optical code division multiple access using carbon nanotubes system

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –

6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 10, October (2014), pp. 01-33 © IAEME

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OPTICAL CODE DIVISION MULTIPLE ACCESS USING

CARBON NANOTUBES SYSTEM

Jafaar Fahad A. Rida, A. K. Bhardwaj, A. K. Jaiswal

1Dept. of Electronics and Communication Engineering, SHIATS -DU, Allahabad, India.

2Dept. of Electrical and Electronics Engineering, SHIATS - DU, Allahabad, India,

3Dept. of Electronics and Communication Engineering, SHIATS - DU, Allahabad, India

ABSTRACT

In recent years, significant progress in understanding of the physics of carbon nanotube

electronics devices and identifying potential application has occurred. In a nanotube low bias (160m

V – 200m V) can be nearly ballistic across distances of several hundred nanometers. The study and

analysis of the optical proprieties through Katuara plot explains the behavior as semiconducting or as

metal, Carbon nanotubes are supporting in optical system applications. The electronic proprieties are

governed by a single parameter named the chiral vector, and there are three parameters affecting the

performance of carbon nanotubes diameter, chirality, and number of walls. The carbon nanotube

supports optical proprieties by three main parameters very important to develop work with optical

system application such as Electronic structure of carbon nanotubes, Saturable absorption, and third

order Nonlinearity. Depending on the chiral vector carbon nanotubes behave as semiconductor or

metal. But here focus on semiconducting carbon nanotubes to improve optical integrated circuit. The

analyze Optical Code Division Multiple Access (OCDMA) with Carbon Nanotubes (CNTs) to

improve three parameters very important in any communication system as data rate (R), bit error rate

(BER), and signal to noise ratio (SNR). It can be divided into broad categories based on the way in

which a particular user’s code is applied to the optical signal. The presents optimized design

performance of incoherent OCDMA as well as coherent OCDMA using carbon nanotubes (CNTs)

based devices with reference to increased Data Rate (R) and reduced Bit Error Rate (BER) which is

far enhanced in comparison to Silicon based Optical Devices. The carbon nanotubes with OCDMA

system supports ultrahigh speed network with data rate upto Tb/s and exceptional BER performance

in the system. As observed and presented in this paper, the carbon nanotubes brought in the

improved performance OCDMA system network with highest data rate and lowest bit error rate.

Keywords: OCDMA, CNTs, Optical Systems, Coherent OCDMA, Incoherent OCDMA and PPM

and OOK Formats.

INTERNATIONAL JOURNAL OF ELECTRONICS AND

COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)

ISSN 0976 – 6472(Online)

Volume 5, Issue 10, October (2014), pp. 01-33

© IAEME: http://www.iaeme.com/IJECET.asp

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INTRODUCTION

Carbon Nanotubes (CNTs) were discovered by Sumio Iijima in NEC in Japan in the early 90s

[1].Carbon is the most important element of the periodic classification for human being. The six

electrons with two of them fill the first orbit as shown figure 1. The remaining four electrons fill the

second orbit as Diamond ( ) and Graphite ( ) as well as Sp hybrid orbital, responsible for

bonding structure of diamond, graphite, nanotubes, and fullerenes [3]. It has since become a

prominent material for an amazing breath of scientific and technological displines of ranging from

structural and material science to chemistry, biology, and electronics [2]. Carbon nanotubes are one

of most commonly mentioned building blocks of nanotechnology, with one hundred times the tensile

strength of steel, thermal conductivity better than all but the purest diamond and electrical

conductivity similar to copper but with the ability to carry much higher currents, they seem to be a

wonder material, thin cylinders of graphite. Graphite ( ) is made up layers of carbon atoms

arranged in a hexagonal lattice like chicken wire. Though the chicken wire structure itself is very

strong [4]. But let’s look at some of the different types of nanotubes and nanotube pretenders such as

One of major classification of carbon nanotubes is into Single – walled varieties (SWNTs), which

have a single cylindrical wall, and Multi-walled varieties (MWNTs), which have cylinders within

cylinders as shown in figure1 which illustrates all stages fabricated for carbon nanotubes (CNTs).

There are three parameters very important in carbon nanotubes (CNTs) as diameter, chirality angle,

and number of walls, and also has unique physical and chemical properties. There are two types for

fabrication first, chemical (chemical vapor deposition (CVD)) and second, other physical methods

(Arc discharge, Laser ablation).The graphite layer appears somewhat like a rolled up chicken wire

with a continuous unbroken hexagonal mesh and carbon molecules at the apexes of the hexagons [5].

They have two conduction bands and and two valence bands and, these are called Van

Hove Singularities observed in their electronic density of state (DOS) of these carbon nanotubes

(CNTs). The direct electronic band gap proportional to diameter for semiconducting carbon

nanotubes, while the direct band gap equal zero for metal carbon nanotubes so, they use in high

electrical current. It has typically have diameters range (1-2) nm for single walled nanotubes and (2-

25) nm for multi-walled nanotubes as well as the length of nanotubes may be (0.2 - 5) µm or some

centimeters, and the spacing distance between walls is 0.36nm. Here, a single wall nanotube is

prepared for optical proprieties applicable with optical system [6]. The potential applications of

carbon nanotubes have been attracting increasing attention from the photonics research community

[7]. It exhibits an exceptionally high third order optical nonlinearity and nonlinear saturable

absorption with ultrafast recovery time and broad bandwidth operation. Thus, carbon nanotubes are

becoming a key component towards the development of fiber lasers and nonlinear photonic

devices.They are making a more significant contribution towards the development of next generation

devises both from an academic and a commercial point of view. General rules have desired the

topology of the termination as a function of the Hamada indices (n, m). Carbon nanotubes can also

be opened ended, according to the integer n and m so, they may behave either semiconducting or

metallic.These calculations electronic structure for carbon nanotube shows about 1/3 of carbon

nanotube is metallic and 2/3 is semiconducting, depending on the nanotube diameter () and chiral

angle (). Another classification for carbon nanotubes depending on chiral vectors (), they are

Zigzag nanotube, armchair nanotube, and chiral nanotube. There are three parameters to develop

carbon nanotubes optical proprieties to work in optical system, Electronic structure of carbon

nanotubes, Saturable Absorption of carbon nanotubes, and Third order nonlinear for carbon

nanotubes. The high pressure carbon mono-oxide (HiPCO) has been one of the fabrication methods

for the mass production of carbon nanotubes.

The typical network architecture for OCDMA with broadcast star is shown in Figure2. It can

be seen that one of the key issues to implement OCDMA networking and communication is how to



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encode and decode the user’s data such that the optical channel can be shared, that is, we need to

develop the practical encoding and decoding techniques that can be exploited to generate and

recognize appropriate code sequences reliably [8]. Therefore, The OCDMA encoders and decoders

are the key components to implement OCDMA systems. In order to actualize the data

communications among multiple users based on OCDMA communication technology, one unique

codeword-waveform is assigned to each subscriber in an OCDMA network, which is chosen from

specific OCDMA address codes, and therefore, different users employ different address codeword-

waveforms.

Figure 1: illustrates all stages fabricated for carbon nanotubes (CNTs) from carbon atoms,

graphite sheet, and rolled as form tube

Optical code division multiple access (OCDMA) technique is an attractive candidate for next

generation broadband access networks [9-10]. Basic architecture and working principle of an

OCDMA passive optical network (PON) network, in the OCDMA-PON network, the data are

encoded into pseudorandom optical code (OC) by the OCDMA encoder at the transmitter and

multiple users share the same transmission media by assigning different OCs to different users. At

the receiver, the OCDMA decoder recognizes the OCs by performing matched filtering, where the

auto-correlation for target OC produces high level output, while the cross-correlation for undesired

OC produces low level output. Finally, the original data can be recovered after electrical

thresholding. Due to the all optical processing for encoding/decoding, OCDMA has the unique

features of allowing fully asynchronous transmission with low latency access, soft capacity on

demand, protocol transparency, simplified network management as well as increased flexibility of

QoS control. In addition, since the data are encoded into pseudo-random OCs during transmission, it

also has the potential to enhance the confidentiality in the network [11- 15]. In an OCDMA network

using on-off keying pattern, the user’s data is transmitted by each information bit “1” which is

encoded into desired address codeword. However, the transmitter does not produce any optical

pulses when the information bit “0” is sent. In terms of the difference of signal modulation and

detection pattern, OCDMA encoders/decoders are roughly classified into coherent optical

encoders/decoders and incoherent optical encoders/decoders. The incoherent optical

encoders/decoders employ simple intensity-modulation/direct-detection technology and the coherent

optical en/decoders are based on the modulation and detection of optical signal phase. As global

network infrastructures expand to support various type of traffic, photonic networks are expected to

take an important role. The increasing demand for bandwidth forces network infrastructures to be

large capacity and reconfigurable [16]. The efficient utilization of bandwidth is a major design issues

for ultra-high speed photonic networks, also it increases data rate (R), and decreases bit error rate

(BER) so as to perform with improved signal to noise (SNR).The roots of OCDMA are found in



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spread spectrum communication techniques. Spread spectrum was developed in the middle -1950s

mainly as a novel form of transmission overcoming the grid restrictions in radio bandwidth

allocations [17-21]. It is based on the idea of spreading the spectrum of the narrow band message

over a much wider frequency spectrum by means of digital codes [22-23].Within the category of

coherent systems, it is useful to further classify OCDMA systems based on the way in which phase

coding is applied to the optical signal field. Since optical phase can be manipulated in either the

frequency domain or the time domain, two types of coherent OCDMA systems are possible, as

Spectral Phase Coded Optical CDMA (SPC-OCDMA) and Temporal Phase Coded Optical CDMA

(TPC-OCDMA) [24-29]. Incoherent schemes use the simpler, more standard techniques of intensity

modulation with direct detection while

Figure 2: Schematic diagram of an OCDMA system

coherent schemes are based on the modulation and detection of optical phase The most common

approaches to incoherent OCDMA are based on spectral-amplitude coding, spatial coding, temporal

(time) spreading, and two-dimensional (2D) wavelength-hopping time-spreading (WHTS) [30-

37].The performance of any communication system is fundamentally limited by the available

bandwidth, the signal to noise ratio of received signal, and the codes used to relate the original

information to the transmitted signal. These limits inevitably lead to increased errors and

corresponding loss of information [16]. An OCDMA network is expected to be able to accommodate

many subscribers and simultaneous access users, and to have high date rate for each user and low bit

error rate [8]. However, since they are strongly associated with each other, optimized performance

analysis of network becomes an issue of multiple target function description, which is very complex.

Next generation of optical communication system may preferably incorporate carbon nanotubes

based devices so as to achieve much higher data rate up to Tb/s in comparison to present systems

using silicon optical devices giving data rate upto Gb/s. Besides, such systems with advanced energy

source power realize in much longer life Nevertheless, future requirements of ultrahigh speed

internet, video, multimedia, and advanced digital services, would suitably be met with incorporation

of carbon nanotubes based devices providing optimal performance. Two novel types of carbon

nanotubes (CNTs) based multiplexers. The new device is a solid – state transmission gate (t-gate)

multiplexer that uses carbon nanotube as channel in the Field Effect Transistor (FET) of both n- FET

and p- FET type. Because it has been shown that carbon nanotubes – based FET switches are reliable

and ultrafast responsivity using much less power than a silicon optical – based devices, and thus

support ultrahigh data rates to Tb/s for ultrahigh speed application networks. The new device will

consume less power than traditional t – gate multiplexer [38]. Nanotechnology is new field of

Research that cuts across many fields of electronics, chemistry, physics, and biology, that analyzes

and synthesize objects and structures in the nano-scale (10) such as nano particles, nanowires, and

carbon nanotubes (CNTs). Carbon nanotube is one of several cutting- edge emerging technologies

and very wide range of applications in many different streams of science and technology [39-46].

Here, we determine some of important parameter in this system as data rate (R) with Pulse Position



5

Modulation (PPM) formats, and bit error rate (BER) and also for On- OFF Keying (OOK) formats

on Incoherent OCDMA 2-D wavelength – hopping / time spread technique and coherent OCDMA

spectral phase encoding and temporal phase encoding for analysis and computing BER for silicon

optical devices and carbon nanotubes. Multiplexing technique is to increase the capacity of an optical

link beyond the limit available for serial transmission, a service provide can either install an

additional fiber or to use some form of multiplexing. Multiplexing allows multiple channels to be

transmitted simultaneously over a single optical fiber giving networkprovides access to the large

bandwidth capabilities of single fiber which can lead to increased throughput in the network without

laying additional fiber. Optical multiplexing can be achieved through multiplexing either in the time

domain, wavelength, or hybrid of both. Due to the large bandwidth (5GHz) and associated high bit

rates, the multiplexing process is beyond the capabilities of pure electronic methods and has to be

implemented optically as well. Code division multiple access (CDMA) is strong candidate for

creating effective multiple methods for the optical subscriber access network because of its

asynchronous access and code multiplexing [47].

ASSUMPTION SYSTEM AND SIMULATIONS

A single wall carbon nanotube (SWTN) can be described as a single layer of graphite crystal

that is rolled up into a seamless cylinder, one atom thick usually with a small number (perhaps 20 -

40) of atoms along the circumference and along length (micron) along the cylinder axis [49]. This

nanotube is specified by the chiral vector ( ).

= ∗ + ∗ (1)

Where n and m are two integers indices called Hamada integers, which often described by the

pair of indices (n, m) that denote the number of unit vectors n* and m* in the hexagonal

honeycomb lattice contained in this vector and where || =|| = || =√3 *

=0.246nm,where = 0.142nm the c-c bond length and are graphite lattice vector ,which two

vectors real space vectors[2], [3],[48][49]. The chiral vector makes an angle () called the chiral

angle with the zigzag or direction.as figure 3. The vector connects two crystallographically

equivalent sites O and A on a two – dimensional (2D) graphene sheet where a carbon atom is located

at each vertex of the honeycomb structure [48]. The axis of the zigzag nanotube corresponds to =

0, while the armchair nanotube axis corresponds to = 30, and the chiral nanotube axis corresponds

to 0≤ ≤ 30. The seamless cylinder joint of the nanotube is made by joining the line AB to the

parallel line OB in figure 3, in terms of the integer (n, m), the nanotube diameter () is given by

equation (2).

= ||∗ !∗"!" # (2)

The nearest – neighbor C-C distance 1.421 or 0.142 in graphite, is the length of the chiral

vector and the chiral angle () is given by equation (3)

$ = %&(√(∗) *!)) (3)

Thus, a nanotube can be specified by either its (n, m) indices or equivalent by and .



6

Next, defined the unit cell OBBA of the 1D nanotube in terms of the unit cell of the 2D

honeycomb lattice defined by vectors and as shown figure 4 a) the unit cell and b) the

brillouin zone of two – dimensional graphite as adopted rhombus and shaded hexagon, respectively,

where and are basis vector in real space, , and ,are reciprocal lattice basis vectors. In the

(x, y) coordinates in figure 4, the real space basis vector and are expressed as equations (4)

and (5).

Figure 3: explaination of synthesis of carbon nanotubes from graphite sheet

-& = .√( ∗ -, - 0 , - = (√( ∗ -, −- ) (4)

And 2& = . 3√(∗- , 3- 0 , 2 = ( 3√(∗- , 3- ) (5)

Figure 4: characteristics of structure the unit cell real and reciprocal

where a= || = || = 0.246nm A is the lattice constant of two – dimensional graphite,

correspondingly the basis vectors , and , of the reciprocal lattice. Corresponding to a lattice

constant of 45√∗6 in reciprocal space, the direction of the basis vectors , and , of the reciprocal

(b=2.949nm A) hexagonal lattice are rotated by 30 from the basis vectors and of the hexagonal

lattice in real space, by selecting the first brilluoin zone as the shaded figure 3, the highest symmetry

points, Γ, K, and M as the center, the corner, and the center of the edge respectively. The energy

dispersion relations are calculated for the triangle ΓMK shown by the dotted lines in figure 3. To

define the unit cell for the 1D nanotube, defined OB as figure 3 as the shortest repeat distance along

the nanotube axis, there by defining the translation vector (T)

7 = 8& ∗ -& +8 ∗ - (6)

Where the coefficient 9 and 9 are related to (n, m) by equation (7)



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8& = ( *!)):; -*:8 =( *!)):; (7)

Where dR is the greatest common divisor of (2n+m, 2m+n) and given by equation (8)

:; = < :, => − =?@9AB9=BC@>3:(:, => − =?AB9=BC@>3: D (8)

In which d is the greatest common divisor of (n, m). The magnitude of the translation vector E = |E| |7| = √(∗F:; (9)

Where L is length of the chiral vector and is the nanotube diameter. The unit cell of the

nanotube is defined as the area delineated by the vector T and. The number of hexagons, N

contained within the 1D unit cell of a nanotube is determine by the integers (n,m) and given by (10)

G = (* !*∗)!) ):; (10)

The addition of single hexagon to the honeycomb structure figure 1 corresponds to the

addition of two carbon atoms. Assuming a value = 0.142 on a carbon nanotube, we

selected here (17,0), (12,5),(10,10),(16,2),(15,0), and (11,11) nanotubes. Since the real space unit

cell is much larger than that for 2D grapheme sheet, the 1D Brilluoin zone (BZ) for the nanotube is

much smaller than the BZ for single two grapheme 2D unit cell. Because the local crystal structure

of the nanotube is so close to that of a grapheme sheet and because the Brillouin Zone is small,

Brillouin Zone – folding techniques have been commonly used to obtain approximate electron and

phonon dispersion relations for carbon nanotubes (n, m) with specific symmetry – whereas the lattice

vector T, given by equation (6), and the chiral vector , given by equation (1), both the unit cell of

the carbon nanotube in real space, the corresponding vectors in reciprocal space are the reciprocal

lattice vectors (k2) along the nanotube axis and (k1) in the circumferential direction, which gives

discrete k values in the direction of the chiral vector . The vectors K and K are obtained from the

relation

;L ∗ MN = 3 ∗OLN, where PQRS are the lattice vectors in real and reciprocal space

respectively. Form KK can be written as

T& = &G (−8 ∗ 2& +8& ∗ 2 )-*:T = &G () ∗ 2& − * ∗2 ) (11)

Where , and , are the reciprocal lattice vectors of a two – dimensional graphene sheet

given by equation (5). The N wave vectors UK(U = 0, … , W − 1) give rise to N discrete k vectors

in the circumferential direction. For each of U discrete values of the circumferences wave vectors a

one – dimensional electronic energy band appears, whereas each U gives rise to 6 branches in the

phonon dispersion relations [48]. A nanotube (n,m) is formed by rolling a graphite sheet along the

chiral vector on the graphite sheet rolled. The nanotube can also be characteristized by the

diameter () and the chiral angle is with respect to zigzag axis = 0 . A Single Wall Nanotube

(SWNT) can be visualized as a hollow cylinder, formed by rolling over a graphite sheet. It can be

uniquely characterized by a vector in terms of a set of two integers (n, m) corresponding to

graphite vectors and. By rolling a graphite sheet in different directions, two typical nanotubes



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can be obtained: zigzag (n, 0), armchair (n, m), n= m, and chiral (n, m), where n>m>0, they are (17,

0), (15, 0), (12, 5), (16, 2), (10, 10), and (11, 11). The lattice constant and intertube spacing are

required to generate a SWNT bundle, and MWNT, the most experimental measurements and

theatrical calculations, agree that on average the C-C bond length and intertube ( = 0.34) [49]. Thus, equations (1) and (2) can be used to model various tube structures and interpret

experimental observation. They now consider the energetics or stability of nanotubes; strain energy

caused forming a SWNT from a graphite sheet is proportional to XY per tube or

XYZ per atom [3].

Typical experimentally observed SWNT diameter is between (0.6 nm – 2.0 nm) while smaller

(0.4nm) or larger (3.0nm). In simplest model [3], the electronic properties of a nanotube derived

from the dispersion relation of a graphite sheet with the wave vectors (K[, K\), [3], [7].

]^T_, T`a = ±cde& + fghi(√(∗T_∗- ) ghi .T`∗- 0 + fjdk (T`∗- ) (12)

Where lmis the nearest neighbor – hopping parameter and a lattice constant (ln = 2.5eV-

3.0eV) from different sources and a=0.246nm. When the graphite is rolled over to form a nanotube,

a periodic boundary condition is imposed along the tube circumference or the C directions. This

condition quantizes the two – dimensional wave vector k = (K[, K\) along this direction. The k

satisfies k.c=2op are allowed where q is an integer. This leads to the following condition at which

metallic conductance occurs as equation (13)

(n - m) = q metallic or (2n + m) = 3q (13)

Semiconducting

The top half of the energy curve corresponds to the conduction o∗ energy band while the

bottom half corresponds to the valence o energy band. The conduction and valence band come into

contact at the six corners (high symmetry points k) in the Brillouin zone, implying that 2D graphite

is a zero – gap semiconductor, when s=0, the valence and conduction band become symmetric a ball

E=qrs this is given by equation (12) and lm = 2.9 eV. The positive sign is for the conduction band

and the negative one for the valence band. In contrast to Si, which is an indirect band gap

semiconductor and asymmetric band structures for electron and holes, grapheme has symmetric

conduction and valence bands. The energy valleys are located at the corners of the Brillouin zones,

which are usually referred as the Fermi points. The basis vectors in the reciprocal lattices,S. The

periodic boundary condition imposed along the circumference direction restricted the wave vectors

to

k.c = 2oq (14)

where k is an allowed wave vector and q is integer which is the quantum number [50] – [58]. The

conductance for SWNT, a SWNT rope, or MWNT given by equation (15)

t = tu ∗ v = .wZ 0 ∗ v (15)

Where tu = .wZ 0 = (12.9K@ℎ) is quantized conductance, M is a apparent number of

conducting channels including electron - electron coupling and intertube coupling effects in addition

to intrinsic channel, M=2 for a perfect SWNT G= (6.5K@ℎ) that means resistance for nanotube



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R= 6.5*10ohm [24]. The knowledge of this limit (which only depends on the communication

channel) allows evaluating the performance of the system, and finding the guidance to its

improvement. In particular, for a linear communication channel with additive noise, and a total

signal power constraint at the input, the fundamental limit to the information capacity is given by the

celebrated Shannon formula [16],[ 37].

= |B@[1 + ] (16)

Where W is the channel bandwidth, u is the average signal power, and is the average

noise power. In comparison, the standard On- Off Keying (OOK) procedure where the information

in encoded via a “ train” of nonoverlapping pulses – with the presence of the pulse in a given time

corresponding to “1” and it’s absence to “0”, leads to the transmission bit rate (data bit rate R) of one

bit per time slot. To avoid the interference of pulses from the adjacent slots, the size of the time slot

is generally chosen to be no less than the pulse width (), leading to the transmission rate up to

bit/sec. Since the corresponding bandwidth is on order of , OOK algorithm performance is by a

factor of log(SNR) less than the fundamental limit. However, the representation of the fundamental

limit to the information capacity in the standard form of equation (16) is unsuitable for applications

to fiber – optical systems, as it was obtained based on the assumption of linearity of the

communication channel, while modern fiber optics systems operate in a substantially nonlinear

regime to improve the performance. Since the optical transmission lines or devices must satisfy very

strict requirements for bit error rate (BER) (10E@10), to use optical fiber for longest distance

and also use integrated circuit from silicon but when the using integrated circuit from silicon does

not support its work enough to transmission rate between these devices and optical fiber has largest

bandwidth to transport most information but it needs the optical devices to support that use here the

new device called carbon nanotubes (CNTs) preferably of the type Single Walled Carbon nanotubes

(SWNTs) to get better improved performance of the system such devices are called biological

device and can be used with human bodies that means it uses in small length maximum 1 centimeter

so they cannot be used like fiber or optical fiber cable but they can also be used in manufacturing

integrated optical circuits like encoder and decoder for optical signal, also mode locked lasers which

have highest efficiency for energy and transferring optical signal with optical code division multiple

access (OCDMA) to develop communication system from increasing data bit rate and to improve the

SNR in the system. For OOK modulation format, the slot length is equal to the length of a frame.

Assuming that both the chip time E = 5.181 ∗ 10?C and throughput are held fixed, the code

length is given by equation (17) [27] [37].

= >@RmZ >@vD (17)

Where M indicates the number of possible slots within a PPM time frame and Pu = 1.0 ∗10 denotes the throughput in bits/chip time. At the receiving end, the data are restored by the

OOK/PPM chip – level optical receiver. Since the chip – level receiver are dependent on the number

of photons (optical energy) per chip in the received frame when it uses silicon optical devices the

optical source power is 35.99 ∗ 1099, whereas when it uses carbon nanotubes the optical source

power is 214.8 ∗ 1099. That means when we use the carbon nanotubes devices the consumed

power is very low. Here, the time duration of time slot E = 3.33 ∗ 10n sec or nanosecond in

silicon optical devices, but the time duration E = 2.58 ∗ 10?C or femtosecond in carbon



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nanotubes, therefore, the carbon nanotubes ultrafast switching based system, are formulated to attain

optimized performance of OCDMA technology. Parameters as indicated in table 1 are assumed for

achieving enhanced performance of carbon nanotubes based OCDMA in comparison to silicon

optical devices based devices which would in turn consume lesser power, miniaturized in dimension

and withstand higher temperature.

Table 1: parameters assumed in simulated OCDMA system

Parameters Silicon optical devices Carbon nanotubes

Time duration (E) 3.33 ∗ 10nsec 2.58 ∗ 10sec

Data rate (P) 3.00 ∗ 10,=9?/?C 7.7519 ∗ 10,=9?/?C

Code weight (w) W=3,5,7 W=3,5,7

Load resistance (RL) 50 ∗ 10Ω 12.9 ∗ 10Ω

Temperature for material 300K 973 K

Refractive index () 2 ∗ 10n/99 1.55 ∗ 10/99 Source power laser (mm) 35.99 ∗ 1099 214.8 ∗ 1099 Recharge electron (e) 1.6 ∗ 10 1.6 ∗ 10

Light of speed 3 ∗ 10 3 ∗ 10

Threshold value (Th) 1 ∗ 1099 1 ∗ 1099 Boltzmann’s constant (R) 1.38 ∗ 10/R 1.38 ∗ 10/R

Area of devices 2.5 ∗ 10 2.5 ∗ 10

Length of code for OOK

formats

n=1000 n=1000

Length of code for PPM

formats

n=375 n=375

Throughput in bits/chip

timePm 1.0 ∗ 10 1.0 ∗ 10

Noise for MAI 6.5 ∗ 1099 6.5 ∗ 1099 Band gap energy (q) 1.12C 2.9C

Time chip (E) 5.181 ∗ 10?C 5.181 ∗ 10?C

Wavelength center () 1550 ∗ 10 1550 ∗ 10

RESULT AND DISCUSSION

3.1 Electronic Structure of Carbon Nanotubes (CNTs)

The electronic properties of a CNT are determined by its chiral vector from (1). This

vector describes how the graphene sheet is rolled when forming the nanotube. Here, we take many

carbon nanotubes as (17, 0), (12, 5), (10, 10), (16, 2), (15, 0), and (11, 11). They consist of (17, 0),

(15, 0) which is called zigzag nanotube that means the integer (n, m) as n= 17, and m=0, the chiral

angle ( = 0) this nanotube is used either as metal or semiconductor depending to prepare carbon

nanotube open fabricated process. Here, we focus on semiconductor chiral nanotubes (12, 5), (16, 2)

wherein of n= 12 and m=5 and the chiral angle (0≤ ≤ 30), further armchair nanotubes (10, 10),

(11, 11) wherein of n=m=10, the chiral angle( = 30), behaving as metal as expressed by equation

(3). In the simulation we have got the diameters of nanotubes as (1.33nm, 1.185nm, 1.35627nm,

1.338nm, 1.175nm, and 1.356nm) respectively. We get the result between the electronic density of

states (DOS) (unit measurement - arbitrary, unit), to Fermi energy in unit cell of the atoms of carbon

nanotubes and energy band gap in semiconductor nanotube focused on semiconducting nanotubes,

wherein band gap is given by equation (18)



11

] = ∗-j¡j∗cd:8 = ¢.£¤¥:8 (18)

where q the energy band gap for semiconductor which has two conduction bands and two

valence bands as shown in figure 5 which illustrates how to work with two van hove singularities ,

with Fermi energy lm = 2.9C. If (2n+m) = 3q ≠ 0, the carbon nanotubes would be 2/3

semiconductor from equation (13). The Kinetic energy (q) form the lowest subband is determine by

the minimum value given by equation (20)

Figure 5: illustrates two van hove singularities in semiconductor carbon nanotubes

Mj.§ = (:8 (19)

Where is the diameter of the carbon nanotube the energy output for CNTs are given by

equations (20)

](M8) = ± (∗-j¡j∗cd ∗ eT8 + ( (:8¨ ) (20)

And

]d =±(∗-j¡j∗cd (21)

Where qm is energy gap with normal temperature for graphite. Subsequently from equations

(20) and (21) we get equation (20) for ]d©8 , the output energy band gap.

]d©8 = ](T8)]d (22)

The output energy band gap for carbon nanotubes depends on doping the electron density of

states in during fabrication and expressed by equation (23).

ª(]T) = £(∗3∗-j¡j∗cd ∗ ](T8)e](T8)(] ¨ ) (23)

From the equations 20, 21, 22, 23 has got results as shown in figure 6 a and b has been

obtained which calculated is nanotubes the energy band gap has positive as well as negative values,

that is the carbon nanotubes show very high symmetry in (a) and (b) of figure 6 which illustrate (17,

0), (12, 5), (15, 0), and (16, 2) for energy gap has two van hove two conduction bands (, )

and two valence bands () symmetries in both side positive and negative in energy gap



12

depend upon doping in electronic density of states (DOS) as in case of semiconductor carbon

nanotubes, while (10,10), and (11,11) these have one conduction band and valence band these

behave metallic carbon nanotubes because band gap is zero as shown figure 6 a and b..In metal

carbon nanotubes the band gap between one conduction band and one valence band is zero while in

semiconductor carbon nanotubes have band gap between two conduction bands and two valence

bands. The incident light (photon) is observed by valence band () to excite electron to conduction

band () leave a hole in and move electron from valence band () to and then leave hole in and move electron from to conduction band () to move to causing the flow of electric

current is called van hove singularities as in figure 5 where energy gap is very symmetrical and low

consumption optical power along life time as shown in figure 6 a and b.

Figure 6 (a): the results for some carbon nanotubes (17, 0), (12, 5), and (10, 10) to get energy

gap with relation DOS in this system

Figure 6 (b): the results for some carbon nanotubes (16, 2), (15, 0), and (11, 11) to get energy

gap with relation DOS in this system

The energy corresponding to the symmetric transition p=q for Semiconducting (S) and

Metallic tubes (M) follows the relations with one p – orbit approximation equation (24) and (25).

[3] - [8], [48-63].



13

]««¬ = ∗«∗-j¡j∗cd:8 (24)

For semiconductance carbon nanotube,

]«« = ®∗«∗-j¡j∗cd:8 (25)

for metallic carbon nanotube, as shown figure 6 part (c).

Wherein the number p (p=1, 2….,) is used to denote the order of the valence and conduction

bands symmetrically located with respect to the Fermi energy as shown figure 6 c . The good

diameter distribution has been chosen from 1nm to 1.5nm, and we select 1.33nm diameter for (17,

0), and 1.185nm diameter for (12, 5) carbon nanotubes respectively. This relation is between

diameters (nm) for carbon nanotubes from (1nm – 2nm) for single walled carbon nanotubes

(SWNTs) and energy gap. The metallic carbon nanotube has high energy because band gap is zero

but for the semiconducting carbon nanotube the energy here the band gap exists and depends on p

where p=1 or p=2 and this results from the equations (24) and (25). [3], [50], [63].

Figure 6 (c): the results for Kataura plot for some carbon nanotubes behavior either as

semiconducting or as metallic energy gap is relation to carbon nanotube diameters in the

system metallic energy gap with relation carbon nanotube diameters in this system

3.2 Saturable Absorption of Carbon Nanotubes (CNTs)

The optical absorption of CNTs is of saturable, intensity-dependent nature, it is a suitable

material to employ for passively mode-locked laser operation. Passive mode locking is achieved by

incorporating an intensity-dependent component into the optical system. The typical absorption of a

suspension of CNT fabricated by the high pressure carbon monoxide method (HiPCO) and measured

by a spectrometer. This is generally a saturable absorber which absorbs the light which is incoming

linearly up to a given threshold intensity, after which is saturates and becomes transparent optical

power intensity for output with losses 5% from input incident optical power intensity. Such saturable

absorbers discriminate in favor of pulse formation over continuous wave lasing. This is one of the

key advantages of carbon nanotube – based devices as has been achieved passive in mode – locked

operation not only in the C (1530nm – 1565nm) and L (1565nm – 1625nm) bands but covering also

the wavelength () range from (1Um - 2Um) using single wall carbon nanotube saturble absorber [7],

[64], [65]. The three parameters the non-linear saturable losses (¯°r = 0.445), the modulation depth

or the linear saturable losses (¯m = 0.05), and saturable intensity(±r6 = 7.89v|/), together



14

response time (²= 1.85 ps) give us the location of the applicability of carbon nanotubes for passive

mode locking applications.

¯(±) = ³´! µµ¶·Y +¯°r (26)

The equation (26) gives the relates between the various parameters where ¯(±) is optical

intensity for carbon nanotubes and comprises of information. We selected for simulation only two

carbon nanotube diameters 1.33nm and 1.185nm carbon nanotubes to get optical intensity

relationship with wavelength () from (500nm – 3000nm). We see increasing optical intensity with

increasing wavelength because the absorption is decreasing also as shown in figure 7 (a). Another

relationship between the energy gap with the wavelength is as per equation (27).

] = ¸∗j¹ (27)

Where h is Planck’s constant is equal (6.626*104J-s) and c is speed of light (3 * 10m/s),

resistance also equals (R= 6.5 *10) ohm, the half width short pulse for this simulation ( = 1.85 ∗10s) or is femtosecond (1 *10s).

Figure 7 (a): illustrates the results for optical intensity (a, u) in satuarble absorption for carbon

nanotubes (1.33nm, 1.185nm)

The saturable absorption in carbon nanotube is achieved from the relationship of wavelength

and absorption that means when the wavelength increases in this system the absorption decreases.

Specifically of the wavelength center (1550nm), the third window in optical frequency, the

absorption is approximately (0.02 d B/km) from equation (28) as also as shown in figure 7 (b). [7],

[66], [67].

º = »h¼&¢(&7) (28)

Where T is transmittance optical intensity and can be derived from equation (29)



15

Figure 7 (b): illustrates the results for optical absorption (a, u) in satuarble absorption for

carbon nanotubes (1.33nm, 1.185nm)

7 = & − ½¾&! ¿¿k-8 +½*k (29)

The transmittance results in figure 7 (c) which illustrates reverse proportion with absorption it

means the absorption is decreasing when the wavelength is increasing but the transmittance is

observed to be increasing as shown in figure 7 (c). This also supports optical system application and

can be used with Erbium Doped Fiber Amplifier (EDFA) for pumping optical power intensity of the

transmitting signal so that it can be used with Wavelength Division Multiplexing (WDM) and

Optical Code Division Multiple Access (OCDMA) to bring in improvement performance of optical

system applications with increasing data rates.

Figure 7 (c): illustrates the results for optical transmittance (eV) in satuarble absorption for

carbon nanotubes (1.33nm, 1.185nm)



16

Figure 8: the results for optical power output (d B m) in saturable absorption for carbon

nanotubes (CNTs)

This also supports optical system application and can be used with Erbium Doped Fiber

Amplifier (EDFA) for pumping optical power intensity of the transmitting signal so that it can be

used with Wavelength Division Multiplexing (WDM) and Optical Code Division Multiple Access

(OCDMA) to bring in improvement performance of optical system applications with increasing data

rates.

Figure 9: the results for optical intensity in saturable absorption for carbon nanotubes (CNTs)

3.3 Third Order Nonlinearity of Carbon Nanotubes

The third order nonlinear material can be considered for optical switching, routing and

wavelength conversion. Optical nonlinearity is due to optical intensity dependent nonlinear response

of dielectric material. When the optical intensity of the propagating light is dielectric material is low,

stimulated polarization is linearly proportional to optical intensity. However, at high optical

intensity, the simulated polarization (P) exhibits a nonlinear response to the optical electric field (E),

as described by equation (30). = Àu(Á(). q +Á(). q +Á(). q (30)



17

Where Á(), Á(), Á() correspond to the linear, the second order nonlinear, and third

order nonlinearity susceptibility respectively. It has been reported that some types of carbon

nanotubes present a highÁ(), however, there is not much active research on exploiting this property.

On the other hand, the high values of Á() calculated theatrically and experimentally are of great

interest. There refractive index in carbon nanotubes can be described by equation (31). [49] - [66].

* = (£* ∗ ;¤Â___(() (31)

Where Re stands for the real part the optical field is assumed to polarized so that only is components Á[[[() , (n=m = 1) is refractive index in free space (air). We have another equation to get

refractive index to get from simple equation (32)

* = jÃ (32)

Where v is the optical frequency if we take wavelength (1550 nm) that means( = 1.5 ∗10 |¨ ) is high. The third order susceptibility of carbon single walled nanotube from Z-Scan

spectroscopy was estimated for the same. Á[[[()can be expressed by equation (33)

Â___(() =(;¤Â() +(¿)Â() (33)

Where ;¤Â( = f(3 ∗ *d ∗ j ∗ Äd ∗ ½*k is real part of Á() ; (Åm = 8.85 ∗ 10), and ¿)Â(() = &(3 ∗ *d ∗ j ∗ Äd ∗ ½*k ∗ ¹is the imaginary part ofÁ(). The values of real and imaginary part of Á() are being of the carbon single wall nanotubes, the vacuum permittivity (Åm). The nonlinear

relationship between the average electrical fields inside materials (D) and the incoming optical (E)

field, nonlinear effects is defined the tensor of optical susceptibility x, which is the transformation

matrix of the incoming E vector to get the result polarization (P) vector inside materials given by

equation (34)

Æ = Ä¾[Â(&) ∗ ] ∗ ghi(Ç²) +Â( ) ∗ ] ∗ jdk (Ç²) +Â(() ∗ ]( ∗ jdk((Ç²)] (34)

We get another expression given by equation (35).

Æ = [& ∗ Ä¾ ∗ Â( ) ∗ ] + .Ä¾ ∗ Â(&) ∗ ] + (f ∗ Ä¾ ∗ Â(() ∗ ](0 jdkÇ² + & ∗ Äd ∗ ] ∗ jdkÇ² +& ∗ Äd ∗ Â( ∗ ]( ∗ jdkÇ²] (35)

According equation (34) and (35) we can get new equation (36)

Æ_ = ½ ∗ ] +½*k ∗ ] + * ∗ ]( (36)

We can get results for optical polarization intensity in third order nonlinearity for carbon

nanotubes the maximum optical intensity between wavelengths (1540nm – 1550nm) for single wall

nanotube by equation (36) as shown in figure 10 (a).



18

Figure 10 (a): explains optical polarization intensity in third order nonlinearity for carbon

nanotubes (CNTs) also single wall nanotubes (SWNTs)

The optical intensity in third order nonlinearity we get maximum in wavelength center at

(1550 nm), the third window in optical systems and covers large bandwidth to support optical

integrated electronic circuit to work in optical frequencies to improve performance for optical system

application as shown figure 10 part (b). The relationship between the potential V (E) and the

electrical field (E) will be symmetrical given by equation (37)

¥(]) = −[.& 0 ∗ ½ ∗] + .&(0 ∗ * ∗ ]( + .&f0 ∗ * ∗ ]f] (37)

The symmetrical potential of the material under the influence of an incoming signal optical E

field implies that the material is contrast electrical that electron polarization in positive and negative

direction as shown figure 10 part (c). The optical potential in third order nonlinearity the ultrafast

optical switches to get approximately (1.85 ps) or few femtosecond ( = 1015

), fast relaxation

process in the order of 100s of femtoseconds combined with an extremely high nonlinear coefficient

can be observed in real carbon nanotubes devices in fabricated optical integrated circuit in ultra large

scale integrated circuits (ULSI). It is also very high third nonlinear and ultrafast respond times [7],

[68], [69].

Figure 10 (b): explains optical power intensity in third order nonlinearity for carbon

nanotubes (CNTs) also single wall nanotubes (SWNTs)



19

Figure 10 (c): explains optical potential in third order nonlinearity for carbon nanotubes

(CNTs) also single wall nanotubes (SWNTs).

3.4 The Coherent OCDMA with the Nonlinearity

In the coherent approach to optical CDMA, the information is first encoded in pulse train

using standard OOK. The OCDMA expresses encoder and decoder; here focus SPC-OCDMA

encoder and decoder for both optical fiber silicon and carbon nanotubes. Here, we get improved

results with parameter signal to noise ratio (SNR) using carbon nanotubes than silicon optical fiber.

When the number of users (M) are increasing, the signal to noise ratio is decreasing because the

carbon nanotubes has high energy band gap and high refractive index third nonlinearity, that means

the enhancement the nonlinearity properties in optical code division multiple access (OCDMA) we

got these result by equation (38) as shown figure 11.

¬G; = Æ«¤-TÆG!Æ«¤-T(&)∗ ² 7 ∗ &&!c ∗: ∗G ∗Æ«¤-T ∗(&) . ² 70 (38)

Where sw6the optical power input for coherent OCDMA system, M is number of users of

the system, d is distance silicon or carbon for area integrated and others parameters mention in

previous section in assumption [16].

Figure 11: represented the SNR in the coherent OCDMA for silicon optical devices and carbon

nanotubes

First, we substitute the optical fiber parameters in equation (38) and get the result as in figure

8 curve 1, decreasing SNR when the increasing number of users in the system, subsequently, we

substitute the carbon nanotubes parameters in same equation to get result as shown figure 11 curve 2.

For improved system, we need to improve SNR values and it is observed that the SNR values with



20

carbon nanotubes are better than silicon optical devices. The figure 12 illustrates about data bit rate

which is observed to be decreasing when the number of users (M) increase, that means that signal to

noise ratio SNR decreases while substituting parameters for silicon optical devices and carbon

nanotubes [16], as governed by equation (39)

P = É [1 − B@ ÊËËÌ1 + CÍÎ ÏÐÑÒÓZ∗ÔZ∗Z∗ÕÖ×·ØZ(Ù¡Ñ)Z∗. ÚZÛ0ZÜÝÞ

Þß] (39)

But the data bit rate (R) in coherent OCDMA with carbon nanotubes are better than silicon

optical devices, this is clearly observed from curve 2 for carbon nanotubes and curve 1 for silicon

optical devices as shown in figure 12.

Figure 12: represented the data bit rate (R) in the coherent OCDMA for silicon optical devices

and carbon nanotubes

The figure 13 illustrates bit error rate (BER) in the same system for carbon nanotubes

increasing from 109@10 while the silicon optical devices BER from109@10n, to make

the improvement in system performance governed by equation 40. This indicates the effect of SNR

to improved coherent system. The encoder works when using silicon optical devices the light spreads

by lens but while using carbon nanotubes ( single walled carbon nanotubes ) (SWNTs) making

narrow band, the light focuses on one point on the filter nanotubes that is observed to be the most

active in applications of passive optical CDMA network [16].

à]; = &á* ¤_«( ¬G;d&Òc ∗: ∗G ∗Æ«¤-T ∗(¡&) ∗. ² 70 ) (40)

Figure 13: represented the bit error rate (BER) in the coherent OCDMA for silicon optical

devices and carbon nanotubes



21

3.5 The Incoherent OCDMA with the Nonlinearity

In the incoherent approach to the CDMA, the original OOK- modulated signal is divided into

several parts and each part is delayed by the amount determined by the code used. The way the OOK

signal is divided depends on the particular realization of the incoherent OCDMA, and poor signal to

noise power SNR in this system as shown figure 14 illustration decreasing the SNR values to take

negative value when the number of users increasing. This performs to effect efficiency performance

OCDMA system with carbon nanotubes curve 2 and silicon optical devices curve 1, given results by

equation (41) [16]. ¬G; = G¹∗Æ«¤-T² 7∗G¹∗∗â¹ã ä .∆æ¾ Ò∆æ 0çÆ«¤-TÒè∆æ Ò∆æ¾ ∆æ∗∆æ¾∗ÆG (41)

Where Wéis the carrier – hopping incoherent OCDMA system with wavelength that is the

original OOK signal is passed through a filter (e.g, prism or grating – based) that separates Wé

components differently by their central wavelength,∆| the single channel spectral width |uis its

central frequency,ê is the frequency spacing between different carriers.té is the gain to the crosstalk

between channels equal (té = 5ë) [70] .

Figure 14: represented the SNR in the incoherent OCDMA for silicon optical devices and

carbon nanotubes

The figure 15 illustrates the data bit rate (R) is also decreasing when the SNR is decreasing

with increased number of users; this is given by equation (42). The data rate in the system with

carbon nanotubes is better than with silicon optical fiber as shown in figure 15. Here, the curve 2 is

for carbon nanotubes results, while the curve 1 for silicon optical devices [16].

; = &7 [& − ád ÊËËËÌ& + ¤_« ¡ 7∗²∗â¹ì í ä ∆æ¾î &Òc ∗: ∗G ∗Æ«¤-T ( (∗√(ÒG¹(¡&)ï¹∗²7

ð

ÝÞÞÞß] (42)

The figure 16 illustrates that the bit error rate (BER) is increasing when the number of users

are increasing, but the SNR is decreasing on proportional relationship between numbers of users (M)

and BER but reverse relationship between BER and SNR. This is given by equation (43) and as

shown in figure 16, the incoherent OCDMA with carbon nanotubes is observed to be better than

silicon optical devices as shown by the curve 2, for carbon nanotubes and the curve1 for silicon

optical devices [8], [16].



22

Figure 15: represented the data bit rate (R) in the incoherent OCDMA for silicon optical


Figure 16: represented the bit error rate (BER) in the incoherent OCDMA for silicon optical


à]; = &á* ¤_«(− 7∗²∗â¹∗ì í ä ∆æ¾î &Òc ∗: ∗G ∗Æ«¤-T ( (√(ÒG¹(¡&)ï¹∗²7ð

) (43)

In this paper, we have investigated the transmission analysis of OCDMA communication

systems using silicon optical devices and carbon nanotubes under the set of the wide range of

operating parameters as shown in table 1. It is aimed to improve the performance of the incoherent

OCDMA systems by OOK formats and PPM formats using carbon nanotubes (CNTs), and silicon

optical devices. Figure17 illustrates that the data rate is decreased when the number of users are

increased in the PPM format for OCDMA system given by equation (44) [16].

; = Mád ∗*∗72 (44)

Where K is the number of simultaneous users, E is the signaling period “symbol interval “, n

is the code of length, where each user is assigned a set of M codes, each corresponding to a particular

“ digit”. In the M-ary system with M=8 [16].The data rate with carbon nanotubes as obtained result

represented by curve 2 is better than silicon optical devices as represented curve 1as shown figure

17. It is indicated that in the simulated system with the existing coding technique for PPM/OCDMA



23

system, the bit error rate increases much more with silicon optical devices but the bit error rate is

very low with carbon nanotubes used = E = 2.58 ∗ 10?C, source power of laser uuñ =214.8 ∗ 1099, and refractive index = 1.55 ∗ 10/99 from table 1 [16],[18],[71][72]

Figure 17: represented the data rate (R) in the incoherent OCDMA by PPM format with

silicon optical devices and carbon nanotubes

Bit error rate in PPM/ OCDMA format is given by equation (45)

à]; = & ò∑ *!)!(*))! õ]8G¹² ∗7j ö) õ& −]8G¹² ∗7j ö*))÷G¹ ø]8 (45)

Let M is the number of simultaneous users and is the single pulse width used in silicon

optical devices and carbon nanotubes, Wé is code with Wé =8 different wavelength channel and

different values of q in silicon optical devices is q =1.12 e V, and carbon nanotubes is q =2.9 e

V. Then, as a function of number of users, the bit error rate (BER) performance codes C is affected

by the multiple access interference (MAI). In the limiting case where the noise due to spontaneous

emission in optical amplifier, detector dark current, etc., can be neglected as compared to the effect

of Multiple Access Interference (MAI). The multiple access interference affects the incoherent

OCDAM system. The bit error rate (BER) increases marginally with carbon nanotube as represented

by curv2 compared with silicon optical devices represented curv1 as shown figure 18.

Figure 18: represented the bit error rate (BER) in the incoherent for silicon optical devices and

carbon nanotubes



24

Therefore, we can say that the Data Rate (R) incoherent OCDMA with OOK/OCDMA

format gives better results than PPM/OCDMA with carbon nanotubes (CNTs). In the OCDMA

system increasing the number of users decreases the data rate, while increasing the bit error rate

enhances the system performance. For the best performance of optical communication with highest

data rate and lowest bit error rate, we investigated the optimized OCDMA performance with carbon

nanotubes in comparison with silicon optical devices.

3.6 The OOK/ OCDMA Chip – Level Receiver and Its Performance Analysis

In the OOK/ OCDMA system uses the (n, w, 1), the signature with optical pulse is sent for

data bit “1” while nothing is sent for data bit “0”. Hence, we focus the Bit Error Rate (BER) for

OOK/OCDMA chip level receiver with carbon nanotubes less than BER with silicon optical devices

and we got result when the number of code length n=1000 is given by equation 17, resulting in

BER with carbon nanotubes as represented by curv2 very less than silicon optical devices

represented by curv1 as shown figure 19.Tthe BER can be given by equation (47) and equation (46).

Æ7 = Ç* ÆddT (46)

Where É the transmitted power is for OCDMA system, w is weight of the code, and n is the length

of the code.

Æ2 = & <∑ (−&)L^ÇL a .& − L Ç *0&ÇL÷& ù (47)

Figure 19: represented the bit error rate (BER) by OOK/OCDMA formats for silicon optical


3.7 The PPM/ OCDMA Chip – Level Receiver and Its Performance Analysis

In M-ary PPm signaling format the ú symbol, j∈ v=0,1,…,M-1 is represented a

signature sequence at the ú slot and otherwise, there is not any pulse within all other slots the result

bit error rate can be given by equation (49) and equation (48)

= (*&)Ç(Ç&) (48)

Æ: = / & <( − &)∑ (−&)L^ÇL a ò& − (L + Ç) Ç*øG& −^& a ò(G&)Ç¤* ø ÇÇL÷¢ ù (49)



25

OCDMA system with PPM receiver can enhance the security of information transmission.

However, in the hardware implementation OCDMA system with PPM chip – level receiver is more

complex than OOK chip level receiver system. Figure 20 illustrates the result for PPM/OCDMA

format with carbon nanotubes as represented by curv2 which is observed to be better than silicon

optical devices represented curv1. The result can be given by equation (49) and equation (48).

Figure 20: variations of the Bit Error Rate (BER) PPM format for silicon optical devices and

carbon nanotubes (CNTs)

Optical overlapping pulse position modulation (OPPM) chip level receiver [16],[8], [73],

whose difference from PPM chip level OCDMA is that it allows partial superposition of two

adjacent modulated signals or two adjacent slot with width and the overlapping depth index l, it’s

hardware is more complex than that of PPM – chip level OCDMA system.

3.8 Performance Analysis of Two – Dimensional Wavelength Hopping/ Time Spread

Incoherent OCDMA System

Comparative analysis is made for BER performance of 2-D incoherent OCDMA system with

carbon nanotubes and silicon optical devices. Figure 21 illustrates that the BER performance

OCDMA system with carbon nanotubes represented by curv2 is better than silicon optical devices

which represented curv1. Because, carbon nanotubes have high optical powermm = 214.8 ∗1099, band gap energy q =2.9 e V, high refractive index = 1.55 ∗ 10/99, and

duration time E = 2.58 ∗ 10sec ,resulting in ultrafast switches performance better than in case

of silicon optical devices which has low power optical source mm = 35.99 ∗ 1099, band gap

energy q =1.12 e V, low refractive index = 2 ∗ 10n/watt , and duration time E = 3.33 ∗10n?C. The result is given by equation (50) and equation (48) [74], [75], [76], [77].

Æ2 = & ∑ ^Ç()&)L a .Ç T0L .& − Ç T0Ç()&)LÇ()&)L÷Ç (50)

3.9 Performance Analysis of Spectral Encoding Coherent OCDMA System

For the On – Off Keying format; when the data is “1”, the ultrashort pulse is fed into the

spectral phase encoder. The spectral phase encoder imposes a specific phase shift on each spectral

component of the ultrashort pulse. Otherwise, when the data is “0”, the output of the spectral

encoder. This encoding process is implemented through a spectral phase code generator multiplying

each spectral component of the ultrashort pulse. Since the phase code generated by the spectral phase

code generator of each subscriber is unique, the solely spectral phase encoding (C) of data from each

user is implemented.



26

Figure 21: represented the BER performance by 2-D WH/TS incoherent OCDMA for silicon

optical devices and carbon nanotubes (CNTS)

The spectral phase code can employ the binary codes with good properties which are widely

applied to the electrical wireless CDMA, such as m- sequences, Gold codes, etc. The optical signal

with spectral phase encoded in time domain. The optical signal with spectral phase encoded in time

domain looks like a low intensity pseudo – noise burst (D), which is fed into the optical

communication network. Figure 22 illustrates the BER performance in spectral phase coherent

OCDMA with carbon nanotubes more better than silicon optical devices, we can say the spectral

phase encoding in OCDMA system is best among other types in OCDMA system, BER is given by

equation (51) and equation (48)

= <∑ ^&¿ a . & M0¿ .& − & M0¿& (& − c(¿)à&(c(¿) − Æ(¿))&¿÷& ù (51)

Where R = ÉüÉý , and is the number of simultaneous subscribers in the network, B is solid lines, I is

number of interfering subscribers, P(I) is a random variable and satisfies a binomial distribution, and l(±) represented the probabilities of false alarm and missed detection. The result obtained BER

performance with carbon nanotubes much better than silicon optical devices [8], [78].

Figure 22: BER performance by spectral phase encoding in coherent OCDMA with silicon

optical devices and carbon nanotubes (CNTS)



27

3.10 Performance Analysis of Temporal Encoding Coherent OCDMA System

The temporal phase encoding coherent OCDMA system is a type of Time – Spreading

OCDMA, whose model is shown in figure 23. Four kinds of noises are presented in this model,

which are the MAI noise from the OCDMA network, the multiplied beat noise and additive shot

noise from photodetector, and the thermal noise of receiver. In the temporal phase encoding coherent

OCDMA, the coherence of the optical signal has to be maintained within the chip duration and thus

the coherent beat noise becomes critical. It has been shown from investigation that the BER

performance of the incoherent OCDMA system mainly confined by the MAIs from the network and

otherwise, the BER performance of the coherent OCDMA system is limited by the beat noise [16],

[8].

Figure 23: model of temporal phase encoding OCDMA system with various noises

The BER performance in temporal phase encoding OCDMA system with carbon nanotubes

represented by curv2 gives better result than silicon optical devices represented by curv1 and

analyzed by equation (52) and equation (48) [8], [79]

Æ2 =∑ Æ(¿)Æ2(¿)&¿÷¢ (52)

Where P(I) indicates the probabilities that subscribers among M-1 interfering subscribers,

and X(±) is the bit error rate with I.

Æ(¿) = ^&¿ a (&) (53)

And

Æ2 = & õò − 7j72ø Æ¤(¿) + 7j72Æ¤(¿)ö (54)

Where w(±) indicates the probabilities of chips 0 and 1 respectively.

Æ¤(¿) = & ¤þj .Æ:(7¸¿)√ * 0 (55)

Where * =8¸ + k¸ + º¿ and 8¸ = fTà7;F ∗ à

Where K is the boltzmann’s constant (1.38 ∗ 10/R) from table 1, T is the ambient

temperature (ÉÉ) Em=300K, B is transmission bit rate for silicon optical devices B= 3.00 ∗10,=9?/?C and for B= 7.7519 ∗ 10,=9?/?C, and load resistance for silicon optical devices is 50 ∗ 10Ω ,while load resistance for carbon nanotubes 12.9 ∗ 10Ω..



28

We can get shot noise by equation (56)

k¸ = ∗ ¤ ∗ à ∗ ¿« (56)

Where e is charge of electron, B is data rate, ±s the current of photodetector for carbon

nanotubes and silicon optical devices. The BER performance in temporal phase encoding OCDMA

system with carbon nanotubes is much better than silicon optical devices as shown figure 24. All

types of coherent OCDMA and all types of incoherent OCDMA with carbon nanotubes provides

comparatively improved performing system by way of getting highest data rate (Tb/s) and lowest bit

error rate (BER) than silicon optical devices.

Figure 24: represented the BER performance by temporal phase encoding coherent OCDMA

for silicon optical devices and carbon nanotubes (CNTS)

CONCLUSION

The carbon nanotube used in this work is single walled nanotubes whose electronic structure

is semiconducting. Optical integrated circuit has many advantages elastic in direction optical incident

and the move almost of optical power intensity and low consumption power, it needs low voltage

like (160mV – 200mV) and input power in microwatt or milliwatt . This performs in bio-electronic

application. It has saturable absorption to efficient saturable absorbers optical power incident to get

output with losses 5% this is very best for work in passive optical network applications. This is one

of the key advantages of carbon nanotube – based devices in passive mode locking operation. It

continues to work even in high temperature environments without affecting in its performance in the

system. The Absorption in carbon nanotube is very low 0.02 dB/km that means very accurate in

transfer the optical signal, their devices offer a very high nonlinear coefficient and fast response time

to reach 100s of femtosecond, ultrafast work optical switches used in many in communication

system applications, information technology, and sensors system.Three important parameters are

very important for any communication system, named signal to noise ratio SNR, Data rate R, and Bit

error rate BER. In optical code division multiple access (OCDMA) utilizing the nonlinear properties

of materials used in silicon optical devices and carbon nanotubes, bring in improvement in the

system performance. In Coherent as well as Incoherent optical CDMA, encoder is in transmitter and

decoder in receiver. But the coherent OCDMA has been observed to be better than incoherent

OCDMA, because of the poor signal to noise ratio in incoherent OCDMA and is demonstrated to be

more robust to the effect of nonlinearity in terms of bit error rate performance and SNR. Considering

the third order nonlinearity, carbon nanotubes are observed to be highly efficient providing very fast

response and are more suited to next generation components required in communication system

consuming much less power with time, extending the life of batteries used. Optimized design



29

performance of OCDMA with carbon nanotubes (CNTs) based devices have been observed

providing highest data rate (R) and lowest bit error rate (BER) incorporating techniques like

OOK/OCDMA and PPM/OCDMA in Coherent as well as Incoherent OCDMA system. Firstly, the

incorporation of carbon nanotube, based devices result in improved system performance in

comparison to silicon optical devices, with increased data rate upto Tb/s and much reduced bit error

rate between 109@10n bits/sec. Next generation of optical communication system may

preferably incorporate carbon nanotubes based devices so as to achieve much higher data rate up to

Tb/s in comparison to present systems using silicon optical devices giving data rate upto Gb/s.

Besides, such systems with reduced energy source power realize in much longer life Nevertheless,

future requirements of ultrahigh speed internet, video, multimedia, and advanced digital services,

would suitably be met with incorporation of carbon nanotubes based devices providing optimal

performance.The Optical Wireless Communications (OWC) is a type of communications system that

uses the atmosphere as a communications channel. The OWC systems are attractive to provide

broadband services due to their inherent wide bandwidth, easy deployment and no license

requirement. The idea to employ the atmosphere as transmission media arises from the invention of

the laser. The visible light communication (VLC) based on Li-Fi (Light Fidelity)-The future

technology in optical wireless communication refers to the communication technology which utilizes

the visible light source as a signal transmitter, the air as a transmission medium, and the appropriate

photodiode as a signal receiving component.The system develops with carbon nanotubes (CNTs) to

improve for space communications but applied for indoor networks. Indoor optical wireless systems

face stiff competition from future WiFi.

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AUTHOR’S BIBLIOGRAPHY

Jafaar Fahad A.Rida Received his bachelor of Electronic and Communication

Engineering Technical Najaf Collage Iraq in 2003. He obtained M.Tech.

Communication System Engineering from SHIATS Allahabad India in 2012. He

is Pursing Ph.D in Communication System Engineering in Depart ment of

Electronics and Communication Engineering in SHIATS, Allahabad. He has

experience for five years with CDMA technical company and MW System. He

has published several research papers in the field of Optical Systems

Communication and Carbon Nanotubes Engineering.

Dr. A.K. Bhardwaj Allahabad, 16.01.1965, Received his Bachelor of

Engineering degree from JMI New Delhi in 1998; He obtained his M.Tech.

degree in Energy and Env. Mgt. from IITNew Delhi in 2005. He completed his

Ph.D in Electrical Engg. From SHIATS (Formerly Allahabad Agriculture

Institute, Allahabad- India) in 2010. He has published several research paper in

the field of Electrical Engineering. Presently heis working as Associate Professor

and HOD in Electrical Engg. Department, SSET, SHIATS Allahabad- India.

Prof. A. K. Jaiswal, Is working as Professor and HOD of the department of

Electronic and Communication in Shepherd school Engineering and Technology

of SHIATS, Allahabad, India. His area of working is optical fiber communication

system and visited Germany, Finland for exploration of the system designing. He

has more than 35 years experience in related fields. He was recipient of national

award also developing electronics instruments.