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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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