Brillouin wavelength-selective all-optical polarization conversion

Diego Samaniego; Borja Vidal

doi:10.1364/PRJ.371513

Abstract

The manipulation of the polarization properties of light in guided media is crucial in many classical and quantum optical systems. However, the capability of current technology to finely define the state of polarization of particular wavelengths is far from the level of maturity in amplitude control. Here, we introduce a light-by-light polarization control mechanism with wavelength selectivity based on the change of the phase retardance by means of stimulated Brillouin scattering. Experiments show that any point on the Poincaré sphere can be reached from an arbitrary input state of polarization with little variation of the signal amplitude (

< 2.5 dB

). Unlike other Brillouin processing schemes, the degradation of the noise figure is small (1.5 dB for a full

2 π

rotation). This all-optical polarization controller can forge the development of new polarization-based techniques in optical communication, laser engineering, sensing, quantum systems, and light-based probing of chemical and biological systems.

1. INTRODUCTION

The ability to manage the state of polarization (SOP) is essential in controlling many polarization-related phenomena in different areas of photonics [1,2]. New tools and techniques have evolved from advanced control of light polarization. In free-space optics, the development of polarization-structured beams has opened new paths in both scientific and engineering applications: for example, spatially dependent polarization beams for optical tweezers [3]. However, in optical fibers and integrated waveguides, there are no tools offering similar potential for polarization structuring.

Polarization management in optical fibers is usually performed by means of (1) multiple stages with fixed linear retardations and variable orientation angles, typically implemented using cascaded mechanically controlled stress-induced birefringence in rotatable waveplates or electro-optical devices exploiting the Pockels effect [4,5]; (2) a single stage with both variable linear retardation and orientation, implemented using fiber implementations of a Babinet–Soleil compensator [6]; (3) multiple stages with variable retardation and fixed orientation [7]. However, all these are broadband devices, and they cannot provide wavelength-selective polarization control analogous to the granularity that can be achieved in spatial dimensions with SLMs.

Nonlinear effects in optical fibers have been proposed to implement different kinds of polarizers through the mechanism known as polarization attraction. The polarization sensitive gain of nonlinear effects such as stimulated Brillouin scattering (SBS) [8–10], stimulated Raman scattering (SRS) [11], and parametric amplification [12] can be used to implement a functionality similar to a polarizer but usually providing polarization-dependent gain instead of loss. A second class of polarizers enabling energy conservation, known as lossless polarizers [13–18], can also be achieved exploiting cross-polarization modulation, but they need rather strong optical powers, typically in the order of watts, and the efficiency of the attractor depends on the pump SOP.

Sign up for Photonics Research TOC. Get the latest issue of Photonics Research delivered right to you！Sign up now

Here, we introduce a new nonlinear optical functionality, i.e., complete polarization control. Instead of the implementation of a polarizer, we report an all-optical analogue of a polarization controller based on a variable linear retarder (such as a wave plate) with fixed orientation plus one variable circular retarder (optical rotator). The variable retarders rely on exploiting the capability of Brillouin scattering to induce arbitrary birefringence in optical fibers to control the phase shift between orthogonal components of the SOP while conserving the energy of the signal through a combination of phase shifting and gain/loss compensation.

2. NONLINEAR POLARIZATION CONTROL

Since Brillouin scattering originates from an interference between counterpropagating waves through electrostriction, its efficiency is polarization dependent, i.e., the gain (or loss) coefficient is maximum when the pump and signal electric fields rotate describing the same ellipses with opposite senses. From this polarization dependence, a controlled phase shift between eigenmodes can be introduced using SBS if the pump is aligned with one eigenmode of the signal. Thus, SBS can induce an optically controlled phase retardance between linearly polarized eigenmodes in a guided medium such as optical fiber. This polarization control is wavelength selective because the Brillouin response bandwidth can be tuned from 30 MHz to tens of GHz due to the short coherence lifetime of hypersonic phonons in fiber. It allows independent control of the SOP of individual optical channels in DWDM scenarios.

The natural response of SBS associates a phase shift with a gain (Stokes) or a loss (anti-Stokes) response, as shown in the inset of Fig. 1(a) (blue solid/dotted curves). However, it is possible to combine Brillouin gain and loss resonances to compensate each other in magnitude while adding the phase shifts provided by both responses, as shown in the inset in Fig. 1(a) (green curve). This combination of two pump waves can easily be achieved by biasing an external modulator at the minimum bias point (MITB) with a microwave signal of frequency $f_{p}$ . The maximum phase shift is obtained when $f_{p} = υ_{B} \pm \frac{Δ υ_{B}}{2}$ , where $υ_{B}$ is the Brillouin frequency shift, and $Δ v_{B}$ is the FWHM bandwidth of the Brillouin gain response. This approach allows the enhancement of the phase response while maintaining the amplitude of the signal minimally affected, as shown in Fig. 1(b). It is analogous to an optical all-pass filter, which has been proposed to control the phase of optically modulated RF signals [19,20].

Figure 1.(a) Concept of the nonlinear polarization controller based on two independently controlled variable elements: a circular retarder and a linear retarder. The SOP of an incoming optical signal at $f_{0}$ with, for example, linear polarization at 45º (Jones vector ${[1 / \sqrt{2} (1, 1)]}^{T}$ ) is altered by a pair of pump signals, gain and loss, respectively, at $f_{0} - f_{p}$ and $f_{0} + f_{p}$ with circular polarization for the circular retarder, and a second pair of pump at $f_{0} - f_{p}$ and $f_{0} + f_{p}$ with linear polarization for the linear retarder. Inset: phase response of the all-optical polarization-dependent SBS all-pass filter. (b) Magnitude of the frequency response of the all-optical polarization-dependent SBS all-pass filter. Combined gain + loss response (green), natural SBS gain response (blue solid), and loss response (blue dotted). (c) Polarization rotation on the Poincaré sphere for the ideal circular retarder. (d) Polarization rotation on the Poincaré sphere for the ideal linear retarder.

From this polarization dependence of the Brillouin all-pass filter response, a polarization controller can be built. In particular, full polarization control can be achieved using SBS to implement two variable retarders with fixed orientations, as shown in Fig. 1(a). Brillouin allows the implementation of arbitrary birefringent elements with dynamic control. The pump SOP defines the birefringence type, i.e., the plane of polarization rotation on the Poincaré sphere, and the pump power controls the phase retardance ( $Γ$ ) between orthogonal polarization eigenmodes, i.e., the angle of rotation on this plane. To perform a circular retarder (Pump #1), the pump polarization has to be circular. In Fig. 1(c), it is shown how a right-handed circular polarization rotates the signal SOP clockwise. A left-handed circular pump would induce a counterclockwise rotation. On the other hand, the second stage, with Pump #2 having a linear horizontal SOP, performs a linear retarder, as shown in Fig. 1(d).

If the Brillouin gain parameter, $G = ζ g_{0} P_{p} L / A_{eff}$ , is high, a significant amount of spontaneous Brillouin noise might be generated. However, this contribution can be considerably reduced if two pump pairs are used. Each orthogonal pump wave must induce a rotation in the same direction, i.e., they need to introduce an inverted Brillouin phase shift. It can be done having pumps with slightly different frequencies. One pump pair will have pump signals at frequencies $f_{0} \pm f_{p 1}$ , and the second pump pair with orthogonal SOP will have $f_{0} \pm f_{p 2}$ , where $f_{p 1} = υ_{B} + Δ v_{B} / 2$ and $f_{p 2} = υ_{B} - Δ v_{B} / 2$ . This doubles the total retardance induced over the signal while suppressing the generation of spontaneous Brillouin noise.

The Brillouin-induced retardance can be calculated, taking into account that SBS in low birefringence single-mode fibers can be viewed as a polarization-dependent gain (loss), where there are two orthogonal input SOPs, each one showing a different gain (loss) [8,21]. The gain of the input SOP with the maximum gain coefficient is twice the minimum one, being 2/3 and 1/3 of the gain in a fiber with no birefringence. Thus, in a birefringent fiber, the Brillouin-induced phase shift is given by $φ_{\max / \min} = \frac{ζ g_{0} P_{p} L_{eff}}{2 A_{eff}} \frac{Δ v_{B} (f_{p} - υ_{B})}{{(f_{p} - υ_{B})}^{2} + {(\frac{Δ v_{B}}{2})}^{2}},$ (1)where $P_{p}$ is the pump power, $g_{0}$ is the Brillouin gain factor, $A_{eff}$ is the effective area, $L_{eff}$ is the effective interaction length of the fiber, and the term $ζ$ is 2/3 for the maximum gain/loss and 1/3 for the minimum gain/loss in birefringent fiber. Therefore, the maximum phase retardance induced by the SBS phase shift in Eq. (1) in a birefringent fiber is $Γ = 2 φ_{\max} - 2 φ_{\min} = \frac{g_{0} P_{p} L_{eff}}{3 A_{eff}} \frac{Δ v_{B} (f_{p} - υ_{B})}{{(f_{p} - υ_{B})}^{2} + {(\frac{Δ v_{B}}{2})}^{2}} .$ (2)It can be seen in Eq. (2) that, despite the combination of gain and loss phase responses, fiber birefringence reduces the maximum phase retardance that can be induced by using SBS to the phase shift induced by a single SBS gain response in a nonbirefringent fiber. Therefore, the Jones matrix of the nonlinear polarization controller is $J_{SBS} = M_{2} M_{1} = (\begin{matrix} G_{\min} A_{\min} \cdot [\cos (\frac{Γ_{2}}{2}) - j \sin (\frac{Γ_{2}}{2}) \cdot \cos (2 δ)] & G_{\max} A_{\max} \cdot jsin (\frac{Γ_{2}}{2}) \cdot \sin (2 δ) \\ G_{\min} A_{\min} \cdot j \sin (\frac{Γ_{2}}{2}) \cdot \sin (2 δ) & G_{\max} A_{\max} \cdot [\cos (\frac{Γ_{2}}{2}) - j \sin (\frac{Γ_{2}}{2}) \cdot \cos (2 δ)] \end{matrix}) (\begin{matrix} G_{\min} A_{\min} \cos (Γ_{1} / 2) & G_{\max} A_{\max} \sin (Γ_{1} / 2) \\ - G_{\min} A_{\min} \sin (Γ_{1} / 2) & G_{\max} A_{\max} \cos (Γ_{1} / 2) \end{matrix}),$ (3)where the Jones matrices, $M_{1}$ and $M_{2}$ , correspond to the linear and circular retarder, respectively. $Γ_{1}$ is the retardance induced by circular birefringence (Pump #1) and $Γ_{2}$ by the linear birefringence (Pump #2). $δ$ is the azimuth angle of the fast axis of the linear birefringence defined by the SOP of Pump #2.

If the gain and loss amplitude responses perfectly compensate each other, i.e., $| G_{\max} | \cdot | A_{\max} | ≅ 1$ and $| G_{\min} | \cdot | A_{\min} | ≅ 1$ , polarization control could be achieved while preserving the energy of the incoming signal.

The system shown in Fig. 2 allows the rotation to an arbitrary output SOP by the combination of two pump pairs with orthogonal polarizations for each wave retarder. Each pump pair introduces a retardance up to $\pm π$ in the Stokes space.

Figure 2.Block diagram of a nonlinear all-optical polarization controller made of one circular retarder plus one linear retarder. HNLF, highly nonlinear fiber; OC, optical circulator; ISO, isolator; VOA, variable optical attenuator; PC, polarization controller; FBG, fiber Bragg grating; OSA, optical spectrum analyzer; PA, polarization analyzer.

For the circular retarder, if the pump at $f_{p 1}$ has a right circular SOP, the signal SOP rotates to the west, as shown in the inset of Fig. 2 (blue solid arrow). The signal SOP can be rotated to the east, as show in Fig. 2 (blue dotted arrow), if frequencies $f_{p 1}$ and $f_{p 2}$ are swapped, such that $f_{p 1} = υ_{B} - Δ v_{B} / 2$ and $f_{p 2} = υ_{B} + Δ v_{B} / 2$ . For the linear retarder, the rotation is obtained in the same way, but the SOPs of the pump waves are linear at 90° and 0° for $f_{p 1}$ and $f_{p 2}$ , respectively.

The polarization modulation speed of the system is restricted by the propagation velocity in the nonlinear medium. For a fiber length of 1 km, the system will have a polarization modulation speed of approximately 200 kHz. However, the use of chalcogenide fiber [22] or photonic-integrated devices [23] would enhance considerably the polarization modulation bandwidth up to the GHz range.

3. RESULTS AND DISCUSSION

A theoretical model of the induced retardance by Brillouin polarization rotation has been developed from SBS equations. It is based on a theoretical analysis of the steady-state-stimulated Brillouin scattering in a single-mode fiber [24]. The model assumes pump depletion but neglects fiber attenuation and takes into account the vector behavior of Brillouin gain in a birefringent fiber. Theoretical estimations have been made assuming a highly nonlinear fiber (HNLF) with $A_{eff} = 11 {μm}^{2}, g_{0} = 7.19 \times 10^{- 12} m \cdot W^{- 1}, Δ v_{B} = 50 MHz$ , $υ_{B} = 9.642 GHz$ , signal power at input fiber $P_{S} = - 8 dBm$ , and operation wavelength of 1548 nm.

The experimental setup used to demonstrate the feasibility of nonlinear polarization control using SBS is the one shown in Fig. 2. In particular, two Brillouin polarization control stages are implemented: a circular retarder and a linear retarder. An optical signal is split into two paths using a fiber coupler: the upper one is used to generate the pump waves, while the lower one experiences polarization rotation. The pump is generated by two x-cut Mach–Zehnder modulators ( ${MZM}_{1}$ and ${MZM}_{2}$ ) at minimum transmission bias (MITB) and fed by two microwave oscillators with frequencies $f_{p 1}$ (9.607 GHz) and $f_{p 2}$ (9.677 GHz). All fibers are standard single-mode fiber but the ones used as nonlinear medium. An optical circulator ( ${OC}_{1}$ ) directs Pump #1 toward the circular retarder, made of 1 km highly nonlinear fiber (HNLF) with $A_{eff} = 11 {μm}^{2}$ , $Δ v_{B} ≅ 50 MHz$ , and $υ_{B} = 9.642 GHz$ at 1548 nm. Another optical circulator ( ${OC}_{2}$ ) is used to inject Pump #2 to the linear retarder, where the nonlinear medium is another HLNF. A fiber Bragg grating (FBG) in reflection mode (bandwidth of 12.5 GHz) is used to filter out backward residual pump waves. The total insertion loss of the system is 9 dB. Polarization rotation is done by adjusting the pump power through the VOAs.

Figure 3(a) shows the evolution of the measured retardance with pump power as well as the output DOP at the output of the circular retarder. Each point in the figure is the average of 100 measurements with a maximum standard deviation of 0.02 and 0.45 for retardance and DOP, respectively. The retardance has been measured using the Poincaré sphere method [25]. It can be observed that, as given by Eq. (2), retardance varies linearly with pump power. The effect of the input power on the induced retardance is small. When input signals of different power (up to 0.6 mW) are rotated, the maximum standard deviation of the retardance was 4.6°. More information is provided in Appendix A. Figure 3(b) shows the evolution of the signal SOP at the output of the circular retarder when the power of Pump #1 is changed from 0.08 to 12.6 mW. It can be seen that a full rotation ( $2 π$ ) on the equator of the Poincaré sphere can be achieved.

Figure 3.Experimental results for a 0.16 mW input signal with linear polarization at 45º (Jones vector ${[1 / \sqrt{2} (1, 1)]}^{T}$ ). (a) (Left) Retardance induced as a function of pump power for the circular retarder: experiment (solid orange) and theory (dotted orange); (right) evolution of the signal degree of polarization (DOP) for the circular retarder as a function of pump power. (b) Poincaré sphere representation of the evolution of the output signal polarization over a circular retarder for an input signal. (c) Rotation of the signal SOP induced by the Brillouin-based circular and linear retarders.

However, there is no need for a full $2 π$ retardance change because the sense of the rotation on the Poincaré sphere can be tuned by swapping frequencies between $f_{p 1}$ and $f_{p 2}$ . Thus, complete rotation of the SOP can be achieved, as shown in Fig. 3(c). For a retardance smaller than $π$ , the DOP remains above 98%.

Due to the combination of gain and loss responses, Brillouin polarization rotation induces only slight changes on the signal power in the range of pump powers that are needed to reach any point on the Poincaré sphere. Figure 4(a) shows measurements of the SBS-induced retardance for an input signal of 0.08 mW as a function of pump power and the variation of the power of the signal for the circular (blue solid and dotted) and linear (red solid and dotted) retarders. Figure 4(a) shows that the nonlinear variable retarder is able to provide different kinds of birefringence with the same efficiency. The same pump power induces the same retardance for the linear and the circular retarders. In addition, there are no preferred SOPs, and the same pump power induces the same rotation angle on Poincaré sphere independently of the input signal polarization state, as shown in Fig. 4(b).

Figure 4.(a) (Left) Retardance induced as a function of pump power for the circular (blue solid) and linear (red solid) retarders for input signal with linear SOP at 45º (Jones vector ${[1 / \sqrt{2} (1, 1)]}^{T}$ ). (Right) Variation of the output signal power versus pump power. (b) Sphere’s rotation angle for input signal with ellipticity of $\pm 0.5$ (Jones vector ${[1 / \sqrt{2} (1, e^{\frac{j π}{4}})]}^{T}$ , ${[1 / \sqrt{2} (1, e^{- \frac{j π}{4}})]}^{T}$ ). (c) Control of the retardance bandwidth; (blue) single pump configuration; (red) multitone pump configuration. (d) Comparison of the change of the noise figure for the proposed method (blue) and polarization pulling (orange).

The power of the signal experiences only a slight variation when it is rotated, whereas the retardance grows with pump power, as shown in Fig. 4(a), which follows a trend similar to the behavior of the SBS gain. In particular, for small signals, the variation of the insertion loss is smaller than 1.2 dB. However, with signals that cannot be assumed to be weak in comparison with the Brillouin threshold, the insertion loss increases; thus, the nonlinear polarization controller is limited to signals with power levels below it. For example, a variation of 2.5 dB is experienced for signals of 0.16 mW when rotated $2 π$ . Further details are provided in Appendix A.

As in other applications of SBS, the bandwidth of the Brillouin response can be tailored. Because the Brillouin response is the convolution of the natural Brillouin gain spectrum with the normalized pump power spectrum, arbitrary polarization responses can be achieved by engineering the pump spectrum. Figure 4(c) shows the frequency dependence of the retardance induced by the Brillouin natural response (blue) and a flat-top retardance obtained with a multitone pump (red), which shows a maximum ripple of 2°. Broadened flat-top Brillouin responses enable control of signals from independent free-running sources, as done, for example, in Ref. [10]. It also allows the rotation of signals with bandwidths of the order of or wider than the natural Brillouin response without partially depolarizing them.

Another interesting feature of the presented nonlinear polarization controller is that, unlike most Brillouin processing schemes, it introduces little additional noise due to the lack of net gain. To assess the noise addition by the polarization controller, the noise figure (NF) is defined as the ratio of SNR of the optical signal when the controller is off and on. Noise figures in both cases have been measured using an electrical method [25] (see additional details in Appendix C). The change of the measured NF for a rotation between linear at 0 and $2 π$ has been measured showing a maximum variation of 1.5 dB. For the sake of comparison, the proposed technique has been compared with polarization pulling, which induces a maximum pulling of $2 π$ . Given the gain induced by polarization pulling, the signal power for polarization pulling has been modified to produce the same RF beat note power. As it can be seen in Fig. 4(d), the polarization rotator experiences an NF variation of less than 1 dB with polarization pulling showing almost a 5 dB increment.

4. CONCLUSION

In this work, we have introduced a new all-optical functionality, nonlinear polarization control. Using stimulated Brillouin scattering, light polarization can be actively tailored, independently of adjacent signals. Experiments have shown that the full Poincaré sphere can be reached while introducing optical power changes smaller than 2.5 dB. Because Brillouin processing has the lowest power threshold among nonlinear effects in silica optical fibers, this effect can be easily harnessed. Thus, SBS can induce any type of birefringence with a single physical mechanism over the same material and with the same efficiency. The combination of gain and loss Brillouin responses avoids the generation of spontaneous Brillouin noise, which conventionally is the main limitation of Brillouin optical processing. This new functionality combined with its low noise feature opens new opportunities in polarization control from the synthesis of light with complex frequency-dependent polarization structures for chemistry, imaging, and optical communications as well as a new approach to revisit applications where Brillouin processing has been constrained by its noisy nature.

APPENDIX A: EFFECT OF CHANGES IN THE INPUT SIGNAL POWER

Given the nonlinear nature of the polarization control method, the effect of the power of the input signal on the behavior of the polarization converter has been experimentally analyzed.

The effect of the power of the input signal on its output state of polarization (SOP) has been experimentally analyzed. Figure 5 shows, for the circular retarder, the retardance variation as a function of pump power for different input signal powers. It can be seen that the induced retardance is remarkably similar in all cases. A maximum change in retardance can be observed for a pump power of 8.3 mW, with a standard deviation of the retardance of 4.6°.

Figure 5.Retardance versus pump power for a Brillouin circular retarder for signals of 0.63 mW (dotted black), 0.16 mW (dotted red), 0.08 mW (dotted green), and 0.04 mW (dotted blue).

Figure 6.Variation of the insertion loss of the polarization controller as a function of pump power for signals with different input power at the HNLF.

APPENDIX B: STABILITY OF THE SOP

Figure 7(a) shows the temporal evolution of the Stokes vector components for a signal with input power at the HNLF of 0.16 mW and linear polarization at 45°, which is rotated with the Brillouin polarization controller to a linear signal at 135°, as depicted in Fig. 7(b).

Figure 7.Temporal stability of the signal SOP at the output of the polarization controller. (a) Stokes parameters of the signal output with linear SOP at 135° as a function of time: S₁ (blue solid curve), S₂ (red solid curve), and S₃ (yellow solid curve). Stokes parameters are normalized to S₀. (b) (Red) signal SOP without SBS; (blue) signal SOP with SBS polarization conversion.

The standard deviation of the Stokes parameters of the signal polarization with and without SBS polarization conversion is shown in Table 1.

APPENDIX C: NOISE MEASUREMENT

The degradation in the signal-to-noise (SNR) ratio of the optical signal introduced by the Brillouin-based polarization converter, i.e., the noise figure (NF) of the nonlinear polarization converter, has been estimated. The NF has been defined as the degradation in SNR induced by the additional noise introduced by the polarization rotation. An electrical method to measure NF has been employed, as it provides a more complete measure of the intensity noise generated by the controller [25]. Noise has been measured using the setup shown in Fig. 8, where an RF signal (2.5 GHz) has been used to modulate the optical signal. After heterodyne detection, the SNR of the beat note has been measured with an electrical spectrum analyzer.

Figure 8.Block diagram of a nonlinear all-optical polarization controller used to measure noise. HNLF, highly nonlinear fiber; OC, optical circulator; ISO, isolator; VOA, variable optical attenuator; FBG, fiber Bragg grating; OSA, optical spectrum analyzer; PA, polarization analyzer; ES, electrical spectrum analyzer; VNA, vector network analyzer.

The Brillouin-induced noise $S_{P} (f)$ must be separated from the total measured noise $S_{ESA} (f) |_{mea}$ , which also includes receiver thermal noise $S_{ESA} (f) |_{th}$ , detected shot noise $2 q i_{mea}$ , and the frequency response of the system [25]. The thermal noise correction has been performed from measurement of the thermal noise density with the input light blocked. The correction of the system transfer function has been performed using an RIN transfer calibration setup. Finally, the shot noise has been corrected from measurements of the optical and electrical spectra of the amplitude modulated optical signal and its associated microwave beat note, respectively.

The intensity noise density produced by the polarization controller $S_{P} (f)$ has been derived from [25] $S_{P} (f) = \frac{S_{ESA} (f) |_{mea} S_{ESA} (f) |_{th}}{\frac{S_{ESA} (f) |_{cal}}{{RIN}_{cal} (f) P_{cal}^{2}}} \frac{2 q i_{mea}}{R^{2}} [\frac{W^{2}}{H z}] .$ (C1)

Then, the noise figure is [25] $NF = \frac{P_{s} S_{P} (f) + 2 G P_{s} h v}{2 h v {G P_{s}}^{2}},$ (C2)where the gain ( $G^{2}$ ) has been derived from spectral analysis of the optical receiver photocurrent, and $P_{s}$ is the power at the fiber input.