## Abstract

Besides coherence degradations, supercontinuum spectra generated in birefringent photonic crystal fibers also suffer from polarization fluctuations because of noise in the input pump pulse. This paper describes an experimental study of polarization properties of supercontinuum spectra generated in a birefringent photonic crystal fiber, validating previous numerical simulations.

©2004 Optical Society of America

Supercontinuum (SC) generation in photonic crystal fibers (PCFs) has recently attracted a great of interest [1]. Both high effective nonlinearity and novel dispersion have made PCFs an excellent medium for ultra-broad SC generation. PCFs-based SC sources have found important applications such as optical coherence tomography [2] and frequency metrology [3].

There have been many experimental and numerical investigations on the mechanisms and properties of SC generation in PCFs [4–12]. These studies provide insights into the SC process and help generate desirable SC sources for various applications. In particular, the properties of SC under influence of input noise have been investigated recently [9–12]. It is shown that the practical noise in the SC process can cause significant fluctuations in the generated SC, resulting in severe coherence degradations. However, these studies are limited to the scalar case by assuming a single polarization state in the SC generation. Recently we extended the study to birefringent PCFs and investigated numerically the polarization properties of SC spectra generated under the influence of quantum noise [13]. The study shows that, due to vector modulation instability, fluctuations in input pulses cause not only coherence degradations but also polarization fluctuations. In this paper we present an experimental study on the polarization properties of SC spectra generated in a birefringent PCF, confirming the previous numerical simulations based on generalized coupled nonlinear Schrödinger equations [13].

We carried out experimental studies of SC generation in a PCF from Crystal Fibre A/S. Although the PCF is designed to have low birefringence, the actual fiber exhibits appreciable birefringence as evident from its SEM image (see Fig. 1) and our initial experiments on SC generation using the fiber. We also used a full vectorial finite difference method [14] to model this fiber and the calculated GVD, effective mode area *A _{eff}* and birefringence as a function of wavelength are shown in Fig. 1. The zero dispersion wavelength is ~770 nm. At wavelength of 800 nm, the nonlinear coefficient

*γ*is ~80 kW

^{-1}m

^{-1}, and the birefringence is ~5×10

^{-5}.

The experiment setup is schematically shown in Fig. 2. Femtosecond pulses emitted from a Ti:Sapphire laser (Spectra Physics Tsunami 3205, repetition rate 81 MHz) pass through an optical isolator and then a prism pair. The isolator blocks reflected light that would go back into the laser and disturb the mode-locking of the laser. The prism-pair is used to compensate the normal dispersion in the optical path and thus narrow the pulse width. The half-wave plate H1 and polarizer A1 are used to adjust the input power, whereas the half-wave plate H2 adjusts the polarization orientation. The average power and width of the input pulse are monitored by a power meter (PM) and an autocorrelator (AC), respectively. A 60× microscope objective couples the laser pulses into the 15-cm-long PCF. The output of the PCF passes through broadband polarization components (half-wave plate H3, quarter-wave plate Q, and analyzer A2) before coupled into an optical spectrum analyzer (Ando AQ-6315A).

With the PCF’s principal axes identified, we examined the polarization properties of the SC spectra generated in the PCF. The measurement principle is described as follows. Assume the output of the PCF have the form $\left(\begin{array}{c}{E}_{x}\left(\lambda \right)\\ {E}_{y}\left(\lambda \right)\end{array}\right)$. The Jones matrices for the half-wave plate H3, the quarter-wave plate Q and the analyzer A2 are, respectively,

${M}_{h}=\left(\begin{array}{cc}\mathrm{cos}\left(2{\theta}_{h}\right)& \mathrm{sin}\left(2{\theta}_{h}\right)\\ \mathrm{sin}\left(2{\theta}_{h}\right)& -\mathrm{cos}\left(2{\theta}_{h}\right)\end{array}\right),{M}_{q}=\left(\begin{array}{cc}{\mathrm{cos}}^{2}{\theta}_{q}+i{\mathrm{sin}}^{2}{\theta}_{q}& \frac{1}{2}(1-i)\mathrm{sin}\left({2\theta}_{q}\right)\\ \frac{1}{2}(1-i)\mathrm{sin}\left(2{\theta}_{q}\right)& {\mathrm{sin}}^{2}{\theta}_{q}+i{\mathrm{cos}}^{2}{\theta}_{q}\end{array}\right),$

and

where *θ _{h}, θ_{q}*, and

*θ*are the angles of the fast axes (or polarizing axis) of H3, Q and A2, respectively, with respect to the slow axis of the PCF. The Jones vector for the light coupled into the optical spectrum analyzer is then given by ${M}_{a}=\left(\begin{array}{cc}{\mathrm{cos}}^{2}{\theta}_{a}& \mathrm{sin}{\theta}_{a}\mathrm{cos}{\theta}_{a}\\ \mathrm{sin}{\theta}_{a}\mathrm{cos}{\theta}_{a}& {\mathrm{sin}}^{2}{\theta}_{a}\end{array}\right),$. Through suitable combinations of

_{a}*θ*and

_{h}, θ_{q}*θ*we can then measure the quantities as listed in the Table 1. Rotation of the half-wave or quarter-wave plate was found to cause negligible change in light coupling efficiency into the optical spectrum analyzer via a standard single-mode fiber. However, rotation of the analyzer A2 was found to significantly affect the coupling of light into the single-mode fiber. So we chose

_{a}*θ*to be fixed at 0 in the experiment.

_{a}As shown in Table 1, *I*
_{1} and *I*
_{2} give the spectral intensities for the slow axis (*x*-axis) and the fast axis (*y*-axis) components, respectively. Simple algebra of *I*
_{1}~*I*
_{5} yields the mean ellipticity and the polarization correlation function as defined in Ref. [13]:

The ellipticity *e _{p}*(λ) is used as a simple measure of the polarization states across the SC spectrum, while the polarization correlation function

*ρ*(λ) is used to quantify the fluctuations in polarization states with value 0 (or 1) denoting maximum (or minimum) fluctuations. Since the quantities

*I*

_{1}~

*I*

_{5}are not simultaneously but sequentially measured by changing the angles

*θ*and

_{h}*θ*, we assume that the effects of input pulse fluctuation are stationary and independent of the measurement timing. This assumption is reasonable because each measurement by the optical spectrum analyzer is carried in a time that is long enough for a large number of shots to be averaged and also short enough so that the laser has good stability.

_{q}As can be seen from Eq. (2), if one of polarization components is significantly smaller than the other, then the polarization correlation function *ρ*(λ) would be severely affected by measurement noise. As a consequence, the value of *ρ*(λ) could be significantly out of the expected range of [0, 1]. This phenomenon was easily observed when the input light is linearly polarized close to the slow or fast axis. Even with the input polarized along 45° to the slow axis, the measured correlation function may still be out of the expected range in some spectral regions where one polarization component is much smaller than the other and thus is susceptible to measurement noise. As we shall see in the experimental results presented below, the measured values of *ρ*(λ) in some spectral regions are bigger than 1.

In Fig. 3 we show the measured SC spectrum, mean ellipticity and correlation function obtained with various input power levels at a pump wavelength of 800 nm. The input light is linearly polarized at *θ*=45° to the slow axis of the PCF. The pulse width (FWHM) is estimated to be about 120 fs. The power values indicated in the figure are the average power measured just before the coupling objective lens L1. As can be seen from the figure, with increasing input power, the SC bandwidth increases and the spectrum becomes smoother, but the correlation function tends to decrease, indicating more polarization fluctuations. The ellipticity of the SC spectrum also tends to be smoother as the input power increases. These observations are qualitatively consistent with the numerical simulations based on generalized coupled nonlinear Schrödinger equations [13]. As an example, in the bottom row of the figure we show the numerical simulation results for the 300mW-input case. The simulation, assuming a coupling efficiency of 40% into the PCF, pulse width (FWHM) of 120 fs and only quantum noise in input pulses [9, 13], does not attempt to best fit the experimental data, because of many uncertainties in the experiments, such as fiber parameters, input pulse properties including noise characteristics. Nevertheless, the observed input power dependence of SC polarization properties validates the numerical prediction presented in Ref. [13].

We also compared the polarization properties of SC spectra obtained from pulses with different central wavelengths. Figure 4 plots the mean spectrum, mean ellipticity and polarization correlation function of SC from pulses with wavelength of 740 nm, 770 nm and 800 nm. These three wavelengths lie in the normal dispersion regime, at zero dispersion wavelength and in anomalous dispersion regime, respectively. As expected, the normal dispersion input generates narrower SC than the near-zero-dispersion input and the anomalous dispersion input, since the input pulse broadens and peak power decreases in the normal dispersion regime. However, the generated SC spectrum has better polarization stability when the input lies in the normal dispersion regime. This wavelength dependence of SC properties is also consistent with the numerical simulations [13].

Finally, we studied the effect of input polarization orientation on the polarization properties of SC spectra. Figure 5 shows, for each of the input orientation angle *θ*=15°, 30° and 45°, the mean spectrum, mean ellipticity and polarization correlation function. As can be seen in the figure, the SC properties depend on the input polarization orientation angle. In particular, the polarization fluctuations increase as the angle increases from 15° to 45°. This observation is consistent with the numerical prediction that the polarization stability improves when the input linear polarization is aligned close to one of the principal axes [13]. We note that the PCF used in the experiment has a relatively low birefringence (~5×10^{-5}); however, high birefringence (~10^{-3}) can also be easily achieved in PCFs. High-birefringence tends to achieve better SC polarization stability, and constant polarization state across the spectrum as well [13].

Numerical simulations have shown that longer input pulses tend to result in larger coherence degradations [9] and polarization fluctuations [13]. Therefore shorter pulses are usually used to obtain a SC source with good coherence property and stable polarization states. In our experiment, the input pulses (FWHM ~120 fs) are relatively long. Even at a low input power, the measured polarization fluctuations are significant (see Fig. 3). Given that the fluctuations in the input pulses are far beyond quantum noise and the presence of other noise in the SC process, the experimentally observed polarization fluctuations are bigger than those from the numerical simulations that only assume quantum noise in the input pulses. Nevertheless, numerical simulations in the quantum noise limit can qualitatively predict the experimentally observed trends describing the polarization dependence on input power, input wavelength and input orientation angle. With a realistic noise model, we expect that the numerical simulations based on the generalized coupled nonlinear Schrödinger equations could provide a better prediction of SC generation in birefringent PCFs.

In summary, the presented experimental results on the polarization properties of SC, in particular the polarization fluctuations, demonstrate for the first time the influence of practical noise on the polarization behavior of SC generated in a birefringent PCF, which qualitatively confirm the previous numerical predictions on the SC polarization properties.

## Acknowledgments

This study was supported in part by a Frank J. Horton fellowship from the Laboratory for Laser Energetics, University of Rochester, and by the National Science Foundation under grant ECS-9816251.

## References and links

**1. **J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. **25**, 25–27 (2000). [CrossRef]

**2. **I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. **26**, 608–610 (2001). [CrossRef]

**3. **R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. **85**, 2264–2267 (2000). [CrossRef] [PubMed]

**4. **A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. **87**, 203901 (2001). [CrossRef] [PubMed]

**5. **A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers,” Opt. Lett. **27**, 924–926 (2002). [CrossRef]

**6. **X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. **27**, 1174–1176 (2002). [CrossRef]

**7. **J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. **88**, 173901 (2002). [CrossRef] [PubMed]

**8. **S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B **19**, 753–764 (2002). [CrossRef]

**9. **J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. **27**, 1180–1182 (2002). [CrossRef]

**10. **K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Webber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. **90**, 113904 (2003). [CrossRef] [PubMed]

**11. **N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. **28**, 944–946 (2003). [CrossRef] [PubMed]

**12. **X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. M. Dudley, S. Cohen, and R. S. Windeler, “Experimental studies of the coherence of microstructure-fiber supercontinuum,” Opt. Express **11**, 2697–2703 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2697 [CrossRef] [PubMed]

**13. **Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B **21**, 249–257 (2004). [CrossRef]

**14. **Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express **10**, 853–864 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853 [CrossRef] [PubMed]