Optics & Laser Technology 44 (2012) 492–496

Contents lists available at SciVerse ScienceDirect

Optics & Laser Technology

0030-39

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/optlastec

Signal amplification based on the local nonlinearMach–Zehnder interferometer

Arpita Srivastava, Man Mohan Gupta, S. Medhekar n

Department of Applied Physics, Birla Institute of Technology, Mesra, Ranchi 835215, India

a r t i c l e i n f o

Article history:

Received 14 June 2011

Received in revised form

22 August 2011

Accepted 23 August 2011Available online 13 September 2011

Keywords:

Cross phase modulation

Mach–Zehnder interferometer

Optical amplifier

92/$ - see front matter & 2011 Elsevier Ltd. A

016/j.optlastec.2011.08.020

esponding author.

ail address: sarangmedekar@rediffmail.com (

a b s t r a c t

Using the phase modulation of spatial solitons, a new scheme for all-optical signal amplification has

been proposed in this paper. The considered structure is composed of the nonlinear Mach–Zehnder

interferometer (NMZI) with the straight control waveguide (CWG), the uniform nonlinear medium

(NLM) and the linear output waveguide. The local NMZI functions like a phase shifter. The light-induced

index changes in the local nonlinear MZI are responsible for the input beam routing in the uniform

nonlinear medium. The coupling of the input beam to the output waveguide depends on its propagation

direction in the NLM. It is shown that the signal launched at CWG can deflect the beam launched at the

NMZI (input beam) and a modulated (amplified) output could be obtained at the output waveguide.

Further, signal pulse may be reshaped by appropriately increasing the NLM length. In addition,

amplification factor may be enhanced by increasing the NLM length and injecting an appropriate

continuous wave beam along with the signal beam at CWG.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

One of the most important components in integrated opticalcircuits is the Mach–Zehnder interferometer (MZI). MZI has beenextensively utilized for optical devices, for example, multiplexing andmodulation, low-loss combiner, WDM applications, optical powerlimiter [1–4], etc. Proposals for various applications using MZI baseddevices exist in the literature. NMZI (one or both arms are made upof nonlinear materials) has thoroughly been studied for all-opticaldevices [5–14]. Recently, all-optical switching and all-optical logicgates are proposed using a novel structure consisting of an NMZIalong with a CWG and uniform nonlinear medium [15,16]. Using astructure similar to that of Refs. [15,16], we propose signal amplifi-cation and signal reshaping in this paper.

2. The device

We consider an NMZI with one arm (NLA) made up of a Kerrnonlinear material as shown in Fig. 1. A nonlinear medium (NLM)is buffered in-between the V-junction of the NMZI and the outputwaveguide. A control waveguide (CWG) has also been consideredas shown.

When a beam is launched into P1, it splits into two equal parts.One part propagates through NLA and its counterpart through LA.

ll rights reserved.

S. Medhekar).

The part propagating through NLA experiences cross phase modula-tion (XPM) if a control beam is present in CWG. The split parts of thebeam recombine at the V-junction of the NMZI placed just beforethe NLM and enter into the NLM in the form of a single beam.The direction of propagation of this single beam in the NLM dependson the relative phase difference of the split parts at the V-junction.As the phase of the part propagating through NLA could be altered byinjecting a control beam at P2, the beam in the NLM can be deflectedin a desired manner by creating appropriate phase differencebetween the split parts at the V-junction. Moreover, if the combinedpower of the split parts is equal to the solitonic or nearly solitonicpower of the considered NLM, they will form a solitonic/nearlysolitonic beam in the NLM (see Fig. 2). It is obvious that the output atP0 will be maximum if the input beam exactly falls on the straightwaveguide (as in Fig. 2b) and it will be zero if the beam falls on eitherside of the straight waveguide (as in Fig. 2a and c). The Decaymedium (DM) is the section of the CWG with a very high loss, wherethe control beam (signal beam) gets lost after accomplishing its job.

The mentioned structure can be thoroughly analyzed usingthe beam propagation method (BPM), i.e., by solving the belowmentioned nonlinear Schrodinger equation (NLSE) using the splitstep Fourier method [17,18] (for the sake of brevity and savingcalculation time, we treat a one-dimensional problem):

@Ej

@z¼�i

1

2kn0

@2Ej

@x2�ik njðx,zÞ�n0

� �Ej; j¼ 1,2 ð1Þ

Here, Ejð ¼ffiffiffiIj

pexpð�x2=2x2

0ÞÞ is the transverse field envelop ofbeams, Ij is the axial intensity, x the transverse coordinate, x0 the

A. Srivastava et al. / Optics & Laser Technology 44 (2012) 492–496 493

width of input beam, k¼2p/l the free space propagation constantand n0 is the refractive index of substrate on which NMZI ofrefractive index nj(x,z) is fabricated; nj(x,z) is expressed as

njðx,zÞ ¼nLðx,zÞ ðfor LAÞ

nNLðx,zÞþDnjðx,zÞ ðfor NLAÞ

(ð2Þ

where nL(x,z) is the refractive index of the linear arm, nNL(x,z) isthe constant part of the refractive index of the nonlinear arm andDnj(x,z) is the intensity dependent refractive index change, whichis expressed as [18]

Dnjðx,zÞ � n2ð9Ej92þk9E3�j9

2Þ; j¼ 1,2 ð3Þ

Here n2 is the nonlinear coefficient of the material of NLA and k isthe coupling coefficient of control beam and the beam propagat-ing through NLA. It is worth mentioning here that the couplingcoefficient defines the interaction between two beams by definingthe effectiveness of XPM with respect to SPM and dependsexplicitly on experimental conditions. In the case of two coherent

Po

NLA

LANLM

CWGDM

P1

P2

Fig. 1. Schematic diagram of the considered structure.an NMZI is consists of one

arm made up of a Kerr nonlinear material (NLA). A local nonlinear medium (NLM)

is buffered in between the V-junction of the NMZI and the straight waveguide.

CWG is the control waveguide. A continuous wave bias is given at P1. P2 is input

port for a signal and P0 is the output port.

Fig. 2. (a) The figure has been obtained by solving Eq. (1) (using BPM) and using param

(b) When the control beam I2 is equal to 1:1� 1010 W=m2 in the control wave guide, (a) i

control wave guide, (b) is modified as shown.

beams of different wavelengths (mutually incoherent), couplingcoefficients are taken to be 2 and 2/3 for parallel and perpendi-cular polarizations, respectively. For other cases like mutuallycoherent/incoherent beams of same wavelengths, it is 1 [19–20].Hence, in present paper (two mutually incoherent beams of samewavelengths), it is taken to be 1.

By considering a constant input I1 at P1 and by varying thecontrol beam I2 (at P2) within an appropriate range (in the presentcase 0 to 3� 1010 W=m2), we have examined the output I0 at P0

and have shown that a signal given at P2 may be amplified at P0

by judiciously setting structure parameters and power levels of I1,I2. Moreover, the signal may be reshaped just by increasing theNLM length.

The output I0 obtained at P0 will be equal to I1T where T is thecoefficient of the power coupling from the V-junction to thestraight waveguide and may be given by [21]

T ¼1

WzW2½ðAþBÞ2þðCÞ2�1=2exp �2D2 AðBÞ2þB½ðAÞ2þðCÞ2�

ðAþBÞ2þðCÞ2

! !

ð4Þ

where A¼ 1=2W2z , B¼ 1=2W2

2 and C¼kB/A; k is the propagationconstant, B¼(1/Wz)qWz/qz the inverse of radius of curvature of thebeam front at the input face of the straight waveguide and Wz isthe width of the beam at the input face of the straight waveguide.It is worth be mentioning that one can know the beam width at agiven propagation distance from the amplitude profile at thatdistance. Variation in beam width, and hence, curvature of thebeam front can be known by knowing beam widths at two closelyspaced propagation distances. W2 is the spot size of the straightwaveguide. D is transverse mismatch parameter. Since length ofNLM is much longer in comparison to D, angular misalignmentcould safely be ignored. It is worth to be mentioned here thatwhen the beam spot size exactly overlaps on the spot size of theoutput waveguide, the centers of both spot sizes coincide andtransverse mismatch parameter D is zero. This situation is favor-able for power coupling to the output waveguide. As the beamshifts from this situation, D becomes finite, resulting in decreasein power coupling.

eters mentioned in the text. There is no control beam in the control wave guide.

s modified as shown. (c) When the control beam I2 is equal to 3� 1010 W=m2 in the

A. Srivastava et al. / Optics & Laser Technology 44 (2012) 492–496494

3. Signal amplification

To show the possibility of signal amplification, we choose corewidth of 8 mm, separation between LA and NLA is 25 mm,branching angle at the splitting Y-junction and combining V-junc-tion is yB¼1.21, separation between CWG and NLA is 6 mm, k¼1and chosen length of LA and NLA is 1200 mm. The Nonlinearitycoefficient n2 is 2� 10�14 m2=W (of semiconductor doped glass[17]), DL¼[nL(x,z)�n0]¼0.3% and DNL¼[nNL(x,z)�n0]¼0.158%.

The width of the local nonlinear medium (NLM) is consideredto be equal to 7500 mm and a continuous wave of axial intensityI1 ¼ 1:95� 1011 W=m2 is considered at port P1.

When mentioned parameters are used in Eq. (1), it producesFig. 2a and c. The output beam deflects upwards (see Fig. 2a) inthe NLM when there is no control beam (I2¼0) at P2, and hence,the output at P0 remains zero. We add here that zero/small widthoscillations with propagation in the NLM indicate solitonic/nearlysolitonic beam propagation in the NLM.

However, when I2 is varied from 0 to 3� 1010 W=m2, theoutput beam sweeps from upward position to downward position.The output at P0 in the extreme situations remains zero (Fig. 2aand c), while the output becomes maximum when the beamexactly falls on the straight waveguide (Fig. 2b). Fig. 3a showscontrol beam (at P2) vs. output (at P0) characteristic of the structure.

It is obvious from Fig. 3a that if a signal that is varying in therange 0�1:1� 1010 W=m2 would be given at P2 and a continuouswave I1 ¼ 1:95� 1011 W=m2 at P1, the continuous wave would bedeflected/modulated according to the signal at P2 and an amplified

Fig. 3. (a)s Output (at P0) vs. control beam (at P2) characteristic of the considered

structure. (b) With structure parameters of (a), when a signal varying in the range

0�1:1� 1010 W=m2 is given at P2 and a continuous wave of I1 ¼ 1:95� 1011 W=m2

at P1, an amplified signal is obtained at P0 as shown.

output could be obtained at P0 as shown by the timing diagramof Fig. 3b.

We now show that a pulse given at P2 may be reshaped atP0 just by increasing the NLM length. To show it, we keep allother parameters unchanged and chose NLM length equal to12,000 mm. The control (at P2) vs. output (at P0) characteristicof the structure in this case is shown in Fig. 4a. In this case, thesignal at P2 gets amplified at P0 as shown in Fig. 4b. One can notein this case that amplification factor of the structure is the sameas in the earlier case; in addition, the output is significantlyreshaped. One can further compress the signal pulse by justincreasing the NLM width. This is evident in Fig. 5a and b, whichcorrespond to Fig. 4a and b, respectively, and are obtained byconsidering NLM length equal to 18,000 mm. The reason for pulsereshaping/compression is quite obvious. The beam spot size goesfarther from the output waveguide in extreme situations (ofFig. 2a and c) when NLM width is larger. When the signal pulseis injected at CWG, the optical power varies with time in the CWGas per pulse shape and duration. The output remains zero duringsmall power levels of the signal pulse. At the pulse peak, wholeof the input I1 ¼ 1:95� 1011 W=m2 at P1, reaches at outputwaveguide, giving peak of the output. After the peak of the signalhas passed, output quickly goes to zero, giving a reshaped andamplified signal.

Next we show that the amplification factor of the mentionedstructure may also be enhanced. This may be done by increasing

Fig. 4. (a) Keeping all parameters of Fig. 3 and choosing NLM width equal

to12,000 mm, the control characteristic vs. output of Fig. 3a is modified as shown.

(b) Using the parameters of (a) the signal at P2 gets amplified at P0 as shown in this

case the amplification factor of the structure is the same as in Fig. 3b. However,

the output is significantly reshaped.

Fig. 5. (a) Control vs. output characteristic of Fig. 3a modified as shown when

NLM width is considered to be 18,000 mm. (b) Timing diagram corresponds to

Fig. 5a. As evident in the figure, one can further compress the signal pulse by just

increasing the NLM width.

Fig. 6. All parameters of the figure are the same as in Fig. 5. A constant continuous

wave of Idc ¼ 0:55� 1010 W=m2 is mixed with a smaller signal varying in the range

0�0:55� 1010 W=m2 at P2. Figure shows the result of mixing Idc with the signal.

Solid and dashed curves of Fig. 5b are plotted again in Fig. 6 (see thick curves of

solid and dahed lines) for comparison. One can see here that a smaller signal (thin

dashed curve) is amplified (thin solid curve) and amplification is more than in the

previous case.

A. Srivastava et al. / Optics & Laser Technology 44 (2012) 492–496 495

width of the NLM and by injecting an appropriate bias beam alongwith the input signal at P2.

One can note in Fig. 5a that P0 remains almost zero for P2

varying from 0 to 0.55�1010 W/m2. Therefore, if other para-meters are kept the same as in Fig. 5 and a constant continuouswave of Idc ¼ 0:55� 1010 W=m2 is mixed with the signal at P2, theinitial operating point of the structure for the signal may be shiftedforward and a smaller signal varying in the range 0�0:55�1010 W=m2 may be amplified at P0 Fig. 6 shows the result of mixingIdc with the signal at P2. Solid and dashed curves of Fig. 5b areplotted again in Fig. 6 for comparison (see thick curves of solid anddashed lines). One can see in Fig. 6 that a smaller signal (thin dashedcurve) is amplified (thin solid curve) and amplification is more thanthe previous case.

We add here that when the beam in the NLM is perfectlysolitonic and its power is stable, in principle, there is no sourceof noise. However, when the beam (in the NLM) is not solitonic,i.e., when its width is oscillating with propagation, noise isgenerated due to width oscillations. In the case of nearly solitonicbeam, noise would be feebly small as width oscillations are small.

At last we emphasize that conventional amplifiers work on theprinciple of one pass lasing/amplification (by stimulated emission)that involves pumping and inverted (active) medium. In suchsystems one of the reasons of noise is amplified spontaneousemission (ASE), i.e., spontaneous emission gets amplified along withthe signals. ASE degrades amplifier output. Signal degradation due

to ASE would be absent in the present proposal as it does not usestimulated emission for signal amplification. Moreover, the presentstructure can amplify a signal of any desired wavelength and canwork as a wavelength converter by choosing different wavelengthsfor P1 and P2. The choice of wavelengths in a conventional wave-length converter is fixed by the pumping and lasing wavelengths ofthe amplifier material. Even, in wavelength conversion with othertechniques, for example, based on four wave mixing using an opticalfiber and semiconductor, or second harmonic generation/differencefrequency generation with a periodically poled lithium niobate, oncepump or signal wavelength is chosen, other is determined by thenonlinear process. The present proposal provides liberty of wave-length conversion from any-to-any wavelength.

4. Conclusion

In conclusion, this paper investigates a structure composed of thenonlinear Mach–Zehnder interferometer (NMZI) with the straightcontrol waveguide (CWG), the uniform nonlinear medium (NLM)and the linear output waveguide. It is shown that the consideredstructure could be utilized in signal amplification and reshaping.Moreover, the amplification factor could be enhanced by increasingthe NLM length and by mixing the input signal with an appropriatebias of a continuous wave. One can also think of using the con-sidered structure as a wavelength converter with desired amplifica-tion. Such a converter could be designed for any two desiredwavelengths, which is not possible with a conventional wavelengthconverter that utilizes a fiber amplifier and therefore, the twowavelengths depend on the energy levels of the active centers ofthe amplifier. The proposed amplification and wavelength conver-sion would also be free from the problem of amplified spontaneousemission (ASE). The present proposal provides liberty of wavelengthconversion from any-to-any wavelength.

Acknowledgment

A.S. acknowledges funding from the Women Scientist SchemeA (WOS-A) of Department of Science & Technology (DST),India [no. SR/WOS-A/PS-19/2008]. M.M.G. and S.M. acknowledge

A. Srivastava et al. / Optics & Laser Technology 44 (2012) 492–496496

funding from Department of Science & Technology (DST), India[SR/S2/LOP-27/2007].

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