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Results: The previous formulation has been applied to the
arrangement shown in Fig. 2, which serves as a feeding system
Indexing term: Optical communications
It is shown that large numbers of optical heterodyne channels may be frequency multiplexed over a single-mode
optical fibre without the intennodulation byproducts of the
photodetection process becoming a problem, provided the
channels are spaced at five times their optical bandwidth, or
11 GHz
Fig. 2 Geometry of the 4/11 GHz feed system analysed
Feeds are placed 20 cm from the FSS and tilted by 3517 = with
respect to FSS normal; £-field in offset plane
for an offset reflector antenna. The FSS is composed of an
array of crossed dipoles of length L = 11-13 mm and width
W = 0-10 mm arranged in a square lattice with size
d = 8-79 mm. The conductors are printed on a Kapton film
(thickness 0-5 mm, er = 3-2 — ;002) supported by a Kevlar
honeycomb structure (thickness = 6.35 mm, er = 105) protected by two Kevlar films (thickness 018 and 0-25 mm, er = 4 1
— jO-024). The characteristics of the dielectric layers are fixed
by technological constraints. With these dimensions, the FSS
has a — 0-5 dB transmission bandwidth extending up to
4-5 GHz and a -0-5 dB reflection bandwidth of 1-4 GHz
centred at 11-2 GHz. The feeds are rectangular and placed at
such a distance from the FSS that the wavefronts cannot be
considered as planar.
Using the technique described before, the transmitted and
reflected primary patterns have been computed, and an
example is shown in Fig. 3. It can be noted that in the £-plane
Introduction: Frequency division multiplexing (FDM) techniques might at first sight appear to offer a very efficient
means of utilising the vast transmission capacity of modern
single-mode opticalfibres.The generation of large numbers of
closely spaced optical FDM channels now seems possible due
to the progress that has been made recently in fibre optic
heterodyne detection techniques.1 Indeed, the use of closely
spaced FDM channels is probably the only efficient way of
exploiting a fibre's full capacity. Unfortunately, light wave
receivers such as photodiodes respond to the incident instantaneous optical power and are therefore nonlinear (or squarelaw) devices. This square-law nonlinearity leads to the
generation of intermodulation terms in the photoreceiver
output spectrum if the incident optical signal comprises
closely spaced FDM channels. This poses the question: what
channel spacing allows maximum utilisation of the fibre's
capacity, and, at the same time, minimises the parasitic intermodulation and crosstalk noise which can occur in these
systems? It is the aim of this letter to address this question.
The receiver model used in the following analyses is shown in
Fig. 1.
-20 r
1250-1700 n
SM window
Fig. 1 Receiver model
PD is the photodetector and SM is the single-mode fibre
-10 0 0
6 , deg
20 3 0 "
Fig. 3 Transmitted field copolar and crosspolar pattern at frequency
4-5 GHz compared with the pattern of the feed: 45C plane cut
feed + FSS
no crosspolarisation is introduced by the FSS because of the
symmetry of the structure. On the other hand a crosspolar
component appears in the H-plane, because of the offset configuration, even if, in this plane, no crosspolarisation is produced by the feeds themselves. This effect is due to the
different TE/TM reflection and transmission coefficients and
to the mode conversion generated by the grid.
Nth December 1984
Dipartimento di Elettronica
Politecnico di Torino and CESPA-CNR
10124 Torino, Italy
* Present address: ESTEC, Postbus 229, 2200 AG Noordwijk,
LOPRIORE, M., SAITTO, A., and SMITH, c K.: 'A unifying concept for
future fixed satellite service payloads for Europe', ESA J., 1982, 6,
pp. 371-396
2 MONTGOMERY, j . p.: 'Scattering by an infinite periodic array of thin
conductors on a dielectric sheet', IEEE Trans., 1975, AP-23, pp.
Vol. 21
No. 3
Theory: It is assumed that the incident optical fields are plane,
spatially coherent waves which, during detection, are normal
to the receiver area. Thus, only temporal effects of the received
radiation need to be considered as the receiver operates as a
point detector.2 The photodetector bandwidth is assumed to
be large enough to pass the wanted signal without distortion.
The photodetector output response r{t) is proportional to
the intensity or low-frequency part of the square of the
modulus of the incident electric field vector s(t),3 i.e.
where L{.} means low-frequency part. (Quantum mechanical
analysis shows that the rapidly varying sum, and double, frequency components never appear for the type of photodetector considered in this letter providing hv f> kT.3)
The optical signal spectrum incident on the photodetector is
shown in Fig. 2.
The purpose of the optical bandpass filter shown in Fig. 1 is
to coarse tune the receiver to the required part of the spectrum and reject most of the unwanted channels. This preselection process helps to reduce the power density falling on the
photodetector and therefore, the total intermodulation and
shot noise. (It is assumed here that the optical filter does not
have sufficient selectivity to reject all unwanted channels.)
A suitable description of the optical bandpass filter in the
frequency domain is
C{f) = S(f±fc) * £(/) = E(f±fc)
where * denotes convolution, and £(/) is the spectral shape of
the lowpass equivalent of the optical filter. 5(f) is a Dirac
delta function.
intermediate frequency (IF) filter characteristic. By increasing
the channel spacing to 5W the resulting guard band would be
33% of the channel bandwidth, and this has been shown to be
realistic.5 Clearly, to meet requirements (i) and (ii) above and
provide channel guard bands at the receiver, we limit the effiS(f)
Fig. 2 Incident optical spectrum
N is the number of channels, q Hz apart, passed by the optical
It is assumed that the optical channels occupy a template,
specified in Woodward's notation4 by
A(f) = rep, [rect
Thus, the composite spectral range incident on the photodetector is specified by
The ideal photodiode output signal spectrum R(f) is therefore
confined to
= L{S*2(f)}
where the notation means the low-frequency part of the self
convolution of the incident optical spectrum 5(/).
The spectrum of S*2(f) is calculated below:
S*2(f) = {C(f)A(f) + B(f)}*2
= {C(f)A(f)}*2 + B*\f) + 2{C(f)A(f) * B{f)}
= {E{f±fc) rep, [rect
+ E(f±fc) rep, [rect
* <5(/±/ 0 )
There are three types of term in this spectrum: the first corresponds to the unwanted crossproduct terms caused by channel
interactions, (i.e. signal-cross-signal); the second results in the
LO DC component; the third corresponds to the wanted
signal-cross-LO terms.
It is straightforward (but tedious) to show, by graphical
constructions of the convolutions in eqn. 7, that the channel
spacing q must be greater than 4 W if we are to simultaneously
satisfy the following requirements:
(i) that image bands must not fall on adjacent channels, given
suitable selection of LO frequency
(ii) that signal-cross-signal spectral terms do not fall into the
photodetector output channel slots.
The photodetector input and output spectra for the special
case of q = 4 W are shown in Fig. 3.
The LO frequency f0 is located W Hz from the wanted
channel edge. It is clear from Fig. 3 that the dominant signalcross-signal term is located around DC. Thus homodyne
systems should be avoided when performing multichannel
detection. In practical systems it will be necessary to introduce
guard bands which allow for a finite attenuation slope in the
7 7 1)1
PI " -
El T - .
where q is the channel spacing, assumed constant, and W is
the width of each hole in the template into which a channel
must fit; rect (x) = 1, | x | < j , or 0 otherwise.
The use of a template, as described above, has the advantage that we need not consider the type of modulation used on
the channels, (i.e. channel spectral shape) or the amplitude of
the signals. We need only ensure that the vast majority of
channel energy falls within the allowed bandwidth W.
The LO, at frequency/0, may be described by
S(f) = C(f)A(f) + B(f)
wanted channel
Fig. 3 Photodetector
a Input spectra
b Output spectra
ciency of spectral usage to about 20%. (Note that the LO
frequency f0 should be located 1-333W Hz from the wanted
channel edge when the optical channel spacing is 5W. This
corresponds to an IF of 1-833W Hz).
If we could use almost unlimited LO power then the wanted
signal-cross-LO terms in the lightwave receiver output could
be made arbitrarily large, thus making the intermodulation
noise insignificant. In this case we need only satisfy condition
(i), for which q>2W is sufficient. In practice channel guard
bands may limit q to ~7>W, leading to a spectral efficiency of
~33%. However, future multiple access (MA) optical FDM
systems may comprise many 10s or 100s of closely spaced
heterodyne channels covering a wide range of signal levels. In
this type of system it may not be possible to achieve the
required performance with the level of LO power available. It
is intended that the LO power requirements for FDM/FDMA
systems be covered in more detail in a future paper. Clearly, a
channel spacing of ~5W or greater is a simple means of
overcoming this problem.
Conclusions: It has been shown that, in principle, large
numbers of FDM heterodyne channels may be multiplexed
over a single-mode fibre without the intermodulation byproducts of the photodetection process becoming a problem, provided the channels are spaced at five times their optical
bandwidth, or greater. The potential usable optical bandwidth
is then restricted to approximately 20% of that available.
Optical preselection prior to photodetection may be necessary
to keep LO power and intermodulation noise within reasonable bounds, particularly if the channels are spaced closer
than SW. Homodyne detection should be avoided since this
gives very poor intermodulation performance, regardless of
channel spacing.
Acknowledgments: The author wishes to thank Mr. J. R. Stern,
Dr. D. W. Faulkner and Mr. D. W. Smith for many useful
discussions, and the Director of Research/Director of System
Evolution & Standards of British Telecom for permission to
publish this letter.
13th December 1984
British Telecom Research Laboratories
Martlesham Heath
Ipswich, Suffolk IPS 7RE, England
No. 3
current. Typical component values for the pulse shaper were
R = 10 Q, L = 7 nH and C = 0-9 to 2 pF.
1 HOOPER, R. c. et al.: 'Progress in monomode transmission techniques in the United Kingdom', IEEE/OS A J. Lightwave Technoi,
1983, LT-1, pp. 596-611
Experiment: Fig. 1 shows a block diagram of the experimental
configuration used to determine the dynamic linewidth. To
maximise the chirp to mean power ratio, the laser was modulated with a 24 bit pattern consisting of four equally spaced
500 ps pulses. Measurements were performed with and
without the pulse shaper using a constant current source to
bias the laser at threshold. The laser light output was split
between a PIN photodiode having a bandwidth of 5 GHz and
a monochromator with a 0-4 A FWHM resolution to enable
both pulse and spectral measurements to be performed.
GAGLIARDI, R. M., and KARP, s.: 'Optical communications' (John
Wiley & Sons, New York, 1976), p. 146
3 THCH, M. c : 'Field-theoretical treatment of photomixing', Appl.
Phys. Lett., 1969,14, pp. 201-203
4 WOODWARD, P. M.: 'Probability and information theory with application to radar' (Pergamon Press Ltd., London, 1953)
BROWN, J., and GLAZIER, E. V. D.: 'Telecommunications' (Chapman
&Hall, 1966), pp. 116-118
Results: Fig. 2 shows the reduction of transient overshoot in
the laser light output achieved when the pulse shaping
network was used. The corresponding reduction in spectral
width is demonstrated in Fig. 3 where the CW spectrum
(Fig. 3a) is included for reference. Figs. 3b and c show a clear
reduction in spectral width using the pulse shaper from 1-4 A
Indexing terms: Lasers and laser applications, Semiconductor
The dynamic linewidth of 1-5 //m ridge waveguide DFB
lasers is shown to be reduced by shaping the pulse of the
laser modulating waveform. Pulse shaping is performed by a
second-order network designed to cancel the small-signal
laser resonance. Results demonstrate a dynamic linewidth
reduction from 1-4 A to 0-55 A FWHM for a 500 ps pulse.
Introduction: The development of single longitudinal mode
lasers, such as the distributed feedback (DFB) device,1 has
enabled the demonstration of high-capacity long-haul optical
fibre transmission systems.23 Such systems have a requirement for a narrow source spectral linewidth to reduce the
effects of chromatic dispersion in unshifted monomode fibre.
Linewidth broadening or 'chirp' of DFB lasers can occur
under high-speed modulation,4 thus reducing the potential
span-rate system product. One method used to overcome this
problem is to bias the laser above threshold at a point where
the spectral linewidth is a minimum; however, this then leads
to an extinction ratio power penalty—as an example, 5 dB
over 130 km at 2 Gbit/s has been reported.5
A reduction in dynamic linewidth has been predicted theoretically by using a small-amplitude prepulse of duration
equal to the relaxation oscillation period.6 In this letter we
present the results of laser modulating waveform shaping to
inhibit the transient overshoot associated with the carrier
density change during laser turn-on.
Pulse shaping circuit: Pulse shaping is provided by a secondorder network (inset, Fig. 1) with a resonant characteristic
equal and opposite to that of the laser resonance, thus giving a
flat overall laser-network transfer function.7 The variation of
laser small-signal resonance with bias current8 was compensated by means of a variable capacitor, such that the transient
overshoot was minimised for any particular value of bias
Fig. 2 Pulse shapes
a Without pulse shaper
b With pulse shaper
data test
2 U bit word
bits 6.12.18,
to chart
pulse shaper
to oscilloscope
Fig. 1 Block diagram of experimental set-up
No. 3
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