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All Optical 2-bit Carry Look Ahead Adder Using
Mach-Zehnder Interferometer
Indranil Jana
Department of Computer Science,
College of Engg. And Management,
Kolaghat, India
jana.indranil@gmail.com
Dilip Gayen
Department of Computer Science,
College of Engg. And Management,
Kolaghat, India
dilipgayen@yahoo.co.in
Abstract—In future for high speed processing all-optical logic
Carry Look Ahead (CLA) Adder is extremely important and it is
proposed and described with the help of semiconductor optical
amplifier (SOA) based Symmetric Mach Zehnder Interferometer
(SMZI) switch. In this present communication, we have tried to
design a all-optical circuit CLA adder circuit. Simulation of
proposed design has also been reported.
Keywords-SOA based SMZI; All-optical; CLA
I. INTRODUCTION
Adder circuit is extremely important for adding data in
CPU. In ripple carry adders, the carry propagation time is the
major speed limiting factor. One widely used approach
employs the principle of carry look-ahead solves this problem
by calculating the carry signals in advance, based on the input
signals. It uses the same carry-look-ahead circuits to construct
the higher-bit CLA recursively. Among the proposed schemes,
the SOA-SMZI switch effectively provides fast switching time
and a reasonably reduced noise figure, with the ease of
integration and jitter tolerance, compactness, thermal stability
and high nonlinear properties, overall practicality that enables
it to compete favorably with other similar optical time division
multiplexing (OTDM) devices. Here all-optical Carry Look
Ahead adder has been constructed using all-optical NAND
circuit developed by SOA-MZI switch, which can decrease the
cost of CLA and increase the speed of CLA [1].
The paper is organized as follows. In Section II, principle
and operation of MZI based optical switch is discussed. In
section III, designing of all-optical carry look ahead adder,
numerical simulation results (by Matlab 10.0) and discussion is
reported in Section 3. The conclusion is given in Section 4.
II. SMZI - BASED OPTICAL SWITCH
A. Function of SOA-SMZI switch
Mach-Zehnder interferometer (MZI) switch, is a very
powerful optical device to realize ultra fast all-optical
switching. In this switch a semiconductor amplifier (SOA) is
inserted in each arm of a MZI. The pulsed signal at the
wavelength ¬1 enters to the upper arm through coupler C2
such that most power passes through upper arm. At the same
time, the incoming signal pulse at the wavelength ¬2 enters
port-1, is split equally by this coupler C1 and propagates
simultaneously in the two arms [2]. The basic diagram is
shown below:
Figure 1. C1, C2, C3, C4 are 3 db couplers; S1, S2 are SOAs;
F1, F2 are optical filters
The operation principle is based on the optically induced
refractive index change within the SOA through appropriately
synchronized optical CP trains that alter the phase conditions of
data signals in the interferometer, thus resulting in switching.
Control and data signals, with orthogonal polarization, are fed
into the switch via 3 dB couplers and co-propagate within the
switch. In the absence of CPs, the data signals entering the
switch via a coupler (C1) split into two equal intensity signals
with 90o
phase shift, E1(0) and E2(ʌ/2), which propagate along
the upper and lower arms of the interferometer, respectively.
Couplers C2 and C3 are in the bar state for data signal
therefore, introducing no additional phase shift ¨ij in the
interferometer. With no CP present, E1 and E2 will experience
the same relative ¨ij during propagation and recombine at the
output of C4. However, with CPs present ¨ij is introduced
between the two arms of the interferometer, thus causing the
data signals to be switched to the bar port, see Fig. 1. To
achieve a complete switching at ¨ij = ʌ, CP1 enters the
C4
CPLS
S1
S2
Bar
Port
Cross
Port
C1
CP1
C2
C3
tdelay
F1
F2
CP2

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interferometer via C2 just before the target data signal. The CP
will then saturate SOA1, thus changing its gain as well as its
phase characteristics. When the data signal enters the
interferometer following the CP1, it will experience a different
¨ij (i.e. ʌ) in the upper arm relative to the lower arm. No signal
will emerges from the cross port. Introducing the second CP2,
delayed by Tdelay with respect to CP1, just after the data
signal, into the interferometer via C3 will saturate SOA2, thus
resulting in the same ¨ij as in the upper arm, thereby resetting
the switch. Therefore, with this mechanism the SMZ switch-
on-and-off time is controlled by fast optical excitation process
which overcomes the slow relaxation time. The output power at
port-1 and port-2 can be expressed as [3],
Pout,1(t) =0.25 Pin(t) [G1(t)+ G2(t) - 2¥ G1(t). G2(t) cos(¨ij)
Pout,2(t) =0.25 Pin(t) [G1(t)+ G2(t) + 2¥ G1(t). G2(t) cos(¨ij)
G1(t) and G2(t) are the temporal gain profiles of SOA-1 and
SOA-2 respectively. The time-dependent phase difference
between the pulses of two arms is
1
1 2
2
( )
ln
2 ( )
G t
G t
α
ϕ ϕ ϕ
§ ·
Δ = − = − ⋅ ¨ ¸
© ¹
where, Į is the line-width enhancement factor, ĭ1 = change of
Phase of SOA-1 and ĭ2 = change of Phase of SOA-2
G1and G2 are the temporal gain profile of the data pulses given
as [4]:
.
1
0
( ) exp[ . ( , ) ]
L SOA
g
z
G t g z t dz
V
= Γ +
³
.
2
0
( ) exp[ . ( , ) ]
L SOA
delay
g
z
G t g z t T dz
V
= Γ + +
³
where, Γ is the confinement factor, g is the differential gain, t
is the time at which the temporal point of the data signal enters
the amplifier, Tdelay the control signal separation, z/Vg the
time increment in z direction and Vg is the group velocity of
the control pulse.
B. The Carry Look Ahead Adder Logic Circuit
The proposed 2 bit Carry Look Ahead (CLA) circuit
contains two partial full adder (PFA) circuit which is shown in
figure 2. This simplified CLA can be used recursively to build
higher bits CLA [5].
Figure 2. Partial Full Adder
Let i be the index of stage. There are three inputs Ai, Bi, and
Ci and three outputs Gi, Pi, and Si in PFA. The variables Ai,
Bi, Ci, and Si are bits of augends, addend, carries, and sums at
stage i, respectively. The carry of the next stage can be
expressed as
Ci+1 = Gi Pi Ci (1)
Generate Function: Gi = Ai.Bi (2)
Propagate Function: Pi = Ai Bi
For 2-bit CLA carry output at each stage is given below:
C0 = input carry
C1 = G0 P0 C0
Using PFA we can develop the 2-bit CLA [6] as shown in
figure 3:
Figure 3. 2 bit Carry Look Adder logic diagram
From the above diagram we get the following equations:
P = P1.P0 --- ----- (3)
G = G1 P1 G0 ---- ---- (4)
Therefore final carry can be produced from G, P and C0 of first
level, which is
C = G P C0 ----- ------ (5)
III. OPTICAL TREE ARCHITECTURE OF CLA USING SOA-
SMZI
A. The PFA Circuit Block using SOA-SMZI
Here we proposed SOA-SMZI tree architecture for
designing an all optical partial full-adder. This PFA block is the
building block of CLA. The block diagram of PFA using SOA-
SMZI is shown in figure 4:
Ai
Bi
Ci
Pi
Gi
Si
A0
PFA
B0 C0
S0
PFA
S1
P0
G0
G1 P1
Ai Bi
Ci
G
P

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Figure 4. Optical Tree Architecture of PFA; S1, S2, S3, S4, S5 are SOA-
SMZI switches
Erbium Doped fiber amplifiers (EDFA) are optical amplifiers
that use a doped optical fiber as a gain medium to amplify an
optical signal. Here the signal to be amplified and a pump laser
are multiplexed into the doped fiber, and the signal is amplified
through interaction with the doping ions.
B. The 2-bit Carry Look Ahead Adder Logic Circuit using
SOA-SMZI Optical switch
In the above block diagram there are three inputs Ai, Bi, and
C0 and three outputs Gi, Pi, and Si in PFA. For 2bit CLA we
require 2 PFA blocks[7]. The NAND gate using SOA-SMZI is
shown in figure 5. The complete 2-bit CLA block diagram is
shown in figure 6.
Figure 5. The SOA-SMZI NAND Block along with XOR and AND block
SMZI-NAND block SMZI - AND block
Figure 6. 2-bit CLA block diagram using SOA-SMZI
This developed model can handle arbitrary data patterns
A(A1A0) and B (B1B0). Let us consider an example for this 2
bit CLA where A = 11, B = 10 and C0 = 0. In PFA-1 two
inputs are A0 = 1 and B0 = 0. According to the operational
principle discussed above, the PFA-1 generates the three
outputs as S0=1, P0=1, and G0 =1.
So the internal carry C1 = G0.C0.P0 = 0
In the next level three inputs are A1=1, B1=1, and C1=0 for
PFA-2 block, which generates three outputs as S1=0, P1=0,
and G1=0.
Finally, it will produce G=1, P=0 (From equation (3) and (4).
Now we can calculate the final carry from equation (5) as
C = G P C0 i.e.,
C = 1, so S2=1.
So the final output is S2S1S0 i.e., 101
C. Results and Discussions
The simulation for CLA is done using Matlab 10.0.The
different parameters used in simulation have been taken from
the literature that reports experimental results and have been
listed in Table 1[7]. Using this parameters we achieved desired
results.
S
1
S
2
Ai
Bi
AiBi
AiBi
AiBi
AiBi
B
C
S
4
S
5
B
C
Pi
Ci
Si
S
3
Gi
AiBi
BC
CPLS
EDFA
Ai
Bi
AiBi
AiBi
Ai
AiBi
B
CPLS
AiBi
XOR
A0
PFA2
B0 C0
S0
PFA1
S1
P0
G0
G1 P1
Ai Bi
Ci
G
EDFA
P

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TABLE I. SOA-SMZI switch parameters
Parameters Value
Injection current of SOA 130 mA
Unsaturated amplifier gain 20dB
Saturation energy of SOA 700 fJ
Control pulse energy 70 fJ
Time delay 5*10-12
s
Confinement factor 0.15
Linewidth-enhancement factor 4
For this simulation we select different parameters as listed
in table-1 so that operational condition is satisfied. For example
we have taken one set of inputs where A = 11, B = 10 and C0 =
0 and the corresponding output waveform are shown in Fig. 7.
Fig. 7(a) shows the output waveform when A = 11, B = 10 and
Cin = 1. Fig. 5(b) shows the output waveform when X = 10, Y
= 11 and Cin = 0.
Input A(A1A0) Input B(B1B0)
IV. CONCLUSION
In this paper we have designed SOA-SMZI-based 2-bit
CLA. This scheme can easily and successfully be extended and
implemented for any higher number of input digits e.g., 4-bits,
16 bits, 32 bits etc. by proper incorporation of optical switches
recursively. Numerical simulation results confirming described
method are given in this paper.
REFERENCES
[1] Xiaohua YeG, Peida Ye, Min ZhangEason, “All-optical NAND gate
using integrated SOA-based Mach–Zehnder” , Optical Fiber Technology
12 , 312--
-316, Elsevier Inc, 2006.
[2] Z. Ghassemlooy, W.P. Ng and H. Le-Minh,” BER performance analysis
of 100 and 200 Gbit/s”, IEE Proc.-Circuits Devices Syst., Vol. 153, No. 4,
August 2006.
[3] Suji seroja sarnim,H.A. Rahaman, Z. Ghassemlooy,”Modelling of All-
Optical Symmetric Mach- Zehnder Switch with Asymmetric
Coupler”,2008 IEEE International Conference
[4] Wei Hong, Minghao Li, Xinliang Zhang, Junqiang Sun, and Dexiu
Huang,” Dynamic Analysis of All-Optical Wavelength Conversion of
Differential Phase-Shift Keyed Signals Based on Semiconductor Optical
Amplifier Mach–Zehnder Interferometer”, JOURNAL OF
LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 24, DECEMBER 15,
2009
[5] Switch with Asymmetric Coupler” Mach–Zehnder switches”
Interferometer’’B. Noble, and I. N. Sneddon, “On certain integrals of
Lipschitz-Hankel type involving products of Bessel functions,” Phil.
Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955.
(references)
[6] Yu-Ting Pai and Yu-Kumg ChenJ, ”The CarryLook Adder”, Second
IEEE International Workshop on Electronic Design, Test and
Applications (DELTA’04)
[7] Dilip Kumar Gayen, Jitendra Nath Roy, Rajat Kumar Pal., “All-optical
carry lookahead adder with the help of terahertz optical asymmetric
demultiplexer” 2011 Elsevier GmbH.
Output S (S2S1S0)
Figure 7. Simulated waveform of Carry Look Adder