A comprehensive guide to intracavity absorption spectroscopy

Abstract

The enormous sensitivity of intracavity absorption spectroscopy (ICAS), as well as its unique ability to tolerate high broadband losses caused by, e.g., optical windows and light scattering, is being exploited by only a few research groups worldwide. The reason seems to be the lack of comprehensive literature, such that the field remains difficult to access for non-experts, in particular for engineers and chemists, who might derive the most benefits from applying ICAS. In particular, the missing connection to this target audience appears to be two-fold: (i) the seeming complexity of the theory, and (ii) the necessity to setup homemade laser systems. However, once some basic understanding and knowledge is obtained, both aspects appear to be of similar complexity as with other spectroscopic techniques. Therefore, the current work is aiming at (i) providing a comprehensive review of the theoretical basics of ICAS, and (ii) describing the most important practical aspects that need to be considered for a successful realization of ICAS measurements. To ensure maximum clarity, illustrative practical examples of recent work are used throughout the paper.

1 Introduction

Intracavity absorption spectroscopy (ICAS), sometimes also called intracavity laser absorption spectroscopy (ICLAS) or intracavity laser spectroscopy (ICLS), is one of the most sensitive spectroscopic techniques, especially for gas-phase applications. The working principle of ICAS is illustrated in Fig. 1.

Fig. 1

Schematics of the ICAS process. Successive interaction of laser photons with the broadband gain G(ν) (homogeneous linewidth Ω_h) and the narrowband absorption κ(ν) (linewidth ∆ν) leads to an imprint of the absorption lines onto the laser emission spectrum I(ν)

The characteristic feature of ICAS is the location of the sample inside the laser cavity. As a consequence, the laser light can accumulate enormous absorption path lengths through the sample of up to L_eff = 70,000 km [1]. However, in contrast to passive-cavity techniques, the intracavity absorption (ICA) effect is not based on high mirror reflectivity, but rather results from laser-dynamics processes, i.e., from successive interaction of light with the laser gain medium and the absorber.

Despite the fact that ICAS has been proposed already in 1970 [2] and several reviews appeared since then [3,4,5,6], its enormous potential is being exploited by only a few groups worldwide. One of the reasons for this situation seems to be of theoretical nature, namely the seeming complexity of the underlying ICA processes (laser dynamics). On the other hand, the limited number of ICAS users may also originate from practical challenges, namely the necessity to set up homemade lasers. Nevertheless, as will be shown in the following, there are only few key concepts (theoretical and practical) that need to be considered to successfully master ICAS. For this purpose, Sect. 2 of the current work is devoted to an illustrative theoretical overview, while Sect. 3 discusses practical aspects that are vital to successfully set up an ICAS system. Illustrative practical examples are used throughout the work, with a focus on recent achievements and emerging trends in this exciting field.

2 Theoretical fundamentals of ICAS

In the following sections, an illustrative summary and a comprehensive interpretation of the most important theoretical findings on ICAS will be given, with the aim of making the technique accessible to a wide range of potential users. Especially engineers and chemists, who sometimes have only basic knowledge in laser physics, might benefit from this approach.

For a better understanding of the theoretical fundamentals of ICAS, a short intuitive explanation of the underlying effect is given first. The main mechanism with ICA is the competition of laser modes (i.e., frequencies) for the common gain, shared within the homogeneous linewidth Ω_h of the laser gain medium (Fig. 1 bottom): Laser modes that coincide with absorption lines of the sample (with a linewidth ∆ν) experience additional losses, i.e., disadvantages in the competition with neighboring (unaffected) modes when passing through the gain medium. It is important to note that mode competition only occurs if ∆ν < Ω_h (otherwise, the situation is equivalent to the presence of a broadband loss). With each roundtrip inside the resonator, this effect accumulates and leads to an imprint of the absorption spectrum of the sample directly onto the broadband laser emission spectrum. During this process, the laser gain compensates broadband losses originating from, e.g., light scattering and absorption by dust, beam steering, or limited transmission through windows, while the narrow-line absorption of the sample (with ∆ν < Ω_h) stays uncompensated. This mechanism is unique for ICAS and eliminates the need for background-free samples, enabling broadband (i.e., multi-line or multi-species) and highly-sensitive measurements, also in challenging environments, e.g., in shock-tubes [7, 8], flames [4, 9,10,11], plasmas [6, 12], or nanoparticle-synthesis reactors [13]. A recent review summarizes the achieved results and new developments particularly in energy and combustion science [14].

2.1 Origins of the technique

Historically, the discovery of the highly-sensitive intracavity absorption (ICA) effect goes back to 1970, i.e., only ten years after the demonstration of the first laser. This was a time, when the understanding of laser processes was still fragmentary and many experimental observations awaited their deeper investigation and theoretical explanation. One of such observations was the line structure of the emission spectra of broadband Nd³⁺ glass lasers. It was the attempt of understanding this line structure that finally led to the discovery of the ICA effect [2]. In that pioneering work, the authors found that the emission spectrum can be extremely sensitive to frequency-dependent losses in the resonator. In particular, they observed that the sensitivity to such losses is strongly dependent on the ratio Ω_h/∆ν between the homogeneous linewidth of the gain Ω_h (~ 20 cm^− 1 in that case) and the linewidth of the introduced loss ∆ν.

Two cases were examined in detail: with Ω_h/∆ν >> 1 and Ω_h/∆ν ≈ 1. The spectrally selective losses have been generated by placing (into the resonator) a glass cell made of two plates with wedged outer surfaces and plane inner surfaces, with a distance l between the inner surfaces. This is equivalent to placing an additional Fabry-Pérot resonator (FPR) inside the laser cavity. As a consequence, interference losses with a linewidth of ∆ν = 1/2l (free spectral range of the FPR) have been generated by using two different cell lengths: l₁ = 0.45 cm (∆ν₁ = 1.1 cm^− 1) and l₂ = 0.025 cm (∆ν₂ = 20 cm^− 1 ≈ Ω_h). Additionally, the magnitude of the induced loss has been minimized by filling the cell with a benzene/chlorobenzene mixture, which had a similar refractive index as glass. The resulting reflection coefficient of the inner cell surfaces was as low as 2 × 10^− 7. Nevertheless, it was shown that for the case of Ω_h >> ∆ν the observed emission spectrum showed a strong modulation (i.e., a pronounced line structure) with a period of ∆ν.

Some spectral modulation has also been observed in the case of ∆ν ≈ Ω_h, however, here, the modulation depth strongly depended on the actual ratio of Ω_h/∆ν: To enable a small variation of that ratio around 1, the gain medium was cooled down, resulting in a reduction of the homogeneous linewidth of the gain. With decreasing temperature, the observed modulation depth reduced gradually, until an almost smooth emission spectrum has been obtained (corresponding to the case Ω_h < ∆ν). These effects were independent of the nature of induced additional losses, i.e., whether they originated from etalon effects or from molecular absorption. In summary, the essence of the work was that high sensitivity to spectrally selective losses was observed when Ω_h >> ∆ν, while a much weaker effect appeared at Ω_h ≤ ∆ν. This was the first evidence of the ICA effect and a clear hint to the strong dependence of this effect upon the Ω_h/∆ν linewidth ratio.

After these pioneering findings, several attempts have been made to explain the observed effects theoretically, e.g., in [5, 15,16,17], but only in 1999, i.e., almost 30 years after the first discovery of the ICA effect, Baev et al. provided convincing theoretical explanations, illustrated by numerical modeling of laser rate-equations for a rhodamine 6G (Rh6G) dye laser [3].

2.2 ICAS with multimode lasers

Since ICAS exploits laser-dynamics processes, it is inevitable to deal with (the results of) laser rate-equations to understand the basic mechanisms. In particular, it is necessary to study the dynamics of multimode lasers. Such lasers are typically based on e.g. rare-earth or transition-metal doped glasses (bulk and fiber geometry) and crystals, or dyes. The common characteristic feature of such lasers is the strong broadening of their absorption and emission lines into bands. Roughly, the widths (FWHM) of these bands are in the range of 10–1000 cm^− 1, while typical absorption-line widths of gas-phase species under atmospheric conditions are about 0.2 cm^− 1. The specific gain-broadening mechanisms are determined by the chosen host material, however, they all can be divided into two general types: homogeneous and inhomogeneous broadening mechanisms.

Homogeneous broadening is characterized by a Lorentzian line shape. It occurs if the whole electronic system, i.e., every laser-active particle (atom, molecule, or ion), experiences the same perturbation. This is the case in, e.g., crystalline materials that are characterized by a regular structure, such that every active ion is surrounded by the same configuration of the host matrix and thus experiences the same crystal field. In contrast, inhomogeneous broadening is characterized by a Gaussian line shape and occurs if individual laser-active particles experience different perturbations, leading to individual shifts of their central frequencies and resulting in an overall broadened spectrum of the whole system. An intuitive example for inhomogeneous broadening is the Doppler-shift in gas lasers (e.g., in HeNe or CO₂ lasers). It should be noted that in real lasers usually both broadening mechanisms are present simultaneously. Glass lasers, for example, are characterized by an amorphous structure of the host material, i.e., each active ion experiences a different crystal field leading to an additional inhomogeneous broadening compared to crystalline materials. In particular, for Nd³⁺-doped silica glass (discussed in Sect. 2.1), the typical inhomogeneous width of the laser transition (at room temperature and wavelength of 1.06 μm) is Ω_inh ≈ 200 cm^− 1 [18], while the homogeneous linewidth is Ω_h ≈ 20 cm^− 1. For comparison, the inhomogeneous broadening in crystalline materials is orders of magnitude smaller, e.g., Nd:YAG typically shows Ω_inh < 0.5 cm^− 1, while Ω_h ≈ 4 cm^− 1 [19].

The following sections will discuss the formation of emission spectra of multimode lasers with intracavity absorption. A distinction will be made regarding the present gain-broadening mechanism(s). The critical question will be: How is the system reacting on narrowband (selective) losses? We will begin with the simplest case, i.e., with single-mode operation, which can be regarded as a basic unit (building block) of multimode operation of lasers with a purely inhomogeneous gain broadening. It will become evident why the sensitivity to intracavity absorption in those cases is much smaller than in the case of homogeneous gain broadening and why the latter mechanism is vital for high-sensitivity ICAS.

2.2.1 Single-mode ICAS

To understand ICAS with a purely inhomogeneously broadened laser gain profile, it is important to have a look on single-mode ICAS first, since the former situation corresponds to ICAS with multiple single-mode lasers. It should be noted that single-mode ICAS is also similar to the case where the absorption linewidth is larger than the homogeneously broadened profile, i.e.,∆ν > Ω_h. In both cases the desired mode-competition effect is absent.

The simple case of ICAS with a single-mode laser is illustrated in Fig. 2 (left). The upper diagram schematically shows the roundtrip gain G(ν) with a linewidth Ω for two cases: When the laser is operated at the wavenumber ν₀ (red) and when it is tuned to ν₁ (blue). The green curve shows the roundtrip cavity-losses γ (sum of all losses) in the steady-state of laser operation, i.e., when all transient laser processes have reached an equilibrium. The frequency-independent part of the losses (horizontal component) originates from, e.g., mirror transmission, or broadband absorption and scattering from optical components, while the small peak located at ν₀ originates from a narrowband absorption line (with a linewidth ∆ν) of, e.g., a gas-phase sample located inside the laser cavity. Note that in general, to obtain laser generation the losses must be compensated by the laser gain. In the case of a single-mode laser emitting at ν₀, this particularly means that also the additional loss due to the gas-phase sample located inside the cavity and absorbing at ν₀, must be compensated by additional gain. Therefore, when operating the laser at ν₀, slightly stronger pumping is necessary to achieve laser threshold compared to laser operation at a nearby wavenumber ν₁, or to the case of absent absorber. In other words, if the pump power is held constant (well above laser threshold) and the laser is tuned from ν₀ to ν₁ (or if the absorber is removed), the laser intensity slightly increases (due to smaller losses), as sketched in the bottom left diagram of Fig. 2. And this difference in laser intensity (with and without absorber) is exploited in single-mode ICAS. The key point here is that the additional selective losses at ν₀ (due to absorption by a sample) must be compensated by the gain.

Fig. 2

ICAS mechanisms with three different laser types. Left: Single-mode laser. Top: Gain of two different modes at ν₀ (red) and at ν₁ (blue) with linewidths Ω. The cavity losses are shown in green. The small peak in the loss curve at ν₀ (linewidth ∆ν) originates from absorption by a sample located inside the cavity. Due to additional losses, the gain at ν₀ (red) must be higher than at ν₁ (blue). Bottom: Resulting laser intensities at the same pump power (well above threshold). Since a fraction of pump power is used to overcome the additional losses at ν₀, the corresponding laser intensity is smaller. Center: Multimode laser with inhomogeneous broadening of the gain. Top: Gain profile (linewidth Ω_inh) at different pump powers, slightly above laser threshold (blue) and well above threshold (red). Bottom: Corresponding laser intensities. When the laser threshold is reached, i.e. the gain profile touches the loss curve, the laser starts emitting at the corresponding frequency ν₁ (blue). When the pump power increases, the threshold condition is also reached for other modes, such that the laser emission spectrum becomes broader (red). The mode at ν₀ experiences additional losses due to intracavity absorption by a sample and, therefore, its intensity is slightly smaller compared to neighboring modes. The red intensity profile is similar to integrated recording of multiple single-mode lasers simultaneously emitting in the spectral range of the gain profile. Right: Multimode laser with homogeneous broadening of the gain. Top: The whole gain profile (linewidth Ω_h) is determined by the modes that touch the loss curve first, here ν₁ and ν₂. As a consequence, the additional selective losses at ν₀ are not compensated by the gain and the corresponding laser intensity (bottom) around ν₀ is much smaller than at ν₁ and ν₂, resulting in high sensitivity to ICA

The evaluation of laser rate-equations for single-mode ICAS [3] shows that when operating the laser well above laser threshold, the effective absorption path length L_eff through the absorber (that is assumed to fill the whole cavity) is given by:

$${L_{eff}} \approx c/\gamma = 2L/T$$

(1)

with L being the cavity length and T the fractional loss of light per cavity roundtrip. For example, if we consider typical values of L = 1 m and T = 0.02, we get L_eff = 100 m. An enhancement factor compared to single-pass absorption is typically defined as ξ = L_eff/L, such that for single-mode ICAS well above laser threshold we get ξ_sm-ICAS = 2/T. Interestingly, this is very similar to the enhancement factor of an (empty) high-finesse passive cavity used, e.g., in cavity-enhanced spectroscopy (CEAS), given by ξ_CEAS = 2R^1/2/(1 − R) [20], with R being the mirror reflectivity, which is typically well above 99%. In fact, when assuming T = 1 – R and R^1/2 ≈ 1, we get ξ_CEAS ≈ ξ_sm-ICAS.

The situation dramatically changes if the single-mode laser with ICA is operated at very low pump powers, i.e. close to threshold. In that case, calculations yield enhancement factors of up to ξ = 10⁷ [3]. However, the practical realization of this scenario is hardly possible due to strict requirements on laser operating parameters, such as, e.g., on the residual instability in laser power that must be held below 10^− 5. It can be concluded that in practice, single-mode ICAS shows a comparable enhancement factor (sensitivity) as passive-cavity techniques.

2.2.2 Purely inhomogeneous broadening of the gain: similarity to single-mode ICAS

The transition from ICAS with single-mode lasers to the case of multi-mode lasers with purely inhomogeneous broadening of the gain is straight forward. Since in the latter case, the gain at different wavenumbers originates from different laser-active particle ensembles, as, e.g., from Ne molecules at different velocities in a HeNe laser, this is similar to the case of multiple independent single-mode lasers oscillating simultaneously.

The central part of Fig. 2 shows inhomogeneously broadened gain profiles G(ν), at threshold with the linewidth Ω_inh (top, blue) and well above threshold (top, red), in presence of an intracavity absorber with a narrow absorption line centered at ν₀. The corresponding laser intensity profiles I(ν) are shown in the bottom diagram. When the pump power is set to the threshold level, i.e., when the gain curve touches the loss curve (top, blue), the corresponding laser mode centered at ν₁ starts to oscillate (bottom, blue). With a further increase of the pump power (top, red), the threshold condition is also reached for neighboring modes and the laser starts emitting in the multi-mode regime (bottom, red). The absorption line centered at ν₀ leads to additional losses in the corresponding laser mode(s). These losses are compensated by the gain, similar to the case of a single-mode laser, such that a small absorption dip can be observed in the broadband emission spectrum (bottom, red). The multi-mode spectrum is shown as a continuous band since the typically used spectral resolution is not sufficient to resolve individual longitudinal laser modes. The mode separation in a linear resonator is given by δν = 1/2L in units of wavenumbers (cm^− 1), or by δf = c/2L in frequency units (Hz). With L = 1 m, this results in δν = 0.005 cm^− 1 (δf = 150 MHz). As a consequence, a typical (practical) interval of spectral resolution of 0.1 cm^− 1 (3 GHz) contains 20 laser modes and the recorded spectrum appears continuous.

In summary, ICAS with lasers exhibiting purely inhomogeneous broadening of the gain shows a limited sensitivity to intracavity absorption due to the fact that each laser mode (frequency) reaches its laser threshold independently from other modes. This particularly means that the loss, including ICA, of each laser mode is individually compensated by a corresponding exclusive portion of the gain. Therefore, only a small sensitivity to ICA can be expected in that case, similar to single-mode ICAS. As will be shown in the following section, the situation radically changes if laser modes share a common gain, i.e., if they start to compete for the same gain. This situation can be achieved with a homogeneously broadened gain.

2.2.3 Purely homogeneous broadening of the gain: Ideal conditions for ICAS

In the case of a homogeneously broadened gain profile, photons of all frequencies within Ω_h interact with all excited laser-active particles (and not with specific classes as in the case of inhomogeneous broadening), resulting in a strong competition among all modes for the common gain. Therefore, the stationary gain of the whole profile (with a linewidth Ω_h) is determined by the frequency at which the gain curve touches the loss curve. Typically, this frequency is the center frequency ν₀ of the profile. However, as shown in the upper diagram of Fig. 2 (right), if additional selective losses due to, e.g., a narrowband absorber are present at ν₀, the stationary gain of the profile is determined by the neighboring frequencies ν₁ and ν₂. And this is the key difference in comparison with the above discussed case of inhomogeneous broadening of the gain, and the origin of the extreme sensitivities achievable in the case of homogeneous broadening (given that the prerequisite of ∆ν < Ω_h is fulfilled). As can be seen from Fig. 2 (right, top), the selective losses at ν₀ stay uncompensated, leading to a significant decay of laser intensity around ν₀ (right, bottom). This is the main effect exploited in ICAS.

Note that broadband cavity losses (due to scattering, beam steering, or dirty windows of an apparatus) are always compensated by the laser gain with ICAS, independent of the particular gain-broadening mechanism. Broadband losses lead to a reduction of the total laser intensity, however, preserving the relative intensity distribution of all laser frequencies. And since the absorption signal is measured as the relative change of the laser intensity (see Sect. 2.3), fluctuations of the total laser intensity do not influence the sensitivity and accuracy of ICAS measurements. This unique characteristic makes ICAS particularly suitable for challenging environments, such as, e.g., combustion [14]. Depending on the employed laser medium, the broadband losses can be tens of percent per roundtrip without significantly affecting the laser process, whereas with passive-cavity techniques, e.g., CRDS, broadband losses are not compensated and the light intensity decays quickly below the noise level [21].

2.3 Spectral dynamics of multimode lasers with homogeneous gain broadening

The previous sections illustrated general mechanisms of the ICA effect. However, to understand ICAS deeper it is necessary to have a look on dynamical aspects, especially on the spectral dynamics of multimode lasers with homogeneous broadening of the gain. As already mentioned, a detailed review of this topic can be found in [3], including explicit solutions and numerical modeling of laser rate-equations, exemplarily illustrated for a typical dye laser. Since the dye laser is close to an ideal four-level laser, it is often used as a model case. In this section, the most important results of the latter work will be summarized and explained by referring to recent practical examples.

When assuming idealized conditions, such as, e.g., the spontaneous emission being the only perturbation of laser dynamics, the laser modes (frequencies) are coupled only via the common gain, and neglecting the wave-nature of light – the rate equations for a typical dye laser are as follows:

$$\dot{M_q}\; = \;{B_q}N({M_q} + \;1) - \gamma {M_q} - {\alpha _q}c{M_q}$$

(2)

$$\dot{N} = P - SN - N{\Sigma _q}{B_q}{M_q}$$

(3)

with B_q being the homogeneously broadened gain (Lorentzian profile) expressed as a rate of stimulated emission per one inverted dye molecule and per one photon in mode q, N the inversion, M_q the mean photon number in q-th mode, γ the broadband losses, α_q the absorption coefficient of the intracavity absorption in mode q, c the speed of light, P the pump rate, and S the rate of spontaneous decay.

The first term in Eq. 2 describes the stimulated emission (plus one photon from the spontaneous emission), the second term the broadband intracavity losses, and the last term is the narrow-band intracavity absorption due to e.g., a gas-phase sample (if present). The consecutive terms in Eq. 3 are contributions by the excitation (pumping), the spontaneous decay, and stimulated emission, respectively.

First, we shall focus purely on the laser dynamics and neglect for a while the intracavity absorption (i.e., the last term in Eq. 2). A characteristic feature of a dye laser is that the lifetime τ of the upper laser level is significantly smaller than the photon lifetime τ_c in the resonator, i.e., τ << τ_c. As a consequence, the population N of the upper laser level almost instantaneously follows any change in the total photon number M in the resonator, i.e. the transition processes between the start of laser excitation (pumping) and stationary laser emission are extremely short and aperiodic. It should be mentioned that this is in contrast to most solid-state lasers, where typically τ >> τ_c, resulting in damped relaxation oscillations of laser intensity in the beginning of the laser process, as illustrated in Fig. 3 for a Nd³⁺-doped fluoride-fiber laser (Nd:ZBLAN) emitting around 1.3 μm [22].

Fig. 3

Laser intensity traces for the pump laser (808-nm laser diode, blue trace) and the corresponding Nd:ZBLAN fiber laser emitting around 1.3 μm (red). For comparison, a typical trace of a dye laser is sketched in grey

As can be seen, shortly after the pump laser (blue) is switched on, the laser emission of the Nd-doped fiber laser (red) starts with a spiking behavior that relaxes to a stationary value only after about 200 µs. In contrast, a dye laser would quickly reach a stationary intensity value, as sketched in Fig. 3 (grey).

In general, the complex laser dynamics of a dye laser can be characterized by four distinct time intervals during which different variables saturate [3]. A qualitative illustration of the characteristic laser-dynamic parameters is shown in Fig. 4 (not to scale).

Fig. 4

Qualitative illustration of the characteristic laser-dynamic parameters for a dye laser (not to scale). The bottom diagram describes the intracavity absorption

Assuming that the pump laser is switched on at t = 0, these intervals can be distinguished as follows:

• 1) Reaching the inversion N_th: 0 < t < t_th

  During this time the inversion N (i.e., the population of the upper laser level in a four-level laser) is growing until the threshold value N_th is reached. At t_th, the laser emission starts with the first few photons.

• 2) Reaching the total photon number M inside the cavity: t_th < t < t_M

  During the second phase, the inversion continues to grow to an intermediate quasi-stationary value and is then quickly depleted to its stationary value by the exponentially growing number of emitted photons M. At t_M, the total number (i.e., from all modes) of emitted laser photons reaches its stationary value M^s.

• 3) Redistribution of the photon numbers among laser modes (frequencies): t_M < t < t_s,0

  After reaching M^s, the spectral distribution among the laser modes continues. The reason is the following: Due to the much higher inversion compared to N_th during the second phase (t_th < t < t_M), the gain is also much higher than in the stationary condition, and in particular the gain exceeds the losses in a wide spectral range, such that the laser starts to emit in a broad spectral range (∆q_th in Fig. 4). However, after the inversion reaches the stationary value at t_M, the gain compensates the cavity losses only for the central mode, similarly to the situation illustrated in Fig. 2 (right), with the only difference of absent ICA now. As a consequence, the intensity of distant modes redistributes towards the central mode, i.e., the initially broad emission spectrum narrows down with time. This phenomenon is often called “spectral condensation”. The stationary value of the spectral emission width ∆q^s is reached at t_s,0. When neglecting spontaneous emission, the whole laser spectrum would condense to just one mode (note that this occurs only in the case of homogeneously broadened gain). However, calculations for a typical Rh6G dye laser (including spontaneous emission) reveal that the spectrum condenses to about 40 laser modes [3].

  As a practical example of this phenomenon, measurements of the spectral condensation of a Cr: forsterite laser (tunable in the 1.2–1.4 μm range) are shown in Fig. 5 [23].

Fig. 5

Adapted from [23], with permission by Optica publishing group Copyright (2019)

Left: Emission spectra of a Cr:forsterite laser recorded at different times t after the onset of laser oscillation. Right: Temporal variation of the emission bandwidths of the laser spectra (circles) and the corresponding fit (solid line).

The recorded emission spectra of the free-running (i.e. without spectrally selective tuning elements) Cr:forsterite laser (Fig. 5, left) show a clear narrowing (condensation) with time. The additional spectral shift towards lower wavenumbers occurs since the laser oscillation always takes place at the maximum of the effective gain profile, given by the difference between gain and cavity loss. And since the gain profile changes between t_th and t_M due to changing inversion, the maximum of the effective gain profile gradually shifts in the very beginning of laser emission. It should be noted that t = 0 in Fig. 5 is set at the beginning of laser oscillations, i.e., at t_th, as usually done with ICAS. The time t > t_th is often referred to as “generation time”, t_g, see also Sect. 3.3 for more details.

The evaluation of the spectral condensation is shown in the right diagram of Fig. 5. The experimentally measured emission width (circles) for t < 100 µs is fitted using the equation ∆ν(t) = At^− 1/2, with A = Ω_h(ln2/γ)^1/2, where Ω_h is the homogeneous linewidth (FWHM) of the gain and γ the cavity loss [23]. It should be noted that this approach enables the determination of Ω_h in practice, particularly resulting in Ω_h = 770 cm^− 1 here, which in turn enables the prediction of the laser tuning range that is typically ~ 50% larger than Ω_h and about 1100 cm^− 1 for the Cr: forsterite laser. The deviation from the fit for t > 100 µs occurs due to, e.g., residual inhomogeneous broadening of the gain that is always present in real lasers, as well as due to mode coupling and spontaneous emission. As a result, the emission width of the Cr: forsterite laser in CW operation does not condense to just one mode (as in the theoretically idealized case of purely homogeneous broadening and absent perturbing effects), but is still about 3 cm^− 1, which corresponds to about 700 oscillating modes (frequencies).

• 4a) Without ICA: reaching stationary conditions: t > t_s,0

  If no intracavity absorption is present, the laser emits in a fully stationary regime after t_s,0.

• 4b) With ICA: reaching the maximum absorption signal/sensitivity: t_s,0 < t < t_s

  Interestingly, when solving the laser rate equations with intracavity absorption (last term in Eq. 2), another characteristic time appears after t_s,0, namely the so-called spectral saturation time t_s, i.e., the time at which the absorption signal saturates, see Fig. 4 (bottom). In particular, it can be shown that t_s = π t_s,0 [3].

When solving the laser rate equations for the photon number M in a mode with ICA, it turns out that the solution has the same form as the well-known Lambert-Beer law:

$$M(t) = {M_0}(t)\;\exp ( - \alpha ct)$$

(4)

with M₀ being the photon number in absence of ICA. The absorption signal is defined as K = ln(I₀/I) = ln(M₀/M) = αct. The product ct is the effective absorption path length L_eff, representing the spectral sensitivity in ICAS measurements. It should be noted that the linearity of K and L_eff with time t is only valid for t < t_s. As can be seen from the bottom diagram of Fig. 4, the linear growth of the absorption signal K(t) = αL_eff(t) saturates at t_s. With this, the effective absorption path length is given by:

$${L}_{\text{e}\text{f}\text{f}}\left(t\right)=\left\{ \begin{array}{c}ct, t<{t}_{\text{s}} \\ {ct}_{\text{s}}, t\ge {t}_{\text{s}}.\end{array}\right.$$

(5)

Note that Eq. 5 needs to be modified by a filling factor if the absorber does not occupy the entire laser cavity. The theoretical upper limit for the spectral saturation time of a dye laser is about 28 s [3], which corresponds to L_eff = 8.4 × 10⁶ km, being more than 20 times the distance from the Earth to the Moon. However, the highest sensitivity achieved so far in practice is about two orders of magnitude smaller: L_eff = 7 × 10⁴ km [1], which still corresponds to about two roundtrips around the Earth. The reason for the deviation of L_eff in a real laser is the presence of various mechanisms that perturb the (theoretically idealized) laser dynamics. A detailed description of these processes is provided in Ref [3]. The essence is that they lead to redistribution of photons (e.g., by scattering and nonlinear effects), thus acting as additional photon sources for modes with ICA and effectively filling up the absorption lines(s) that appear less deep. Depending on the used gain medium and the laser operation parameters, the dominating processes can be, e.g., four-wave mixing (FWM), Rayleigh- and Brillouin-scattering. While some of these parasitic effects are intrinsic for specific types of laser gain-media (e.g., crystals, glass fibers, dye solutions), others can be controlled by appropriate operation parameters of a laser. In this context, it should be noted that any kind of mode coupling is highly detrimental for ICAS since it circumvents the necessary mode competition. This is the main reason why the nowadays popular frequency combs, as well as quantum cascade lasers that intrinsically show strong nonlinearity (in particular FWM), cannot be used for ICAS.

As an illustration of the influence of nonlinear effects on spectral sensitivity, Fig. 6 shows the growth and saturation of the effective absorption path length L_eff of a real ICAS system based on the above-mentioned Cr:forsterite laser [23].

Fig. 6

Adapted from [23], with permission by Optica publishing group Copyright (2019)

Effective absorption path length L_eff vs. generation time t for different pump rates η (colored dots). The straight line corresponds to L_eff = ct.

Since nonlinear effects strongly depend on the pump rate, the ICAS measurements were performed at three different relative pump rates η = P/P_th, with P and P_th being the applied and threshold pump rates, respectively. The evaluation was accomplished by measuring the absorption signal K = ln(I₀/I) of the oxygen absorption line at ν = 8030.17 cm^–1 at several laser generation times t and subsequently calculating the effective absorption path length L_eff = K/α by using the absorption coefficient α listed in the HITRAN database [24]. As can be seen, the effective absorption path length grows according to L_eff = ct in the beginning of the laser process for all pump rates. However, depending on the applied pump rate, it starts saturating at different generation times. The shortest spectral saturation time of t_s ≈ 1.3 ms is reached with the highest applied relative pump rate of η = 4.5 and corresponds to a sensitivity limit of L_eff = ct_s ≈ 400 km. In contrast, when operating the laser near the threshold, i.e., at η = 1.1, the sensitivity continues growing and is not yet saturated at t = 9 ms.

3 Frequent experimental challenges

The previous sections provided a summary of the fundamental aspects of ICAS. This section is devoted to describing some of the most important practical aspects that need to be considered for a successful realization of ICAS measurements.

The main experimental difference between ICAS and other spectroscopic techniques (besides the requirement for a high-resolution spectrometer) is the necessity to set up homemade laser systems. In general, comparably simple lasers consisting of a gain medium, a two-mirror cavity and a tuning element (e.g., prism, lens, or thin pellicle) are suitable for ICAS. Nevertheless, several typical obstacles might appear during the setup and operation of an ICAS system. The most frequent challenges and the corresponding solutions are described in the following.

3.1 Detrimental spectral structures

The enormous sensitivity of ICAS to selective losses unfortunately also implies high sensitivity to any narrow-band non-absorption losses. As a consequence, optical effects, such as interference or birefringence, can lead to detrimental spectral structures and significantly hamper spectroscopic measurements.

3.1.1 Interference effects

One of the most frequent obstacles is the ordinary etalon effect arising from plane-parallel optical surfaces inside the laser resonator. The solution is also well-know: All optical elements, i.e., lenses, absorption-cell windows or gain elements, must either be set at the Brewster angle, or have a very good anti-reflection (AR) coating. In particular, it is recommended to use thick and wedged glass substrates as resonator mirrors, with their backside ideally being AR-coated.

The use of optical fibers deserves a special note since there are several pitfalls to be considered. When it comes to the setup of fiber lasers, several commercial components, such as wavelength-division multiplexers (WDM), splitters, optical diodes, or circulators, might appear useful, in particular for the setup of ring cavities. The latter configuration allows avoiding standing waves and the associated spatial hole-burning. Therefore, in comparison with linear cavities, ring-based ICAS setups allow to double the maximum effective absorption path length [25]. However, it must be considered that commercial components are tailored for specific requirements, e.g., for telecommunication applications in the 1.55 μm range, i.e., their suitability for ICAS cannot be guaranteed.

As a practical example, Fig. 7A and B show two variants of ring-cavity setups based on an erbium-doped active fiber and different commercial fiber components, such as WDM, optical diode, circulator, and 1/99 splitter [25]. Preliminary tests of the WDM (performed in a linear cavity) enabling the input of the pump light at 980 nm through one fiber port, while preventing the ~ 1.55-µm laser light from exiting the same port, have shown that the WDM produces no spectral structures. However, as shown in the right diagram of Fig. 7, the straight-forward implementation of a fiber-based optical diode and the 1/99 splitter (variant A) led to severe spectral structures already in the very beginning of laser emission (blue curves), which became particularly pronounced in continuous (CW) operation (red curves). The origin of the observed spectral structures could not be identified since the inner architecture of the commercial components was unknown. Only the replacement of the optical diode by a fiber circulator that fulfills the same function of unidirectional light circulation, and the splitter by a coated glass wedge (OC in Fig. 7B) that enables the outcoupling of laser light towards a spectrometer, facilitated the elimination of the spectral structures in the ring laser, as shown in the upper panel of Fig. 7 (right). Note that all fiber end surfaces were AR coated to suppress back reflections that also could lead to etalon effects.

Fig. 7

Left: Two variants of ring cavities based on an Er-doped fiber laser. Both variants use a 980-nm laser diode (LD) as pump source and a WDM for its injection into the ring cavity, with L being lenses and AR anti-reflection coatings. While variant A is based upon an optical diode and a 1/99 splitter, variant B uses a circulator and a wedged glass substrate (OC) instead. Right: Emission spectra of the Er-doped fiber ring lasers based on different fiber-optic elements. Blue spectra are recorded in the beginning of (pulsed) laser oscillation, while red spectra represent the CW operation

Another source of spectral structures arises if multi-mode fibers are used with ICAS. In this case, interference between transversal fiber modes results in strong spectral channeling, similar to the conventional etalon effect. An example of the influence of this effect is shown in Fig. 8.

Fig. 8

Emission spectrum of the Nd:ZBLAN fiber laser showing strong spectral structures due to the interference of different transversal fiber modes. Inset: Sketch of a fiber cross-section with the two first transversal modes LP₀₁ (red) and LP₁₁ (green). The arrows represent possible orientations of the electric fields

In this case, a Nd³⁺-doped fluoride fiber with a cut-off wavelength that was slightly longer than the lasing wavelength of 1050 nm, was used [22]. As a result, the recorded emission spectrum (blue) showed strong fringes. The inset in Fig. 8 illustrates a fiber cross-section and the two first guided transversal fiber modes, the LP₀₁ (red) that is similar to the TEM₀₀ mode in free space, and the LP₁₁ mode (green). The arrows represent the orientations of the electric fields. Even in this simplest case, there are areas where the transversal modes interfere constructively (parallel arrows) or destructively (antiparallel arrows). And since each transversal mode carries various longitudinal modes (frequencies), there are always frequencies experiencing destructive interference, resulting in strong spectral channeling. Consequently, to avoid these effects, only single-mode fibers should be used for ICAS thus ensuring the oscillation of only the LP₀₁ mode.

3.1.2 Birefringence effects

Besides interference effects, birefringence can also result in spectral structures. This effect needs to be considered in many solid-state lasers, e.g., in the wide-spread Ti:sapphire or the mentioned Cr:forsterite laser [23] that is used for illustrations in the following. In general, if the polarization of the incident laser light is not aligned with one of the axes of the refractive-index ellipsoid of the gain medium, the polarization splits into individual components that experience different refractive indices, i.e., they accumulate different phase shifts when passing through the gain medium. As a result, only wavelengths with a net phase shift of a multiple integer of 2π experience no net polarization rotation, i.e., no additional reflection losses at the Brewster-cut surfaces of the crystal. The remaining wavelengths experience selective losses that transform into spectral structures, similar to an etalon effect. Note that this is the working principal of the so-called Lyot filter that is often used for wavelength tuning. Consequently, to avoid these effects, the birefringent gain medium (in most cases a crystal) must be rotated accordingly to match the orientation of the crystal axis with the polarization of the optical field. The influence of a mismatch of these axes is illustrated for the Cr:forsterite laser in Fig. 9.

Fig. 9

Adapted from [23], with permission by Optica publishing group Copyright (2019)

Influence of crystal rotation on the emission spectrum of the Cr:forsterite laser, shown for different angles between the crystallographic b-axis and the polarization of optical field in the cavity. The absorption lines originate from atmospheric O₂ and H₂O, as illustrated by the calculated transmission spectrum from the HITRAN database (top, green).

The broadband emission spectra of the Cr:forsterite laser have been recorded with an absorption path length of L_eff = 10 km and contain various absorption lines of atmospheric O₂ and H₂O (see the corresponding calculated transmission spectrum from the HITRAN database shown in the upper diagram in green). As can be seen, strong spectral structures appear already at an angle mismatch of 2° between the crystallographic axis (b-axis in that case) and the polarization of the optical field (bottom diagram). Therefore, a proper adjustment/alignment is crucial when setting up ICAS systems based on birefringent active media.

3.2 Spectral noise and its reduction

The major source of spectral noise in pulsed multimode lasers is the presence of quantum fluctuations [26, 27]. It should be noted that this spectral noise component is random and, consequently, it can be reduced by averaging. In the case of static or periodic processes, the averaging can be performed over n spectra (or n periods) leading to a total noise reduction by a factor of $\sqrt{n}$. On the other hand, effective averaging can also be achieved by increasing the number of oscillating laser modes inside the interval of spectral resolution of the recording system, as illustrated in Fig. 10 (left). The frequency separation of individual (longitudinal) modes in a linear cavity with the length L is given by ∆f = c/2L, with c being the speed of light. Therefore, an increase of the cavity length by a factor n leads to a noise reduction by $\sqrt{n}$.

Particularly time-resolved measurements can benefit from the latter averaging approach and the reason is the following: The minimum time interval between two pulses ∆t (highest time-resolution) with ICAS consists of the three components: the buildup time of the inversion t_i, the laser pulse duration t_l and the photon lifetime in the resonator t_p. While t_l and t_p change proportionally to the cavity length, t_i changes only slightly. Consequently, when increasing the cavity length by a factor of n, the same noise reduction is achieved in a time that is approximately nt_i shorter than in the case of a short cavity and averaged recording of n spectra. In other words, this concept allows faster noise reduction and enables low-noise single-shot measurements, as already demonstrated in the 1.5–1.6 μm spectral range [7, 12]. A similar strategy can also be applied for non-fiber cavities, as e.g. demonstrated by folding the cavity of a dye laser [8], however, only the fiber geometry allows to maximize this effect and achieve substantial noise reduction.

In general, the fiber geometry offers several unique advantages. First of all, a fiber can be coiled up to a diameter of about five centimeters, thus enabling very compact experimental setups. Second, fibers facilitate highly modular laser systems, since different active fibers can be spliced to passive fibers with appropriate coatings, i.e. highly-reflective (HR) or anti-reflective (AR). Figure 10 (right) illustrates a realization of a very compact ICAS system [28] based on an Er-doped fiber that is splices to 50 m of passive fiber.

Fig. 10

Adapted from [28] with permission by Springer Copyright (2017)

Left: Illustration of the number of oscillating laser frequencies with a short (top) and a long (bottom) cavity. The higher density of laser modes in a long cavity ensures effective averaging within the interval of spectral resolution. Right: Experimental setup exploiting a long fiber cavity, with LD being the pump laser-diode, L: lenses, M: mirrors, AR: antireflection coating, CCD: charge-coupled device (line camera). All components of the fiber laser shown in the dashed box are incorporated into a small housing (fiber laser unit). The spectral tuning of the laser is accomplished by moving the lens L3 along the optical axis.

Most of the components of the fiber laser are integrated into a small box (approx. 6 × 8 × 4 cm³), such that only the second mirror M2 of the resonator is needed for a typical ICAS system. It should be noted that the lens L3 not only focuses the light from the fiber onto the mirror M2 and back, but it is also movable along the optical axis of the resonator thus serving as a wavelength tuning element: When translated along the optical axis, chromatic aberration leads to optimal fiber-coupling of only a specific center wavelength.

To maximize the detection sensitivity with ICAS, the concept of noise reduction by using long fiber cavities needs to be transferred to the MIR spectral range, where the fundamental vibrational bands of many species are located [24]. And this possibility recently became feasible through the development of suitable low-loss chalcogenide glasses, as reviewed in [29]. As a result, the first fiber lasers emitting beyond 4 μm have already been demonstrated with Tb-doped [30] and Ce-doped [31] glasses. These developments appear particularly promising for future ICAS applications.

3.3 Determination and control of the sensitivity

This section will illustrate the proper determination and control of the sensitivity with ICAS. Since the sensitivity is routinely characterized by the effective absorption path length L_eff defined in Eq. 5, the task is to properly measure and control the generation time t (often also denoted as t_g). These aspects are particularly important to ensure correct ICAS measurements.

3.3.1 Accurate determination of the generation time/sensitivity

When recording measurement data with ICAS, it appears particularly important to understand where the time t = 0 is located, from which the generation time t is measured. Figure 11 (left) shows a typical oscilloscope picture of the relevant signals observable during an ICAS measurement sequence.

Fig. 11

Left: Typical signals during an ICAS measurement sequence: Pump-laser excitation (green), laser generation (red), and the detection using a narrow detection window of a CCD (blue) that can be shifted to different times (dashed lines). Right: Typical evaluated absorption signal (dots) and corresponding fits (lines) determining the times t = 0 and t_s

The starting point t = t₀ is determined by the start of the excitation source (green), i.e., a pump laser in most cases. A short time later, the actual ICAS laser (red) starts to oscillate. However, it would be a mistake to simply set the location of the rising edge as t = 0: Since the ICAS process already starts with the very beginning of the lasing process, intuitively the time t = 0 should be determined by the threshold of the laser emission, i.e., by the time when the very first laser photons have been generated. However, since the corresponding intensity is extremely low, this time cannot be directly captured by a photodiode and the rising edge of laser intensity becomes visible only at some later time, compare also Fig. 4. Nevertheless, as illustrated in Fig. 11 (left, blue) the relevant times can be determined by recording absorption spectra at different times t₁–t_n by, e.g., using a CCD camera with a narrow detection window and consecutively shifting this recording window relative to, e.g., the excitation signal. The evaluated absorption signal typically looks similar to Fig. 11 (right). As can be seen, the linear part of K(t) can be fitted to determine the exact location of t = 0. Moreover, the crossing point of the linear fit with the horizontal line originating from the saturated absorption defines the spectral saturation time t_s.

It should be noted that the described recording procedure of ICAS spectra by using a narrow detection window of a CCD camera is not always possible and, instead, the entire laser pulse must be recorded. This is particularly the case when working with short laser pulses and/or in unconventional spectral regions, where corresponding cameras are not available. As an example for integrated recording, the case of the Fe:ZnSe laser emitting ns-pulses in the spectral range of 3.7–5.3 μm [32] is briefly illustrated in the following. Figure 12 shows the corresponding experimental setup (left) and the recorded pulses (right) of the pump laser (green) and the Fe:ZnSe laser (red). A notable specialty of the experimental setup is that conventional aluminum mirrors are used to form the resonator of the Fe:ZnSe laser (M1 and M2). The outcoupling of laser light towards detection is assured by slightly tilting the crystal from the Brewster angle, such that the crystal surfaces reflect about 5% of the light. Such a scheme can be of great help if corresponding dielectric mirrors are not available for a specific spectral range.

Fig. 12

Adapted from [32], with permission by Optica publishing group Copyright (2021)

Left: Experimental setup of the Fe:ZnSe laser, with M and Al being aluminum mirrors, PR: photodetector. A CaF₂ prism is used for spectral tuning of the laser. Right: Temporal profiles of the pump (green) and laser (red) pulses.

In general, the integrated absorption signal has a complex dependence on the absorption coefficient α [33]

$$K=\text{l}\text{n}\left(\frac{\underset{0}{\overset{p}{\int }}{I}_{0}\left(t\right) dt}{\underset{0}{\overset{p}{\int }}{I}_{0}\left(t\right)\text{exp}\left[-\alpha \left(\nu \right)ct\right]dt}\right)$$

(6)

with I₀(t) being the temporal laser-pulse shape and p the laser-pulse duration. A detailed discussion of this equation can be found in, e.g., Ref [6]. In the following, only general consequences will be highlighted. In particular, Eq. 6 suggests that for non-symmetric laser pulses the high-intensity parts have a stronger contribution to the integrated absorption signal than low-intensity parts. Nevertheless, in most cases the integrated absorption signal can be represented by an integrated absorption path length L_{eff, I}, or the corresponding time t_i, similar to the commonly used relation originating from the Lambert-Beer law, K = αL_{eff, i} = αct_i. Experimentally, L_{eff, i} can be determined from a calibration measurement with a known concentration of a sample and a fit of the integrated experimental absorption spectrum by using, e.g., the HITRAN database [24] and varying the absorption path length until an agreement with the experimental spectrum is obtained. In the case of the Fe:ZnSe laser, the fitting procedure resulted in L_{eff, i} = 5.8 m, corresponding to t_i ≈ 20 ns. Considering the strong asymmetry of the Fe:ZnSe pulse, the shift of t_i towards the beginning (high-intensity part) of the laser pulse appears intuitive. It should be noted that in the case of a symmetric laser pulse, t_i would be located in the center of the pulse. Similarly, in the case of a narrow detection window of a CCD, t_i is located in the center of the recording window, as shown in Fig. 11 (left).

3.3.2 Control of the sensitivity

The proper control of the sensitivity of ICAS measurements is particularly important when working with laser materials that have long inversion times t_th (compare Fig. 4), i.e., relatively long delay between the start of excitation and beginning of laser emission. As an example, the excitation sequence of the mentioned Cr:forsterite laser [23] will be discussed in the following. Figure 13 (left) shows typical signals recorded during a laser-pulse sequence.

Fig. 13

Adapted from [23], with permission by Optica publishing group Copyright (2019)

Diagrams of the control signal for the pump laser (green), the pump laser emission (blue), and the Cr:forsterite laser emission (red). Left: Modulation of the pump laser at full modulation depth. Right: Modulation with a DC offset of the control signal by 0.4 V.

The pump laser in this case was an Yb-doped fiber laser, which was pumped by a diode laser, whose output power was determined by the applied voltage. Figure 13a shows a full-depth modulation of the applied voltage, from zero to 0.7 V. As can be seen from Fig. 13b, the fiber laser starts emitting about 250 µs after the onset of excitation (marked by a dashed vertical line). A strong relaxation spike appears at the beginning of the pump-laser emission, which is typical for most solid-state lasers, where the upper-state lifetime is much larger than the photon lifetime in the cavity (see also Fig. 3). After additional 20 µs, the Cr:forsterite laser also starts to oscillate (Fig. 13c). The crucial point in this excitation scheme is the following: The delay between the onset of excitation and the start of laser emission depends on the time required to build up the required inversion in the pump and Cr:forsterite lasers. Therefore, this delay varies with pump power (and its fluctuation), cavity loss and spectral tuning. In contrast, the position of the detection window of the CCD camera is fixed, typically to the beginning of excitation. Consequently, induced relative shifts of the start of laser emission will result in measurements with different effective absorption path lengths (L_eff = ct), thus reducing the accuracy of absorption measurements.

To solve this problem, a DC offset of 0.4 V has been added to the modulation amplitude of the control voltage, as shown in Fig. 13d. With this, the output power of the pump laser was constantly held just below the threshold of the Cr:forsterite laser (Fig. 13e and f), while a slight increase in the control voltage immediately initiates the emission of the Cr:forsterite laser. Note that in this case the delay between the excitation of the pump laser (green) and the beginning of Cr:forsterite laser emission (red) is very small (Fig. 13f). Consequently, this excitation scheme enabled time-resolved absorption measurements with a fixed L_eff. Additionally, the strong spikes in the beginning of the pump- and Cr: forsterite-laser emission almost disappeared.

It should be noted that controlling the sensitivity with e.g. dye lasers is much easier, because the inversion time is typically very short, e.g., only few nanoseconds for Rh6G [3]. As a consequence, the possible induced shift between the excitation and laser emission is negligible for most practical situations.

4 Summary

This work provides a comprehensive review of theoretical basics of ICAS and highlights the most important practical aspects that need to be considered for a successful realization of ICAS measurements. In particular, the basic requirement for the enormous sensitivity of the technique, namely that the homogeneous linewidth of the gain must exceed the absorption-line width, has been explained and illustrated in detail. Besides that, the most important aspects of laser dynamics of multimode lasers have been highlighted. Finally, several typical obstacles that might appear during the setup and operation of an ICAS system have been discussed. To reach a broad audience, illustrative practical examples have been used throughout the work, with a strong focus on recent achievements and emerging trends in this exciting field.