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Optik 123 (2012) 489– 493

Contents lists available at ScienceDirect

Optik

jou rna l homepage: www.elsev ier .de / i j leo

imulation of two photon absorption in silicon wire waveguide formplementation of all optical logic gates

ousik Mukherjeea,∗, Dharmadas Kumbhakara,b

Dept of Physics (UG & PG), B.B.College, Asansol, West Bengal, IndiaDept of Electronics and Communication Engineering, Asansol Engineering College, Asansol, West Bengal, India

r t i c l e i n f o

rticle history:eceived 22 November 2010ccepted 10 May 2011

a b s t r a c t

All optical switching action of silicon wire waveguide for the design of the proposed logic gates is simu-lated. This is one possible building block of the future all optical computer or photonic devices. All opticallogic gates NOT, NAND and AND gates using two photon absorption in silicon wire waveguide are pre-

eywords:ilicon wire waveguidewo photon absorptionogic gate

sented. Use of ultra short pulse has negligible free carrier absorption effect; hence the operating speed ofthe gates is very high and has potential application in photonic processing. NAND gate is universal oneand thus one can perform any logical operation using this. The device (Si wire WG) requires low energypulse and is ultrafast one.

© 2011 Elsevier GmbH. All rights reserved.

hotonic integration

. Introduction

All optical logic gates are needed to perform future high speedptical signal processing digitally. Optical logic gates have beenemonstrated using different techniques such as semiconductorptical amplifier (SOA) [1], nonlinear optical fiber [2], and periodi-ally poled lithium niobate (PPLN) [3]. In SOA, there is some speedimitation and latency, the high power level for the nonlinear oper-tion in the fiber and temperature and polarization sensitivity ofPLN make them less attractive. Recently NOR gate using Si wireaveguide (Si WG) have been demonstrated [4–6]. The high refrac-

ive index contrast (n = 3.5 for Si and 1.45 for SiO2) makes it possibleo realize submicron size single mode planar waveguide [7]. Dueo small effective area (<0.1 �m2) and high optical confinement,he Si waveguide can produce high intensity in low input opticalowers used in telecommunications [8]. Thus photonic integra-ion is possible more efficiently in this Si wire waveguide basedevices compared to other devices. The operating speed of theevice depends on the pulse size and shorter the pulse faster wille the speed of operation. In this communication, the authors sim-lated the basic mechanism, TPA for ultrafast all optical logic gatesOT, NAND and AND using Si waveguide.

∗ Corresponding author.E-mail address: lipton007@indiatimes.com (K. Mukherjee).

030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2011.05.012

2. Working principle and theory

An optical pulse of high intensity propagating along Siwaveguide experiences two photon absorption (TPA) which isproportional to the square of the intensity and the maximum trans-mitted power is therefore limited. The absorption of photon has twodirect effects – the optical power depletion (TPA) and the genera-tion of photo carriers. The former is an ultrafast process and thesecond one is slower. So TPA has no speed limitation due to photogenerated carriers [9]. In Fig. 1, nondegenerate and degenerate TPAprocesses are shown.

When the sum of the energies of two pump photons is largerthan the band gap of silicon, they will be absorbed by the processof phonon mediated degenerate two photon absorption (TPA) asin Fig. 1(a). When the sum of the pump photon and probe photonenergies is larger than the band gap, phonon assisted nondegener-ate TPA causes absorption of the two photons. This results in crossmodulation of the probe light. Here excess free carrier absorptionloss is neglected because both the pump and probe photons areultrashort pulses.

By proper choice of the pump (ultra-short pulses) one canachieve high peak power and low average power [8], the amountof free carrier generated is small (since ultra-short pulses are used)and the corresponding loss is negligible.

The evolution of the pump and signal field intensities Ip (z) andIs (z) of two different frequencies, along the propagation direction

z, is governed by following expressions [10]

dIpdz

= −(˛p + ˛FCA)Ip − ˇI2p − 2ˇIpIs (1)

490 K. Mukherjee, D. Kumbhakar / Optik 123 (2012) 489– 493

Phono n Ec phonon Ec

Probe photon pump photon

………virtu al stat e….. Eg ………virtu al state….. Eg

Pump photon pump photon

Ev Ev

a b

TPA, (b): nondegenerate TPA.

wi

N

˛

i[

N

wp1aTn

3

ri1oFtaoflsei

4

0 0.2 0.4 0.6 0. 8 1 0

0.01

0.02

0.03

0.04

0.05

2

FCA

incm

/GW

T=1ps

T=0.5ps

T=0.1ps

in the fraction of intensity is less for pump with less initial peakpower I0 (1 GW and 0.5 GW is shown in the figure here). So suit-ably we can choose the pump intensity keeping in mind the factorof pulse width T for more proper operation of the device.

0.99

1 T=0.1 ps

Fig. 1. (a): Degenerate

dIsdz

= −(˛s + ˛FCA)Is − ˇI2s − 2ˇIPIs (2)

here ˛p,s the linear propagation loss, ̌ is the TPA coefficient, ˛FCAs the free carrier absorption loss.

The free carrier absorption loss is related to the carrier density(z) as [11]

FCA(z) = 1.45 × 10−17N(z) (3)

Here N(z) is the carrier density created from a single pump pulsenside the waveguide along propagation direction z and is given by12] (taking Gaussian temporal profile of the pump).

(z) = ˇ√

�TI20(z)

4h�(4)

here ̌ is the TPA coefficient, T is the pulse width; I0 is the peakower and h� is the photon energy. For Gaussian pump pulse with.6 ps pulse-width and 2 W peak power, the calculated free-carrierbsorption loss after 1 cm long waveguide will be less than 0.18 dB.hus the additional loss from photo-generated carriers is almostegligible [8].

. Simulation and result

The simulation of Eqs. (1)–(4) has done using MATLAB and theesults are shown in Figs. 3–6. In Fig. 3, the variation of ˛FCA withnput pump power for different pulse width (T = 0.1 ps, 0.5 ps and

ps) is shown. The linear loss ̨ and free carrier absorption loss ˛FCAf both the pump and probe beam can be neglected as discussed.rom Fig. 3, it is clear that the value of ˛FCA is negligibly small inhe power range 0–1 GW/cm2 and thus we have taken ˛FCA = 0. It islso interesting to note that less is the pulse width less is the valuef ˛FCA and a pulse width of the order of 1 ps is very much effectiveor proper operation of the devices proposed. The linear absorptionoss ̨ is also neglected since the waveguide has very small dimen-ion and the non linear effects are more dominant. We have also

xcluded the dispersive terms and the real part of the nonlinearndex which is also in effect leads to some kind of dispersion only.

In Fig. 4, the transmitted intensity shows a little variation about% for T = 1 ps and the variation decreases for low values of T. For

Si

SiO2

W= 480nm h = 220nm L= 1cm h

W

L

Fig. 2. Silicon wire waveguide.

Power in GW/cm

Fig. 3. Variation of ˛FCA with input power for different pulse widths.

T = 0.5 or less the intensity transmitted is almost negligible. But alarge pulse width (2 ps) may cause sufficient decrease in the inten-sity. So the selection of the pulse width of the input probe is a crucialfactor. Any pulse width of the order of 1 ps is best for the operationof the devices. It is also interesting to note in Fig. 4 that the decrease

0 0.2 0.4 0. 6 0.8 10.95

0.96

0.97

0.98

z in cm

Fra

ctio

n of

Inte

nsity

T=1 ps

T=0.5 ps

Fig. 4. Variation of fraction of transmitted intensity with length z of the waveguidefor different pulse width and for two different initial intensity I0.

K. Mukherjee, D. Kumbhakar / Optik 123 (2012) 489– 493 491

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2x 10

-->

Pro

be In

tens

ity in

GW

/sq

cm

With pump

Without pump

F

hbsuo

iIpapiimppTmptz

aveslmo

F

--> z in cm

ig. 5. Variation of intensity of the output probe intensity with waveguide length.

The experimental value of ˇTPA = 0.5 − 0.9 cm2/GW [13]; andere we have taken ̌ = 0.9 cm2/GW in our calculation. The probeeam intensity used in the calculation is 1 MW/cm2 which is quitemall in view of the nanoscale size (∼0.01 �m2) of the Si waveg-ide. The solution of Eq. (2) gives Is, the probe intensity as a functionf propagation distance z from the input end of the waveguide.

The output probe intensity is plotted against waveguide length zn the propagation direction in Fig. 5 with and without pump beamp. There is almost no variation of probe intensity with z when theump is absent. But when the pump is applied, there is a large vari-tion of the probe intensity along the z direction. For z = 1 cm, therobe intensity falls to 15% of the input intensity and for z = 2 cm

t goes down to 5% of the input probe intensity when the pumps applied. This can be explained on the basis of cross absorption

odulation or TPA assisted by the pump. When there is no pumpulse, there is very small two photon absorption since TPA is pro-ortional to the beam intensity and the probe beam intensity is low.he probe is transmitted almost full without any cross absorptionodulation. When the pump is applied there is nondegenerate two

hoton absorption and the intensity of the probe beam falls due tohe dominant term IpIs in place of I2

s . For larger interaction length, there is larger reduction in transmitted probe intensity.

In Fig. 6, the variation of transmitted probe intensity for vari-tion in the input pump intensity is shown. The profile of theariation of the pump probe intensity readily matches with thexperimental curve in reference [8]. The transmitted probe inten-

ity is extinguished more than 95% as shown in figure within aength 1 cm of the waveguide. When the pump is absent, the trans-

itted probe intensity is high and when the pump is present theutput probe intensity is low. If we encode the absence light as off

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

90

100

--> Pump Intensity in GW/sq cm

-->

Pro

be p

ower

tran

smis

sion

(%)

Probe depletion with pump power

ig. 6. Variation of intensity of the output probe intensity with pump intensity.

Fig. 7. NOT gate based on Si wire waveguide.

and presence of light as on state, then the above device can be usedas an efficient all optical switch.

4. Realization of different logic gates

The basic principle of operation lies on the transmission charac-teristics of the Si wire waveguide (Si WG). By adjusting the pumppower we can control the pump depletion and hence two photonabsorption can be created or photons can be transmitted accordingto our purpose. If there are two light beams with slightly differ-ent energies (or wavelengths), with one source at high peak power(pump) and the other one at low power (probe) are injected intothe Si WG, the high power pump source will then induce absorp-tion of the low power probe signal. So in the output of the Si WGthere will be no signal. If the pump is not present then there willbe no absorption and hence the probe will be transmitted.

4.1. NOT gate

Fig. 7 shows the schematic diagram of a NOT gate. Pulse signal Ais used as pump which is multiplexed by 12.5 ps MUX. The probe ismultiplexed by a 25 ps MUX is also pulsed probe. The detail of thegeneration of the pump and probe pulse is described in Section 4.

When the pump signal is present (bit ‘1’), then nondegeneratetwo photon absorption (TPA) effect causes significant absorptionof the probe and no probe is transmitted. So the output is LOW(‘0’ bit). When the pump signal is absent (‘0’ bit), the probe pulseis transmitted through the waveguide without any nonlinear lossbecause in that case two photon absorption is not present. Thus theoutput is HIGH (‘1’ bit). This is the NOT operation.

4.2. NAND gate

The next gate which will be realized is the NAND gate. The out-put of a NAND gate is HIGH (‘1’ state) if any one or both of the inputsare LOW (‘0’ state). When both the inputs are HIGH the output is

LOW. The schematic diagram of a NAND gate using TPA in Si wirewaveguide is shown in Fig. 8.

When both the signals A and B are absent there is no non degen-erate TPA in the both Si wire WG I and II and hence the probe pulse

Fig. 8. NAND gate based on Si wire waveguide.

492 K. Mukherjee, D. Kumbhakar / Optik 123 (2012) 489– 493

iblnttiWstwa

4

wS

bTLiTWTHc

5t

5

osl[4

ppf

twMfi

Fig. 9. AND gate realization using Si wire waveguide.

s transmitted and the output is HIGH. When the signal A is absentut B is present there will be TPA in the Si wire WG II and the probe

ight will be transmitted through the Si wire WGI since there is noondegenerate TPA in this waveguide. So the output is HIGH dueo the transmitted probe light through the WG I. Similarly whenhe signal A is present and B is absent, nondegenerate TPA happensn the Upper WG I and transmission of probe light through Lower

G II results in HIGH output State again. Finally when both theignals A and B are present, non degenerate TPA is induced on bothhe waveguides and resulting absorption of the probe on both theaveguides and hence the output is LOW. This is the operation of

NAND gate.

.3. AND gate

The experimental realization of the AND gate using Si wireaveguide is shown in Fig. 9. In this experimental design three

i wire waveguides are used.When both A and B are LOW, the probe I is transmitted through

oth the WG I and II and the input to the WG III is HIGH. This makesPA to happen in the WG III and the final output of the WG III isOW. Again when either one of A or B is LOW, the input to the WG IIIs HIGH resulting a HIGH output in the WG III due to nondegeneratePA in WGIII. When both of the A and B are HIGH, the outputs ofG I and II are both LOW and hence the input of the WG III is LOW.

his result in a transmission of the probe II i.e. the final output isIGH. This is the operation of an AND gate. The filters I and II areentered at wavelengths of probe I and II respectively.

. Physical requirement for experimental demonstration ofhe gates

.1. Si wire waveguide

A typical waveguide is shown in Fig. 2. The basic designf the waveguide is shown in the figure; the core is a silicontrip of transverse dimension W × h and length L over a SiO2ayer. The details of the structure and characteristics are given in11]. The waveguide core may be taken as a strip of dimension80 nm × 220 nm × 10 mm (Fig. 2) for a typical experiment.

For the realization of different logic gates the pump and therobe pulse may be generated from a broadband femto-secondassive mode locked fiber (MLFL) laser by spectral slicing in theollowing process (Fig. 10).

The output of the MLFL is divided into two parts, the upper and

he lower part. The upper part is passed through a tunable filterith a center wavelength 1545 nm and multiplexed by a 12.5 psUX and then amplified. The lower part is passed through tunable

lter with center at 1550 nm, 25 ps MUX and then an attenuator to

Fig. 10. The scheme for generation of probe and pumps signals necessary for theexperimental set up.

generate probe pulse. The use of two different pump and probebeams with modulation formats 12.5 ps for pump and 25 ps forprobe lies in the fact of time scales of the two processes of opticalpower depletion by two photon absorption and free carrier gener-ation effects. The former is ultra fast with time scale 5 ps and thefree carriers generated has life time of the order of 1–10 ns. Therelative pulse repetition rate of pump and probe for the differentlogic gates are shown in the figures of the corresponding gates. Theprobe II in the Si wire WG III should be different from probe I and itmay be of wavelength 1560 nm. Before cascading the output in thenext stage, the outputs of the silicon waveguides should be passedthrough a MZI [14] for inversion of the pulse and an amplifier tofeed the next stage.

6. Conclusion

In this paper, the simulation of pump probe intensity variationthrough two photon absorption is reported and three very usefulgates for optical data processing are presented with ultrafast oper-ating speed. The result shows that the device can be used as anefficient switch for all optical computation and communication.Using this switching action logic gates NOT, NAND and AND areproposed [15] but in this communication the simulation of the TPAis shown and the corresponding conditions for pulse width choicesare also simulated. As mentioned in [9] the speed of operation isultrafast one can utilize these gates for future high speed compu-tation and communication technology. In the output, for properdetection of the pulse one should use amplifier to enhance thepower of the output signal. The device required for the implemen-tation of the gates is very small in size and the operating powersrequirement is very low and operation at any wavelengths between1200 nm and beyond 1700 nm range is possible. For successfuloperation of the devices, the sum of the pump photon energy andprobe photon energy should be greater than the band gap of the sil-icon. Actually the NOT gate proposed in this communication mayalso be used as controlled NOT (CNOT) gate but in the presence ofthe probe it acts like a NOT gate. So this is a two bit gate but if degen-erate four wave mixing is used then it can be made a single inputNOT gate. In that case the pump and probe has same frequency andcan be derived from a single input by a proper coupler (90:10).

The implementation of the logic gates also shows that siliconwire waveguides have potential applications in ultrafast opticalphotonic signal processing and very much applicable to telecom-munications. Before cascading the output in the next stage, theoutputs of the silicon waveguides should be passed through a MZIfor inversion of the pulse and an amplifier to feed the next stage.

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[[

[

[

[

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