1. Introduction

Since the groundbreaking achievements of Ranka et al., who first demonstrated a suitability of microstructured fibers for supercontinuum generation [1], a significant progress was done in spectra quality, especially in terms of shot-to-shot spectral stability, as well as in understanding of supercontinuum generation processes [2, 3]. In particular, it was shown that normal dispersion fibers are suitable for generation of coherent supercontinuum [4, 5], which can be used as a source for an optical coherence tomography [6, 7], an ultra-high repetition rate spectroscopy [8], and optical telecommunication [9, 10].

There are a few factors limiting the quality of supercontinuum generated in normal dispersion fibers. It was shown recently that at certain conditions spectral coherence is deteriorated by incoherent cloud formation and incoherent optical wave breaking [11]. However, for femtosecond pulse pumping, coherence degradation appears only after a very long propagation. The other limiting factor is a weak unintentional birefringence intrinsic to microstructured nonlinear fibers [12]. Tu et al. investigated depolarization phenomena in a commercially available normal dispersion fiber pumped with a solid-state Yb:KYW pulse laser giving 229 fs pulses with the central wavelength at 1041 nm. They showed by solving a system of coupled-generalized nonlinear Schrödinger equations that in case of weakly birefringent fibers, vector nonlinear processes drive to pulse depolarization. They suggested that the depolarization could be suppressed in a highly birefringent normal dispersion fiber. The polarized all-normal dispersion continuum of approximately 30 nm width was generated in a highly birefringent fiber by Domingue et al. [13]. Polarization properties of supercontinuum generated in birefringent microstructured fibers were also investigated numerically [14] and experimentally [15] by Zhu and Brown. They showed that pumping in a slow axis is preferred to achieve a stable polarization state of supercontinuum spectrum [14].

An important parameter of supercontinuum is its spectral range. The mid-infrared is of a particular interest because of the presence of strong absorption lines of numerous chemical compounds. Initially, pushing a long wavelength range of an all-normal dispersion supercontinuum towards the mid-infrared in silica fibers seemed not possible due to the difficulty in shifting the maximum of normal dispersion in silica microstructured fibers beyond 1.3 µm [5]. As a result, the all-normal dispersion generated in silica fibers reached only 1.5 µm [4] and in consequence a silica transparency window was not fully covered. The all-normal supercontinua in mid-infrared were demonstrated in more exotic glasses like boron-silicate/silicate [16, 17], ZBLAN/chalcogenide [18], chalcogenide [19], and tellurite [20].

Recently, we addressed the problem of a long wavelength limit of the silica all-normal dispersion supercontinuum in our theoretical [21] and experimental [22] works. The all-normal supercontinuum reaching 2.2 μm was demonstrated in microstructured silica fibers with a germanium doped core and very small air channels in the microstructured cladding [22]. Our results showed that in such fiber it is possible to overcome a positive material dispersion with a waveguide contribution and obtain a flat normal dispersion suitable for the supercontinuum generation reaching mid-infrared. Recently, also another silica microstructured fiber design with air holes diameter varying in subsequent rings was investigated numerically for the all-normal dispersion supercontinuum generation reaching mid-infrared [23].

Here, we present a microstructured silica fiber which has high birefringence and normal dispersion up to 2.5 µm. In this fiber we generate a polarized all-normal dispersion supercontinuum (so called PolAND SC) by pumping with 70 fs pump pulses. We investigate both experimentally and numerically the wavelength broadening and degree of polarization of the generated supercontinuum spectra.

2. Birefringent microstructured silica fibers for PolAND SC

Scanning electron microscope (SEM) images of the fiber fabricated by the Laboratory of Optical Fiber Technology, Maria Curie-Sklodowska University, Lublin, Poland are presented in Fig. 1. The fiber preform was made using the stack and draw technology. The fiber core fabricated with the MCVD method is moderately doped with germanium dioxide (18 mol%), while the fiber cladding was stacked from silica rods and capillaries. The capillaries were arranged in two groups located symmetrically with respect to the fiber core, Figs. 1(a) and 1(b). By applying a high pressure during a fiber drawing process, we achieved lattice squeezing and consequently high fiber birefringence. The SEM images were numerically post processed [Fig. 1(c)] to evaluate the fiber geometrical parameters with better precision. The germanium doped core was approximated with an ellipse (semi-major axis $r_{do}^{\left(x\right)}=1.74\text{μm,}$semi-minor axis $r_{do}^{\left(y\right)}=1.45\text{μm}$). The first ring of air holes formed an ellipse (semi-major axis $r_{co}^{\left(x\right)}=3.11\text{μm,}$ semi-minor axis $r_{co}^{\left(y\right)}=2.76\text{μm}$) and defined location of air holes in subsequent rings according to the Kagome lattice. The air holes’ shapes were also approximated with ellipses (elongated in x direction) and their dimensions were averaged in successive rings. Their averaged semi-axes in the first ring are $r_{h1}^{\left(x\right)}=250\text{nm,}$ $r_{h1}^{\left(y\right)}=230\text{nm}$while in the following rings (from the second to the fifth) $r_h^{\left(x\right)}=210\text{nm}$, $r_h^{\left(y\right)}=200\text{nm}$.

 

Fig. 1 Images of fabricated fiber: SEM images (a), (b); post-processed image (c): white – germanium doped silica, grey – silica, black – air; calculated normalized electric field distributions in fundamental modes at different wavelengths λ with effective area A_eff values given (d), (e), (f).

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The parameters presented above were used in the fiber numerical model developed with Comsol Multiphysics Wave Optics for modeling optical parameters using the finite element method (FEM) and Structural Mechanics module for modeling material birefringence induced by thermal stress. In order to decrease computational effort we reduced the model size 4-fold taking advantage of the fiber symmetry. The model accounted a materials’ refractive index dispersion [24, 25] and a refractive index change due to anisotropic thermal stress induced during fiber drawing process [26–28]. The calculated electric field distributions in the fundamental mode for selected wavelengths (1.8 µm, 2.0 µm, and 2.4 µm) are presented in Figs. 1(d)-1(f), while in Fig. 2 the model used in the calculations is shown. According to FEM simulations, the fiber supports six modes at 0.75 μm and becomes a single mode one beyond 1.1 μm.

 

Fig. 2 Fiber model used in FEM calculations. The small air holes are connected with solid line to indicate the five full rings accounted in the model.

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Simultaneously, we measured the fiber properties such as spectral dependence of the chromatic dispersion and the phase modal birefringence. We used a white light interferometric technique [29–31] according to the procedure described in [22] to determine the chromatic dispersion. For measurements of the phase modal birefringence we applied a combination of the spectral interferometry method and the lateral force method [28, 32, 33].

We obtained a very good agreement of experimental and simulation data for the chromatic dispersion, Fig. 3. The chromatic dispersion reaches a local maximum of −2 ps/km/nm at 1.6 µm and according to numerical results is negative up to 2.56 µm. The difference between the chromatic dispersion of slow and fast axes is very small and ranges between −0.2 and 0.4 ps/km/nm. Simultaneously, the chromatic dispersion is flat (fits between −20 ps/km/nm and 0 ps/km/nm) in a broad range from 1.23 µm to 2.56 µm.

 

Fig. 3 Comparison of measured (blue points) and calculated (black solid line) chromatic dispersion for the considered fiber.

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In case of the phase modal birefringence, we did not obtain such a good agreement as for the chromatic dispersion, but the birefringence slope is restored correctly, Fig. 4. The phase modal birefringence originates from both geometrical and stress effects. To show their relative importance, we performed FEM calculations neglecting thermal stress. The difference between black lines in Fig. 4 (dashed and solid) shows that in the short wavelength range, the stress related birefringence makes a principal contribution to the overall birefringence, while in the long wavelength range the form birefringence dominates. The underestimation of the calculated birefringence can be related to the inaccuracy in creating an idealized fiber geometry for the finite element model used in the numerical simulations. Nevertheless, both the numerical and the experimental results show that the considered fiber is highly birefringent.

 

Fig. 4 Comparison of measured (blue) and calculated (black) phase modal birefringence for the fabricated fiber. Black solid line represents the calculated overall birefringence, while black dashed line represents the contribution of form birefringence (stress effect disregarded).

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3. Supercontinuum generation

3.1 Experimental setup

In the performed experiments of the SC generation we pumped our birefringent microstructured silica fiber with high peak power femtosecond pulses, with central wavelength from 1.8 µm to 2.4 μm, delivered by a tunable non-collinear optical parametric amplifier (NOPA). The NOPA was pumped by a chirped pulse amplified Ti:sapphire system providing pulses centered at 790 nm with 3.2 mJ energy (100 fs pulse duration) at 1 kHz repetition rate. The maximum energy of the infrared pulse delivered by the NOPA is about 300 μJ, and the pulse duration was measured to be ~70 fs. Neutral density filters were first used to reduce the high pulse energy. Additionally, a conventional half-wave plate and a polarizer were used for fine tuning of the input power, while keeping the input linear polarization parallel to one of the fiber birefringent axes. By means of a 20X microscope objective, the pumping beam was then introduced into the fiber mounted onto a 3-axis holder. At the fiber output, the generated SC was collimated with a ZnSe microscope objective and then focused with an off-axis gold coated parabolic mirror on the input slit of the monochromator. A second polarizer was used to check the linear polarization state of the output SC. Our motorized monochromator was equipped with a diffraction grating adapted for the wavelength range of interest (1.1 μm-5.0 µm range with a 90% peak efficiency at the blaze wavelength of 2 µm), and providing a spectral resolution of almost 5 nm. The SC light at the output slit was imaged by means of another off-axis gold coated parabolic mirror on the liquid nitrogen cooled HgCdTe detector. The detector signal was then extracted by means of a lock-in amplifier operating at the laser repetition rate. The near infrared part of the supercontinuum was also measured with a spectrometer operating in the 890-2520 nm range (NIRQUEST, Ocean Optics). The full SC spectrum is then reconstructed by merging the two spectra.

3.2 Scalar simulations

To get insight into the SC generation process, we conducted corresponding nonlinear simulations, first focused on spectral broadening. For this purpose, we used a self-developed software solving scalar generalized nonlinear Schrödinger equation (GNLSE) with split-step Fourier method [2, 3, 34] accounting a Raman scattering term. In the nonlinear simulations, we used the fiber parameters obtained in the FEM modelling, such as chromatic dispersion, Fig. 3, dispersive effective mode area [35], and confinement loss. To estimate the total attenuation coefficient, we summed up the contributions coming from waveguide confinement loss, material loss [36] and OH loss, Fig. 5. In the infrared range, the OH absorption and confinement loss are the dominant factors. In the simulations we accounted OH absorption peaks at 1.38 µm, 2.21 µm and 2.72 µm with relative strength given by Humbach [37]. Our estimation was based on the attenuation value of 2.4 dB/m measured in the investigated fiber at 1.38 µm using a cut-back method.

 

Fig. 5 Total attenuation coefficient applied in the simulations of nonlinear propagation.

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3.3 Supercontinuum broadening and dynamics

We began our studies with analysis of SC spectral broadening under pumping at 1.8 µm in a 122 mm long piece of fiber, Fig. 6(a). With increasing power (average pump power given in Fig. 6(a)), we observed significant spectral broadening. Measured spectra filled normal dispersion wavelength range up to 2.56 µm and extended beyond zero dispersion wavelength in anomalous dispersion range up to 2.62 µm. Similar results were obtained with numerical simulations, Fig. 6(b). We estimated the highest pump peak power (P₀) to be 400 kW. The pump peak powers in the simulations were adjusted in such a way to obtain the same ratios between the peak powers as between the average powers used in the experiment (the average powers were measured before the microscope objective). The measured and simulated spectra are in good agreement in terms of broadening and shape, however simulation spectra extend more towards shorter wavelengths. This may be related to the fact that the fiber is not a single mode one below 1.1 μm. As a result, there exists an additional mechanism of attenuation in a short wavelength range caused by nonlinear coupling to leaky higher order modes, which is not accounted in the single mode simulations. Moreover, a fine structure related to Raman scattering is present in the simulations for the highest pump powers around 1.4 µm, which will be discussed in the next paragraph.

 

Fig. 6 Comparison between measured (a) and calculated (b) spectra for different pump power levels. Pump central wavelength is 1.8 μm. Fiber length is 122 mm. For experimental data average pump power is given; P_a and P_b denote powers, which were too low to be measured accurately. For simulated data the highest peak power P₀ is 400 kW.

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In the next step, we compared the spectra generated in the same piece of fiber for different pump wavelengths equal to 1.8 µm, 2.0 µm, 2.2 µm, 2.4 µm, respectively, Fig. 7(a). We verified that up-shifting of the pump wavelength does not up-shift significantly a long wavelength edge of the generated SC. This is due to high OH absorption peak at 2.72 µm, which is over 2 orders of magnitude greater than the peak at 1.38 µm [37]. The average pump power was almost equal for all pumping wavelengths (respectively 440 µW, 420 µW, 430 µW, 430 µW), therefore in the simulations we assumed the same peak power P₀ = 400 kW for all pumping wavelengths. Again, we obtained very good agreement between measurements and simulations, except the fine structure visible in the simulated spectra around 1.4 µm, Fig. 7(b). To clarify this discrepancy, we performed the simulations disregarding Raman scattering, which resulted in disappearance of the fine spectral structure, Fig. 7(c). It means that the fine structure observed in the simulations is related to Raman scattering, but is present only above certain threshold power like in Fig. 6. The mentioned earlier loss mechanism related to nonlinear coupling of higher order modes decreases the power guided in the fiber for shorter wavelengths and most probably obstructs observation of this fine spectral structure in the experiment. For this reason, from this point onwards we neglected the Raman term in the numerical simulations.

 

Fig. 7 Comparison between measured (a) and calculated (b), (c) spectra for different pump wavelengths 1.8 µm, 2.0 µm, 2.2 µm, 2.4 µm (indicated by vertical dashed lines in corresponding colors). Measured average pump powers were 440 µW, 420 µW, 430 µW, 430 µW, respectively. Simulation peak power was 400 kW. Simulations conducted with Raman scattering accounted for (b) and disregarded (c).

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Finally, we investigated the dynamics of the supercontinuum generation in a short fiber piece. The shortest possible piece we could handle in the experimental setup was 48 mm long. In Fig. 8, we present the comparison of measured and simulated spectra for two wavelengths 1.8 µm and 2.4 µm. The spectra obtained for pumping at 1.8 µm were much broader than for 2.4 μm and covered the wavelength range from 1.0 µm to 2.5 µm. The short-wavelength side of SC spectra for 2.4 μm pumping was limited by the chromatic dispersion curve. The broadening was not so effective in this case since the pump wavelength was beyond local minimum of the chromatic dispersion located around 2.25 μm. This difference can be also seen in the Fig. 9, presenting the SC spectral evolution over the propagation distance obtained with the numerical simulations. With this figure, we conclude that about 30 mm of a fiber is enough to reach the SC spectral saturation and 48 mm long piece of the fiber used in the experiments allowed us to observe full broadening.

 

Fig. 8 Comparison between measured (a), (b) and calculated (c), (d) spectra generated in 48 mm long fiber for different pump power levels. Vertical dashed lines indicate pump central wavelengths: 1.8 μm (a), (c), and 2.4 µm (b), (d). For experimental data the average pump power is given; P_a and P_b denote powers too low to be measured accurately. For simulated data the highest peak power P₀ was 400 kW.

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Fig. 9 Simulated SC spectral evolution over propagation distance for pumping at 1.8 μm (a) and 2.4 μm (b). The peak power was 400 kW. Black dashed lines denote pumping wavelengths and white dashed lines denote distances at which maximum spectral broadening is reached, respectively 26 mm (a) and 14 mm (b).

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In our work, we did not focus on coherence properties of the generated spectra, but one can expect that for pump pulse duration of only 70 fs and short propagation distances of 48 mm and 122 mm, the generated spectra are coherent according to recent analysis presented in [11].

4. PolAND supercontinuum generation

After the investigation of spectral broadening for pumping at different wavelengths and power levels, we verified if the generated supercontinuum maintains the linear polarization state of the pump. To model the process of the PolAND supercontinuum generation, we extended our modeling software to solve coupled nonlinear Schrödinger equations system for both polarizations with the split-step Fourier method [38]. As in scalar simulations, we used the fiber parameters obtained by FEM modelling, Figs. 1–4, and the estimated fiber loss, Fig. 5.

In Fig. 10(a) we present the measured spectra generated with the average pump power of 420 µW at 2.0 µm, which show that there exists an asymmetry between propagations in both polarization axes. We observed more light coupled to orthogonal polarization when pump polarization was aligned in parallel to a fiber fast axis than for pumping in a slow axis. For pumping in the fast axis, the polarization extinction ratio is greater than 10 dB in most of the spectral range, except the region around 2.17 µm at which it approaches 6 dB. For pumping in the slow fiber axis, the polarization extinction ratio is much better and significantly exceeds 10 dB in the almost full spectral range.

 

Fig. 10 Comparison between measured (a) and calculated (b), (c) spectra generated in 122 mm long fiber under pumping at 2 µm in each polarization axis: ss – pumping in slow axis, observation in slow axis, sf – pumping in slow axis, observation in fast axis, ff – pumping in fast axis, observation in fast axis, fs – pumping in fast axis, observation in slow axis. Ideal excitation is assumed in (b), and 1 degree polarization misalignment is assumed in (c).

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With numerical simulations we restored these results qualitatively. The peak power was set to 400 kW. For an ideal excitation, i.e. the pump polarization aligned in parallel to one of the fiber polarization axes [Fig. 10(b)], we see a power transferred from the fast to slow axis and there is not such transfer in the opposite direction (visible only a noise level related to one-photon per mode noise used in simulations). The ratios of power in orthogonal axis to total power at the fiber end are: for pumping in slow axis P_f/(P_f + P_s) = 9.7 × 10⁻¹⁰ and for pumping in fast axis P_s/(P_f + P_s) = 1.1 × 10⁻⁷, where P_f and P_s are powers in fast and slow axis, respectively. Similar results have been obtained numerically by Zhu and Brown [14]. For pumping in an anomalous dispersion regime they observed that separation between two polarization components depends on initial pump polarization. The same conclusions for normal dispersion were drawn by Tu et al. [12]. This asymmetry in polarization properties can be explained as follows. The high birefringence results in a great phase mismatch between orthogonal polarizations. When pump polarization is parallel to the slow axis, then due to the fiber nonlinearity the effective refractive index in a slow axis increases thus making the phase mismatch greater. In the opposite situation, when the pump light is coupled into the fiber fast axis, the phase mismatch lowers and as a result, a nonlinear coupling between orthogonal polarizations is observed. The maximum nonlinear change of the effective refractive index is Δn = 2γP ≈10⁻³ for the nonlinear refractive index n₂ = 2.6 × 10⁻²⁰ m²/W, the effective mode area A_eff = 20 μm² and the peak power P = 400 kW. This change is great enough to compensate the phase mismatch between polarization modes and to enable vector nonlinear coupling.

We repeated the simulations, assuming that the pump polarization is misaligned by 1 degree arc with respect to the fiber polarization axis [Fig. 10(c)]. This corresponds to 3 × 10⁻⁴ of power coupled to orthogonal axis. In this case, the ratios of power in orthogonal axis to total power at the fiber end are: for pumping in slow axis P_f/(P_f + P_s) = 2.7 × 10⁻⁴ and for pumping in fast axis P_s/(P_f + P_s) = 0.13. Again, the pumping in the slow axis is resistant to depolarization in contrast to pumping in the fast axis [12]. It can be concluded that vector nonlinear processes lead to depolarization and that slow polarization axis is much more resistant to this process. The quantitative differences between the simulation and measurements results can be attributed to the difference between measured and calculated birefringence, Fig. 4, and to the low signal-to-noise ratio achieved in the experiment.

5. Summary

In this work, we demonstrated the all-normal dispersion supercontinuum generated in a silica fiber up-shifted for the first time beyond 2.5 µm. The all-normal operation limit is related to the zero dispersion wavelength located at 2.56 µm according to FEM simulations. For the maximum pump power, the generated spectrum reached up to 2.67 µm, slightly into the anomalous dispersion regime and was limited by OH absorption peak at 2.72 µm. It seems that further fiber optimization is possible to shift the zero dispersion wavelength more towards mid infrared and obtain flatter SC spectrum filling the full transparency window of silica glass. The fiber used in the experiments was highly birefringent and allowed to generate the polarized supercontinuum. We identified the asymmetry in propagation properties in both fiber polarization axes, and showed that pumping in the slow fiber axis is beneficial for higher degree of polarization.