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Spectral Shift and Broadening of DFB
Lasers Under Direct Modulation
Avi Zadok, Hamutal Shalom, Moshe Tur, Fellow, IEEE, W. D. Cornwell,
and Ivan Andonovic, Senior Member, IEEE
Abstract—The spectrum of DFB lasers, directly modulated at
144 and 622 Mb/s, is found to be considerably wider than the
modulating random sequence rate. The broadening, which may
be as high as ten times the data bandwidth, is accounted for by
frequency changes (chirp) along each bit, incorporating a recently
observed short time constant on the order of 10–20 ns. These
changes will also introduce a few gigahertz spectral shifts as a
function of the bit rate.
Index Terms—Distributed-feedback lasers, optical communication, optical modulation/demodulation.
HE PRESENCE of dispersion in optical fibers requires
the transmitting laser to have the narrowest possible optical spectrum under modulation conditions. However, even the
most currently used single frequency source, the distributedfeedback (DFB) laser is spectrally broadened by direct modulation. Three main mechanisms are involved: 1) transient chirp,
associated with the relaxation oscillations following a sudden
current change [1], [2]; 2) adiabatic chirp, introduced by the
effect of the injection current on the refractive index of the
cavity [3]–[5]; and 3) a more slowly evolving thermal chirp,
where the junction temperature affects both the refractive index
and the cavity length, thus changing the optical frequency [6],
[7]. While the adiabatic chirp follows the instantaneous injection current, the thermal chirp maintains correspondence with
the active region temperature. The various chirp mechanisms
broaden the laser spectrum significantly beyond the original
laser linewidth and the modulation bandwidth.
Transient chirp could greatly increase the linewidth when
modulation rates reach several gigabits per second [8], [9],
though modern DFB’s display very little transient chirp at
subgigahertz-per-second rates. Broadening due to adiabatic
chirp would be dominant in many modulation schemes [10],
[11]. However, in digital modulation systems with high extinction ratios, its effect is negligible since “zero” bits carry
almost no light, and the entire signal is characterized by a
single current level.
Commonly stated values for time constants associated with
thermal chirp range from 150 ns to several milliseconds [6],
[11]–[13], suggesting that the optical spectrum of a digitally
Manuscript received June 26, 1998.
A. Zadok, H. Shalom, and M. Tur are with the Faculty of Engineering,
Tel-Aviv University, Tel-Aviv, Israel.
W. D. Cornwell and I. Andonovic is with the Department of Electronic
and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW,
Scotland, U.K.
Publisher Item Identifier S 1041-1135(98)08760-6.
modulated laser at rates of several hundred megabits-persecond would be of the same order as the data rate, and will
not be influenced by thermal chirp. In a recent experiment,
however, chirp of five different DFB lasers was characterized
using a high-resolution Mach–Zender interferometer, indicating for the first time the existence of much shorter chirp
time constants, of the order of 10–20 ns [14]. Such a short
time constant may lead to considerable spectral broadening of
directly modulated lasers, at bit rates as high as 622 Mb/s.
Chirp also causes a shift of the central optical frequency, as
a function of the bit rate.
This letter examines the effect of the short time constant on
the spectrum of a DFB laser, directly modulated by a random
bit sequence. Section II presents simulation results, Section III
displays the experimental results, and concluding remarks are
given in Section IV.
The impulse response of the thermal chirp is often stated
different time constants, associated with the
in terms of
various elements of the laser structure [6], [11], [14]
The step response of the thermal chirp would be of the same
form. The instantaneous optical frequency of the laser can be
obtained by applying an th-order digital filter, equivalent to
(1), to the input current waveform. This procedure was taken
ns and
for a MQW laser that is best described by
ns, with respective frequency shifts
GHz/mA and
GHz/mA. Fig. 1 shows the resulting
instantaneous frequency for a 32-bit sequence at three different
modulation rates: 5, 100, and 622 Mb/s. Zero bits are assumed
to carry no light, and the modulation current is 20 mA.
Fig. 1 suggests that thermal-like chirp should have two
effects on the spectrum of a DFB laser under random-sequence
direct modulation. 1) The central optical frequency
change with the bit rate. When the bit duration is longer
than the chirp time constants, the optical frequency moves
, resulting in a red shift of the
average frequency. On the other hand, for bit rates much
, no frequency shift is expected. 2) Chirp
faster than
broadens the spectrum of the modulated laser as the bit rate
slows down. Since the frequency shift associated with the short
1041–1135/98$10.00  1998 IEEE
Fig. 1. Simulated instantaneous optical frequency of a DFB laser along
a direct modulation sequence, at bit rates of 5 Mb/s (dashed curve), 100
Mb/s (dotted curve) and 622 Mb/s (solid curve). The modulating sequence is
displayed at the bottom of the figure. Modulation amplitude is 20 mA.
Fig. 2. Simulated optical spectrum for PRBS direct modulation, at bit rates
of 100 Mb/s (dashed curve), 300 Mb/s (dotted curve), and 640 Mb/s (solid
curve). Modulation current is 32 mA.
time constants of 10–20 ns is on the order of 200 MHz/mA
[14], chirp induced by a modulation current of 10–40 mA
should dominate the spectral linewidth even when the bit rate
is several hundred megabits per second.
In order to calculate the resulting optical spectrum we
express the complex field of the directly modulated laser as
is determined by the input modulation
where the power
is expressed as an integral
sequence, and the phase
calculated using (1).
of the instantaneous frequency
Phase noise and phase discontinuities when the laser is turned
off are neglected. Therefore, the power spectral density of
(2) incorporates the combined effect of both chirp and data
sequence, and produces the overall optical spectrum induced
by the specific direct modulation sequence. The obtained
spectral density can be perceived as a convolution of the data
AM spectrum and a related chirp induced FM term, and the
overall linewidth is approximately the sum of the data rate and
the width of chirp distribution.
Fig. 3. Simulated (solid curves) and experimental (dotted curves) spectra of
DFB lasers, PRBS direct modulation. (a) DFB 1, 10 mA, 144 Mb/s. (b) DFB
2, 32 mA, 622 Mb/s.
Spectral shifting and broadening is demonstrated in Fig. 2,
where the optical spectrum of the same laser is simulated for
a pseudorandom bit sequence (PRBS). The bit rates are 100,
300, and 600 Mb/s and the modulation current is 32 mA. The
full-width at half-maximum (FWHM) is 4.8, 3.1, and 2.4 GHz,
respectively, significantly broader than the data spectrum in all
three cases. The optical spectrum is broadened and shifted by
1.4 GHz as the bit rate slows down from 600 to 100 Mb/s.
The existence of short time constants suggests, therefore,
that the spectrum of directly modulated lasers is both shifted
and broadened by the nonadiabatic chirp, even for bit rates of
several hundred megabits per second.
The spectrum of two directly modulated DFB lasers was
measured under PRBS current modulation, using a scanning
Fabry–Perot interferometer. The impulse responses of the
tested lasers were previously determined experimentally in
terms of (1) [14], and the response parameters are summarized
in Table I.
The two lasers were tested using two similar experimental
setups. Due to equipment limitations, measurements over a
wide range of bit rates could not be performed at either
Fig. 3(a) shows the simulated and experimental spectra for
Laser 1, at a bit rate of 144 Mb/s and modulation current
of 10 mA. High-resolution interferometric measurements of
the optical frequency verified the absence of transient chirp
(the pulse rise and fall times were 2 ns). The effect of the
nonsquare pulse shape on the resulting chirp was simulated
and found to be negligible. The measured FWHM of 1.4 GHz
is in very good agreement with the predicted value of 1.2 GHz,
while the spectral width of the data sequence is of the order
of only 70 MHz. Fig. 3(b) refers to Laser 2, the one used
for Figs. 1 and 2, at 622 Mb/s and 32 mA modulation. Once
again, the measured FWHM of 1.85 GHz agrees reasonably
well with the simulated value of 2.4 GHz, although the overall
spectrum is not as broad as expected. The obtained width is
approximately three times larger than the data rate.
Both experiments indicate that the spectral width of a DFB
laser under direct modulation is dominated by thermal-like
chirp, and is much broader than the data bandwidth even at
bit rates up to 622 Mb/s.
The existence of thermal-like chirp with a 10–20 ns short
time constant is shown to be responsible for a significant
spectral broadening of DFB lasers under direct digital modulation. This resulting optical spectrum is broader that the
data bandwidth for bit rates of up to several hundred Mb/s.
The whole output spectrum is also expected to shift by
several gigahertz as a function of the bit rate. While this
broadening has negligible effect on applications dominated
by adiabatic chirp, such as frequency modulation in coherent
communication [6], [11], [14]–[19], it may greatly affect the
performance of direct detection communication systems [20],
[21]. Furthermore, the spectral broadening enables successful
radio-frequency filtering of interferometric phase noise, at bit
rates of up to several hundred megabits-per-second [22].
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