A design algorithm for VIPA-based spectral-phase-coded OCDMA encoder

A design algorithm for VIPA-based spectral-phase-coded aCOMA encoder A. Mokhtari 1 , A. A. Shishegar1 1: Department of Electrical Engineering, Sharif University of Technology

Abstract: We propose a design algorithm for VIPA-based OCOMA encoder used in WOM-compatible COMA networks based on the problem requirements. Analyzing this device by our previous formulation leads to some useful suggestions to improve the device.

coefficients of highly reflective surfaces; d, VIPA thickness and n2 is the applied etalon refractive index. Using the VIPA and etalon similarities and considering paraxial and Fourier assumptions, some simple relations can be collected from [3], [6], [7] and [8] that are listed here:

mAo

Keywords: Optical COMA, VIPA, Oesign algorithm

0)0

Introduction Following the successful implementation of codedivision-multiple-access exploitation in wireless domain [1], its prospective usages in optical domain are also under investigation. Optical COMA is the most promising photonic switching technology in next generation optical networks to realize optical internet. Etemad [2] showed the possibility of OCOMA implementation in conventional WOM networks. OCOMA encoder is the key element in this scheme that has three main functions namely, WOM channel demultiplexing to the frequency bins, inducing prescribed phase change and then multiplexing the phase coded bins [3]. Novel spectral dispersers such as Virtually-Imaged-Phased-Array (VIPA) and Micro-Ring-Resonator (MRR) are introduced to provide the required high resolution [3]. VIPA first introduced by Shirasaki [4] is a tilted version of etalon. VIPA function is mainly explained by its common characteristics with Fabry-Perot etalon. VIPA function can be viewed best as the interference of an infinite number of waves of progressively smaller amplitudes all with equal phase difference [5]. It acts as periodic (comb) filter with sharp peaks as a function of frequency with two major parameters describing it as sketched in figure 1; i.e. free spectral rang (the maximum frequency range that the phase coding can be performed independently.) (FSR) and 3-dB bandwidth commonly referred as Full width at Half Maximum (FWHM). VIPA principal system used in SPC-OCDMA application is depicted in figure 2. The focused beam light is emitted from a laser source enters the device and intercepts the highly reflective surface, majority of light beam reflects but a portion emits out of device in each round-trip that build a set of virtual sources. They interfere with each other and are collimated by lens on the phase mask. Consequently, the different wavelengths of input pulse are separated and spectrally phase coded by the phase mask.

2. Design algorithm The Gaussian source with wavelength Ao and beam waist of (vo emits light with angle Bi relative to the normal line. The device is characterized by Rand r , reflection

2n2dcos(B) (m E Z)

~Aod /(n 2 1t) (beam waist)

Bi == focused beam size/ d

FSR

c /(2n 2d cos(B))

FWHM

c 1- Rr 2n21td cos(B) . jji;

[1] [2] [3]

[4]

[5]

In the proposed scheme, FSR is extended to an optical passband to use efficiently from an optical window bandwidth. Meanwhile, to increase the number of code length so that the network can support more users, FWHM must be decreased. The ratio of FSR/FWHM is a measure of supporting code length. Oue to poor coupling into single mode fiber receiver, the device insertion loss is high. Trying to design better OCOMA encoder (i.e. lower multi-user-interference) translates to the design of a demultiplexer with high contrast ratio and reduced channel crosstalk and increasing security. There are seven steps to design the OCOMA encoder: 1) Regarding Gaussian beam input wavelength and FSR, the term n2dcos(B) is extracted form (4). 2)

Oue to small input angle, cos(B) is close to 1. Based on the previous step, n2d is calculated.

3) 4) 5)

6) 7)

Choosing the VIPA material (here; glass n2

1.5),

VI PA thickness (d) is extracted from previous step. From known parameters, beam waist is calculated from (2). To reduce device insertion loss, fiber mode size should be equal to focused beam width. For single mode fiber, Bi is calculated from (3). Having code length and assuming R == 1, the other reflection coefficient r is calculated from (5). "m" an integer is determined so that equation (1) is satisfied. There may be a small variation in FSR value.

We propose the following flowchart to design the required encoder (figure 3). The problem parameters are denoted by rectangular while the calculated parameters are shown in circles. Following the flow chart (tracing the arrows and performing the above-mentioned procedure) and utilizing

the fundamental equations, the problem parameters are calculated in table1.

6. References [1]

S. Yang, "3G CDMA2000: WIreless englneenng', Artech House, 2004

[2]

P. Toliver, et.al. "Optlcalnetworklngdemonstratlonof O-CDMA basedon hypemne spectralphase codtng'; LEOS'04, 2004.

[3]

P. R. Prucnal, OptlcaICodeDiV/slonMu!tlpleAccess: Fundamentals and Appllcallons, CRC Press, New York, 2006.

[4]

M. Shirasaki: "Largeangulardtsperslonbya VIrtually Imaged Phased Array and Its applicatIon to a wavelength demu!tlplexe~, Optical Letter, vol. 21, pp. 366-368, 1996. E. A. Saleh Bahaa &. Teich Malvin: "Fundamentalsof PhotonIcs', Chap. 2, p.1 06, John Wiley & Sons, Inc., New York, 1991.

3. Numerical Results We use our previous proposed formulation to simulate the design device function [8]. The output 3-D pattern also obtains the 3-D distribution of power in the output plane. Due to spherical lens usage at the output of the device, the symmetry is disturbed and spectral components are distributed over the whole plane; in other word, spectral dispersion happens in two-dimension in contrast with the conventional cylindrical lens usage. Utilizing this characteristic may lead to higher code length and lower multi-user-interference (MUI) encoder/decoder due to more channel discrimination (i.e. lower channel crosstalk, higher contrast ratio and increased confidentiality). 4. Conclusion We proposed an algorithm to design VIPA-based spectral-phase-coded aCOMA encoder. The designed device is also simulated by our previous proposed formulation and the numerical results are presented.

3-dB

[5]

[6]

M. Shirasaki, et al: " VIrtually Imaged PhasedArray WIth Graded Rellecllvily It, IEEE Phot. Tech. Lett., Vol. 11, 1443-1445,1999.

[7]

S. Xiao, "ExpeniJJental and TheoretIcal Study of Hypemne WDM Demultiplexer Pedormance USIng the VIrtually Imaged Phased-Arra)l, IEEE JLT, vol. 23, no. 3, March 2005. A. Mokhtari, A. A. Shishegar: "A RIgorous Vectonal GaussIan Beam Modeling of Vlitually-ImagedPhased-Arrajl, AOE'07, (Shanghai, China), 2007.

[8]

.... ~BW

system

+--+

FSR

Table1: VIPA parameters designed for SPC-OCDMA encoder

Figure 1: Periodic filter and main describing parameters

1ll1l.. 11A Encoded pulse

F Phase mask

Parameter

Value

,.10' aJ 0 [CQ1l]

1.55,18.2

(}i [degree]

1.14

R,r

1,0.975

d[mm]

1

n2

1.5

F[cm]

18

Figure 2: VIPA as an OCDMA encoder/decoder CD

ia.. E

~ 0.5

•

:t:f (I

E o

Zo o X-Direction Ou1put Angle (Degree)

Figure 3: Design flow chart and the corresponding steps

Figure 4: 3-D output pattern of designed VIPA on the lens focal plane (before phase mask)