Femtosecond all-optical parallel logic gates based on tunable saturable to reversesaturable absorption in graphene-oxide thin filmsSukhdev Roy and Chandresh Yadav Citation: Applied Physics Letters 103, 241113 (2013); doi: 10.1063/1.4846535 View online: http://dx.doi.org/10.1063/1.4846535 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/103/24?ver=pdfcov Published by the AIP Publishing

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

134.99.128.41 On: Thu, 26 Dec 2013 15:29:44

Femtosecond all-optical parallel logic gates based on tunable saturableto reverse saturable absorption in graphene-oxide thin films

Sukhdev Roya) and Chandresh YadavDepartment of Physics and Computer Science, Dayalbagh Educational Institute, Dayalbagh,Agra 282 005, India

(Received 24 September 2013; accepted 17 November 2013; published online 12 December 2013)

A detailed theoretical analysis of ultrafast transition from saturable absorption (SA) to reverse

saturable absorption (RSA) has been presented in graphene-oxide thin films with femtosecond

laser pulses at 800 nm. Increase in pulse intensity leads to switching from SA to RSA with

increased contrast due to two-photon absorption induced excited-state absorption. Theoretical

results are in good agreement with reported experimental results. Interestingly, it is also shown

that increase in concentration results in RSA to SA transition. The switching has been optimized

to design parallel all-optical femtosecond NOT, AND, OR, XOR, and the universal NAND and

NOR logic gates. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4846535]

The design of all-optical ultrafast devices is a major

challenge to achieve the next generation ultrahigh bandwidth

information processing. This requires a nonlinear optical

(NLO) material that exhibits fast response, strong nonlinear-

ity, broad wavelength range, low optical loss, high damage

threshold, low-power consumption, low cost, and ease of

integration into optical systems.1

Graphene oxide has emerged as an attractive photonic

material due to its unique properties.2 It exhibits (i) heteroge-

neous chemical and electronic structures, (ii) can be proc-

essed in solution, (iii) interacts with a wide range of organic

and inorganic materials that facilitates synthesis of functional

hybrids and composites with unusual properties, and (iv) its

band gap can be tuned by controlling the sp2 and sp3 fractions

to tailor its electrical, optical, and chemical properties.2

A wide range of applications has been proposed for

graphene-oxide (GO) and reduced graphene oxide (rGO).2–6

Its high transparency in the visible spectrum has been inves-

tigated for transparent conductor applications as a possible

replacement for indium-tin oxide (ITO) in organic solar

cells, organic light-emitting devices (LEDs), and displays.2

Its intrinsic tunable fluorescence in the visible and near infra-

red (NIR) has led to biological applications for bio-imaging,

sensing, and drug delivery.2 GO films with very high dielec-

tric constant have been used as spacers to realize thin film

super capacitors.3 rGO obtained from chemical vapor depo-

sition or thermal reduction of GO has been used as one elec-

trode in diode-based memories, solar cells, and LEDs.4 The

strong modulation conductance by strain has been used to

fabricate rGO channel field-effect transistors for ultrasensi-

tive strain sensing.5 The strong saturable absorption (SA) of

GO has also been used for Q-switching and femtosecond (fs)

mode-locking of erbium-doped ring-cavity fiber lasers.6

The NLO properties of GO have been experimentally

investigated in the nanosecond (ns), picosecond (ps), and fs

regimes at different wavelengths, primarily for broadband

optical limiting.2,7–9 These studies show that the NLO prop-

erties of GO are determined by the combined action of the

sp2 and sp3 domains. For ns and ps pulse excitation at

532 nm and also for fs pulse excitation at 800 nm in GO dis-

persed in different solvents and thin films, a transition from

SA to reverse saturable absorption (RSA) takes place on

increase in intensity with increased contrast.7–9 The charge

carriers with SA from the sp2–hybridized domains dominate

the NLO response at low pump intensities while the influ-

ence of the two-photon absorption (TPA) from the sp3–

hybridized domains on the transient absorption signal

becomes stronger on increase in pump intensity.

Logic gates based on switches are the basic building

blocks of computing circuits. In a variety of materials, the

SA characteristics have been used to design all-optical OR

and AND logic gates whereas RSA characteristics have been

used for NOT and the universal NAND and NOR logic gates,

in a pump-probe setup.10,11 These designs require different

samples that exhibit either SA or RSA based on the lower or

higher lifetime of the excited-states, respectively. However,

the intensity-dependent ultrafast SA to RSA transition can be

advantageous in simultaneous realization of various all-

optical ultrafast logic gates with the same sample.

In this letter, we theoretically analyze ultrafast transitions

in GO thin films to study the effect of excitation intensity,

pulse width, concentration, two-photon and three-photon

absorption (3PA) coefficients, and pulse frequency on the SA

to RSA switching and optimize it to design all-optical ultra-

fast parallel OR, AND, XOR, NOT, and the universal NAND

and NOR logic gates.

We consider the four-level energy diagram to analyze

the fs nonlinear absorption (NLA) dynamics in GO thin films

as shown in the inset of Fig. 1. Ultrafast transitions in GO

involve only the singlet states (S0! Sn). One-photon absorp-

tion (S0! S1) and TPA (S0! S2) are as shown in the figure.

TPA from S1 to Sn is not allowed as it occurs between states

of even parities. Electrons in S2 absorb another photon to

reach Sn through excited-state absorption (ESA) as TPA from

S0 to S2 is predominant. TPA and ESA contribute to the vari-

ation in intensity with absorption coefficients b and c, which

correspond to the third and fifth-order nonlinear coefficients,

respectively. The rate of change of the population densities ina)E-mail: sukhdevroy@dei.ac.in.

0003-6951/2013/103(24)/241113/4/$30.00 VC 2013 AIP Publishing LLC103, 241113-1

APPLIED PHYSICS LETTERS 103, 241113 (2013)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

134.99.128.41 On: Thu, 26 Dec 2013 15:29:44

different energy states can be described by the following

equations:

dN0

dt¼ � r0IN0

�hxþ N1

s1

� bI2

2�hx; (1)

dN1

dt¼ r0IN0

�hx� r1IN1

�hx� N1

s1

þ N2

s2

; (2)

dN2

dt¼ r1IN1

�hx� r2IN2

�hx� N2

s2

þ N3

s3

þ bI2

2�hx; (3)

dN3

dt¼ r2IN2

�hx� N3

s3

; (4)

where N0, N1, N2, N3 are the population densities of S0, S1,

S2, and Sn states, respectively, r0, r1, and r2 are the absorp-

tion cross-sections of S0! S1, S1! S2, and S2! Sn transi-

tions, respectively, and s1, s2, and s3 are the corresponding

life times. The transmitted intensity through the film can be

written as

dI

dz¼ �aI ¼ �½aef f þ bI þ cI2�I; (5)

where aeff¼ a0/(1þ I/Is) with a0 as the linear absorption

coefficient and Is as the saturation intensity. The Gaussian

modulating excitation laser pulse is given by

I ¼ I0

x20

x2ðzÞ exp �ct2

s2p

! !exp � 2r2

x2ðzÞ

!; (6)

where x(z)¼x0{1þ (z/z0)2}1/2, c¼ 4ln2 as the pulse profile

parameter, I0 as the peak pulse intensity, and z0¼ px02/k,

with x0 as the radius of the beam waist.

To analyze two input logic gates configurations, we con-

sider two single laser pulses such that the four input combi-

nations (0,0), (0,1), (1,0), and (1,1) can be considered in

terms of phase differences of their peaks.11,12

NLA characteristics have been computed using Eqs.

(1)–(6) considering the experimental parameters for GO thin

films.9,13,14 We consider a laser pulse from a Ti:sapphire

regeneration amplifier at 800 nm of pulse width sp¼ 100 fs

to excite the film. The experimental values of various param-

eters used in the computation are r0¼ 5.5� 10�19 cm2,

r1¼ 1.5� 10�17 cm2, r2¼ 7.4� 10�19 cm2, s1¼ 66 ps,

s2¼ 4.3 ps, s3¼ 0.37 ps, Is¼ 7.0� 1010 W/cm2, concentra-

tion 25 mM, film thickness 140 nm, and wo¼ 20 lm.9,13,14

The contributions of ESA and multi-photon absorption are

difficult to distinguish using z-scan experimental technique;

hence, the reported fitting experimental results which give

effective TPA (beff¼ 31� 10�9 cm/W) and 3PA coefficients

(ceff¼ 0.47� 10�18 cm3/W2) have been used for computation.9

The variation of normalized transmitted intensity with

time at different peak input pulse intensities is shown in

Fig. 1. At I0¼ 5.0� 1010 W/cm2, SA is observed as mole-

cules get excited from S0 to populate S1 and S2 states,

which increases on increase in I0 to 11� 1010 W/cm2. At

I0¼ 11.3� 1010 W/cm2, there is a transition from SA to

RSA due to TPA-induced ESA. Further increase in I0

results in increased contrast due to increase in ESA. This is

evident from the corresponding variation in normalized

population density with time at different I0 values as shown

in Fig. 2. Continuous increase in N2 and N1 leads to

increased ESA from S2 to Sn so that the normalized trans-

mitted intensity exhibits a dip with increasing contrast. At

I0¼ 55� 1010 W/cm2, 68% modulation can be achieved

with switch off/on time of 80 fs. Theoretical simulations

are in good agreement with experimental results shown

recently.9

NLO response is sensitive to concentration. Interestingly,

the variation of transmittance with time for different concen-

tration values exhibits a reverse behavior with regards to peak

pump intensity. In this case, the transition from RSA to SA

takes place at 11.8 mM on increase in concentration as shown

in Fig. 3. The population of N2 reduces with increase in con-

centration. The variation indicates that concentration affects

TPA-induced ESA that is greater at lower concentration. It

has been shown in 4-methoxy-2-nitroaniline that both effec-

tive TPA and ESA cross-sections decrease with increase in

concentration and the effective lifetimes of TPA-induced

ESA increases.15 The variation of percentage modulation with

concentration at different I0 values is also shown in Fig. 4. It

FIG. 1. Variation of transmittance with time during a single 100 fs laser

pulse for different I0 values. Inset shows the four-level energy diagram to

describe NLA in the fs regime.

FIG. 2. Variation of normalized population density with time for different I0

values (a) and (b).

241113-2 S. Roy and C. Yadav Appl. Phys. Lett. 103, 241113 (2013)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

134.99.128.41 On: Thu, 26 Dec 2013 15:29:44

is evident that the RSA-SA transition occurs at higher concen-

tration for higher values of I0. At higher values of I0, beff, and

ceff contributions become significant. The SA to RSA transi-

tion intensity (TI) value is sensitive to beff and ceff. The de-

pendence is shown in inset of Fig. 4. There is a monotonic

decrease in the transition intensity on increase in the value of

the TPA and 3PA coefficients, respectively.

The intensity-induced SA-RSA transition (Fig. 1) can be

used to theoretically design all-optical OR, AND, XOR,

NOT, and the universal NOR and NAND logic gates. For

this, the rate equations have been solved and optimized by

considering two Gaussian pulsed laser beams of equal inten-

sity at 800 nm and pulse width 50 fs, to excite the GO film of

thickness 380 nm. The SA that takes place at lower I0 values

(4.0� 1010 W/cm2) has been used to design the all-optical

OR and AND logic gates. The peak transmittance through

the film for each of these pulsed beams individually is 0.81.

However, when both the pulses are incident together, they

result in increased transmittance due to SA. The all-optical

OR logic can be realized if no threshold is considered, for

which the output is high when either one or both the pulses

are present and is low, when none of the pulses is present, as

shown in Fig. 5(a). The same configuration results in an

all-optical AND logic gate by considering a threshold at 0.81

(solid line) such that the output is high only when both pulses

are incident simultaneously.

The RSA characteristics at higher intensities lead to the

design of NOT and the universal NOR and NAND logic

gates with the same input pulsed laser beams. For this case,

we consider two pulses each at I0¼ 25� 1010 W/cm2. There

is a dip in the transmittance through the film when each of

these pulses is incident individually that results in the NOT

logic, without considering any threshold (Fig. 5(a)).

However, when both the pulses are incident together, the

transmission decreases further due to increased absorption.

The all-optical NOR logic gate is realized considering a

logic 0 below 0.73 such that the output is low when either

one or both the pulses are present and is high when none of

the two pulses is present. The same configuration also results

in an all-optical NAND logic gate by considering a threshold

at 0.52 (dashed line). In this case, the output is low only

when both pulses are incident simultaneously and is high for

all other cases. It has been experimentally shown that excita-

tion with 400 nm fs pump pulse leads to RSA at relatively

lower I0 values compared to 800 nm excitation9; this can also

be used for designing logic gates at lower intensities with

higher contrast.

FIG. 3. Variation of transmittance with time for 100 fs pump pulse excita-

tion for different concentration values at I0¼ 5� 1010 W/cm2.

FIG. 4. Variation of percentage modulation with concentration. Inset shows

the variation of SA to RSA transition intensity with (a) ceff and (b) beff.

FIG. 5. Variation of output transmittance with time and design of all-optical

logic gates: (a) OR and AND gates (solid line as threshold), NOT gate (with-

out threshold), and NOR and NAND gates (dashed lines as thresholds); (b)

XOR gate (dotted line as threshold); (c) combined normalized input pulse

profiles.

241113-3 S. Roy and C. Yadav Appl. Phys. Lett. 103, 241113 (2013)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

134.99.128.41 On: Thu, 26 Dec 2013 15:29:44

The all-optical XOR logic gate can be realized by oper-

ating near the SA-RSA transition (Fig. 5(b)). For this case,

we consider two pulses each of I0¼ 9.7� 1010 W/cm2 and a

threshold at 0.73. Now, the output is high for each of

these pulses incident individually. However, when both the

pulses are incident together, RSA results in greater absorp-

tion that leads to a strong dip in the output to result in a 0

logic state. Hence, the intensity-induced ultrafast SA-RSA

transition in GO thin film can effectively be used to realize

various multiple input Boolean logic operations in the fs

domain, with the same setup by only controlling the excita-

tion intensity.

For continuous operation, repeated pulse excitation is

required. The minimum pulse interval that can be achieved

keeping the same contrast as in Fig. 5 is 115 fs. This can lead

to repetition rates as high as 8.69 Tbits/s. For parallel com-

puting, it is important that various logic operations are simul-

taneously realized in parallel. A schematic setup for

realization of parallel logic gates is shown in Fig. 6 with two

input pulses of intensities I1 and I2 splitting into two equal in-

tensity pulse trains at each beam splitter, made to be colli-

nearly incident on the GO thin film. Different logic gates can

be simultaneously realized in parallel for combinations of

incident fs pump pulses at 800 nm in a small area on the same

film.

In comparison to the SA-RSA transition in Cu-Pc thin

films,12 a number of significant advantages appear in GO thin

films. GO exhibits higher values of nonlinear coefficients

(beff and ceff); as a result, all-optical switching in GO thin

films takes place at two orders of magnitude lower I0 values.

For the same film thickness (200 nm), pump pulse width

(50 fs) and concentration (28 mM), 50% modulation in both

GO and Cu-Pc thin films takes place at 43� 1010 W/cm2 and

36� 1012 W/cm2, respectively. Moreover, GO thin films ex-

hibit a concentration dependent RSA to SA transition with

faster switch off/on time and high switching contrast whereas

in Cu-Pc thin films, either SA or RSA is observed on increase

in concentration (1 to 100 mM) at lower or higher I0,

respectively.12 The NLO properties of GO can be tailored

over a wide wavelength range by various techniques that

include, varying the number of layers and the chemical com-

position or covalently functionalizing it with materials with

large optical nonlinearities to form hybrid materials that

include porphyrins, fullerenes, oligothiopines, Fe3O4 nano-

particles, and phthalocyanines.2,8,14 The combination of non-

linear mechanisms and the strong interaction due to

photo-induced electron or energy transfer in hybrid materials

leads to enhanced NLO response. The present analysis high-

lights the suitability of the proposed model for ultrafast tran-

sitions in GO, with near-IR pulsed excitation, as theoretical

results are in good agreement with reported experimental

results.9

In conclusion, the present analysis is the first demonstra-

tion of the applicability of GO thin films for all-optical ultra-

fast operations with fs switch off/on time and high switching

contrast, at relatively lower pump intensities compared to

other organic molecules, and opens up exciting prospects in

ultrafast and ultrahigh bandwidth information processing.

The advantages of fs operation, simplicity, tunability, high

contrast, stability of these thin films, and realization of dif-

ferent ultrafast parallel logic gates (OR, AND, XOR, NOT,

NAND, and NOR), with the same film and set up, by only

varying the input pulse intensity make them attractive for

practical applications.

The authors are grateful to the University Grants

Commission and Department of Science and Technology,

Government of India, for partial support of this work and a

research fellowship to C.Y.

1O. Wada, New J. Phys. 6, 183 (2004).2K. P. Loh, Q. Bao, G. Eda, and M. Chhowalla, Nat. Chem. 2, 1015 (2010).3J. Liu, D. Galpaya, M. Notarianni, C. Yan, and N. Motta, Appl. Phys. Lett.

103, 063108-1 (2013).4J. Liu, Z. Yin, X. Cao, F. Zhao, L. Wang, W. Huang, and H. Zhang, Adv.

Mater. 25, 233 (2013).5T. Q. Trung, N. T. Tien, D. Kim, M. Jang, O. J. Yoon, and N.-E. Lee, “A

flexible reduced graphene oxide field-effect transistor for ultrasensitive

strain sensing,” Adv. Funct. Mater. (published online 2013).6J. Xu, J. Liu, S. Wu, Q. H. Yang, and P. Wang, Opt. Express 20, 15474

(2012).7Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, Appl. Phys. Lett.

94, 021902-1 (2009).8N. Liaros, K. Iliopoulos, M. M. Stylianakis, E. Koudoumas, and S. Couris,

Opt. Mater. 36, 112 (2013).9X. F. Jiang, L. Polavarapu, S. T. Neo, T. Venkatesan, and Q. H. Xu,

J. Phys. Chem. Lett. 3, 785 (2012).10F. Z. Henari, K. H. Cazzini, D. N. Weldon, and W. J. Blau, Appl. Phys.

Lett. 68, 619 (1996).11C. P. Singh and S. Roy, Opt. Commun. 218, 55 (2003).12S. Roy and C. Yadav, Opt. Commun. 284, 4435 (2011).13Z. B. Liu, X. Zhao, X. L. Zhang, X. Q. Yan, Y. P. Wu, Y. S. Chen, and J.

G. Tian, J. Phys. Chem. Lett. 2, 1972 (2011).14M. B. M. Krishna, V. P. Kumar, N. Venkatramaiah, R. Venkatesan, and D.

N. Rao, Appl. Phys. Lett. 98, 081106-1 (2011).15B. Gu, W. Ji, X.-Q. Huang, P. S. Patil, and S. M. Dharmaprakash, J. Appl.

Phys. 106, 033511-1 (2009).

FIG. 6. Schematic for realization of two-input parallel all-optical logic

gates. (a) Block diagram. (b) Circuit diagram with two pulse trains I1¼ I2

with I0¼ 38.7� 1010 W/cm2; BS: beam splitter, M: mirror.

241113-4 S. Roy and C. Yadav Appl. Phys. Lett. 103, 241113 (2013)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

134.99.128.41 On: Thu, 26 Dec 2013 15:29:44