All-Optical Logic Gates Using Nonlinear Effects

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All-optical logic gates using nonlinear effects

in silicon-on-insulator waveguides

Mohammadreza Khorasaninejad and Simarjeet Singh Saini*

Department of Electrical and Computer Engineering, University of Waterloo,

200 University Avenue West, Waterloo N2L 3G1, Ontario, Canada

*Corresponding author: [email protected]

Received 3 February 2009; revised 11 May 2009; accepted 17 May 2009;

posted 19 May 2009 (Doc. ID 107082); published 9 June 2009

We propose multiple all-optical logic operations in complementary metal oxide semiconductor compatiblesilicon-on-insulator waveguides based on three nonlinear phenomena, stimulated Raman scattering, freecarrier absorption, and cross phase modulation. The performance of three optical logic operations issimulated by use of the finite-difference time-domain method. We achieved an extinction ratio of approxi-mately 13dB between two logic levels. 2009 Optical Society of America

OCIS codes: 190.0190, 130.3750, 290.5910, 040.6040.

1. Introduction

Stimulated Raman scattering (SRS), a third-ordernonlinear effect, has been proposed as a unique me-

chanism to achieve optical amplification and lasingin silicon [1,2]. To realize Raman amplification, ahigh intensity input pump is required that leads toanother nonlinear effect, two-photon absorption(TPA), which results in the generation of free carriers[3,4]. Although the detrimental effect of TPA is neg-ligible by itself, the TPA-generated free carriers playan important role in decreasing the performance ofsilicon-based active devices [4,5]. It has been shownthat the lifetime of the free carriers and, hence, theexcess loss that is created due to them can be reducedconsiderably by integrating a reverse biased p-i-ndiode structure along a waveguide [6]. In addition

to amplifiers, several different devices such as opticalmodulators [7], optical switches [810], and opticallogic gates [1114] have been proposed using nonli-nearity in silicon. For realization of an optical mod-ulator, an embedded modulated reverse biased p-i-ndiode is used to cause a phase shift inside a siliconwaveguide by changing the free carrier density. Anall-optical switch was proposed by Xu et al. [8] by

use of the cross phase modulation (XPM) effect of Ra-man pump-generated free carriers. In other words, afrequency-shifted signal that is shifted in wave-

length due to XPM can pass through a designed filterat the output and results in the ON state of theswitch. Similarly, Boyraz et al. [9] demonstrated a

XPM based interferometric switch with a MachZehnder configuration. Another all-optical switchwas achieved in a fiber Bragg grating by use of

XPM [10]. In addition, all-optical logic gates havealso been proposed by Xu et al. [11] based on a siliconmicroring resonator that needs electron beam litho-graphy (EBL). Liang et al. [12] designed a NORgate using the TPA in a silicon waveguide. Someother logic operations in silicon-on-insulator (SOI)waveguides were achieved by Raman [13] and inter-ference effects [14] by use of a Y coupler and multi-mode interference (MMI) coupler, respectively.

All-optical logic gates have attracted considerableresearch interest because of their numerous poten-tial applications in optical signal processing systems,such as switching, addressing, and data encoding. Wepropose three different optical logic gates that usenonlinear effects in a SOI waveguide. Unlike [79],a control pump along with a Raman pump is usedto create free carriers to take advantage of their non-linear effects and achieve logic between two inputs asopposed to optical switching. In this context, first we

0003-6935/09/250F31-06$15.00/0 2009 Optical Society of America

1 September 2009 / Vol. 48, No. 25 / APPLIED OPTICS F31
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describe a model used to simulate the proposed de-vices. Next, we study nonlinear loss caused by thefree carriers and investigate the dependence of thefree carrier generation on the pump power and itspulse width. It is shown that by appropriate adjust-ment of the free carrier density with the width andthe peak power of the pump pulse, amplification andattenuation processes can be controlled. In particu-lar, the dependence of free carrier absorption(FCA) on the pulse width and the peak power canbe utilized to achieve all-optical logic operations. Fi-nally, we explore the plasma dispersion effect of freecarriers and use this effect to achieve another logicgate. Performance of the gates is analyzed for thepropagation, TPA, FCA, and SRS by means of thefinite-difference time-domain (FDTD) method.

2. Modeling

In a typical silicon Raman amplifier, a Raman pulsepump at wavelength p and a continuous-wave (cw)probe beam at a Stokes wavelength s are injectedinto a waveguide. During propagation of these two

waves along the waveguide, Raman coupling takesplace between the pump and the Stokes signalsresulting in an amplified Stokes at the output. Theevolution of the pump Ip and the first-order StokesIs intensities along the waveguide are governed bythe following:

dIpt;z

dz Ipt;z I

2pt;z 2gIpt;zIst;z

Nt;zIpt;z; 1

dIst;zdz Ist;z I

2s t;z 2gIst;zIpt;z

Nt;zIst;z; 2

where z is the propagation direction, is the propa-gation loss, is the TPA coefficient, g represents theRaman gain coefficient, shows the FCA crosssection, and N is the free carrier density. A modifica-tion to the standard model in [2] was made to includethe effect of Raman coupling on the Raman pump.Moreover, N is given by

dNt;z

dt

2hpI

2

pt;z

2hsI

2

s t;z

Nt;z

; 3

where p and s are the frequencies of the Ramanpump and the Stokes probe, respectively. Also, isthe effective lifetime of the free carriers. To have abetter understanding of Raman amplification, aRaman net gain constant G is defined as

G 10 log

IoutIin

; 4

where Iin and Iout are the input and the output probeintensities, respectively. To assess the validity of ournumerical method, first we calculate the net gain of ademonstrated amplifier in [2]. In this simulation, weassume a linear propagation loss of 0:22dB=cm, aTPA coefficient of 0:5 cm=GW, a free carrier crosssection of 1:45 1017cm2, a carrier lifetime of 25ns, a Raman gain coefficient of g 10:5 cm=GW, and a 4:8 cm long SOI rib waveguide with an ef-fective area of1

:57m2, all of which are the same as

in [2]. Figure 1 shows the net gain G for both simula-tion and the published experimental results of [2]when the peak pump intensity varies from 0 to50MW=cm2. It is evident that our simulation andexperimental results are in good agreement.

3. Free Carrier Effect

It has been shown that the efficiency of Ramanamplification is reduced by the TPA generated freecarriers since the free carriers not only absorb thepower of the input pump thereby decreasing the cou-pling power to Stokes, but they also attenuate the

amplified Stokes signal along the waveguide [4,6].A simulated detrimental effect of the generated freecarriers on reduction of the input pulse power alongthe length of the waveguide is shown in Fig. 2. Theinput pump power depletes significantly while it pro-pagates along the waveguide. One can avoid generat-ing the free carriers by pumping the waveguide witha pulse of a full width at half-maximum (FWHM)narrower than the effective carrier lifetime. The si-mulated density of free carriers is shown in Fig. 3when the waveguide is pumped with a Gaussianpulse with an intensity ofI 50MW=cm2 for differ-ent FWHM values of15ns and 150ps. It is apparentthat, although the peak pump power in both the pi-

cosecond and the nanosecond pulses is equal, thedensity of the free carriers is reduced considerably

Fig. 1. Net Raman gain versus pump intensity when the wave-guide is pumped by a 17ns long Gaussian pulse at wavelength of1545 nm and a cw probe,Stokes signal at a wavelength of1680 nm.Solid curve, the modeling result; symbols, experimental resultsadopted from [2].

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in the picosecond regime. Figure 3 also shows thefree carrier density for another 150ps long Gaussian

pulse, such as the previous one, but with an in-creased peak power. As seen it is possible to generatethe free carriers as large as a nanosecond pulse by ahigh peak power picosecond pulse. Therefore, one caneither avoid or increase the FCA effect by adjustingthe pulse width or its peak power. This property ofcontrolling the free carriers can be used to build all-optical logic gates. Two levels of a logic gate aredefined by switching between amplification andattenuation of the Stokes signal. In other words,an amplified Stokes signal corresponds to a logicone and an attenuated Stokes signal correspondsto a logic zero. Alternating between the amplification

and the attenuation is possible by controlling the

density of the free carriers and this can be achievedby using an additional input pump power (hereaftercalled the control pump). Some important para-meters that should be considered about this controlinput pumpIp include its wavelengthp, pulse width,peak power, and pulse position in comparison withthe Raman pump. The wavelength of this pumppower is selected at a slightly different wavelengthof the Raman pump so as not to have any Raman am-plification between the control pump and the Stokessignal at a wavelength ofs. Furthermore, its widthor peak power should be large enough that it cangenerate considerable free carriers for attenuationpurposes. However, if we consider its width in the na-nosecond range, it restricts the speed of the device.Therefore, we utilize a 150ps long Gaussian pulsewith a peak pump power of10W and a wavelengthof1530nm to control free carrier density. To considerthe effect of the control pulse, Eqs. (1)(3) must bemodified as follows:

dIpt;z

dz Ipt;z I

2pt;z 2gIpt;zIst;z

2Ipt;zIpt;z I

st;z

Nt;zIpt;z; 5

dIst;zdz

Ist;z I2s t;z 2gIst;zIpt;z

2Ist;zIpt;z I

st;z

Nt;zIst;z; 6

dIpt;z

dz Ipt;z I

2p t;z 2gI

pt;zI

st;z

2Ipt;zIpt;z Ist;z

Nt;zIpt;z; 7

dIst;zdz

Ist;z I2s t;z 2gI

st;zI

pt;z

2Ist;zIpt;z Ist;z

Nt;zIst;z; 8

dNt;z

dt

2hpI2pt;z

2hsI2s t;z

2hpI2p t;z

2hsIst;z

Nt;z

; 9

where Is is the Stokes signal associated with Ip. Inaddition, p and

s are the frequency of the control

pump and its generated Stokes, respectively. As is

Fig. 2. Modeled profile of a Gaussian pulse with a peak pumpintensity of 50MW=cm2 and a FWHM of 17ns along a 4:8 cmSOI waveguide at three different positions.

Fig. 3. Free carrier density profiles generated by TPA for differ-ent pulses with a carrier lifetime of1ns. Solid line, free carriergenerated due to a 15ns long Gaussian pulse with a peak powerof I 50MW=cm2; dashed line, free carrier generated due to a150ps long Gaussian pulse with a peak power of I 50MW=cm2;dasheddot line, free carrier generated due to a 150ps longGaussian pulse with a peak power of I 160MW=cm2.

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clear from Eqs (5)(9), propagation of the controlpump along the waveguide is considered by includingthe propagation, TPA, and FCA losses in conjunctionwith the SRS gain. The principal role of the controlpump is in its generated free carriers imposedin Eq. (9).

In the two logic operations reported below, we alsocreate a time delay of25ps for the Raman pump incomparison with the control pump. By this time de-lay, overlap of the Raman pump takes place with thefree carriers generated by the control pump near themaximum level of free carrier density resulting in ahigher extinction ratio. Realization of different all-optical logic operations based on various effects ofgenerated free carriers is discussed in the followingsections.

4. Logic Operations by Free Carrier Absorption

A schematic diagram of an all-optical logic gate isshown in Fig. 4. Inputs for the gate are as follows:A, a Gaussian pulse with a FWHM of 100ps at awavelength of p 1545nm and a peak intensity

of50MW=cm2

to generate Raman amplification; B,a Gaussian pulse with a FWHM of150ps, a wave-length of p 1530nm and a peak power of 10Wused to change the density of the free carriers inthe SOI waveguide. A cw probe signal at the Stokeswavelength for pump A is injected into the wave-guide and monitored at the output to investigatethe amplified or the attenuated signal and thusthe logic output of the gate. The output of the logicgate is denoted by C. The C wavelength is selectedsuch that Raman coupling occurs between A andC. By considering the input pump power at a wave-length of1545nm, the wavelength of the first-orderStokes is calculated at a wavelength of s 1680nm [2].

The output of the waveguide for different logic va-lues ofA and B is shown in Fig. 5 for a free carrierlifetime of1ns, achievable by either integrating a re-

verse biased p-i-n diode [6] or using a small effectivearea waveguide [8]. Other simulation parameters arethe same as mentioned in Section 2. In the absence ofB, no dominant free carriers are generated, as shownin Fig. 3, because of the narrow pulse width and mod-erate power ofA. This leads to efficient amplificationbetween A and C, corresponding to logic one. Asshown the output has a perfect Gaussian shape,the same as the Raman pump because of the negli-

gible density of the generated free carriers. In otherwords, there is no excess loss in the trailing edge thatis expected for a nanosecond Gaussian pulse. Whenwe pump the waveguide with A and B simulta-neously, the detrimental effect of FCA caused by Bdecreases the Raman amplification; hence, the out-put on C drops, corresponding to logic zero. The otherconfigurations that can be considered are A B 0and A 0, B 1. In the case ofA B 0 as shownin Fig. 5 a cw Stokes appears at the output as it onlysees the propagation loss in the waveguide. This sig-nal can be filtered simply by a high-pass filter in theelectronics part of the circuit after detection of theoptical power. The output power for A 0, B 1 isnot shown but it is apparent that, in this case, thesignal will be attenuated more than in theA 1,B 1 cases since there will be no Raman gain on C. Thusthe extinction ratio for the A 0, B 1 input caseswill be larger than for the A 1, B 1 cases. Conse-quently, the structure provides logic operation ofA:B.One can see that the output power that correspondsto logic one is approximately 13dB higher than logiczero assuming that the dc signal, when A 0 and

B 0, can be filtered and is greater than8dB assum-ing it is not removed. This gate can also be used as aNOT gate by considering B as an input and withpulse A always present. From an experimental pointof view a simple long-pass filter can be used at theoutput facet of the waveguide to have only the Stokessignal at the output of the gate.

By changing the time translation betweenA andB,A and its generated Stokes will experience XPM thatis imposed by B. This effect can be utilized to haveanother logic operation and is described in Section 5.

5. Logic Operation by Cross Phase Modulation

In this proposed device, the schematic diagram of alogic gate is the same as what is shown in Fig. 4. Herewe use XPM to realize an AND gate. XPM occurs

Fig. 4. Schematic diagram of a SOI waveguide used as an all-optical logic gate media. A and B are the Raman and the controlpumps, respectively. Also, C is the output power at the Stokeswavelength.

Fig. 5. Output power of thelogicfor different logic values ofA andB. A, 100ps long Gaussian pulse with a peak intensity of50MW=cm2; B, 150ps long Gaussian pulse with a peak powerof10W.

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because the B-generated free carriers can also per-turb the refractive index of the waveguide. The rela-tion between the change in free carriers and the

variation rate of the refractive index is as follows:[15]

nt e22

82c20n

Net

mceNht

mch

; 10

where e is the electron charge, is the wavelength ofthe pump, 0 is the free space permittivity, n is therefractive index of unperturbed silicon, Ne andNh are the number of excess electrons and holesgenerated by TPA, respectively. In addition, mceand mch represent the effective mass of the electronsand the holes, respectively. Because of the refractive-index change, the phase of a signal varies as follows:

t 2L

nt; 11

where L is the waveguide length. The time depen-

dence of the phase causes a frequency shift given as

t d

dtt: 12

Using Eqs. (10)(12), the total wavelength shift forthe 4:8 cm long SOI waveguide is calculated by theFDTD method and is indicated in Fig. 6. IfA overlapswith the leading part of the B-generated freecarriers, the XPM effect of B is enough to changethe carrier frequency ofA. This effect has been pre-

viously used to create an optical switch [8]. Perfor-mance of an optical AND gate based on this effectis described in the following.

To have an A:B logic operation, i.e., an AND gate,we use a bandpass filter at the output of the wave-guide such that its center frequency is at the wave-length of the Stokes signal minus the maximumabsolute value of the wavelength shift that is due

to XPM. Operation of the gate is simulated usingthe FDTD method to determine pulse propagationinside the waveguide, the concentration of the freecarriers, and also the free carrier induced wave-length shift. Output powers of the AND gate are de-picted in Fig. 7 for various configurations ofA and B.

At these A and B arrangements, the output power ofthe AND gate is defined by the properties of thebandpass filter, mainly its bandwidth. Therefore, en-

ough extinction can be achieved by the proper designof the filter. In the presence of both A and B, at theoutput of the waveguide we have an amplified Stokessignal with its center frequency changed because ofthe dispersion effect ofB. Therefore, the Stokes sig-nal can pass through the designed filter. It is notablethat, in this section, we used a reduced Raman gain,g 5 cm=GW, that is due to the small width of theRaman pump that decreases the Raman gain.

In the presence of only B, the Stokes signal experi-ences FCA generated by B in addition to the fre-quency change so the amplitude of Stokes is smallin comparison with the previous case. However, weobtained an extinction ratio of 13dB, which differ-entiates between logic one and logic zero. For A 0 and B 0, Stokes signal C does not receive eitherany Raman amplification or any frequency shift andis highly attenuated at the output after the opticalfilter.

Here we considered a fifth-order bandpass Butter-worth filter with a FWHM of0:25nm. Butterworthbandpass filter designs are interesting because oftheir flatness and their equiripple characteristics.Different designs of Butterworth filters have beenapplicable by use of fiber-optic interferometers andring resonators [16]. The filter is centered at a wave-length that is 0:35nm shorter than that of the cw

probe. The effect of the filter bandwidth and its shapeis taken into account in the simulations. As shown inFig. 7, the amplified Stokes is distorted in the

Fig. 6. Time transientwavelengthshift dueto pump pulseBwitha FWHM of50ps and a peak power of10W.

Fig. 7. Normalized output power for different logic values ofAand B after a fifth-order bandpass Butterworth filter with aFWHM of0:25nm. A, 5ps long Gaussian pulse with a peak powerof3W; B, 50ps long Gaussian pulse with a peak power of10W.

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presence of both A and B because of the FCA effect ofB and the filtering effect. While such distortionsmight be of consequence in optical switches [17], theyshould not matter much in optical logic gates inwhich a thresholding circuit is used to make the de-cision. In addition, the effect of the output filter isalso observable by comparing the peak-to-zeroamplitude of the output pulses in Fig. 7 with theircounterparts in Fig. 5.

6. Conclusion

In summary, we have investigated two different as-pects of the free carrier effect, FCA, and XPM. Wehave demonstrated how FCA can be used as a leverto alternate between amplification and attenuationto achieve logic operation. Use of another effect offree carriers, XPM, an AND gate was proposed.Further improvement in the extinction ratio betweenthe two logic levels could be applicable with a taperedwaveguide [5] because of Raman gain enhancement.The effective area reduction of a tapered waveguidealong its length enhances nonlinear effects such asSRS and FCA. Although gate speed is limited bythe carrier lifetime, it can be boosted by dc biasingthe waveguide to sweep out free carriers.

This research was supported by the CanadianNational Science and Engineering Research Council(NSERC) through the Discovery Program.

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All-Optical Logic Gates Using Nonlinear Effects

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