Supercontinuum (SC) generation occurs when relatively narrow-band incident light is transformed through nonlinear processes into a broad continuous spectrum [1]. The emergence of the photonic crystal fiber (PCF) in the late-1990s has led to a revolution in the field by offering enhanced modal confinement, widely engineerable group velocity dispersion, and the possibility of single-mode guidance over a broad wavelength range [2,3]. SC generation in optical fibers is now well understood and has diverse applications in science and technology [4,5]. The polarization properties of SC light generated in PCFs have been investigated by many research groups [6–12]. A long-standing issue is the difficulty in generating a SC that is robustly maintained in one polarization state across its entire spectrum. In straight PCFs, the polarization state of the SC varies over its spectrum due to random fluctuations in the weak linear birefringence, coupling between orthogonally polarized components induced by modulational instability [13] and the vectorial nature of soliton fission [8]. Previous studies have indicated that an optical fiber with circular birefringence $B_C$ large enough to dominate linear birefringence could simplify the nonlinear polarization dynamics [14,15]. Chiral fibers, created by spinning a linearly birefringent fiber preform during the draw, support elliptically polarized modes [16]. A continuously twisted PCF, on the other hand, exhibits perfect circular birefringence [17], thus preserving circular polarization states against external perturbations, making it an ideal candidate for generating broadband light in a single circular polarization state. We note that high-order orbital angular momentum modes in special fibers with annular cores have been successfully used to produce octave-spanning supercontinua whose polarization states mimic those of the pump light [18]. Here we report, to the best of our knowledge, the first experimental generation of a broadband circularly polarized SC in a helically twisted, circularly birefringent, solid-core PCF. The results are confirmed by vector numerical simulations of pulse broadening.

A schematic of the experiment is shown in Fig. 1(a). Light from a linearly polarized 40 ps pump laser at 1064 nm, oscillating at a repetition rate of 0.2 MHz (Fianium FP-1060-10-pp-01), was passed through a quarter-wave plate to allow switching between the left-circular (LC) and right-circular (RC) polarization states. An aspheric lens with $20\times$ magnification was used to launch the light into a 60 cm long twisted endlessly single-mode PCF with a hollow channel diameter $d=1.6\mathrm{\mu m}$, inter-hole spacing $\mathrm{\Lambda }=3.8\mathrm{\mu m}$, and core diameter $\sim 6.0\mathrm{\mu m}$ [see the inset in Fig. 1(b)]. The PCF was fabricated from fused silica using the standard stack-and-draw technique, and the twist (period 4.7 mm) was created by spinning the preform during fiber drawing [19]. The loss spectra of the LC and RC polarized core modes, measured by the cutback method [20] using circularly polarized broadband light, are shown in Fig. 1(b). The attenuation peak at 1.38 μm is due to vibrational OH absorption. The circular birefringence $B_c$ of the fiber was measured to be 1.1 μRIU at 1064 nm, a value that agrees well with the results of finite element (FE) modelling based on a scanning electron micrograph (SEM) of the fiber microstructure [Fig. 1(c)]. For this fiber, there are no loss bands (caused by anti-crossings with leaky cladding modes) within the SC bandwidth, and the core mode is optically active, with a circular birefringence that scales linearly with the twist rate [17]. At smaller twist periods ($\sim 500\mathrm{\mu m}$), it is possible that spectral dips in transmission, caused by the twist, will modify the SC spectrum (see Ref. [21]). A $20\times$ microscope objective was used to collimate the output light, and the generated spectrum was recorded with an optical spectrum analyzer (Yokogawa AQ-6315A, operating wavelength range of 350-1750 nm). To monitor the polarization state at different wavelengths, a pair of calcium fluoride equilateral prisms was placed after the output objective to separate the SC spectrum into its constituent spectral components, followed by a commercial polarimeter with a slit aperture. The prism was used at close to normal incidence so as to avoid any polarization-dependent effects and to ensure that the polarization state was not perturbed. The polarimeter was mounted on a translation stage perpendicular to the laser beam so that the individual narrow spectral bands could be analyzed.

 

Fig. 1. (a) Schematic of the experiment. Inset: photograph of the side of the twisted PCF, showing the periodic pattern caused by the spiraling hollow channels. The distance between the bright regions is one-sixth that of the helical pitch. (b) Measured loss of the LC (blue) and RC (magenta) polarized core modes as a function of the wavelength for the twisted PCF (twist period 4.7 mm). The loss peak at $\sim 1.4\mathrm{\mu m}$ is caused by water absorption. Inset: SEM of the PCF microstructure. (c) Dispersion $D$ for both circular polarization states and circular birefringence $B_c$ (green) as a function of the wavelength for the twisted fiber, calculated by FE modeling based on the SEM. The measured value of $B_c$ at 1064 nm (1.1 μRIU) is in good agreement with the modelling.

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The measured SC spectra and polarization properties for LCP and RCP pump light are summarized in Fig. 2(a) for an average pump power of 232 mW (peak power $\sim 29\mathrm{kW}$). The beam-to-fiber coupling efficiency was typically 56%. To avoid damaging the PCF input face, we did not increase the power further. The PCF was kept straight and unstretched between the input and output coupling stages. The zero-dispersion wavelength (ZDW) of the twisted PCF is at 1.1 μm, so that the pump wavelength was in the (weakly) normal dispersion regime. For the picosecond pump pulses used, the spectral broadening is dominated by four-wave mixing (FWM) and stimulated Raman scattering [3]. Applying the dispersion in Fig. 1(c) to the standard analytical FWM phase-matching condition predicts Stokes and anti-Stokes sidebands at 1754 and 764 nm, respectively, which is in good agreement with the experiment. Two further higher-order anti-Stokes bands at $\sim 590$ and $\sim 485\mathrm{nm}$ can also be identified in the measured spectra, equally spaced by $\sim 111\mathrm{THz}$.

 

Fig. 2. (a) Measured SC spectra for the twisted PCF when the pump source is LC (blue) or RC (magenta) polarized and the average pump power is 232 mW. The measured 1064 nm pump spectrum is plotted in red. The drop in spectral intensity at wavelengths $>1.4\mathrm{\mu m}$ is the result of Raman-shifting solitons encountering the 1.4 μm loss band [Fig. 1(b)]. The two FWM sidebands are marked by dotted vertical lines, spaced 111 THz from the pump frequency. (b) Measured output ellipticity (Stokes parameter $S_3$) at selected wavelengths for three different average pump powers, showing that the circular polarization state is robust against power fluctuations.

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The measured output polarization state remains circular across the SC bandwidth, as shown in the insets of Fig. 2(b), where the measured values of ($S_3\pm 1$) (+ for LCP and − for RCP light) are plotted against the wavelength for three different pump powers. Although the circular birefringence is only of the order of ${10}^{-6}$, the polarization state was maintained, even when the twisted PCF was bent to a 30 cm radius over 50 cm. The measured values of $S_3$ vary very little with pump power, showing no sign of depolarization, so that the circular polarization state of the SC is negligibly affected by fluctuations in pump power.

For comparison, the experiment was also carried out using a 60 cm length of untwisted PCF with the same transverse microstructure, drawn from the same preform. Based on FE modelling of the PCF cross-section from the SEM, the linear birefringence $B_L$ is 6.1 μRIU at 1064 nm, and the ZDW is 1.1 μm. The measurements of the polarization state at the output are plotted against wavelength in Fig. 3, showing severe depolarization; at some wavelengths, the handedness of output polarization is even opposite to that of the pump light.

 

Fig. 3. (a) Measured SC spectra for the untwisted PCF when the pump source is LC (blue) or RC (magenta) polarized and the average pump power is 232 mW. (b) Measured Stokes parameter $S_3$ of SC light generated in an untwisted PCF at an average power of 232 mW. Although the overall spectral shape of the SC is identical to that in the twisted PCF (Fig. 2), there is severe wavelength-dependent depolarization for both LCP and RCP pump light.

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To illustrate the striking difference between twisted and untwisted PCFs, the Stokes parameters [$S_1,S_2,S_3$] for the data points in Figs. 2(b) and 3 are plotted on Poincaré spheres (Fig. 4). For twisted PCFs, the polarization state remains close to the north (RC) and south (LC) poles of the Poincaré sphere, following the pump polarization [Fig. 4(a)]. For the untwisted fiber [Fig. 4(b)], the Stokes parameters are spread all over the Poincaré sphere and exhibit a strong power dependence. The twisted circularly birefringent PCF significantly outperforms the linearly birefringent PCF in terms of polarization stability, without any reduction in SC bandwidth.

 

Fig. 4. Poincaré sphere representations of the output polarization state for the data in Figs. 2(b) and 3. (a) Twisted PCF and (b) untwisted PCF.

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A numerical study of the polarization properties of the SC generated in twisted and untwisted PCFs was also carried out to verify the experimental results. The simulations were based on coupled generalized nonlinear Schrödinger equations in the slowly varying envelope approximation, using a circular polarization basis and including birefringence, chromatic dispersion, loss, Kerr and delayed Raman nonlinearities, and self-steepening [22,23]. The pump was taken to be a 40 ps pulse at 1064 nm with a peak power of 29 kW, and the system was seeded with one photon per mode of delta-correlated noise. The effective mode area was taken to be $22.2{\mathrm{\mu m}}^2$ at 1064 nm (estimated from FE simulations), and the nonlinear refractive index was $3.2\times {10}^{-20}{\mathrm{m}}^2/\mathrm{W}$ [24]. The calculated SC spectra generated in the 60 cm long chiral PCF and the corresponding ellipticity $S_3$ as a function of the wavelength for RCP and LCP pump light are shown in Fig. 5(a). The simulated and measured SC spectra show good qualitative agreement, and the calculated values of $S_3$ are $\pm 1$ and wavelength independent. No shot-to-shot variations were detected.

 

Fig. 5. (a) Simulated SC spectra at 232 mW average pump power for a 60 cm length of twisted PCF (twist period = 4.7 mm) pumped by LCP (blue shaded) and RCP (red shaded) light. Ten ensemble simulations were used to model the effects of noise seeding. (The SC spectrum generated in the untwisted PCF is almost identical, so it is not shown.) The measured SC spectra from Fig. 2(a) are included for comparison. (b) Simulated ellipticity $S_3$ as a function of the wavelength for the twisted PCF. The pump polarization state is LCP (blue) and RCP (red). (c) Same as (b), but for the untwisted PCF. Note that the polarization state of each SC spectral component generated in the untwisted PCF is subject to shot-to-shot fluctuations.

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We attribute the strong polarization fluctuations in the wavelength range of 1–1.6 μm to fission-generated vector solitons, which exhibit different states of polarization [3,8,9]. The simulations also reveal that the polarization state fluctuates from shot to shot, especially in the wavelength range of 1.0–1.4 μm, and that the circular polarization state is preserved in the twisted fiber independently of pump power, in sharp contrast to the untwisted case, when it varied strongly with power, in agreement with the experimental results [Fig. 4(b)].

In conclusion, SC light generated in a twisted PCF, when pumped by circularly polarized laser light, is robustly circularly polarized across its entire spectrum, sharing the same polarization state as the pump. The experimental and numerical results are in very good agreement. Circularly polarized broadband SC sources based simply on twisted PCF, by avoiding the need for achromatic quarter- and half-wave plates, cholesteric liquid crystals, or chiral nanostructured surfaces, are likely to find many applications in fields such as biochemistry (spectroscopy of chiral proteins and pharmaceutics), astronomy, and sensing.