse as max(∂U(t)/∂t) ∝ 1/T ₀, with the input pulse duration T ₀ , and the expression for the OWB distance (Finot et al., 2008)

$$ {L}_{\mathrm{OWB}}\simeq {L}_D/N={T}_0{\left(\gamma {P}_0\left|{\beta}_2\right|\right)}^{-1/2} $$

(6.4)

and obtain

$$ {\left|{\omega}_{\mathrm{SPM}}\left({L}_{\mathrm{OWB}}\right)-{\omega}_0\right|}_{\mathrm{max}}\propto {\left(\frac{\gamma {P}_0}{\beta_2}\right)}^{1/2} $$

(6.5)

In consequence, the spectral broadening in ANDi fibers can be enhanced by higher peak power of the input pulse, as well as higher nonlinearity or decreased and flattened dispersion of the fiber, which is a very intuitive result. However, there is usually a trade-off between spectral bandwidth and flatness. As the ratio of nonlinearity to dispersion is increased, the OWB process progressively depletes the central frequency such that a spectral “dip” with magnitude of >10 dB can form around the pump wavelength. This is especially an issue when the MDW approaches zero (Heidt, 2010). The spectral flatness can be improved by increasing the dispersion at the pump wavelength, but at the cost of decreased bandwidth (and vice versa).

Not quite so intuitive is the fact that the spectral bandwidth, and in extension also the coherence properties and temporal compressibility, is independent of the input pulse duration if the peak power remains constant. This has been verified by numerical simulations (Heidt et al., 2017), and is valid as long as incoherent nonlinear effects do not play a significant role, i.e., up to input pulse durations of about 1 ps (see also Sect. 6.5). However, since the wave breaking distance grows linearly with the pulse duration (Eq. (6.4)), the nonlinear dynamics are slowed down for longer pulses, and the fiber length needs to be increased accordingly. Therefore, the loss profile of the fiber may play a more significant role, particularly if technologically less mature non-silica glasses are used for fiber fabrication (Price et al., 2012).

Note also that the spectral broadening is only weakly dependent on β₂. It is therefore not a critical necessity to match the pump wavelength exactly to the MDW of the fiber. If the dispersion profile is sufficiently flat, pump wavelengths several hundred nanometers on either side of the MDW can be acceptable and can still create more than octave-spanning SC spectra (Heidt et al., 2011a; see also Sect. 6.6.1). In this case, spectral broadening occurs preferentially toward the side where the MDW is located, i.e., toward wavelengths with low and flattened dispersion where the temporal broadening of the pulse is limited and continuously high peak powers are maintained during propagation. This can be effectively used to steer the SC generation process toward a desired spectral region (Price et al., 2012).

6.5 Noise Properties of Fiber Supercontinuum Sources

With every new edition of this book, a variety of new applications are emerging for the supercontinuum laser source, and as such these versatile broadband coherent light sources have become undispensable tools for spectroscopy, biomedical imaging, optical coherence tomography, advanced microscopy, and many more applications. However, due to the ever-increasing sensitivity and speed of spectroscopic detection and imaging techniques, the noise properties, shot-to-shot stability, and temporal characteristics of fiber-based SC sources are now becoming increasingly relevant.

Commercially available sources, often constructed from pico- or nanosecond pulsed lasers pumping an anomalous dispersion fiber, suffer from huge pulse-to-pulse fluctuations of spectral amplitude and phase that arise from nonlinear noise amplification processes dominating the SC generation dynamics. While the correspondingly large relative intensity noise (RIN) in the order of 50% or more can often be reduced by long-term averaging (Dupont et al., 2014), SC noise has become the predominant factor limiting the precision, speed, resolution, or sensitivity of many applications (Jensen et al., 2019).

In this section we explore the origin of this noise in more detail in an effort to identify strategies and fiber designs that can effectively suppress any nonlinear noise amplification during SC generation. While it is well-known that SC noise depends on input pulse duration and fiber length, only recent results have highlighted the fact that the noise characteristics of fiber-based SC sources can be effectively controlled both by the dispersion profile and the cross-sectional geometry of the nonlinear fiber. In particular, highly birefringent polarization-maintaining ANDi fibers are currently emerging as the key-enabling technology for the realization of the next generation of ultra-low noise SC sources.

6.5.1 Origin of Supercontinuum Noise

A typical fiber-based SC source operates at MHz repetition rates and thus emits millions of pulses per second. So far in this chapter, we have considered only the evolution of a single ultrashort pulse and its transformation into a supercontinuum as it propagates along the fiber. However, since there is always a certain level of quantum or technical noise on the input pulses, the evolution of subsequent pulses inside the fiber is not necessarily identical. The properties of the generated SC might change considerably from shot to shot if the nonlinear effects responsible for the spectral broadening are sensitive to this noise.

We can investigate this sensitivity numerically by including quantum noise terms into the simulations, e.g., as described by Dudley et al. (2006), and comparing the results of multiple simulations obtained with different random noise seeds. It is common to characterize the shot-to-shot fluctuations using the spectrally resolved modulus of first-order coherence at zero path difference:

$$ \left|{g}_{12}\left(\lambda \right)\right|=\left|\frac{\left\langle {S}_1^{\ast}\left(\lambda \right){S}_2\left(\lambda \right)\right\rangle }{\sqrt{\left\langle {\left|{S}_1\left(\lambda \right)\right|}^2\right\rangle \left\langle {\left|{S}_2\left(\lambda \right)\right|}^2\right\rangle }}\right| $$

(6.6)

where angle brackets indicate an ensemble average over independently generated SC pairs [S ₁(λ), S ₂(λ)] obtained from a large number of simulations. At each wavelength bin, this yields a positive number in the interval [0;1] with the value 1 representing perfect stability in amplitude and phase and the value 0 indicating completely uncorrelated fluctuations from pulse to pulse (Dudley & Coen, 2002).

In order to illustrate the origin of SC noise, we consider again our representative ANDi fiber from the previous sections, but increase the pump pulse duration to 5 ps and limit the peak power to 5 kW. Figure 6.5a shows the calculated evolution as well as the spectral fluctuations and coherence properties after 1 m of propagation through the fiber, extracted from 20 simulations with independent quantum noise seeds. In the central part of the spectrum, the coherent dynamics dominated by SPM/OWB discussed in Sect. 6.4 are at work, which are seeded by wavelength components within the pump pulse itself and, therefore, maintain high coherence. After about 40 cm of propagation, a broad peak starts to develop redshifted from the central spectrum by a frequency of around 13.2 THz, which corresponds to the peak frequency of the Raman gain in silica. Consequently, the origin of this peak is stimulated Raman scattering (SRS), which provides enormous exponential gain to any seed signal injected into its gain bandwidth. If the Raman gain remains unseeded, like in this case, then quantum noise serves as the seed and is amplified to become significant and even dominate the spectral broadening dynamics. The noise-seeded spectral components contained in the Raman peak exhibit random fluctuations in amplitude and phase from shot to shot and are thus incoherent with the pump. With further propagation cascaded Raman Stokes (redshifted) and anti-Stokes (blueshifted) peaks appear, which are also noise-seeded and show similarly large fluctuations and low coherence.

Fig. 6.5

(a) Origin of SC noise. Bottom: simulated spectral evolution of 5 ps, 5 kW pulses in the ANDi fiber from Fig. 6.1. Arrows indicate primary gain bands for amplification of quantum noise. Center: spectrum at the fiber exit. The mean spectrum is displayed in red, obtained from averaging 20 simulations with random noise seeds. Gray traces show single-shot spectra. Top: coherence calculated according to Eq. (6.6). (b) Mixed parametric Raman (MPR) gain g _MPR, normalized by the standard Raman gain g _R. We use the MPR gain to describe the dispersion dependence of noise-amplifying incoherent nonlinearities in SC generation dynamics. Typical conditions for octave-spanning SC generation for ANDi and conventional SC from Fig. 6.2 are indicated

Raman anti-Stokes components are rarely observed in fibers, since neither SRS nor other nonlinear mechanisms such as parametric FWM are efficient enough to generate them by themselves—the ANDi profile excludes phase matching of Stokes and anti-Stokes Raman components with the pump wave. Instead, the presence of anti-Stokes peaks can only be explained by the combined action of SRS and FWM, which couple in a high peak power/low dispersion environment, i.e., exactly in conditions that are usually employed for SC generation (Bloembergen & Shen, 1964; Coen et al., 2002a). In single-mode fibers, this nonlinear coupling of SRS and FWM can be described by the mixed parametric Raman (MPR) gain (Coen et al., 2002b), which amplifies and distributes noise across the SC spectrum and can generally be regarded as the main noise-amplifying nonlinear effect responsible for incoherent spectral broadening (Heidt et al., 2017).

6.5.2 Supercontinuum Noise Control by Fiber Dispersion Engineering

Clearly, the noise properties of SC sources can be understood in terms of a competition between coherent and noise-amplifying incoherent nonlinear processes. While the coherent nonlinearities preserve the coherence and stability of the input pulses, the MPR gain builds up new spectral components from noise and quickly distributes it throughout the SC pulse. By comparing the strength of these two sets of nonlinearities and their dependence on input pulse and fiber design, we can develop strategies how to reduce noise amplification or even suppress it altogether.

As discussed in Sects. 6.3 and 6.4 of this chapter, the coherent dynamics are dominated by OWB in the normal dispersion and soliton fission in the anomalous dispersion regime. Interestingly, by comparing Eqs. (6.1) and (6.4), we note that the characteristic length scales of these two processes are virtually identical. In particular, for the low dispersion conditions employed for SC generation and for a given pump peak power, it is only weakly dependent on the fiber design and mainly proportional to the pump pulse duration.

In contrast, the MPR gain g _MPR, which we use here to describe the strength of noise-amplifying incoherent dynamics, is independent of the pump pulse duration, but highly dependent on the fiber dispersion. It is shown in Fig. 6.5b normalized to the standard peak Raman gain g _R ≃ 0.5γP₀ in dependence of $K=-{\upbeta}_2{\Omega}_R^2/\left(2\upgamma {P}_0\right)$, which is essentially the ratio of dispersion and nonlinearity (Vanholsbeeck et al., 2003). Here Ω_R is the angular frequency shift of the Raman gain peak. For large |K|, SRS and FWM decouple and g _MPR ≃ g _R. However, in the region |K| < 1 relevant to SC generation, the incoherent dynamics are strongly suppressed in the normal dispersion, while noise amplification is strongly amplified in the anomalous dispersion region. The peak of the MPR gain is located at K ≃ 1 − f _R/2, where f _R (~ 0.18 for silica) is the fractional contribution of the Raman effect to the nonlinear material response (see Chap. 3, Eq. (3.6)). At the peak, Stokes and anti-Stokes Raman sidebands are effectively amplified by FWM, a process that is also known as modulational instability (MI) and whose role in the coherence collapse of conventional SC has been investigated since the early days of fiber-based SC generation (Nakazawa et al., 1998; Corwin et al., 2003). Describing incoherent nonlinear dynamics in terms of the MPR gain therefore incorporates previous literature results, while providing a broader and more universal perspective on SC noise and the opportunities arising from its control via dispersion engineering.

Returning to our representative fiber designs and SC dynamics discussed in Sect. 6.3 pumped with high peak power femtosecond pulses for generating octave-spanning bandwidths, K ≃  − 0.02 for the ANDi SC and K ≃ +0.28 for the conventional SC. The corresponding MPR gains are indicated in Fig. 6.5b. Hence, we find that the MPR gain and associated noise amplification can be decreased by over one order of magnitude by changing from the conventional to the ANDi fiber design. In fact, this order of magnitude difference in noise susceptibility is a recurrent factor found in many theoretical and experimental studies, as we detail below, and can be seen as the main reason behind the attraction of ANDi fibers for low-noise SC source development.

From this fundamental physics perspective, we expect ANDi SC to be significantly more stable than conventional SC for any given pump source. These analytical arguments are confirmed by the numerical simulations in Fig. 6.6 illustrating the significantly different noise amplification behavior of conventional and ANDi SC. Displayed are the calculated coherence properties and spectral fluctuations for various input pulse durations using our representative fiber designs.

Fig. 6.6

Temporal coherence and stability calculations for (a) conventional SC and (b) ANDi SC in dependence of input pulse duration. Pump peak power and fiber lengths are fixed and values given in the text. The temporal coherence function ∣g₁₂(λ)∣ (Eq. (6.6)) is displayed on top of each spectrum. The gray traces show spectra from 20 individual simulations including shot noise, while the mean spectrum appears in red

The competition between the coherent and incoherent dynamics typically leads to a threshold pulse duration T _crit or threshold soliton number N _crit above which the nature of the SC changes from coherent to incoherent (Dudley et al., 2006; Genty et al., 2007). For the conventional SC, significant spectral shot-to-shot fluctuations and coherence degradation indicate the beginning dominance of incoherent dynamics governed by the MPR gain already for pump pulses as short as T _crit ≈ 100 fs or N _crit ≈ 10. Consequently, very short pump pulses, low pulse energies, and short fiber lengths are necessary to maintain coherence. In contrast, for ANDi fibers noise amplification becomes significant only for much longer pump pulse durations. At about 1000 fs, we observe first low-level fluctuations, especially at the long-wavelength edge, while the coherence function is still relatively unaffected. Only at pulse durations exceeding 1500 fs, incoherent dynamics become significant and the coherence function starts to collapse. In a comprehensive study on the coherence limits of ANDi SC, Heidt et al. (2017) clarified the role of the MPR gain in the decoherence of ANDi SC and revealed the complex interaction between coherent and incoherent dynamics in the long-pulse regime, which leads to novel mechanisms such as incoherent cloud formation and incoherent optical wave breaking. In ANDi fibers, coherent octave-spanning SC can be generated with pump pulse durations T _crit > 1000 fs and “soliton” orders of N _crit ~ 600, corresponding to an approximately 50 times increase of the coherent regime compared to conventional SC generation. Consequently, ANDi SCs allow for much higher pulse energies and power spectral densities in the order of mW/nm.

Since quantum noise amplified by the MPR gain grows exponentially with propagation distance (Smith, 1972), the coherence properties are also dependent on the fiber length. Shorter fibers generally yield better coherence, but might also result in narrower spectral bandwidths. In practice, balancing coherence and bandwidth with the correct choice of fiber length becomes more and more critical as the pump pulse duration is increased (Heidt et al., 2017).

The superior coherence and noise properties of ANDi SCs over conventional SCs were also experimentally verified, for example, by measurements of relative intensity noise (RIN), spectral coherence, dispersive Fourier transformation, and RF beating with stabilized laser diodes (Nishizawa & Takayanagi, 2007; Nishizawa et al., 2018; Klimczak et al., 2016). While initial results indicated a coherence collapse of ANDi SC when technical noise such as pump laser power fluctuations is considered (Genier et al., 2019), it was later shown that coherence is not a useful figure of merit to quantify SC stability in the presence of technical noise (Sierro & Heidt, 2020). In fact, ANDi SCs exhibit a remarkable resistance against technical noise (Sierro & Heidt, 2020, Eslami et al., 2020), and further studies have highlighted that the RIN of ANDi SC can actually be lower than the RIN of the pump laser in the central part of the spectrum (Genier et al., 2019; Rao et al., 2019). In contrast, in conventional SC technical noise is amplified by factors up to 20 dB, even in the regime where coherent dynamics dominate (Newbury et al., 2003).

6.5.3 Supercontinuum Noise Control by Designing Fiber Geometry and Birefringence

Although the above analysis suggests excellent stability of ANDi SC sources up to the picosecond regime, it assumes that the linear polarization state of the pulses remains unchanged during propagation in the fiber. In reality, every fiber exhibits a certain amount of birefringence that breaks the degeneracy of polarization states. This birefringence might be introduced, for example, by geometrical asymmetries of the fiber core and cross section, stresses introduced around air-hole microstructures, stresses due to different thermal expansion coefficients of multiple glass compositions, or twisting of the fiber during the drawing process. Consequently, linear and nonlinear mode coupling between the polarization modes leads to several nonlinear effects that, in addition to the MPR gain, have the potential to amplify quantum noise and results in unpredictable fluctuations of the polarization state. Table 6.1 provides an overview of the most relevant polarization-dependent noise-amplifying nonlinear processes in optical fibers. Polarization modulation instability (PMI) is especially relevant as it was shown to cause a significant degradation of coherence and stability of SC generated in low-birefringence ANDi fibers, even when the polarization of the pump pulses is aligned to one principal axes of the fiber (Gonzalo et al., 2018).

Table 6.1 Overview of the most relevant polarization-dependent nonlinear processes for (quantum) noise amplification in birefringent optical fibers, including the fiber or input pulse parameter that can be used for their control and suppression

In general, the nonlinear noise amplification is a complex function of fiber birefringence and dispersion, as well as relative orientation of input pulse polarization and fiber axes. This can be visualized by the high-resolution polarization-dependent RIN measurements shown in Fig. 6.7. For these measurements, pulses from an ultrafast Er-fiber laser (80 fs, 40 MHz, 0.05% RIN) were coupled into ANDi fibers with similar dispersion profiles, but very different geometries and birefringence, generating SC with comparable spectral bandwidths in the range 1.2–2.2 μm. A rotating half-wave plate in front of the fiber and a synchronized analyzer at the fiber exit control the plane of pump pulse and detection polarization with respect to the fiber geometry. Polarization-dependent RIN values are measured with an angular resolution of approximately 0.2° using a photodiode and electronic spectrum analyzer and visualized in polar plots. These plots were found to be unique for each tested fiber and are therefore referred to as “noise fingerprints.”

Fig. 6.7

Noise fingerprints of various ANDi SC (a–c) and conventional SC sources (d) pumped by an Er-fiber laser (80 fs, 40 MHz) at 1550 nm, generating comparable bandwidths in the range 1.2–2.2 μm. Shown are SC RIN values (in %) in a polar plot in dependence of pump pulse polarization orientation. The corresponding fiber geometry is shown in the background. The fiber’s slow axis is aligned to zero degrees. The red-dotted line shows the RIN of the pump laser (0.05%). The birefringence at 1550 nm is given below each measurement. (a) Low-birefringence all-solid ANDi PCF with SF6 glass core (Klimczak et al., 2017). (b) Weakly polarization-maintaining (PM) air-hole microstructured PCF with Ge-doped silica core (Tarnowski et al., 2017). (c) Extremely birefringent nanohole suspended-core pure silica ANDi fiber (Hartung et al., 2019). (d) Commercial conventional fiber NKT PM-1550-01

We observe a strong correlation between the noise fingerprints and the cross-sectional geometry of a particular fiber, which we attribute to the unique stress profile associated with each fiber structure. The ANDi fiber in Fig. 6.7a is designed as an all-solid microstructured PCF made from two different soft glasses forming the photonic lattice and inclusions (Klimczak et al., 2017). The structure causes a complex stress pattern due to different thermal expansion coefficients of the two glasses. Since there is no intentional stress axis defined in this design, the resulting birefringence is random, and the polarization axes are not well defined. This enables all of the nonlinear effects listed in Table 6.1 to occur at various angles; a more detailed analysis reveals PI as origin of the narrow noise spike around the fast axis, for example, while a combination of PMI and XMI is responsible for the noise peak at 49°.

Figure 6.7 also illustrates that birefringence is an effective control parameter to reduce polarization-dependent noise in ANDi SC generation. With increasing birefringence the noise fingerprints become more regular and environmentally stable. Near the slow axis of birefringent ANDi fibers, the noise of the SC is found to be virtually identical to the noise of the pump laser. Eventually, complete suppression of noise-amplifying nonlinear processes is observed ANDi fiber designs exhibiting extreme birefringence, such as the nanohole suspended-core fiber in Fig. 6.7c, even when the pump polarization is not aligned to one of the principal fiber axes. In contrast, the noise fingerprint of a comparable polarization-maintaining conventional SC source in Fig. 6.7d is significantly more complex, and shows noise amplification up to a factor of 40. In the test conditions, the soliton number is N ≃ 6, such that stable and coherent conventional SC is generated when the polarization of the pump pulses is exactly aligned to a principal axis of the fiber. However, even slight misalignment of the polarization in the order of just 1° causes a significant rise of the SC noise.

These measurements highlight the importance of the cross-sectional fiber geometry and the homogeneity of the stress profile, in addition to dispersion engineering, for the realization of high-quality, low-noise SC sources. As we discuss in the following section, ANDi SC sources designed with these considerations in mind are currently emerging and provide further experimental evidence for the excellent quality and stability of these broadband coherent light sources.

6.6 Experimental Results and Fiber Designs for Various Spectral Regions

Based on the discussions in the previous sections, we can establish general fiber design guidelines for efficient SC generation in the normal dispersion region:

• The fiber should exhibit a convex and flattened all-normal dispersion profile. This ensures broadband uniform and smooth spectral and temporal profiles and suppresses soliton dynamics and MI gain entirely. The spectra can therefore be generally expected to be highly coherent if the MPR gain is negligible, i.e., for sub-picosecond pump pulses and 10s of cm fiber lengths.

• The fiber should have a birefringence in the order of 10^-4 or higher in order to properly suppress polarization-dependent noise amplification processes, such as PMI. Alignment of the pump laser polarization to a principle fiber axis is generally recommended.

• For generating high-quality SC spectra, high-quality pump pulses are required. Nonideal pump pulse shapes containing satellite pulses or low-level pedestals lead to spectral and temporal fine structure (Rampur et al., 2020).

• The MDW should be close to the desired pump wavelength to ensure minimum temporal spreading of the input pulse and maximum generated SC bandwidth.

• For maximizing spectral bandwidth, the dispersion at the MDW should be close to zero and the dispersion profile as flat as possible. However, this can compromise spectral flatness and result in the formation of a depletion region around the MDW with a dip in spectral intensity larger than 10 dB.

• For maximizing spectral flatness, the dispersion at the MDW should be slightly normal to balance nonlinearity and dispersion and avoid the depletion region around the MDW. For typical input pulse parameters, the range −10 ps/(nm km) ≤ D ≤ −30 ps/(nm km) has led to good results.

• For asymmetric broadening toward a preferred wavelength region, the MDW should not be located at the pump wavelength, but further toward the preferred side of the spectrum.

• For a given fiber design, the generated spectral bandwidth is determined by the peak power and is independent of the input pulse duration (if MPR gain is negligible). However, the fiber length should be chosen according to input pulse duration: longer pump pulses require longer fibers for the SC to fully develop. For pump pulses approaching the picosecond regime, careful adjustment of fiber length is required to maximize spectral bandwidth while maintaining coherence.

In the following paragraphs, we give examples of fiber designs that fulfill these guidelines and discuss important experimental results of SC generation pumped in the normal dispersion regime in different spectral bands.

6.6.1 Visible and Near-IR Spectral Region

In order to realize an all-normal GVD profile in the visible and near-IR spectral region, the material dispersion of silica, which has a single ZDW in the vicinity of 1300 nm, has to be substantially modified. In optical fibers, the geometry-dependent waveguide dispersion can counteract the material dispersion. This requires a high refractive index contrast between fiber core and cladding materials in combination with a small core diameter in the order of one wavelength. This can be realized using microstructured optical fiber technology, which enables the fabrication of fibers with small silica core surrounded by a photonic crystal cladding of air holes running longitudinally along the optical fiber (Knight, 2003). The structure of the photonic crystal cladding has a significant influence on the waveguide dispersion and hence allows the engineering of GVD profiles with large design freedom. Two kinds of microstructured optical fibers, PCF and suspended-core fibers (SCF), have been considered for the realization of ANDi fibers with MDW in the visible and near-IR region, and we discuss them here in more detail.

6.6.1.1 Photonic Crystal Fibers (PCFs)

Silica PCFs, in which the air-hole inclusions are arranged in a hexagonal lattice structure and a single lattice defect represents the guiding core, offer an enormous potential for dispersion engineering. By tuning the two design parameters, pitch Λ and relative air-hole diameter d/Λ, ANDi fibers with MDWs virtually anywhere between 500 and 1300 nm can be realized. Figure 6.8 demonstrates the full versatility of the concept, which is discussed in detail by Hartung et al. (2011a). The position of the MDW is predominantly determined by Λ, while d/Λ serves to reduce the GVD into the normal dispersion regime, accompanied by a slight decrease of the MDW. Consequently, small Λ and large d/Λ are required for the MDW to be located at visible wavelengths, while large Λ and small d/Λ shift the MDW further into the near-IR. Note that the absolute diameter d of the air holes stays almost constant at about 500 nm for every design.

Fig. 6.8

Variety of possible ANDi PCF designs, optimized for various pump wavelengths in the visible and near-infrared spectral regions. The schematic cross section of the PCF illustrates the definition of the basic design parameters, pitch Λ and air-hole diameter d. (Adapted with permission from Hartung et al. (2011a). © The Optical Society)

Relative air-hole diameters near unity are approached for pumping at short wavelengths, which corresponds to a pure silica strand with submicron diameter suspended in air that can be fabricated simply by tapering of a standard single-mode fiber. Such nanofibers could therefore be an interesting approach for deep ultraviolet SC generation (see Sect. 6.6.2). On the long-wavelength side, the extremely flat profiles should result in ultra-broadband SC generation. However, the small d/Λ values result in large confinement losses and require a large number of rings in the photonic crystal cladding as counterbalance, which is challenging in fabrication. Additionally, a limit is imposed by the material dispersion of silica, and it is not possible to place the MDW further than around 1300 nm using the simple hexagonal PCF design considered here. However, using slightly modified PCF designs, the MDW can be shifted toward 1550 nm to create coherent and uniform spectra for telecommunications or optical coherence tomography (Hansen, 2003; Chow et al., 2006; Rao et al., 2019). In Sect. 6.6.3, we consider additional approaches how this limit can be overcome and discuss ANDi fiber designs for longer near-IR and mid-IR wavelengths.

ANDi PCF structures have usually been in-house fabricated, e.g., with MDWs around 650 nm (Heidt et al., 2011a), 800 nm (Humbert et al., 2006), and 1050 nm (Tse et al., 2006; Hooper et al., 2011). But the most extensively studied ANDi PCF to date is commercially available (NKT Photonics NL1050-NEG1) and optimized for pumping with femtosecond ytterbium fiber lasers at 1 μm, but also works well for pumping with widespread Ti-sapphire femtosecond systems around 800 nm. Figure 6.9 shows experimental ANDi SC generated in this fiber as well as in other selected low-birefringence PCF structures optimized for pump wavelengths in the visible and near-IR spectral regions.

Fig. 6.9

Experimental SC generation results in low-birefringence ANDi PCF. Measured SC spectra in a commercially available ANDi PCF (NKT NL1050-NEG1) with MDW near 1020 nm using a central pump wavelength of (a) 1050 nm and (b) 790 nm in dependence of pump pulse energy. The pump pulse duration is 50 fs. The fiber cross section is shown in (e). (c) Visible ANDi SC generated in fiber (f) under 50 fs, 1.1 nJ, 650 nm pumping. (d) Near-IR ANDi SC generated in fiber (g) under 125 fs, 1550 nm pumping in dependence of peak power. (Adapted with permission from Heidt et al. (2011a) and Rao et al. (2019). © The Optical Society)

The commercial NKT fiber has a dispersion profile very similar to our example fiber from Fig. 6.1 used in the numerical simulations in the previous sections. It has a core diameter of 2.3 μm and a photonic crystal cladding with design parameters Λ ≈ 1.46 μm and d/Λ ≈ 0.39, resulting in a peak dispersion parameter of D ≈ −11 ps/(nm km) at a wavelength of 1020 nm. Since the ratio d/Λ is smaller than 0.4, this fiber fulfills the criterion for endlessly single-mode guidance (Birks et al., 1997; Koshiba & Saitoh, 2004). Despite the relatively small core, input coupling efficiencies from free space in the order of 60% or more are achievable with properly sealed and cleaved or polished end facets. The SC spectra generated in this fiber exhibit the flatness and smoothness expected from the numerical simulations, and with a bandwidth of up to 1.5 octaves, they are among the broadest SC spectra generated in the normal dispersion regime of a silica optical fiber to date. These experiments demonstrate that a single fiber can consistently generate smooth, coherent, and broadband SC spectra with a variety of different pump sources if the dispersion curve is sufficiently flat. Note also the preferential broadening toward the side of the spectrum where the MDW is located in the case of 790 nm pumping. Experiments could also confirm the high temporal coherence of the SC and the conservation of single ultrashort pulses in the time domain (Heidt et al., 2011a), as well as their excellent compressibility (e.g., Heidt et al., 2011b; Demmler et al., 2011; Liu et al., 2012b).

Other experiments have demonstrated ANDi SC covering the entire visible spectral region (400–950 nm; Fig. 6.9c, f), where the small air-hole diameter (~400 nm) of the PCF structure leads to large confinement losses for longer wavelengths, which were minimized by using short pump pulses and fiber lengths (Heidt et al., 2011a). A different approach was chosen by Rao et al. (2019) for overcoming confinement losses of PCF structures above 1300 nm, highlighted in Fig. 6.9d, g. They fabricated a fiber with nonuniform design, where the air holes in the first three rings define the extremely flat dispersion according to the design criteria in Fig. 6.8, while rings 4–11 exhibit an increased diameter to reduce the losses. As a result, 9 kW pump peak power was sufficient to generate low-noise broadband ANDi SC in the 1300–1900 nm region with RIN as low as 0.5%.

A major advantage of ANDi SC is the extraordinarily good agreement of experimentally measured spectral intensity and phase with numerical simulations, which was shown by Tu et al. (2010, 2012a). So far, the same level of predictability has not been possible to achieve for conventional SC generation.

In Sect. 6.5.2 we stressed the critical importance of designing polarization-maintaining (PM) ANDi fibers with high birefringence and homogeneous stress profiles for avoiding quantum noise amplification via incoherent polarization-dependent nonlinear processes. Consequently, first prototypes of PM-ANDi fibers are now emerging. Figure 6.10 shows two recent examples of such fibers based on silica PCF, optimized for pumping at 1050 nm and 1550 nm, respectively. While Genier et al. (2021) demonstrated the extraordinary flatness, quality, and stability of their source, Tarnowski et al. (2019) realized an extremely simple and compact solution by splicing their PM-ANDi fiber directly to the output of a femtosecond Er-fiber laser. Both results impressively demonstrate the importance of highly birefringent ANDi fibers as the key-enabling technology for the next generation of ultra-low noise ultrafast SC sources. Nishizawa et al. (2004, 2007, 2018) describe multi-octaves for OCT and clocks.

Fig. 6.10

Experimental SC generation results in high-birefringence, polarization-maintaining ANDi PCF. (a) Measured SC spectra and polarization extinction ratio (PER) in a PM-ANDi fiber (birefringence 4.7 × 10⁻⁴) with MDW at 1040 nm pumped with 180 fs, 48 kW pulses at 1049 nm. The inset shows a microscope image of the fiber facet. Figure kindly provided by E. Genier, T. Sylvestre, Institut FEMTO-ST, Université de Franche-Comté (Genier et al., 2021). (b) Measured (black), simulated (green) SC spectra from an all-fiber ANDi SC source realized by splicing a PM-ANDi fiber (birefringence ~ 10⁻⁵) with MDW at 1.7 μm directly to the output of an Er-fiber femtosecond laser. Dispersive Fourier transformation (individual traces, gray; mean, red) highlight the excellent shot-to-shot stability of the spectrum. Insets show microscope images of the fiber facet. Adapted from Tarnowski et al., 2019

6.6.1.2 Suspended-Core Fibers (SCF)

For the realization of silica fibers with ANDi profile, PCFs with a large number of closely spaced air holes in the cladding are necessary for reducing confinement losses, as seen in the previous section. SCF exhibit similar design freedom as PCF, but can be much simpler to fabricate (Hartung et al., 2011a). In these fibers, a core is suspended in air in the central section of a fiber, connected to the walls typically via three or more silica bridges. The dispersion parameters of such fibers depend on the core diameter d as well as on the number n of silica bridges and hence implicitly on the geometry of the core. Such structures have been exploited to generate ANDi SC in the visible range covering the spectral range 350–900 nm (Hartung et al., 2011b), but have not gained practical relevance to date.

An interesting new development in this area is the introduction of an additional degree of freedom into SCF design, achieved by including a nanohole into the center of the core with variable diameter (Hartung et al., 2019). As shown in Fig. 6.11a, this design facilitates ANDi fibers with MDWs between 500 nm and 1900 nm, but without the confinement loss challenges associated with PCF structures. By elongating one side of the core, extremely birefringent fibers with Δn > 10⁻² can be realized that exhibit very different dispersion characteristics of the two principal polarization modes. In one such design, shown in Fig. 6.11b, both principal polarization modes exhibit an ANDi profile, but with vastly different MDWs, 800 nm and 1600 nm, depending on the polarization direction with respect to the long core axis. Preliminary experiments using femtosecond pump pulses from an Er-fiber laser have confirmed highly polarized, high-quality ANDi SC generation in the region 1200–2000 nm. Such new fiber designs could in the future enable, for example, ultra-broadband ANDi SC by synchronized simultaneous pumping at different central wavelengths.

Fig. 6.11

(a) Calculated dispersion profiles of nanohole suspended-core fibers (SCF) with n = 3 struts in dependence of the core diameter, hole diameter, and strut width. Microscope image of SCF with n=4 struts are shown in the insets. (b) Dispersion characteristics of the fundamental polarization modes of highly birefringent nanohole SCF. Polarization direction is given with respect to the long core axis. The insets show microscope image and preliminary SC spectrum using an Er-fiber femtosecond pump laser. (Adapted with permission from Hartung et al. (2019). © The Optical Society)

6.6.2 Deep-UV Spectral Region

A long-standing challenge in SC generation is the generation of significant power densities in the deep ultraviolet (UV) region at wavelengths below 350 nm. Especially applications in spectroscopy and fluorescence microscopy require light sources in the UV, as many photo-induced processes are excited in this wavelength region (Prasad, 2003). Therefore, many studies have tried to extend the bandwidth of the conventional SC generation on the short wavelength edge (e.g., Kudlinski et al., 2006; Travers, 2010). However, it is difficult to generate significant spectral power densities below 350 nm wavelength, mainly due to the fact that many approaches rely on dispersive wave generation from soliton effects. This requires phase matching with the original soliton, which is difficult to achieve for short wavelengths.

In contrast, the generation of short wavelengths in ANDi fibers is extremely fast and independent of any phase-matching condition, and could therefore be an interesting approach to extend short wavelength edge of fiber-generated SCs deeper into the UV region. In addition, the coherence and temporal properties of the ANDi SC would be favorable, e.g., for broadband transient absorption spectroscopy at UV wavelengths. As discussed in the previous section, ANDi fibers with MDWs between 400 and 500 nm can be realized either with freestanding nanofibers or SCF with core diameters of approximately 500 nm, which can be easily obtained in taper configurations. However, SCF are generally the better choice as the tapered core is also protected by the surrounding silica cladding, which offers improved stability, ease of handling, and improved protection against surface contamination. Spectral broadening down to wavelengths of 250 nm can be expected when pumped with femtosecond pulses from frequency-doubled Ti-sapphire systems around 400 nm and peak powers of about 20–50 kW (Hartung et al., 2012). Although this approach is promising, it has not yet been verified experimentally.

Using a related technique exploiting nonlinear dynamics both in normal and anomalous dispersion regime of a tapered PCF, Stark et al. (2012) have succeeded to experimentally demonstrate deep-UV SC generation down to 280 nm—the current record for SC generation in solid-core silica fibers. In these experiments, summarized in Fig. 6.12, the pump pulses are launched in the normal dispersion regime at the input face of the fiber, but undergo soliton fission in the anomalous dispersion of the taper waist, where the nonlinearity is strongly enhanced. In order to achieve this, a PCF with high air-filling fraction (d/Λ = 0.85) and single ZDW at 1040 nm was tapered from an original core diameter of 5.4 μm down to ~620 nm using taper transition lengths of ~20 mm. The 130 fs, 50 kW peak power pump pulses are launched at 800 nm in the normal dispersion regime of the original fiber and experience SPM broadening. During propagation, the ZDW shifts toward shorter wavelengths as the fiber diameter decreases, and eventually sweeps across the pump pulse. The pulse, now experiencing anomalous dispersion and the high nonlinearity in the waist, undergoes a strong temporal compression to up to ten times higher peak power than the input pulse. Eventually soliton fission dynamics take place, generating the short wavelength components down to 280 nm. The energy conversion efficiency from the pump to UV (<400 nm) is about 20%.

Fig. 6.12

(a) Simulated spectral evolution of SC generation in a 24-mm-long PCF taper, pumped by 110 fs, 50 kW pulses at 800 nm. The black lines show the evolution of ZDWs as the fiber core diameter decreases from 5.4 μm to 620 nm. (b) Experimental results from PCF tapers with different lengths. The lower spectral boundary is 280 nm. (Reproduced with permission from Stark et al. (2012). © The Optical Society)

The fundamental limit of the UV generation in solid-core silica fibers is ultimately given by both linear and nonlinear absorption in the material, defined by the relation

$$ -\frac{\partial I}{dz}=\alpha \left(\omega \right)I+\beta \left(\omega \right){I}^2, $$

(6.7)

where α(ω) and β(ω) are the frequency-dependent coefficients of linear and two-photon absorption (TPA), respectively, and I is the intensity. Although α rises sharply at UV wavelength in silica, it typically remains below 0.1 dB/cm and therefore almost negligible when considering a short taper as above. The TPA threshold, however, is reached at approximately 250 nm and causes an exponential increase in β (Brimacombe et al., 1989; Taylor et al., 1988). While the loss due to TPA depends on the intensity and hence the experimental conditions, Stark et al. (2012) estimated it to be as high as 100 dB/mm for their experiment described above. Such a strong attenuation would, of course, represent a hard barrier for any experiment, and therefore it seems hard to imagine a significant further UV extension of SC generation in solid-core silica fibers.

Further extension is possible in other fiber materials, and conventional SC spanning 200–2500 nm in ZBLAN PCF has been demonstrated (Jiang et al., 2015). However, hollow-core fibers filled with noble gases have emerged as the most successful approach for generating considerable spectral power density and powerful ultrashort pulses in the deep-UV hollow-core fibers filled with noble gases. Such fibers guide the light in the gas with minimal overlap with the silica cladding, avoiding the material-induced nonlinear absorption (Markos et al., 2017).

6.6.3 Mid-Infrared Spectral Region

We mentioned in Sect. 6.5.1 that the achievable bandwidth toward the mid-infrared (mid-IR) spectral region is limited with the traditional hexagonal silica PCF designs. For the extension of ANDi SCs toward the mid-infrared (mid-IR) spectral region, different fiber designs have to be considered. Since the material dispersion of silica is anomalous but fairly low and flat above 1300 nm, it can be compensated by modest waveguide dispersion and hence a relatively low refractive index step between core and cladding material, which can be realized also in standard solid silica fiber by doping a small diameter core with GeO₂, for instance. In their early work, Hori et al. (2004) and Nishizawa and Takayanagi (2007) could demonstrate broadband SC generation spanning up to 2.1 μm in such highly nonlinear fibers with extremely flat and low normal dispersion in most of the near-IR region, but pumping required more complex schemes and not much detail was given about fiber design and composition.

Ultimately, new fiber materials need to be introduced in order to realize ANDi fiber designs at wavelengths of 2 μm and beyond, where silica is intransparent. Soft glass materials offer low losses in the mid-IR and ZDWs between 1.6 μm for fluoride and 5 μm for chalcogenide glasses (Price et al., 2007). The variety of available soft glass materials provides a whole new dimension for the design of ANDi fibers at mid-IR wavelengths, because significant dispersion design flexibility is given not only by the inclusion of air-hole microstructures but also by combining glass materials with different characteristics in all-solid designs. An excellent example how this design freedom offered by soft glass materials can be exploited is given by the work of Klimczak et al. (2014), who realized ANDi SC generation in the range 900–2300 nm in an all-solid PCF combining commercial N-F2 glass used for the core and lattice structure with an in-house synthesized, thermally matched boron silicate glass used for lattice filling (Martynkien et al., 2014; Stepien et al., 2014). Of course, the SC has the typical excellent coherence and temporal properties associated with ANDi fibers, and the overlap with the amplification bandwidths of both thulium- and holmium-doped fiber amplifiers offers intriguing prospects for ultrafast coherent seeding and few-cycle pulse generation at wavelengths around 2 μm, which we discuss in Sect. 6.7.1. The design freedom offered by this approach is more comprehensively reviewed by Klimczak et al. (2017) as well as in Chap. 15 of this book.

Large freedom in dispersion design can not only be achieved in microstructured fibers but also in solid step-index fibers by combining core and cladding glasses with large refractive index difference and choosing an appropriate core size (Poletti et al., 2011). Chalcogenide glasses are good candidates for this approach as they exhibit extremely large refractive index variations depending on their composition, and additionally offer a transparency window covering the molecular fingerprint region up to 12 μm and above as well as orders of magnitude larger nonlinearity than silica (Price et al., 2007). A fiber design using these beneficial properties in an ANDi fiber context is shown in Fig. 6.13. It consists of Te-based chalcogenide core and cladding glasses with numerical aperture NA ≈ 0.4, embedded in a thermally matched polymer jacket (Zhang et al., 2019). The compatibility of thermal and mechanical properties of the three materials enables the tapering of this fiber in its entirety, i.e., without removing the polymer, which makes these devices mechanically extremely robust and in practice allows the precise control over the fiber dimensions via straightforward post-processing (Shabahang et al., 2013). By choosing an appropriate core diameter in the taper waist, ANDi profiles with MDWs between 7 and 8 μm can be realized, as illustrated in Fig. 6.13a. When pumped by 150 fs pulses with central wavelengths in the range 4.5–6.5 μm, SC spectra covering the range 2–12 μm were generated (Zhang et al., 2019) (Fig. 6.13c). Similar experimental results were obtained by Wang et al. (2017) in As-S-based chalcogenide fiber tapers, albeit with slightly narrower spectral bandwidth. Several other, more complex ANDi fiber designs have been proposed for increased flatness or other pump wavelengths (Baili et al., 2014; Ben Salem et al., 2016). In combination, these efforts represent important steps toward fiber-based broadband coherent and ultrafast photonics in the mid-IR, but the realization of birefringent fibers in this wavelength regime remains a challenge.

Fig. 6.13

(a) Dispersion profiles of a chalcogenide step-index fiber (Ge₂₀As₂₀Se₁₅Te₄₅ core, Ge₂₀As₂₀Se₂₀Te₄₀ cladding) in dependence of the core diameter. Effective dispersion control can be achieved by tapering the fiber to the desired size. (b) Robust handling of the tapers enabled by the polymer coating. Insets show microscope images of the taper in different regions. (c) Experimental measurement of the SC spectrum generated in a taper with 13.4 μm waist, pumped with pulses of about 150 fs duration at different central wavelengths. (Adapted with permission from Zhang et al. (2019). © The Optical Society)

6.7 Selected Application Examples

It is clear that SCs generated in ANDi fibers will be particularly relevant for applications in which the spectral uniformity, the temporal profile, or the stability of the continuum is of importance and that have hence struggled to incorporate the noise-sensitive and complex conventional SCs. Two salient areas stand out and have received particular attention: ultrafast photonics and advanced imaging and spectroscopy. We therefore discuss them in more detail in this section.

6.7.1 Ultrafast Photonics

The generation and application of short laser pulses is at the heart of ultrafast optics, and the motto “shorter is better” usually applies. Today, laser pulses containing only a few or even just a single oscillation of the light field¹ enable the time-resolved study of fundamental processes in physics, chemistry, and biology (Kärtner, 2004), or drive the generation of coherent soft X-rays and attosecond pulses, which open up new frontiers in atomic spectroscopy (Krausz & Ivanov, 2009). Although Ti-sapphire oscillators are commercially available that can deliver few-cycle pulses directly in the near-IR, these systems are costly and sensitive to environmental changes, and the shortest pulses have relatively poor quality, i.e., are accompanied by pre- and post-pulses. Spectral broadening of longer femtosecond pulses in optical fibers with subsequent external compression has therefore long been considered as an inexpensive and robust alternative, and the extreme bandwidths of microstructured fiber SCs are particularly attractive. But although it is theoretically possible to compress octave-spanning conventional SCs to single-cycle pulses (Dudley & Coen, 2004), in practice the sub-two cycle regime could never be reached and the pulse duration remained above ~5.5 fs (Schenkel et al., 2005). Even when maximizing the coherence using very short 15 fs pump pulses and only a few millimeters of fiber, the noise sensitivity and the spectro-temporal fine structure are the main practical limitations to reach the predicted Fourier-limited pulse durations.

These fundamental limitations do not apply to ANDi SCs, and consequently numerous studies have investigated their compressibility. When considering nonlinear pulse compression based on solid-core optical fibers, the ANDi fiber design has enabled:

• (i) The highest compression ratio to the sub-two optical cycle regime. Liu et al. (2012b) obtained a compression ratio of almost 30×, shortening 180 fs input pulses to high-quality, near transform-limited 6.4 fs (1.8 cycle) pulses after full phase compensation using a liquid crystal-based spatial light modulator (SLM). This is an impressive result, transforming a compact and reliable commercial 180 fs oscillator into a sub-two cycle pulse source. Even when taking coupling efficiencies and losses in the compressor into account, the compressed pulses can have more than 10× higher peak power than the pulses available directly from the oscillator.

• (ii) The best pulse quality. Demmler et al. (2011) demonstrated the compression of an octave-spanning SC to Fourier-limited, single-cycle pulses with a quality superior to any other technique. Almost 20 dB suppression of sub-pulses was achieved, as shown in Fig. 6.14a. Similarly high-quality sub-two cycle pulses could even be obtained using linear chirp compensation only, as Heidt et al. (2011b) could demonstrate using a static chirped mirror compressor and extremely short fiber lengths that limit the influence of higher-order dispersion.

• (iii) The shortest pulse duration. Pulses as short as 3.67 fs (1.3 optical cycles) were measured by Demmler et al. (2011) by recompressing an octave-spanning ANDi SC using a SLM. This is the shortest pulse duration obtained from nonlinear pulse compression in solid-core fibers to date.

Fig. 6.14

Applications of ANDi SC sources in ultrafast photonics. (a) Generation of a single cycle of light via compression of an octave-spanning ANDi SC. Up to 19 dB pre- and post-pulse suppression (note the logarithmic scale!) and pulse durations as low as 3.7 fs (1.3 optical cycles) were measured. Adapted with permission from Demmler et al. (2011). © The Optical Society. (b) Measured spectrum of a Tm-/Ho-codoped chirped pulse fiber amplifier (CPFA) seeded by an ANDi SC, which is generated by an ultrafast Er-fiber laser at 1550 nm. (c) Measured pulse at the output of the all-fiber CPFA system. Adapted from Heidt et al. (2020). (d) Noise spectra of amplified pulses in an all-PM CPFA implementation in comparison with the Er-fiber seed laser. The integrated RIN of the ultra-low noise CPFA system is as low as 0.03% (10Hz–10 MHz). Adapted with permission from Rampur et al. (2019). © The Optical Society

Such sub-two cycle, high-quality ultrashort ANDi SC pulses are the ideal seed source for ultra-broadband optical parametric chirped pulse amplification (OPCPA) systems, and have consequently facilitated the generation of carrier-envelope phase stable 5.0 fs pulses with up to 22 W average power at 1 MHz repetition rate (Rothhardt et al., 2012). Such high-power few-cycle laser systems have already enabled unique applications such as efficient generation of coherent soft X-ray radiation and isolated attosecond pulses at up to 0.6 MHz repetition rate (Krebs et al., 2013). In the future, many more applications such as photoelectron spectroscopy and XUV microscopy might benefit from modern high-power few-cycle lasers based on amplified ANDi SC pulses (Rothhardt et al., 2017).

Low-noise ultrafast ANDi SC sources have recently also been considered as seed source for the next generation of ultra-low noise high-power ultrafast fiber amplifiers and frequency combs operating in the 2 μm spectral region. This waveband is particularly important as stepping stone for the exploration of the molecular fingerprint region in the mid-infrared via nonlinear frequency conversion. Pumped by robust, turnkey mode-locked Er-fiber systems with ultra-low amplitude and phase noise, ANDi fibers with MDW near 1550 nm were recently employed in proof-of-principle experiments for low-noise spectral broadening into the 2 μm region and subsequent coherent seeding of thulium (Tm)- or holmium (Ho)-doped fiber amplifiers (Rampur et al., 2019; Heidt et al., 2020). Figure 6.14b shows the spectrum of such an amplifier system with a -20 dB bandwidth of 320 nm and the comparison to the ANDi SC seed. High-quality 66 fs pulses with 70 kW peak power could be obtained at the output of the all-fiber system (Fig. 6.14c). When constructed with highly birefringent ANDi fibers in an all-PM architecture, the amplified pulses exhibit a RIN of only 0.03%, which is virtually identical to the Er-fiber seed laser (Fig. 6.14d). These excellent noise characteristics are enabled by the suppression of incoherent nonlinearities in the PM-ANDi fiber (as discussed in Sect. 6.5), as well as by the coherent seeding of the entire amplifier gain spectrum with the broadband ANDi SC, which effectively suppresses amplified spontaneous emission noise in the amplifier. These results represent an order of magnitude improvement of amplifier noise over comparable conventionally seeded implementations, overcoming the major challenge limiting the further development and power-scaling of frequency comb sources at 2 μm (Gaida et al., 2018).

Recent experiments also convincingly demonstrated the advantages of ANDi SC over conventional SC in the construction of stabilized frequency combs (Nishizawa et al., 2018). In combination with the progress of fiber amplifiers described above, these studies have laid the foundations for exciting opportunities arising from using ANDi SC seed sources for the next generation of ultra-low noise frequency combs and ultrafast fiber amplifiers operating in the 2 μm spectral region and beyond in the mid-IR.

6.7.2 Advanced Imaging and Spectroscopy

SC sources in the visible and near-IR have been commercially available for over a decade, and are the excitation source of choice for a range of advanced microscopy techniques, such as multiphoton- and stimulated emission depletion (STED) microscopy (Wildanger et al., 2008). In optical coherence tomography (OCT), SC sources facilitate high-speed, high-resolution 3D imaging across several medical specialities, including ophthalmology and cardiology (Moon & Kim 2006). Pumped by high repetition-rate pico- or nanosecond pulsed lasers and equipped with the high beam quality of optical fibers, the brightness of these fiber-based SC sources is unparalleled. However, due to the stochastic nature of the nonlinear processes involved in spectral broadening, these SC sources provide spatially but not temporally coherent light and exhibit very large pulse-to-pulse fluctuations of spectral amplitude and phase. This SC noise has become the predominating factor limiting acquisition speed, sensitivity, and resolution in many applications (Jensen et al., 2019).

The adaptation of low-noise ultrafast ANDi SC sources has therefore started to push the boundaries in several spectroscopy and imaging modalities. Their recent implementation in hyperspectral stimulated Raman scattering microscopy for label-free, chemical-specific biomedical, and mineralogical imaging is particularly impressive, as source noise is critically important in this technique and has excluded the use of many other nonlinear spectral broadening schemes (Abdolghader et al., 2020). In high-resolution spectral-domain OCT, ANDi SC sources have enabled, for the first time, imaging limited by detection shot noise and not by SC source noise (Rao et al., 2020). ANDi SCs are also starting to replace white light generation in bulk media like YAG, sapphire, and CaF₂ in ultrafast spectroscopy, removing the need for expensive amplified laser systems (Kearns et al., 2019).

The combination of an ANDi SC source with a SLM-based pulse shaping device and subsequent imaging or spectroscopy system has proven to be an especially powerful and versatile tool in biophotonic imaging and spectroscopy (Fig. 6.15a) (Tu & Boppart, 2013). It offers full digital and programmable control over the spectro-temporal profile of the incident light field at the sample and allows the realization of numerous coherently controlled applications in a single setup. Conveniently, the incorporation of the pulse shaper facilitates the complete or partial compression of the SC pulses at the sample position via digital algorithms, such as multiphoton intrapulse interference phase scanning (MIIPS) and time-domain ptychography (Tu et al., 2011; Dwapanyin et al., 2020). Of course, an additional arbitrary spectral phase may be applied with the same pulse shaper to enable the desired coherently controlled applications.

Fig. 6.15

(a) The combination of ANDi SC source, SLM-based pulse shaping device, and subsequent imaging or microspectroscopy system is a powerful setup in biophotonics. Multiple coherently controlled modalities can be realized, including label-free nonlinear microscopy with various contrast methods and single-beam CARS microspectroscopy. (b) Label-free multimodal multiphoton imaging of human mammary tumor using compressed pulses from the ANDi SC source. The image contains two-photon fluorescence (yellow), third-harmonic generation (magenta), and second-harmonic generation (cyan) signals used as contrast methods. Representative image data from the study detailed in Liu et al. (2012a), courtesy of Y. Liu, H. Tu, and S. Boppart, University of Illinois. (c) Schematic operational principle of CARS microspectroscopy and experimental single-beam CARS spectrum of para-xylene. (Adapted with permission from Viljoen et al. (2020). © The Optical Society)

Using such amplitude and phase shaping of an ANDi SC, alignment-free and programmable-contrast multimodal multiphoton microscopy of biological samples over a broad spectral range becomes possible (Liu et al. (2012a); Dwapanyin et al., 2020). Figure 6.15b illustrates such imaging of a human breast tumor. By carving different spectral slices out of the SC and compressing the resulting ultrashort pulses at the focus of a scanning microscope, selective and efficient nonlinear optical imaging using three different modalities (two-photon fluorescence, second-harmonic generation, and third-harmonic generation) was shown with a single beam and an easily tunable setup. The enhanced multiphoton signals enable the selective visualization of various intrinsic molecules and internal structures.

The full power of combining an ANDi SC source with a pulse shaper is revealed when implemented in a modality that requires full coherent control of the field incident on the sample, such as single-beam coherent anti-Stokes Raman scattering (CARS) spectroscopy (Fig. 6.15c). Due to the coherence and ultrafast properties of the ANDi SC, pump, probe, and reference beam can be carved from a single SC pulse, and using the pulse shaper, it is possible to compress, stretch, and delay them independently as well as separating the coherent information from the incoherent background (Liu et al., 2013; Tu and Boppart, 2014; Viljoen et al., 2020). Ultimately, the combination of multiphoton microscopy and hyperspectral CARS imaging based on digitally programmable ANDi SC pulses has led to the development of an extremely versatile platform for optical alignment-free programmable-contrast imaging, offering the potential to translate stain-free molecular histopathology for disease diagnosis into routine clinical use (Tu et al., 2016). Even without the relatively expensive SLM device, broadband multimodal CARS and multiphoton imaging systems based on ANDi SC sources have been developed (Herdzik et al., 2020).

6.8 Conclusion

In this chapter, we provide a comprehensive review of SC generation in ANDi fibers, fiber design possibilities, and related applications. While coherent SC generation in normal dispersion fibers has been studied since the early beginnings of nonlinear fiber optics, the emergence of the ANDi fiber design concept has pushed the obtainable bandwidths to magnitudes previously only known from anomalous dispersion pumping. In combination with their high stability, the conservation of an ultrashort compressible temporal pulse, and their uniform and flat spectral profiles, ANDi SCs are a truly unique “white light” source whose full potential is yet to be explored. The possibility to achieve these characteristics with relatively long pump pulses and the relaxation of previously demanding pump source requirements to maintain coherence increases availability and applicability of broadband coherent SC sources.

It should have become clear that the ANDi fibers are an important complement to the fibers with single ZDW conventionally used for SC generation, and both have their unique advantages and drawbacks. Ultimately, the choice of fiber design depends on the application demands. The ANDi design is preferable if coherence, stability, temporal profile, or spectral flatness is required, but for a given input peak power, the achievable spectral bandwidth is usually narrower in comparison with anomalous dispersion pumping. For applications in which stability and the presence of fine structure are less important, the classic approach of anomalous dispersion pumping close to the single ZDW still provides the broadest achievable spectral bandwidth and allows pump sources from the femtosecond to the CW regime. ANDi fibers do not offer the same flexibility in the choice of pump source; the high peak powers required for substantial spectral broadening put a practical limit on the pump pulse duration and imply a sub-picosecond pulse source.

Highly birefringent ANDi fibers are emerging as the key-enabling technology for the next generation of ultra-low noise ultrafast SC sources and are already beginning to push the boundaries in several spectroscopy and imaging applications. From our perspective this is really just the beginning of a movement that will see these versatile sources of broadband, low-noise, and ultrashort pulses being used in an increasing numbers of applications which so far were not able to use conventional fiber-based SC sources due to their noise or complex temporal pulse shapes. It will also be interesting to follow the further development of ANDi fibers made of soft glass materials like chalcogenides, which will enable the extension of coherent and ultrafast photonics based on optical fibers to the emerging mid-IR waveband.