Broadband dispersion measurement of photonic crystal fibers with nanostructured core

Chromatic dispersion is one of the most fundamental phenomena affecting propagation in optical fibers. Chromatic dispersion is of particular importance in telecommunication systems, where wavelength dependence of the refractive index results in detrimental broadening of propagating pulses.

Photonic crystal fibers (PCFs) enable control of dispersion characteristics in a broad spectral range by means of lattice constant and linear filling factor (Saitoh et al. 2003). In practice, the range of changes is limited by material dispersion of glass and effective mode area of the designed fiber. In supercontinuum generation, dispersion critically defines formation of new wavelength components in nonlinear optical fibers during broadening of spectrum (Dudley et al. 2006). Therefore, dispersion characteristic of optical fiber is a crucial criterion in designing of nonlinear optical fibers for supercontinuum applications.

All-solid photonic crystal fibers (ASPCFs) are an alternative approach to the more popular air-glass solid core PCFs. In this case, air holes are replaced with glass inclusions of a different refractive index to that of the background glass. The advantage of APCFs, as compared to the air hole-based PCFs, is the possibility of dispersion control with an additional parameter, which in this case is material dispersion of the second type of glass used for lattice design. Moreover, control of the fiber parameters during the drawing process is simpler and obtaining fiber parameters similar to the designed ones is straightforward (Buczynski et al. 2012a, b). The development of ASPCFs has been reported by several groups (Feng et al. 2003; Luan et al. 2004; Buczynski et al. 2012a, b) and successfully reported for supercontinuum generation (Kibler et al. 2009; Wang et al. 2012; Stepniewski et al. 2014). Introduction of subwavelength inclusions in the core enables an additional degree of freedom in shaping of dispersion profile, while maintaining a constant value of effective mode area (Buczynski et al. 2011).

Widely used techniques for dispersion charaterization, like the time-of-flight method or the modulation phase shift method (Cohen 1985), require use of long sections of optical fiber. Apart from high cost, mentioned techniques are inapplicable for optical fibers made of highly nonlinear glasses due to their high attenuation. Another approach is to use an interferometer combined with a broadband light source (Diddams and Diels 1995). A modified Mach–Zehnder interferometer technique enables measurement of dispersion characteristic in short lengths of optical fiber (Hlubina et al. 2007). We used this relatively cheap and easily applicable method for dispersion measurements of all-solid microstuctured fiber with nano-inclusion in the core.

Interferometer presented in Fig. 3a is unbalanced, which means that the calculation of the dispersion is not based on the absolute group index measurements, but on the relative measurement of \(N\). It follows, that the \(N\) value obtained in the measurements is reduced by an unknown constant \(C\) and can be named as a relative, or a differential value of \(N\). Therefore, using the Michelson interferometer, we estimated the optical path difference introduced by every optical component placed in the arms of the MZI: MO2, MO3 and NDF in the spectral range of 450–1,600 nm, and approximated the obtained data points with a polynomial fit.

This procedure simplifies the dispersion estimation using MZI in the following way:

$$\begin{aligned} 2\Delta L=\underbrace{d_{MO2} (N_{MO2} -1)}_{OPD\;\;of\;MO2}+\underbrace{d_{MO3} (N{ }_{MO3}-1)}_{OPD\;\;of\;MO3}-\underbrace{d_{NDF} (N_{NDF} -1)}_{OPD\;\;of\;NDF}+z(N_{FUT} -1), \end{aligned}$$

(1)

where \(2\Delta L\) is the doubled reference arm compensation length, and the subsequent elements of this formula are optical path differences measured for the second and third microscope objectives (MO2 and MO3) and for the NDF. The last part is the unknown optical path difference of the fiber of length \(z\). It is obvious, that all group refractive indices, as well as the \(2\Delta L\) are wavelength functions, which was not included in formula (1) for clarity. Concluding, the relative group refractive index can be calculated using formula (2):

$$\begin{aligned} N_{FUT}^{relative} =\frac{2\Delta L-{ OPD}_{MO2} -{ OPD}_{MO3} +{ OPD}_{NDF} }{z}+1. \end{aligned}$$

(2)

Measured relative group index as a function of wavelength is shown in Fig. 4a and can be fitted with typical approximation curve, for instance the Laurent polynomial:

$$\begin{aligned} N_{FUT}^{relative} (\lambda )=\frac{A_1}{\lambda ^{4}}+\frac{A_2}{\lambda ^{2}}+A_3 +A_4 \lambda ^{2}+A_5 \lambda ^{4}. \end{aligned}$$

(3)

The dispersion of the fiber is defined as:

$$\begin{aligned} D=\frac{1}{c}\frac{dN_{abs}}{d\lambda }, \end{aligned}$$

(4)

where \(c\) is the velocity of the light in the vacuum and \(N_{abs}\) is absolute value of the group refractive index. We can apply formula (4) in following way:

$$\begin{aligned} D=\frac{1}{c}\frac{dN_{FUT}^{relative}}{d\lambda }, \end{aligned}$$

(5)

because the absolute and relative value of the group index are related by the unknown constant \(C\):

$$\begin{aligned} N_{abs} =N_{FUT}^{relative} +C \end{aligned}$$

(6)

and the derivative of a constant is zero. The dispersion dependence upon wavelength calculated this way is presented in Fig. 4b, c, where circles are representing measurement data points.

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The modal and dispersion properties of the PCFs were calculated using the finite element method (FEM) commonly used for modelling of PCFs. The material dispersion of the considered glasses is taken into account through the Sellmeier coefficients. We then compared the measurement results with simulated profiles obtained numerically, as described in details in our previous work (Pniewski et al. 2013) (blue curve).

We obtained a good agreement between modeling and experimental results. Both profiles match perfectly for short wavelengths. A small difference was observed for longer wavelengths above 1,100 nm. Slope of the dispersion profile is very small in this area. Small variation of dispersion value results in relatively large difference in wavelength. Based on performed simulation we predict the location of zero dispersion wavelength at 1,516 nm. Measurement results indicate that ZDW is located at 1,680 nm. Difference between modeled and measured results are related to some approximation assumed in the modeling. First of all we assumed sharp transition between SF6 and NC21 glasses. However diffusion occurs between glasses and transition between glasses is smoothed in a real fiber structure. Second source of error introduced into the simulation is uncertainty of geometric dimension reading from the SEM images. In addition, calculations introduce errors with limited mesh size and assumed material dispersion characteristics. As a result, developed fiber has ZDW shifted by 164 nm toward longer wavelengths with respect to design and cannot be used for efficient supercontinuum generation with 1,550 nm femtosecond fiber lasers as pump source as it was predicted in (Pniewski et al. 2013). For this purpose, further optimization of fiber design and fiber drawing is required for use with 1,550 fiber femtosecond sources. The dispersion curve can be lifted up and the zero wavelength can be pushed into the shorter wavelengths in a new fiber with larger pitch and with larger inclusion in the core. Currently the developed fiber can be considered for supercontinuum generation in anomalous dispersion range with thulium femtosecond lasers which operate around \(2\,\upmu \hbox {m}\) (Wan et al. 2013).

New type of microstructured fiber with flat dispersion was designed and fabricated. A modified method of spectral interferometry for the chromatic dispersion measurements was used to verify its properties. The dispersion of an all-solid nano-inclusion microstructured fiber was measured in a wide spectral range between 600 and 1,800 nm. Taking into account the approximation curve of the measured dispersion, the zero dispersion wavelength was located in this fiber at 1,680 nm. The discrepancy between experimental and numerical results is assigned to the uncertainty of dimensions of the fabricated structure, taken from its SEM images for the calculations, which was related to the diffusion effect between the glasses.