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The spatiotemporal dynamics of linearly and trumpet flared high brightness semiconductor lasers are compared and contrasted using a comprehensive model built up from the microscopic physics. While both devices display complex multi longitudinal mode dynamics, the trumpet flared device is less susceptible to transverse filamentation instabilities and, hence, displays superior time-averaged far-field imaging properties.
©1998 Optical Society of America
1. Introduction
Wide aperture semiconductor lasers, designed to deliver output powers exceeding 1 Watt, are extremely complex nonlinear dynamical systems displaying weakly turbulent near-field outputs. By weak turbulence, we mean persistent random intensity bursts throughout the device which leads to random beam steering in the far-field. These dynamic intensity filaments lead to severe broadening of the far-field, when time-averaged and, generate local hot-spots which can damage the output facet. High power, high brightness (single longitudinal mode diffraction limited) semiconductor lasers are of great importance because of their wide applications potential ranging from space based communications to fiber laser pump sources. Two laser device geometries have proved partially successful so far: those based on the utilization of tapered gain regions (for a full review see Ref. 1) and so-called Alpha DFB devices. Tapered amplifier sections reduce the possibility that the local intensity reaches filamentation or damage threshold [2]. A nominally single mode laser and amplifier system has been integrated in a single device: the Monolithically Flared Amplifier-Master Oscillator Power Amplfier (MFA-MOPA) device [3]. Longitudinal mode filtering is provided by DFB grating distributed reflectors at each end of the narrow stripe master oscillator section. This laser is extremely complicated and expensive to fabricate. Even though the output facet is antireflection coated (R ≈ 0.05% - 0.1%), the flared amplifier structure in the MFA-MOPA can lase at high pumping levels. One can therefore expect persistent multi-longitudinal mode dynamics at these pumping levels. The fact that there are a large number of applications that do not require strict CW output power means that these lasers have great potential if a simple way can be found to to maintain near-diffraction limited outputs (i.e control the transverse filamentary behavior) to high current pump levels.
Introducing an aperture for the backward field (“cavity spoilers,”[1]) controls the unstable transverse filamentary behavior to a degree: more of the far field is concentrated in a single lobe but there is still a lot of energy at wider angles. The addition of a long thin gain section to the narrow end of the laser to act as a spatial (“mode”) filter seems to work better [4] although it is difficult to compare pulsed with continous operation.
Of critical importance is the need to minimize the build-up of unsaturated carrers within the lasing structure, thereby avoiding strong amplification of backward reflected fields arising either from finite PA facet reflectivities or spurious external back reflections. In this letter, we study the full spatio-temporal dynamics of flared laser structures with the goal of maintaining good far-field imaging properties even though the device may run in multiple longitudinal modes. We find that a nonlinear taper shape of the type used for an MFA-MOPA structure in Ref. 5 provides both a gain shape that the forward field fills as is expands, leaving less uneven gain for the backward field and some spatial filtering. This combination of effects increases the transverse instability threshold and increases the diffraction limited output power almost by a factor of three over a linear taper laser.
2. Theory
Our theoretical model resolves the multi-longitudinal and transverse mode dynamics and is built on a self-consistent microscopic physics basis (for further details see Refs. 6,7). The model has been extensively tested and has shown good agreement with more complicated many body theories. Basically, the semiconductor gain/absorption and refractive index spectra extracted from a many-body computation of the semiconductor optical response function, are fitted with a background term and a series of Lorentzians whose width, height, and peak position can all vary with carrier density. In our case just the backgound index variation and a single Lorentzian with variable gain peak height suffices to capture the behaviour of the gain around the operating frequencies of the laser. We neglect the small shifts in gain peak and width. The counterpropagating optical fields (F(x, z, t), B(x, z, t)) and total carrier density (N(x, z, t)) evolve throughout the laser structure according to the following coupled partial differential equations.
Figure 1. Shaded surface contrast of the linear and nonlinear (trumpet) flare current pump profiles.
The polarization dynamics (PF,PB) is extracted from the Lorentzian fit to the microscopic gain/index and provides the all-important gain discrimination between many competing longitudinal modes. The coefficients a 1(N), a 4(N), and δ are fit parameters. We use the full manybody semiconductor Bloch equations to compute the optical gain and refractive index spectra for a single 90Å strained In0.19Ga0.81As/GaAs quantum well emitting at a wavelength of about 980nm.
The shape of the two current pump stripes (j(x, z)) can be seen in Fig. 1. The nonlinear (trumpet) flare is overlaid on the linear flare. Each device is 2mm long. The left narrow end is 2μ wide with an intensity reflection coefficient RL = 0.35 and the right open end is 200μ wide with RR = 0.001.
We integrate these equations employing a split operator technique that combines a Fourier transform method to solve the diffraction and diffusion parts and a scheme due to Fleck [8] to deal with the plane wave (z, t) part of the equations. The equations were integrated on a grid 256×151 (nx×nz) and the time step we used was 0.2046ps.
3. Results
We now compare the spatiotemporal behavior of the lasers with linear and nonlinearly tapered current stripes. The complicated multi-longitudinal mode dynamics of these lasers, although resolved in our simulations, is not the central issue here. Rather we wish to see if the time averaged output produces near diffraction limited far-field outputs. The gain band width is very large and with the output facet antireflection coated, the cavity has a very low finess. This allows many longitudinal modes to oscillate and beat together leading to very complicated short time scale temporal dynamics. The spectrum shows a large number of very well defined modes (ie, narrow peaks separated by the free spectral range) until the onset of transverse filamentation dynamics in the laser when these peaks broaden significantly. Typically we see tens of longitudinal modes oscillating together and we would see more if we used a finer longitudinal space and time resolution.
Figure 2. The near field intensity of both nonlinear (left) and linear (right) flares for pump currents of 1A, 2A, 3A, 4A and 5A time averaged over a period of 2ns. The nonlinear flare has the same shape at any instant in time whereas in the linear flare, at 3A and beyond (dashed lines), the transverse profile begins to evolve significantly (even the 2ns time average evolves). At 4A and 5A the nonlinear flare output is slightly asymmetric, whether it emits more strongly on the left or the right depends on initial condition.
The time-averaged (over 2 ns) near-field output intensity of the laser at the output facet (see Fig. 2) at differing pump levels of 1A, 2A, 3A and 4A displays significant differences between the two flare geometries. Changes in the near field of the nonlinear taper laser are moderate in comparison to those of the linear taper laser. In fact studying the time evolution of the near fields one sees that the linear taper laser near field wobbles for all currents and the time average is not constant for pump currents greater than 2A. In contrast, although the total intensity of the nonlinear taper laser oscillates up and down due to the longitudinal mode dynamics, there is no noticeable change in the shape until we reach pump levels of 5A where there are some minor changes in the central lobe which do not manifest themselves in the time average.
The overall beam quality is examined by looking at the far field divergence of the beam and estimating how close to diffraction-limited it is. To collimate the diverging beam from the expanding flare, we choose a lens of a suitable radius of curvature. For each pump current there is an optimal focal length of lens that will give the best collimation. We choose a focal length that optimizes the output beam quality for as large a range of pumping as possible. The far fields calculated in this manner are shown in Fig. 3. Again there is clear evidence that the nonlinear taper laser outperforms the linear taper laser. In the case of the nonlinear taper laser the majority of the far field intensity remains within the central lobe and only at 5A pumping do the side lobes have power comparable to the central lobe. In contrast the far field of the linear taper laser has apreciable side lobes and beyond 2A pumping one cannot distinguish a central lobe.
Figure 3. The corrected far field intensity of both nonlinear (left) and linear (right) flares for pump currents of 1A, 2A, 3A, 4A and 5A time averaged over a period of 2ns. The nonlinear flare far field remains well collimated with less than 0.5° of divergence up to 4A whereas the linear flare beam quality degrades rapidly as the power increases. The far fields are calculated using a fixed focal length lens: 0.48mm for the nonlinear flare and 0.8mm for the linear flare.
Clear evidence of the better control of the backward field in the nonlinear taper laser can be seen in Fig. 4. Here we plot the carrier density and backward fields for both devices just before the linear flare becomes unstable. As the forward field is much larger than the backward field everywhere except at the narrow end of each flare, we can consider the shape of the carrier density as being dictated by the forward field. Low carrier density means high forward field except near the narrowest regions where carrier diffusion spreads, and consequently reduces, the carrier density.
The large carrier density regions at the side of the linear taper indicate that the field does not fill the gain region. Unsaturated carriers at the edges cause the backward field to buildup along these edges. This has two adverse effects. The narrow end of the linear flare will be a less effective mode filter: it acts like an aperture for the backward field as there is absorption outside the gain region. The field propagating down the the edges also penetrates into the unpumped regions making them more transparent and the “aperture” less effective.
In contrast the nonlinear taper shows a good match between the expanding forward field and the shape of the flare. This means that the backward field is almost purely single lobed, travelling up the centre of the taper. The contrast between half maximum contours of the linear and nonlinear tapers is marked. There is still some slight channelling of the backward field down the edges of the taper as evidenced by the 90% contour. However, the long narrow section of the taper filters this out very effectively producing a clean single lobed field at the back facet.
Figure 4. An instantaneous comparison of the carrier density (top) and backward field intensity (bottom) distributions for a nonlinear (left) and linear (right) flare laser. Dark shading signifies high and light shading, low values. The contours in the density plots correspond to Nth and 0.1Nth, where Nth is the threshold carrier density. The backward field contours correspond to 90% of maximum and half-maximum.
4. Conclusions
We have shown that a nonlinear taper laser performs far better than a linear taper laser. The two key features giving this performance enhancement are the tailoring of the shape of the gain to ensure that the expanding field always fills the gain region and the longer narrow section able to filter out transverse structure. Both lasers always show whole beam oscillations consistent with longitudinal mode beating but the nonlinear taper laser is much less susceptable to transverse instability. The nonlinear taper laser shows very good beam quality. It is very close to diffraction limited with a typical FWHM of 0.35° for the central lobe (to be compared with the ideal 0.84λ/D=0.26°).
Acknowledgement
The authors acknowledge support from the U.S. Air Force Office of Scientific Research under grants AFOSR F49620-97-1-0002, F49620-97-0142, an NSF international collaborative research grant INT 9404732, and Forbairt (Irish Science Research Council), Ireland.
References
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