scopic model of the facet temperature characteristics and related degradation phenomena of semiconductor lasers. M. C. KRANTZ H. J. ROSEN W. LENTH IBM Almaden Research Center 650 Harry Rd. San Jose, C a 95120, U S A level systems (such as N-PSK and N-APK) and, for a suffciently high number of levels, polarisation modulated systems (N-PSK). 18th April 1990 References 1 ETTENBERG, M., and K R ~ E L ,H.: ‘The reliability of (A1Ca)As cw laser diodes’, IEEE J. Quantum Electron., 1980, 16, p. 186 2 HENRY, C. H., PETROFF, c. M., LOGAN, R. A.. and MERRIT, F. R.: ‘Catastrophic damage of Al,%a, -,As double heterostructure laser material’. .IAppl. . Phys., 1979, SO, p. 3721 3 BRUGGER, H., and EPPERLEIN, P. w.: ‘Mapping of local temperatures on mirrors of GaAs/AlGaAs quantum-well graded-index separateconfinement heterostructure lasers’, submitted to Appl. Phys. Lett. 4 TOWROKIS,S . : ‘Influence of local heating on current-optical output power characteristics in Cia, -.AI,As lasers’, J. Appl. Phys., 1986, 60,p. 61 5 KAWANISHI, H., M O R I M 0 7 0 , T., YAMAGUCHI, M., KANEIWA, S., MIYAUCHI, N., YISHIUA, T., HAYASHI, H., YANO, S., and HIIIKATA, T.: ‘High-power CW operation in v-channel substrate inner-stripe lasers with “torch”-shaped waveguide’, Jap. J. Appl. Phys., 1988, 27, p. L1310 6 DEVLIN, G . E., DAVIS, 1. L., CHASE, L., and GESCHWIND, s.: ‘Absorption of unshifted scattered light by a molecular I, filter in Brillouin and Raman scattering’, Appl. Phys. Lett., 1971, 19, p. 138 7 ASPNES, D. E., KELSO, s. M., LOGAN, R. A., and BHAT, R.: ‘Optical properties of Al,Ga, -,As’, J . Appl. Phys., 1986, 60,p. 754 8 LAX, M . : ‘Temperature rise induced by a laser beam’, J. Appl. Phys., 1977,48, p. 3919 9 PAOLI, T. L.: ‘A new technique for measuring the thermal impedance of junction lasers’, IEEE J. Quantum Electron., 1975, QE-11, p. 498 IO ESMAN, R. D., and RODE. D. L.: ‘Semiconductor laser thermal time constant’, J. Appl. Phys., 1986.59, p. 407 11 FUJITA, 0.: ‘A new method of measuring the thermal time constant ofjunction lasers’, J. A p p l . Phys., 1985,57, p. 978 S y s t e m description a n d analysis: When dealing with the optical field propagating through a conventional single-mode fibre, fibre birefringence must be considered since it causes an unpredictable polarisation fluctuation of the fibre output field. This phenomenon can be accomodated in the described system by means of the electronic adaptive algorithms’ based on the estimation of the Jones metrix of the fibre as shown in Reference 5. In order to simplify the system scheme this problem has been neglected in this letter and the fibre is supposed to preserve at its output the input field polarisation. The electrical field of a n electromagnetic wave propagating through an optical fibre can be written as follows: U t ) = E,(t)x = [(x, + E,(t)Y + ix,)x + ( x j + i~,)y]e’”’~‘ (1) where x and y are the reference axes unit vectors, so that it can he then represented by means of a vector X of components x r (i = 1, . . . , 4). In the space of the vectors X, indicated as the signal space (SS), it is useful to introduce a Euclidean metrix so that the norm of a vector coincides with the electromagnetic field power. In the following, for the sake of simplicity, only constant power signals will be considered, however even more efficient signalling can be achieved using the full four-dimensional space in a way similar to N-APK format on the plane. The transmitter must be capable of producing at its output an arbitrary electrical field with a given power P o . Such a field is represented by the vector X whose components satisfy the condition x: + x i + x: + x: = Po so that in the S S each transmitted field is associated with a point lying on a spherical surface. On such a surface, with an increasing number of levels, the distances among the points that represent the transmitted fields decrease more slowly in comparison with conventional multilevel systems (e.g.. N-PSK and N-APK) working on plane metrics, as shown in Table 1. Therefore, Table 1 MINIMUM DISTANCES BETWEEN POINTS EXPLOITING FIBRE OPTICS TRANSMISSION CAPACITY: 4-QUADRATURE MULTILEVEL SIGNALLING Indexing t e r m . Optical communications, Polarisation The principle scheme of a new multilevel coherent optical system is presented which shows how to exploit the four degrees of freedom of the optical field. The proposed system performance gets nearer to the theoretical Shannon limit than conventional and polarisation modulated multilevel systems for a high number of levels. Introduction: Recently novel optical coherent systems have been proposed allowing the two polarisation modes of a conventional sngle-mode fibre to be exploited either to realise polarisation modulation,'^* or to send, together with the transmitted phase-modulated signal, a phase noise reference carrier.’ It has been demonstrated that the polarisation characteristics of the electromagnetic field propagating through the fibre allows the design of new multilevel modulation schemes. Using polarisation modulation the transmitted symbols can be associated to points on the Poincare sphere so that a performance improvement is obtained with respect to traditional multilevel system^,^.^ due to the characteristics of the spherical metrix. In this letter the conceptual scheme of a new multilevel coherent optical system is presented that exploits all the four degrees of freedom of the electromagnetic wave propagating through the fibre. It allows system performance to get nearer to the theoretical Shannon limit than the conventional multi- 992 N M = 2 M = l M = 4 2 4 2 1.414 2 6 1 0.765 0.518 2 1,633 1.414 1.211 0.983 0.390 om7 1 . n ~ 8 12 16 1.633 1.414 1.400 1.220 because of the fact that error probability depends essentially upon the distance between points representing adjacent levels, a sensitivity improvement is expected. A suitable modulation can be realised starting from a CW linearly polarised field by simultaneously modulating the field phase and polarisation so that the transmitter can he designed as a cascade of a phase and a polarisation m o d ~ l a t o r . ~ . ~ The block diagram of the receiver is shown in Fig. 1. The received field is decomposed in its polarisation components U Fig. 1 System block diagram ELECTRONICS LETTERS 5th July 1990 Vol. 26 No. 14 with respect to the reference axes which, under the above hypothesis, coincide with those adopted at the transmitter. Each polarisation component is coherently detected by means of a 4 2 balanced receiver using polarisation diversity so to obtain at intermediate frequency (IF) an estimate of the four components of the transmitted X vector. In particular, after an ideal bandpass I F filtering, the four IF currents have the following expressions: yk(t)= 2ax,(t) cos [WtF t + cp] + Even better performance can be obtained if the constant power constrain is abandoned. . 0 20 [email protected]) (k = 1, . . . , 4) 0 ; ’ (2) a being the fibre attenuation and cp the phase mismatch between the transmitting laser and the local oscillator (LO) that is common to all the four currents. The power of each L O polarisation component is assumed to be normalised to unity so that the power of the four handlimited, white, Gaussian detection noise processes nk(t) can he considered equal to the I F bandwidth. Both laser phase and amplitude noise have been neglected in order to obtain the quantum noise limited system performance. After I F filtering the signals are coherently demodulated by means of a conventional PLL that can be driven, using the algorithms detailed in Reference 5, by a suitable combination of all the signals in order to estimate the slow varying phase mismatch, cp. The demodulated signals, tk,are an estimate of the components of the transmitted X vector. The decision is then performed by correlating the estimated transmitted vector with the vector corresponding to the possible transmitted symbols in the signal space (reference vectors, RVs). In particular the N decision variables / , 101 2 1 . 3 1 5 spectral efficiency ,log N , 6 1197111 Fig. 2 Shot noise limited system performance W N-PSK U N-APK 0 N-SPSK 0 N-4Q A c k n o w l e d g m e n t : Work carried out in the framework of the agreement between Fondazione Ugo Bordoni and the Italian P T Administration and under the partial financial support of the National Research Council (CNR) in the frame of the Telecommunications Project. S. BETTI 17th M a y 1990 F. CURTI G. DE MARCHIS E. IANNONE Fondazione Ugo Bordoni Viale Europa 190,00144 Roma, Ifaly References 1 and IANNONE, E.: ‘Phase-noise and polarization state insensitive optical coherent systems’, IEEE BETTI, S.. CURTI, F., DE MARCHIS, G., J . Lightwaue Technol., 1990,LT-8, (3,pp. 756767 2 CALVANI, 0 are calculated, being T, the symbol interval, xf ( i = 1, .. . , 4) the co-ordinates of the kth RV, n:(t) and n f ( t ) the baseband Gaussian components of the noise process nh(t),and k = 1, . . . , N . The jth symbol is considered the one transmitted if q, > qk ( k #J). All the decision variables are Gaussian distributed so the performance evaluation problem can be solved with standard methods’ obtaining the system symbol error probability, P,. S y s t e m performance: In order to obtain the best system per- formance the transmitted field states must be chosen such in a way so as to minimise the received optical power required to achieve the desired bit error probability. This is equivalent to choosing N points on the sphere in the signal space so that the error probability, P,, function of their co-ordinates is a minimum. This problem cannot be solved analytically and the solution must be found numerically, for example by using the downhill simplex method. However the obtained optimum configurations are highly regular, as shown in Reference 5. In Fig. 2 the system sensitivity corresponding to an error is shown as a function of the number of probability of levels and compared with the performance of N-PSK, N-APK and N-SPSK.’ The classical Shannon limit for the channel capacity is also reported. From Fig. 2 it is seen that systems based on a spherical S S metrix (as N-SPSK and the proposed one) have higher sensitivity than that of the systems based on a plane metrix (as N-PSK and N-APK). With an increasing number of dimensions of the SS, the sensitivity is increased and therefore, for a high number of levels, the proposed system performance results are better than that of N-SPSK. The performance gain of the proposed system tends to increase when increasing the number of levels. In particular, considering N-APK as a reference, it is 0.8dB for N = 16, it rises to 1.6dB when N = 32 and, for N = 64 it is equal to 3-5dB. ELECTRONICS LETTERS 5th July 1990 Vol. 26 No. 14 3 4 5 6 R., CAFONI, R., and CISTFXNINO, F.: ‘Polarisation phase shift keying: A coherent transmission technique with differential heterodyne detection’, Electron. Lett., 1988, 24,(lo),pp. 642-643 DE MARCHIS, G., BETTI, s.. CURTI, F., and IANNONE,E.: ‘Multilevel coherent optical system based on Stokes parameters modulation’, IEEE J . Lightwave Technol., 1990,LT-8, (7) BENEDETTO, s., and POGGIOLINI, P.. ‘Performance evaluation of multilevel polarisation shift keying modulation schemes’, Electron. Lett., 1990,26, (4),pp. 244-246 BETTI, S., CURTI, F., DE MARCHIS, G., and IANNONE, E.: ‘A novel multilevel coherent optical system: 4-quadrature signalling’, suhmitted for publication to IEEE J . Lightwave Technol. BETTI, S., CURTI, F.. DE MARCHIS, G., and IANNONE. E.: Patent filed, April 1990 OPTICAL SECOND H A R M O N I C GENERATION FROM LAMINATED POLY M ER IC LANG MUIR - B LO D G E l T M U LTI LAY ERS Indexing terms: Optical properties of substances, Harmonic generafion Alternating polymeric LB films have been formed using a performed polymer dye. SHG efficiency has been shown to be substantially increased by forming a laminated layer structure using cadmium arachidate. Introduction: In an earlier letter’ we reported on a LangmuirBlodgett’ device consisting of alternate layers of a polymer and a suitable chromophore (merocyanine) which could be used to generate second harmonic radiation from an incident 993

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