Performance comparison of pseudonoise sequences for optical CDMA networks

The reflectances and transmittances in Ž14. and Ž15. then are given by 2 r 11 s yr 22 s Ž ␩a y ␩ b . Ž ␨ 12 y ␨ 22 . r⌬ ,

Ž 17 .

r 12 s 2 i␩a Ž ␩a2 y ␩ b2 . ␨ 2 Ž ␨ 1 q ␨ 2 . r⌬ ,

Ž 18.

r 21 s y2 i␩ay1 Ž ␩a2 y ␩ b2 . ␨ 1Ž ␨ 1 q ␨ 2 . r⌬ ,

Ž 19.

t 11 s

␩b ␩a

t 22 s 8␩ b Ž ␩a q ␩ b . ␨ 1 ␨ 2r⌬ ,

Ž 20.

t 12 s y4i␩a␩ b Ž ␩a y ␩ b . ␨ 2 Ž ␨ 1 y ␨ 2 . r⌬ ,

Ž 21 .

t 21 s y4i Ž ␩a y ␩ b . ␨ 1Ž ␨ 1 y ␨ 2 . r⌬ ,

Ž 22.

2

2

⌬ s Ž ␩a y ␩ b . Ž ␨ 1 q ␨ 2 . q 16␩a␩ b ␨ 1 ␨ 2 .

Ž 23.

Expressions Ž17. ᎐ Ž22. reduce correctly to those for isorefractive nonchiral media w6, 7x on setting ␤ s 0 Ži.e., ␨ 1 s ␨ 2 . therein.

3. DISCUSSION

Let us note from Ž17. ᎐ Ž22. that a left Žresp. right-.-handed plane waveᎏthat is incident on the planar interface of two isorefractive chiral mediaᎏis reflected as well as transmitted with both left- and right-handed components. We can thus conclude that isorefractivity is not germane to left l righthandedness conversions. But we know that the satisfaction of the isoimpedance condition Ž6. suppresses left l righthandedness conversions w2, 3x. This confirms that the impedance match is sufficient to prevent handedness conversions on scattering by the interface of two chiral media. Finally, let us note that when both Ž6. and Ž7. are satisfied simultaneously, Ž17. ᎐ Ž22. yield r 11 s r 12 s r 21 s r 22 s t 12 s t 21 s 0 and t 11 s t 22 s 1. Theses reductions come about because isoimpedant isorefractive chiral media must be identical media.

REFERENCES 1. A. Lakhtakia, Beltrami Fields in Chiral Media, World Scientific, Singapore, 1994. 2. A. Lakhtakia, V. V. Varadan, and V. K. Varadan, ‘‘What Happens to Plane Waves at the Planar Interfaces of Mirror-Conjugated Chiral Media,’’ J. Opt. Soc. Amer. A, Vol. 6, 1989, pp. 23᎐26. 3. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, ‘‘Influence of Impedance Mismatch between a Chiral Scatterer and the Surrounding Chiral Medium,’’ J. Modern Opt., Vol. 36, 1989, pp. 1385᎐1392. 4. A. Lakhtakia, ‘‘On the Crucial Role of Impedance Matching in Chirolens Design,’’ Microwa¨ e Opt. Technol. Lett. Vol. 7, 1994, pp. 66᎐68. 5. A. Lakhtakia, ‘‘On Homogenization of Impedance-Matched Chiral-in-Chiral Composites,’’ J. Phys. D: Appl. Phys., Vol. 29, 1996, pp. 957᎐962. 6. C. L. Giles and W. J. Wild, ‘‘Fresnel Reflection and Transmission at a Planar Boundary from Media of Equal Refractive Indices,’’ Appl. Phys. Lett., Vol. 40, 1982, pp. 210᎐212. 7. A. Lakhtakia, ‘‘On Pathological Conditions and Fresnel Coefficients,’’ Int. J. Infrared Millim. Wa¨ es, Vol. 11, 1990, pp. 1407᎐1413. 8. P. L. E. Uslenghi, ‘‘Exact Scattering by Isorefractive Bodies,’’ IEEE Trans. Antennas Propagat., Vol. 45, 1997, pp. 1382᎐1384.

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9. A. Lakhtakia, ‘‘Brewster Condition for Planar Interfaces of Natural Optically Active Media,’’ Z. Nat. forsch. A, Vol. 47, 1992, pp. 921᎐922. 䊚 1998 John Wiley & Sons, Inc. CCC 0895-2477r98

PERFORMANCE COMPARISON OF PSEUDONOISE SEQUENCES FOR OPTICAL CDMA NETWORKS Celso de Almeida1 and Sandro Moraes Modenese1 1 Departamento de Comunicac ¸˜oes Faculdade de Engenharia Eletrica e de Computac ¸˜ao ´ Universidade Estadual de Campinas 13.083-970 Campinas, SP, Brazil Recei¨ ed 21 April 1998 ABSTRACT: In this letter, a performance comparison between two classes of pseudonoise sequences for optical CDMA networks is presented: Gold sequences and optical orthogonal sequences. 䊚 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 352᎐354, 1998. Key words: optical CDMA; optical orthogonal sequences; pseudonoise sequences INTRODUCTION

CDMA has been analyzed intensively, mainly in RF applications. Also, much has been written about optical CDMA systems that use optical orthogonal sequences ŽOOSs. w1x. In this letter, we show performance advantages using Gold sequences ŽGSs. over OOS in optical CDMA networks. We explore receivers with p-i-n diodes and APDs. SYSTEM MODELS

Figures 1 and 2 show the transmitter and receiver models when GSs are being used. Spreading is obtained by multiplying bipolar, information, and GSs, both with levels y1, 14. In the transmitter, a level translator must be provided to obtain unipolar sequences, with levels 0, 24, before driving the laser. In the receiver, before multiplying by the despreading sequence, we consider another translater that eliminates the dc level, and converts the unipolar received sequence into a bipolar one.

Figure 1

Optical CDMA transmitter for GSs

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 19, No. 5, December 5 1998

Figure 2

Optical CDMA receiver for GSs

␭ a is the maximum off-sync autocorrelation value, and ␭ c is the maximum cross-correlation value. Given the period N and the weight K, where K Ž K y 1. F N y 1, and ␭ a s ␭ c s 1, then M F ?Ž N y 1.rŽ K Ž K y 1..@ OOSs can be constructed, where ? x @ is the integer part of x w1x. An algorithm was developed in w3x to find some OOSs that were used in this simulation. SIMULATION RESULTS

Figures 3 and 4 shows the transmitter and receiver models when OOSs are being used. In this case, spreading is obtained by multiplying unipolar sequences 0, 14, information, and OOSs. In this case, we have to use in the transmitter two different spreading sequences associated with the information bits, to guarantee transitions in the channel, when bit 0 is to be transmitted. The topology assumed in this network is that of a star, where it is assumed that the signals from different users arrive at a given receiver with the same power. We consider in the receiver a transimpedance amplifier that introduces thermal noise and, depending on the photodetector employed, shot or avalanche noise is also present. We do not consider in this letter the interference due to multiple optical carriers w2x because CDMA is very robust against interference, and the probability of having two monomode lasers aligned in 30 Žmaximum number of users considered. to generate strong interference is very low, as shown in w3x. GOLD SEQUENCES

In w4x, an algorithm is described to find 2 m q 1 sequences with length 2 m y 1 that have good properties of autocorrelation and cross correlation, where m is the number of shift registers. OPTICAL ORTHOGONAL SEQUENCES

An optical orthogonal sequence is determined by the quadruple  N, K, ␭ a, ␭ c4, where N is the length, K is the weight,

Figure 3

Figure 4

In this section, we show some performance curves, obtained by a Monte Carlo simulation method, with the following parameters: responsitivity of both photodetectors R s 0.75, transimpedance R f s 120rN k ⍀, number of chips per bit N s 31, bit rate R b s 45.8 Mbitsrs, temperature TR s 300 K, ionization constant k s 0.04, extinction ratio Fext s 0.01, and weight of OOSs K s 2. It is important to mention that, for reasons of reliability, the laser peak power must be limited, so that the mean power for OOSs is less than the mean power of GSs, and this amount is given by w3x Po PG

s

2

K

1 q Fext

N

Ž 1 y Fext . q Fext

Ž1.

where Po is the mean power for OOSs and PG is the mean power for GSs. For simplicity, avalanche noise was considered as a Gaussian process. Invoking the central limit theorem, CDMA systems have its decision variable nearly Gaussian, even for APDs. N s 31 chips per bit is used in this simulation for both kind of sequences, which limits the number of users to 33 for GSs and 7 for OOSs Žusing K s 2 marks, and two sequences for each user.. Notice in Figure 5, for GSs, that the performance of systems using a p-i-n diode does not worsen too much when the number of users grows. For APD, we notice exactly the opposite. This can be explained as follows. When the number of users grows, there is more optical power in the receiver, and consequently, we have more avalanche noise, which worsens the bit-error rate. For only one user, we have a gain of approximately 17 dB, using APD instead of p-i-n for a BER of 10y3. When more users are added to the system, we

Optical CDMA transmitter for OOSs

Optical CDMA receiver for OOSs

Figure 5 Mean bit-error rate for GSs with p-i-n and APD. % APD: one user, ⽧ APD: ten users, q APD: 30 users, B p-i-n: one user, 䢇 p-i-n: ten users, ' p-i-n: 30 users

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 19, No. 5, December 5 1998

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2-D NUMERICAL SIMULATION OF LASER-INDUCED PLASMA Z. H. Shen,1 W. Z. Wen,1 J. Lu,1 and X. W. Ni1 1 Department of Applied Physics Nanjing University of Science & Technology Nanjing, 210094 P. R. China Recei¨ ed 21 April 1998

Figure 6 Mean bit-error rate for OOSs with p-i-n and APD. B APD: one user, 䢇 APD: seven users, ' p-i-n: one user, % p-i-n: seven users

ABSTRACT: In this paper, second-order accurate upwind schemes of the total ¨ ariation diminishing (TVD) type are employed for numerically calculating axisymmetric silicon plasma field interactions induced by a Q-switched Nd:YAG laser. The numerical results are in good agreement with the experimental results. 䊚 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 354᎐358, 1998. Key words: laser-induced plasma; gas dynamics 1. INTRODUCTION

conjecture, based on simulation results, that APD performance tends to p-i-n performance. We notice from Figure 6, for OOSs, that the performance does not change significantly with the number of users. This occurs because these sequences are almost orthogonal. When comparing the total transmission loss between GSs and OOSs, we have to subtract the negative value of Ž1. in decibels from the sensitivity of OOSs. So, we observe that OOSs present a smaller total transmission loss when compared with GSs for the same number of users and bit-error rate. CONCLUSIONS

We have shown, for optical CDMA networks, that GSs present a greater total transmission loss than OOSs for the same number of users and BER. For GSs and a great number of users, the p-i-n diode presents approximately the same performance as APD. ACKNOWLEDGMENT

This work was supported in part by CNPq, CAPES, and CPqD-Telebras. ´ REFERENCES 1. J. A. Salehi, ‘‘Code Division Multiple-Access Techniques in Optical Fiber NetworksᎏPart I: Fundamental Principles,’’ IEEE Trans. Commun., Vol. 37, 1989, pp. 824᎐833. 2. C. Desem, ‘‘Optical Interference in Lightwave Subcarrier Multiplexing Systems Employing Multiple Optical Carriers,’’ Electron. Lett., Vol. 24, 1988, pp. 50᎐52. 3. S. M. Modenese, ‘‘Desempenho de Sistemas CDMA Aplicados a ´ Redes de Comunicac¸˜ oes Opticas,’’ M.Sc. thesis, UNICAMP, Brazil, 1997 Žin Portuguese.. 4. J. G. Proakis, Digital Communications, McGraw-Hill, New York, 1993.

䊚 1998 John Wiley & Sons, Inc. CCC 0895-2477r98

When a high-power laser pulse irradiates a target surface, a high-temperature and high-pressure plasma occurs, and a high-pressure shock wave is developed when plasma propagates in air. To simulate this procedure, there are many methods, including the Lax Wendroff scheme, the ADI scheme w1x, and the feature-line method, but there is effacing or pseudo-oscillation to a certain extent behind the shock wave when using those traditional differential schemes. However, the upwind TVD scheme developed by Harten w2x not only can capture a high-resolution shock wave accurately, but also might avoid defects in the above differential schemes. In this paper, on the basis of the physical features of laser-induced plasma, second-order accurate upwind schemes in the TVD method are employed for numerically simulating the laser-induced plasma field, and the numerical results are in good agreement with those obtained by experiment w3, 4x. 2. PHYSICAL MODEL AND NUMERICAL METHOD

2.1. Physical Model. We assume that cohesiveness and thermoconduction can be neglected, and the specific heat rate is constant in the procedure. Accordingly, the axisymmetric fluid gas-dynamical equation can be written as

⭸U ⭸t

q

⭸ F ŽU . ⭸x

q

⭸ G ŽU . ⭸r

q H ŽU . s 0

Ž1.

where vectors U, F, G, H represent Usw␳

m

n

e xT

F ŽU . s m

m 2 r␳ q p

G ŽU . s n

n⭈u

H Ž U . s nrr

n 2 r␳ q p

␳ ⭈ u ⭈ ¨ rr

Ž e q p . mr␳

m⭈¨

Ž e q p . nr␳

␳ ¨ 2rr

T

T

Ž e q p . ¨ rr

T

.

Here, ␳ is the plasma fluid density, u and ¨ are the axial and radial velocity, respectively, m s ␳ ⭈ u and n s ␳ ⭈ ¨ are the axial and radial momentum of unit fluid, respectively, and p is the pressure. The gross internal energy per unit mass is e s pr Ž ␥ y 1 . q 12 Ž u 2 q ¨ 2 .

Ž2.

where ␥ is the specific heat rate of vapor plasma of silicon.

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