J.V. Moloney, A. Egan, C.Z. Ning, R.A. Indik
Index Keywords: semiconductor device modeling, semiconductor lasers, modulation/demodulation, laser resonators, electromagnetic propagation.
Abstract -- We provide the first comprehensive theoretical evidence for nonlinear space-time dynamical behavior which seriously degrades the performance of a monolithically integrated master oscillator power amplifier laser under direct current modulation of the master oscillator. A host of instabilities, reflecting dynamical behavior of different sections of the device, are possible. These instabilities are due to the combination of weak feedback from the Power Amplifier section of the device causing leakage into the Master Oscillator section, from the buildup of unsaturated carriers along the narrow edges of the expanding flare and differential saturation of the passive regions under the DBR grating sections.
Tapered amplifiers have been shown to be more resistant to filamentation than traditional broad-area devices. The MOPA device which integrates a master oscillator (MO) (with grating feedback to provide single-frequency output) and a tapered power amplifier (PA) was proposed[1] and experimentally realized[2]. This device has demonstrated single longitudinal mode and lateral mode operation within finite MO and PA current ranges. Experimental investigations have shown that near-diffraction-limited beams are possible to high power [2, 3, 4] and the quantum efficiency is generally around 60%.
Modulation of MOPAs is an important consideration in potential communications applications. Experimental investigations of integrated MOPAs under current modulation of the MO [5] have demonstrated some of the their advantages and limitations. The complex geometry of the MOPA laser makes in particularly susceptible to dynamic instabilities, even in the absence of current modulation[6]. By simply adjusting the bias current in the separately pumped MO or PA sections, the device can be shown to display sustained relaxation oscillations, multi-longitudinal mode and dynamic transverse filamentation instabilities. It is of critical importance therefore, to be able to quantitatively predict device performance under modulation.
The Beam Propagation method (BPM) has been the accepted approach to modeling wide aperture high power semiconductor laser devices. When applied to steady state analysis of Fabry Perot devices such as wide aperture semiconductor lasers, the method is essentially a nonlinear shooting technique. Convergence of the iteration scheme implies the existence of a stationary solution but it does not guarantee stability of that solution. Unfortunately, the BPM has recently been used to infer intrinsic dynamics of the laser[7, 8] when the iterations fail to converge.
In this letter, we apply a model that resolves the full spatiotemporal dynamics of an arbitrary geometry wide aperture, single or multi-section, edge emitter[9] to study current modulation of a MOPA device. It has been suggested that this device has the attractive feature that the full MOPA power can be modulated with a 100 mW swing of the MO current[5]. We will show that many of the phenomena already observed experimentally, conspire to produce extremely complex spatiotemporal behavior when the MO section of the laser is modulated directly. These phenomena include a longitudinal mode hop in an isolated MO and spontaneous lasing of the PA section beyond some threshold current value.
Severe degradation of the modulated output can arise from different sources. At the high power end, when the PA current is below the transverse filamentation instability threshold of the device in the absence of modulation, there is severe degradation of the output due to a combination of transverse and longitudianl mode instabilities. This situation is particularly severe for lower frequencies where the PA can spontaneously lase during the off-cycle. Our studies suggest that the MOPA can be optimally modulated at frequencies close to the relaxation oscillation frequency of the MO i.e around 5 Ghz. The main problem that limits the modulated output power, is the spontaneous lasing of the PA section of the laser. As long as the PA section current is held above its threshold for lasing ( about 800 mA in the device modeled here), energy is apt to leak back into the MO, destroying the integrity of the whole device.
The counterpropagating wave model, described in detail elsewhere [9], is reproduced below,
Here 
, 
are fitted induced polarization terms,
are the forward and backward traveling electric fields and N is
the total carrier density. Parameter values for the MOPA are taken
from reference [6]; the output facet reflectivity is 
here. The total current I(x,z) consists of a section
pumping the MO and a flared section pumping the PA. Here the current
applied to the MO can be expressed as
,
where 
is the DC or mean value of the current, 
is the
MO threshold current, 
is the repetition frequency of the applied
modulation signal and m is the modulation depth. We use
sinusoidal modulation and relaxation oscillation frequency is 
GHz when 
mA. The general features observed
here should be insensitive to the details of the modulation and we could
easily implement a square-wave modulation for instance.
Figure 1 shows the total modulated output power of the device at
relatively low PA currents spanning the threshold for spontaneous
lasing of the PA itself. Figure 1d shows a clean near-sinusoidal
modulation signal when 
at a modulation depth of 
and a frequency 
. This is the expected behavior of
a conventional diode when subjected to an external modulation signal
and a change of modulation depth or frequency leads to expected
behavior. Simply increasing the PA current to the PA lasing threshold
( 
leads to a complete deterioration of the modulated
signal. The output of the MOPA shows sustained relaxation oscillations
which appear weakly modulated at a 
modulation depth (Figure 1c) and as
intermittant bursts at modulation depth (Figure 1b). The only
evidence of
the external modulation is the periodic repetition of the relaxation
oscillation bursts. Just above the PA lasing threshold, the same
complex dynamics prevail. At 
and close to the relaxation
oscillation resonance frequency ( 
), one still sees
complicated but sustained bursts at the relaxation oscillation
frequency (Figure 1a). Here the device is switching between DC and modulated
operation in a very complicated fashion. Clearly the usual small and
large signal type analysis is inapplicable to the situations depicted
in Figure 1a-c. The transverse profile remains
clean and the far-field output is close to diffraction limited.
At the high PA current end but at about 0.25A below the onset of
transverse dynamic filamentation ( 
), we still observe
transverse filamentation when the MO is modulated. Here there is a
complete spatiotemporal breakdown of the modulated output. Reducing
the PA current to 
avoids transverse filamentation
instabilities and offers the possibility of useful modulation with
near-diffraction limited far-fields. Figure 2 succinctly presents the
salient features of the modulation response as a function of varying
modulation frequency at 
modulation depth. We have also
explored other modulation depths and these exhibit similar qualitative
dynamical characteristics to what is shown in Figure 2. Close to the
resonance frequency ( 
), the output signal is
relatively clean but very strongly distorted from a sinusoidal
shape (Figure 2a). At progressively lower modulation frequencies, the
PA tends to want to spontaneously lase as we are well above its
threshold for lasing. The sequence in Figure 2b-d shows a progressive
degradation in the signal quality and ultimately, complete breakdown
(Figure 2d). The strong kink in the signal at 
is a
signature that the PA is trying to lase when the MO current is low.
The characteristic time for the PA to switch on when 
is
. At 
, we see the first evidence of
multi-longitudinal mode beating appearing on the envelope of the
strongly distorted output waveform (Figure 2c). This fine structure is
well-resolved and corresponds to longitudinal mode beating ( 
) within the MO
section of the MOPA device. This destabilization comes from a
combination of weak optical feedback from the PA output facet and the
buildup of unsaturated carriers near the narrow edge of the PA section
[6]. Finally at a low modulation frequency
( ), the output degrades into a complicated
chaotic signal. Figure 2d shows random bursts of longitudinal mode
beating, switching back and forth between longitudinal mode beats
within the MO (dark shading) and the PA (light shading) sections. The
beat frequency in the PA is about 10 GHz.
In summary, we have shown that the monolithically integrated nature of the MFA-MOPA device makes it susceptible to a host of instabilities that severely degrades its performance under current modulation. Sources of the diverse instabilities highlighted here arise from weak feedback from the PA output facet, buildup of unsaturated carriers at the edges of the linearly expanding flare and differing degrees of saturation of the unpumped regions under the DBR gratings.
