Quantum Well GaAs/GaAlAs Lasers

Applications of the model for a typical structure, a conventional double heterostructure, and an advanced structure are presented. The gain flat state that single quantum well lasers exhibit near the beginning of the second quantized state lasing is introduced.

Terminology and Background

The energy scale for holes in the valence band is therefore inverted relative to the energy scale for the electrons in the conduction band; this term is consistently used in this thesis. In the case of injection lasers, the density of electrons and holes in the active region is made so great that inversion is achieved between the band edges.

Outline

The requirement for carrier confinement and optical mode guidance via material-dependent scaling laws is examined. It is clarified that quantum well lasers are superior to double heterostructure lasers in providing wide gain spectrum due to pump current density.

Units

In most cases, it is desirable to have the quantum well in the center of the optical mode. The meaning of the curve (r c, tc) is that it specifies the part of the two-dimensional parameter space O < r < 1, 0 < t ~ 1 of the composite cavity, where continuous tuning is impossible (t < r).

Theory of Unstable-Resonator Semiconductor Lasers

Geometric Theory, Ray Tracing

An example of an unstable resonator geometry is shown in Figure 2.1 along with a diagram showing the entire range of possible unstable resonators. Consequently, the fraction of energy remaining in the cold cavity (assuming full transparency and total reflection) after a round trip is .

Figure 2.1 (a) Confinement diagram for optical resonators [Ref. 2, page 1364]. The shaded part of the parameter space presents unstable resonators (high loss)

Quantum Efficiency and Optimized Resonator Design

The average intensity is considered dumped and laterally lost, which does not contribute to the output of the unstable-resonator laser. Q is the sum of the anti-propagating optical power per width at the location of interest.

Figure 2.2 ( a) Explanation of treatment of lateral losses in unstable-resonator lasers

Conclusion

The shape of the gain spectrum under this pumping condition is specific to quantum well lasers. This is a parameter directly related to the inversion established in the gain region of the laser.

Figure 3.1 (a) Schematic of the layer structure. (b) Top view of the laser with geometrical ray description of the unstable-resonator semiconductor laser

Experiments with Unstable-Resonator Semiconductor Lasers

Focusing Properties of Unstable-Resonator Semiconductor Lasers

After reflection on the cylindrical surface, the depth of the virtual source point is obtained in the small-angle approximation [9]: D = double slit in the image plane of the microscope objective with respect to the laser aspect; M1 , M2 = plane mirrors;.

Figure 3.2 Schematic of near-field ( a) and virtual-source point (b) measurement or an unstable-resonator semiconductor laser

Coherence Properties of Unstable-Resonator Semiconductor Lasers

At higher currents, the feedback effect dominates and the laser output exhibits the mode characteristics of the unstable resonator. Figure 9.,tb and S.4c are examples of interference patterns recorded with an edge visibility function of approx. 0.6.

Conclusion

A high degree of spatial coherence was observed over the entire spatial extent of the laser output, independent of lateral position. When the injection current was increased beyond 3 · Ith, feature visibility decreased, presumably indicating the onset of higher-order modes.

Spectrally resolved near-field, high-resolution far-field and coherence measurements showed lateral modes with nearly planar phase fronts across most of the device widths.

Introduction

The transverse profile of the aluminum concentration of the GaAlAs/GaAs structure is shown together with its refractive index in the vicinity of the laser wavelength. All of the above approaches involve increased processing complexity and suffer from a variety of specific problems.

Figure 4.1 Single-quantum-well, graded-index wave-guide, separate-confinement heterostructure (SQW-GRINSCH) as used in these experiments

Design and Basic Performance

In Figure 4.2, the pulsed, biased output power versus driving current of the wide-area laser with a single quantum well is shown. This high external quantum efficiency is a combined result of the low threshold current density a.VJ.cl and the very high differential quantum efficiency.

Figure 4.2 Optical output power against current under pulsed conditions (400 ns, 25 Hz) for a broad-area laser with a stripe width of 100 µ,m and a cavity length of 480 µm

Near- and Far-Field Pattern and Coherence

For currents starting at threshold and up to 15 times threshold, a differential quantum efficiency of 0.84 is derived considering the symmetric resonator, resulting in a maximum absolute quantum efficiency of 0. A typical interference pattern from two near-field point sources around 50 µm apart is shown in figure 4.4.

Figure 4.3 Far-field pattern parallel to the junction plane for a 100 µm-wide, broad-area laser at two different pump currents as indicated

Spectrally Resolved Near-Field Pattern

Several of these lateral modes do not show high intensity over more than a fraction of the width of the active region. In this case, the narrow, far-field contribution may be off-center, indicating a slope in the nearly flat phase front of the contributing lateral modes.

Figure 4.5 Spectrally resolved near-field intensity distribution for I = 1.6 • Ith

Conclusions

The lower half of the picture also shows a mode whose lateral width makes it a candidate for a very narrow, far-field distribution, if its phase is nearly flat and the other modes do not make its contribution subdominant. As can be seen from the near fields, the mode is not specially located on a small portion of the width of the device, but rather spans the entire width, which is.

The scaling nature of the density function of states is represented by the Heaviside function H. This electromagnetic mode has a spatial extent that is large compared to the size of the quantum well.

Figure 5.1 Measured lasing wavelength versus modal gain (derived from measured length via in Equation 5.1) shown in comparison to predictions of the simple model

Second Quantized State Lasing of Single-Quantum-Well

Experimental Approach

In Figure 5.1, the measured wavelength of the first mode to laser (at threshold) is shown as a function of the modal gain constant. The vertical bar indicates the distribution of the data, while the horizontal bar gives the mean value.

Figure 5.2 Schematic of a quantum well and its confined states causing a staircase density-of-states function

Basic Theoretical Approach

Part (a) shows states of high pump density, part (b) of very high pump density, leading to the gain maximum at the onset energy of the second quantized state. The broken curve follows the maximum gain of the spectra with varying quasi-Fermi energy.

Figure 5.3 Gain spectra as computed using Equation (5.2} from the shown electron density

Refined Theoretical Approach

Consequently, the laser wavelength must shift to shorter wavelengths as the required gain (i.e., cavity loss) increases. By tracing the peak of the gain spectrum (5,4) for varying quasi-Fermi energies, as shown in Figure 5.4, the laser wavelength as a function of modal gain is obtained in this model.

Threshold Current Density as a Function of Required Gain

The upper curve in Figure 5.4 shows the upper limit of the available gain as a function of the photon energy, that is, the value that ,s: could result from an infinite pump current in this model. It should be noted that the very high threshold current densities limit measurements well above the threshold.

Figure 5.5 Threshold current density versus lasing gain measurements. For expla- expla-nation, refer to text

Conclusion

Yariv: "Theory of Gain, Modulation Response, and Spectral Linewidth in AlGaAs Quantum Well Lasers." IEEE J. Weisbuch: "Threshold Current of Single Quantum Well Lasers: The Role of the Confining Layers." Appl.

Introduction

The two-dimensional density of states of the charge carriers and the effective width of the optical mode are identified as the relevant parameters for gain calculations. Basically, the quantum well laser is similar to the conventional double-heterostructure laser, except for the special effects of the very small layer thickness.

Eigensolutions of the Transverse Structure

The effective mass is a function of the Al concentration, which changes in the transverse direction into the double heterostructure or quantum well structure. In this thesis, the Al concentration is taken as a piecewise constant as a result of the stepwise representation of the Al concentration in the cross-section.

Figure 6.1 a. Overall transverse structure in the potential of the electrons

Static Density-of-States Function

This parameter is called the effective measure, meJJi will be used in this thesis most often in the form of a number, Me/ 1 ; the sum of the rest mass of the electron ( m,fl = Mefi · me). The starting energy of the Heaviside function is the eigenvalue of the one-dimensional problem.

Figure 6.2 Scale drawing of the dispersion relation of the parabolic band approxi- approxi-mation (as used in this thesis), k versus E

Effective Density-of-States Function

Second, the uncertainty introduced in the energy of the states is only reflected in the transition, not in the state density function. There are two additional mechanisms by which the efficiency of the density of states changes.

Figure 6.3 Effective density of states for a structure as in Figure 6.1. The smearing of the onset of the subbands is evident; the scale does not allow the effect of the outer parabolic structure on the density of states in the

Quasi-Fermi Levels and Selection Rules for Transitions

The two-dimensional density of occupied states (electrons in the conduction as well as holes in the valence band) is found by integration over energy of the effective. The negative value indicates that the Fermi energy of the conduction band is actually in the band gap.

Figure 6.5 Effective density of state for a single quantum-well structure (Scaled from Figure 6.3 by a factor of 42)

Theory of the Gain Spectrum of Semiconductor Lasers

The derivation of the gain is based on relating the density of subband transitions of quantum well structures to the photon density. Below, the modal gain of quantum well lasers is derived directly from the Einstein coefficient by relating the energy density of the transitions to the photon density.

Appendix

The local behavior given in equation 6.30 expresses the excess of the eigenvalue above the potential, and fi(z) and h(z) determine the value of the phase density, that is, the rate at which the phase progresses with a change of position as long as E > P(z). Assigning a zero phase to the outside of the cladding layer results in an integrated phase of n · 1r I /2 at the svmmetrv olan.

The distinct onset of sub-bands in the quantum well laser allows for more than one local maximum in the gain spectrum. In Figure 8.5, the left pole region corresponds to the case of dominant crystal face reflection (t < r) and hence non-continuous tuning.

Figure 1.1 The inner structure of the parabolic-graded index, single-quantum-well laser as used for the numerical calculations

Gain Calculations of Semiconductor Lasers

Numerical Results of the Gain Spectrum Model

Comparison of Quantum-Confined Structures

The density of carriers for transparency at the starting energy of the subbands is one of the key parameters of the laser medium. The ratio gives the effective asymmetry of the valence band with respect to the conduction band.

Table 1.1 Comparison of GaAs/GaAlAs lasers with different confinement struc- struc-tures leading to dimensionalities from three to zero

Figure of Merit of Quantum-Well Size

For the given effective mass of the heavy hole, room temperature and the figure of merit of 1, the width of the well is 87.5 A (about 90 A). Substituting the effective mass of the electron for the heavy hole in Equation 7.6 results in a width of 209 A.

Conventional Double-Heterostructure Laser

Direct bandgap material requires the Al concentration to be less than 0.42 and therefore limits the depth of the quantum well. Also, the region of the inner transition structure next to the quantum well must also be of direct bandgap material.

Figure 7.6 Gain spectra of bulk GaAs as it is effective in conventional, double- double-heterostructure lasers

Conclusion

A single structure for optical guidance and electron confinement, as used in traditional double heterostructure lasers, is significantly mismatched. The improved performance of single quantum well lasers over conventional double heterostructure lasers and in many cases multi-quantum well lasers has not yet led to dominance of this structure in the commercial laser market.

Quantum well lasers are shown to exhibit flattened broadband gain spectra at a specific pump condition. The possible tuning range of double-heterostructure lasers is compared with that of quantum well lasers.

Introduction

Experimentally, the flattened gain spectrum of quantum well lasers is demonstrated by broadband tuning in a grating-tuned external cavity. This chapter shows the existence of a flattened gain spectrum in quantum well media under proper pumping.

Figure 8.1 Computed gain spectra of a single-quantum-well laser under various pumping strengths

Gain-Flattened Condition of Quantum-Well Lasers

With increased separation, the spacing between the two maxima increases and can become a practical limiting factor for increasing the width of the flattened gain region in single quantum well lasers. The dip depth in the gain spectrum can be reduced by using a multi-quantum well structure with a slightly different well width.

Figure 8.2 Schematic of ( a) the external resonator configuration, and (b) the two main contributing beams for the rear side reflectivity

Tuning of Uncoated Crystal Cavities

In (b) the expanded part of the spectrum is shown and the 39 wavelengths where the phase condition equation 8.4 is satisfied are marked with vertical dashed lines. In this section, only operating conditions close to the crystal cavity resonance are described.

Figure 8.3 Computed phase modulo 21r and gain requirement of the composite cavity laser tuned to a crystal cavity resonance

Continuous Tuning

Using s = -1 in the case of t > r results in constructive interference with a round trip to the external cavity due to the reflection coefficient - r. The case corresponding to the round-trip phase condition with the crystal cavity, Figure 8.6a, results in a minimum gain requirement of 48.5 c:n of.

Figure 8.5 Computed gain requirement of the composite cavity laser as a function of external-resonator transmission coefficient for three values of facet reflectivity:

Width of Spectral Tuning Range

The quantum well laser operates at a shorter wavelength and the detuning region as a function of pump power exhibits a structure caused by the subbands of the individual quantized states. Apart from these differences, the tuning ranges of the two types of semiconductor lasers.

Figure 8.9 Spectral tuning range of (a) conventional double heterostructure and (b) single-quantum-well laser as a function of band filling (refer to text for expla-nation)

Broadband Tuning

The quantum well laser exhibits only a moderately (less than or equal to 25%) larger tuning range near the gain-flattened state. The practical issue is that high current densities are undesirable; it is this limitation that determines the superiority of the quantum well laser.