266 PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013

Wavelength-dependent Switching of a Nonlinear Optical LoopMirror

O. Pottiez1, B. Ibarra-Escamilla2, and E. A. Kuzin2

1Centro de Investigaciones en Optica, Loma del Bosque 115Col. Lomas del Campestre, Leon, Gto. 37150, Mexico

2Departamento de Optica, Instituto Nacional de Astrofısica Optica y ElectronicaL. E. Erro 1, Puebla, Pue. 72000, Mexico

Abstract— We propose and study a Nonlinear Optical Loop Mirror (NOLM) whose switchingcharacteristic is wavelength-dependent. The device operation relies on a polarization imbal-ance between counter-propagating beams in the loop, which is created by the insertion of ahigh-birefringence fiber (HiBiF). Wavelength-dependent switching arises from the fact that thepolarization of one of the beams is altered by the HiBiF in a wavelength-dependent manner. Thesetup is proposed for wavelength-confined switching and for simultaneous regeneration of twowavelength signals presenting uneven power levels.

1. INTRODUCTION

The Nonlinear Optical Loop Mirror (NOLM) [1] is a versatile and low-cost device whose poten-tial has long been recognized for applications like ultrafast optical switching and signal processing(regeneration, wavelength conversion, demultiplexing, etc.) [2, 3]. Switching is obtained throughthe optical Kerr effect, when the symmetry in the Sagnac interferometer structure of the device isbroken in some way. Although conventional schemes are power-asymmetric (by the use of an asym-metric coupler, or by inserting asymmetrically a gain or loss element in the loop), a birefringenceasymmetry (e.g., a wave retarder (WR) inserted asymmetrically in the loop) is also effective, takingadvantage of the polarization dependence of the Kerr nonlinearity. Such a polarization-imbalancedNOLM, including a 50/50 coupler and a quarter-WR, was proposed and studied previously [4],and the enhanced flexibility of its switching characteristic, which can be controlled though theWR angle and input polarization, makes it very promising for applications like high-quality dataregeneration [5] or passive mode locking of fiber lasers [6].

With most NOLM schemes, the nonlinear response does not depend on the signal wavelength.For some applications however, in particular in Wavelength Division Multiplexing (WDM) systems,wavelength-dependent operation is highly desirable. Unfortunately, very few wavelength-sensitiveNOLM designs can be found in the literature. In [7], wavelength dependence was introduced in aNOLM though the insertion of a chirped grating. Wavelength-confined switching (switching at thegrating wavelength only) was demonstrated experimentally. In the frame of signal regeneration,efforts are being made to concentrate functions such as amplitude equalization and regenerationof different channels into a single device, for obvious cost-saving reasons. Most of the fiber-basedschemes that have been proposed so far for these tasks are based on nonlinear spectral broadeningfollowed by offset filtering [8, 9]. These schemes usually conserve a certain degree of parallelism,as at some point the channels are demultiplexed and processed separately, so that the number ofsome components (fiber sections, filters, attenuators, delay lines etc.) remains proportional to thenumber of channels. Therefore, in a sense simultaneous regeneration is not performed through atruly single device.

2. DEVICE DESCRIPTION AND MODELING

As mentioned before, the polarization-imbalanced NOLM relies on a birefringent element, a WR,to provide switching, taking advantage of the polarization-dependent nonlinear phase shift. If theWR is replaced by a piece of high birefringence fiber (HiBiF), consisting of a large number of beatlengths, the phase shift between the x and y components of light propagating through it is muchlarger than 2π and is given by

∆φ =2π

λ0∆nLHB = 2π

LHB

LB(1)

where ∆n is the refractive index difference, LB the beat length, LHB the HiBiF length and λ0

the wavelength. At a slightly different wavelength λ1 = λ0 + ∆λ (∆λ ¿ λ0), the phase shift ∆φ

Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 267

changes by an amount δ = −2πLHB∆λ/(LBλ0), which is a substantial fraction of 2π and thusalters significantly polarization at the HiBiF output if LHB/LB is large. This wavelength shiftthus alters the polarization imbalance in the NOLM loop, and therefore its switching characteristicbecomes wavelength-dependent.

50/50

45

HiBiF

LHB

L

Non-PM fiberA

CW

ACCW

ο

Figure 1: Scheme under study. The case of linear input polarization is illustrated.

The proposed scheme is illustrated in Fig. 1. It includes a 50/50 coupler, a length L of non-polarization-maintaining (non-PM) fiber and a piece of HiBiF inserted asymmetrically in the loop.For proper NOLM operation, polarization imbalance has to be maintained, so that the ellipticityof each beam must be conserved as it propagates down the non-PM fiber, a condition hardly metin practice due to the residual birefringence of the fiber and its typically long length. A nearlyisotropic behavior can be easily obtained in practice, however, by applying twist to the fiber [10].Finally, the HiBiF birefringence (and thus ∆φ) can be slightly tuned in a range of ∼ π (e.g.,mechanically or thermally), allowing transmission adjustments.

In the continuous-wave approximation, the NOLM behavior can be easily modeled using theJones matrix formalism. In the circular [C+; C−] base, the matrix of the HiBiF (whose axes areset parallel and perpendicular to the plane of the loop) is given by

HB =[

cos (∆φ/2) j sin (∆φ/2)j sin (∆φ/2) cos (∆φ/2)

]. (2)

In the weak nonlinearity limit [4], the Kerr effect does not alter light ellipticity, so that the Stokesparameter, A = [|C+|2−|C−|2]/P (where P = |C+|2+|C−|2 is the optical power) remains constant.In this case, the nonlinear phase shift in the non-PM loop is conveniently accounted for by a Jonesmatrix, which writes as

FCW/CCW =[

exp[jγ

(1− 1

3Acw/ccw

)Pin

2 L]

00 exp

[jγ

(1 + 1

3Acw/ccw

)Pin

2 L]

], (3)

where Pin is the NOLM input power, and the subscripts CW and CCW refer to clockwise andcounter-clockwise beams, respectively. Acw is equal to the Stokes parameter at the NOLM input(assuming that the coupler does not alter polarization) and Accw is calculated from the Jonesvector of the CCW beam at the HiBiF output. Finally, each crossing of the 50/50 coupler is takeninto account by a multiplication by 1/

√2 for the CW field and by j/

√2 for the CCW field. For

a given Jones vector Ein at the NOLM input, the output fields of the CW and CCW beams,Eout,cw = 1/2HB.FcwEin and Eout,ccw = −1/2Fccw.HB.Ein, respectively, are easily calculatedand summed to yield the total output field Eout. The NOLM transmission is finally obtained byT = |Eout|2/|Ein|2.3. RESULTS AND DISCUSSION

Figure 2 shows the power-dependent NOLM transmission at four different wavelengths and for twoparticular input polarization states, namely circular and linear at 45◦ with respect to the HiBiFaxes. A 500-m long high-nonlinearity fiber (nonlinear coefficient γ = 10 /W/m) is chosen as thenon-PM fiber, and the HiBiF consists of 50.25 beat lengths (at λ0 = 1550 nm). It is clear fromthe figures that the NOLM transmission is strongly wavelength-dependent. At wavelength λ3, thetransmission even vanishes (T = 0 for any power), which means that the signal at that wavelengthis completely reflected back to the input port. This behavior can be useful for demultiplexing.Indeed, assuming for example a dual-wavelength signal at λ0 and λ3, and adjusting the peak power

268 PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013

of the signal at λ0 to the switching power Pπ(λ0) = 3.77W, the signals at λ0 and λ3 are transmittedand reflected, respectively.

Except when ∆φ = π/2 or 0, the curves of Figs. 2(a) and (b) are different, which means that, aswavelength is varied, the transmission evolves in a way that depends on input polarization. The caseof linear input polarization at 45◦ is particularly interesting: as observed in Fig. 2(b), a wavelengthshift only affects switching power, whose value is then given by Pπ = 6π/(γL| sin ∆φ|), whereasminimal and maximal transmission values T (0) = 0 and T (Pπ) = 1 are unaltered. Moreover,through slight mechanical/thermal adjustments of the HiBiF, the ratio between switching powers attwo given wavelengths can be readily tuned. This configuration is applied to amplitude regenerationof two signals at λ0 and λ2 having different power levels. If the average peak powers at eachwavelength are in the same ratio than the values of Pπ of the corresponding transmission curves,and if total input power is adjusted to set the peak powers slightly above the values of Pπ (at∼ 4.4W and ∼ 8.8W, respectively), then the intensity limiting effect of the NOLM significantlyreduces amplitude fluctuations (regeneration of the “1” level). Moreover, the low transmissionat low power for any wavelength also allows regeneration of the “0” level in both signals. Such aregeneration is illustrated in Fig. 3 (channels were shifted temporally to avoid nonlinear interactionsbetween them in the loop). This figure was obtained resolving a system of coupled nonlinearpartial differential equations to take into account the small dispersion of the high-nonlinearity fiber(0.3 ps/nm/km with 0.02 ps/nm2/km dispersion slope) and the twist-induced group delay difference(assuming a twist of 2 turns/m), however the results do not differ significantly from those of thecontinuous-wave approach presented here.

0 1 2 3 4 5 6 7 8

0

.5

1

0 1 2 3 4 5 6 7 8

0

.5

1

λ0

∆φ = π/2

λ2

∆φ= π/6

λ1

∆φ = π/4

λ3

∆φ= 0

λ0

∆φ = π/2

λ2

∆φ = π/6

λ1

∆φ= π/4

λ3

∆φ= 0

(b)(a)

Input power (W) Input power (W)

Tra

nsm

issio

n

Tra

nsm

issio

n

Figure 2: NOLM transmission at four different wavelengths λ0 = 1550 nm, λ1 = 1553.85 nm, λ2 = 1555.14 nmand λ3 = 1557.71 nm, in the case of (a) circular input polarization and (b) linear input polarization makinga 45◦ angle with the HiBiF axes.

λ2

λ0

0

2

4

6

8

10

-30 -20 -10 0 10 20 30

λ2

-30 -20 -10 0 10 20 30

0

2

4

6

8

10

λ0

(b)(a)

Time (ps) Time (ps)

Po

wer

(W)

Po

wer

(W)

Figure 3: Eye diagrams at the NOLM (a) input and (b) output of a 2-wavelength signal at λ0 = 1550 nmand λ2 = 1555.14 nm with a power ratio of 1 : 2, assuming that each channel consists of 12-ps pulses with10% Gaussian amplitude noise as the “1” level and 10% ghost pulses with 50% noise for the “0” level.Transmission curves of Fig. 2(b) (linear input polarization at 45◦) were used.

Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 269

4. CONCLUSION

In this work we propose and study a novel wavelength-sensitive polarization-imbalanced NOLM. Itconsists of a symmetric coupler, a loop of twisted non-PM fiber and a HiBiF inserted asymmetricallyin the loop. Switching is due to the polarization imbalance introduced by the HiBiF and wavelength-dependent operation is obtained as a consequence of the wavelength-dependent phase shift of theHiBiF. The case of linear input polarization at 45◦ with the HiBiF axes is particularly attractive,as the transmission curve is then a simple sinusoidal function of input power whose switchingpower only varies with wavelength. The setup is considered for wavelength demultiplexing and foramplitude regeneration of two wavelength channels with uneven power levels. This work contributesto pave the way for the design of a range of novel wavelength-sensitive ultrafast processing devicesfor WDM systems.

ACKNOWLEDGMENT

This work is funded by CONACYT grant #130681.

REFERENCES

1. Doran, N. J. and D. Wood, “Nonlinear optical loop mirror,” Opt. Lett., Vol. 13, 56–58, 1988.2. Boscolo, S., S. K. Turitsyn, and K. J. Blow, “Nonlinear loop mirror-based all-optical signal

processing in fiber-optic communications,” Opt. Fiber Technol., Vol. 14, 299–316, 2008.3. Sotobayashi, H., C. Sawaguchi, Y. Koyamada, and W. Chujo, “Ultrafast walk-off-free nonlinear

optical loop mirror by a simplified configuration for 320-Gbit/s time-division multiplexingsignal demultiplexing,” Opt. Lett., Vol. 27, 1555–1557, 2002.

4. Kuzin, E. A., N. Korneev, J. W. Haus, and B. Ibarra-Escamilla, “Theory of nonlinear loopmirrors with twisted low-birefringence fiber,” J. Opt. Soc. Am. B, Vol. 18, 919–925, 2001.

5. Pottiez, O., E. A. Kuzin, B. Ibarra-Escamilla, F. Gutierrez-Zainos, U. Ruiz-Corona, andJ. T. Camas-Anzueto, IEEE Photon. Technol. Lett., Vol. 17, 154–156, 2005.

6. Pottiez, O., R. Grajales-Coutino, B. Ibarra Escamilla, E. A. Kuzin, and J. C. Hernandez-Garcia, “Adjustable noise-like pulses from a figure-eight fiber laser,” Appl. Opt., Vol. 50,E24–E31, 2011.

7. Pattison, D. A., P. N. Kean, W. Forysiak, I. Bennion, and N. J. Doran, “Bandpass switchingin a nonlinear-optical loop mirror,” Opt. Lett., Vol. 20, 362–364, 1995.

8. Vasilyev, M. and T. I. Lakoba, “All-optical multichannel 2R regeneration in a fiber-baseddevice,” Opt. Lett., Vol. 30, 1458–1460, 2005.

9. Kouloumentas, Ch., P. Vorreau, L. Provost, P. Petropoulos, W. Freude, J. Leuthold, andI. Tomkos, “All-fiberized dispersion-managed multichannel regeneration at 43 Gb/s,” IEEEPhoton. Technol. Lett., Vol. 20, 1854–1856, 2008.

10. Tanemura, T. and K. Kikuchi, “Circular-birefringence fiber for nonlinear optical signal pro-cessing,” J. Lightwave Technol., Vol. 24, 4108–4119, 2006.