Quantum design of semiconductor active materials: laser and amplifier applications

Transcription

1 24 Laser & Photon. Rev. 1, No. 1, (2007) / DOI /lpor Abstract: We present an overview of a novel first-principles quantum approach to designing and optimizing semiconductor quantum-well material systems for target wavelengths. Using these microscopic inputs as basic building blocks we predict the light-current (LI) characteristic for a low power InGaPAs ridge laser without having to use adjustable fit parameters. Finally we employ these microscopic inputs to develop sophisticated simulation capabilities for designing and optimizing end packaged high power laser structures. As an explicit example of the latter, we consider the design of a vertical external cavity semiconductor laser (VECSEL). Experimental (circles and squares) and theoretical (solid lines) photoluminescence (green/blue) and modal gain (black/red) for a 5-nm wide InGaAs quantum well sandwiched between GaAs barriers Quantum design of semiconductor active materials: laser and amplifier applications Jerome V. Moloney 1,,Jörg Hader 1, and Stephan W. Koch 2, 1 Nonlinear Control Strategies Inc 5669 N Oracle Rd, Suite 2201 Tucson, AZ 85704, USA 2 Department of Physics and Material Sciences Center Philipps-Universität Marburg Renthof 5, Marburg, Germany Received: 22 December 2006, Accepted (revised version): 4 January 2007 Published online: 22 January 2007 Key words: semiconductor lasers, microscopic modelling, quantum-well lasers, gain spectra, photo luminescence, VECSEL (vertical external cavity surface emitting lasers) PACS: Px, Ap, De, Be 1. Introduction Semiconductor amplifiers and lasers are pervasive as critical components in modern day technologies spanning low to high power applications [1, 8, 9, 11, 43, 45, 48]. The design and optimization of virtually every operational aspect of a semiconductor laser or amplifier requires a quantitative knowledge of the semiconductor material optical response. Important ingredients of the optical material properties are J.V. Moloney and J. Hader are also with the Arizona Center for Mathematical Sciences and the College of Optical Sciences, University of Arizona, Tucson AZ 85721, USA. absorption/gain and refractive index, as well as radiative and nonradiative recombination processes. All of these quantities critically influence semiconductor amplifier or laser performance. Static properties such as threshold, slope efficiency, gain saturation, emission wavelength etc and dynamic properties including modulation response/ bandwidth, gain switching, mode-locking are cases in point. With very few exceptions, current semiconductor amplifier or laser design and modeling strategies involves a topdown approach whereby important macroscopic influences such as electrical and thermal transport within the complex semiconductor heterostructure are modeled with sophisticated packaged software tools [10, 21, 39 41]. The Corresponding author: stephan.w.koch@physik.uni-marburg.de

2 Laser & Photon. Rev. 1, No. 1 (2007) 25 Achilles Heel of these approaches lies in the ad hoc manner in which they treat the semiconductor optical response for the most part the above material properties are represented by phenomenological models that rely on external input which at best can be extracted from prior experimentally measured data. For example the optical gain is usually represented by a linear gain model with gain saturation included and the current losses by individual defect, radiative (spontaneous) and Auger recombination parameterizations. Clearly, such an approach lacks almost entirely any predictive capability. For example, if one wants to design a new active structure optimized for a very different wavelength possibly using a different material combination, one needs generally unavailable input from experimentally measured data for that novel structure. Semiconductor wafer growth can now produce heterostructures of very high quality with stoichiometrically correct growth of individual mono-layers. Despite these significant advances in modern growth technologies, a critical void remains in predicting the performance of final packaged functional amplifier or laser devices. The lack of predictive semiconductor device design and growth monitoring capability can be traced to the extreme complexity of calculating the above semiconductor optical response from basic principles. The culmination of a series of important research breakthroughs over the past decade on the systematic calculation of semiconductor optical properties recently has led to the first ever prediction of an end-packaged semiconductor multiple quantum well (MQW) laser device performance without resorting to the use of adjustable fit parameters [16]. Now critical ingredients such as absorption/gain and refractive index (α-factor), spontaneous and Auger recombination rates can be computed for a wide range of material systems. The systematic optimization of these systems and the potential cost savings of being able to fast-track to a final optimized semiconductor optical amplifier (SOA) or semiconductor laser (SL) structure for a targeted wavelength in very few, ideally a single wafer growth cycle promises to have a wide economic impact across all semiconductor laser technologies. This has to be contrasted with current practice typically involving costly and time consuming multiple wafer growth/re-growth and packaging cycles before finalizing on a commercially feasible end product. At the end, one never knows whether the structure is truly optimal. This paper will review the key breakthroughs made in the microscopic many-body approach to quantitatively calculating all of the above important ingredients of the semiconductor optical response of an active structure comprising one or more quantum wells. We will provide illustrative examples of a bottom up approach to designing final laser structures. The closed-loop approach will generally entail designing the initial semiconductor epitaxial (epi) structure for a targeted wavelength, followed by wafer growth accuracy and quality verification and finally prediction of the end laser device performance. Section 2 reviews the microscopic gain calculations for a range of material systems that generate light from the UV/Visible through mid-ir. All of these calculations have been validated by experimental measurements over the past decade giving us confidence in their predictive value. We then provide in Section 3, more recent results on calculations of the spontaneous (radiative) and Auger (non-radiative) recombination rates for the same material systems. These calculations have again been validated by experiment but there are limited experimental data available in this case. Having placed the critical semiconductor optical properties on a firm foundation we are now ready to carry out the first fully predictive closed-loop approach to designing a low power semiconductor edge emitting laser L-I characteristic without having to use adjustable fit parameters. An example of such a prediction for an InGaPAs 1.3 µm emitter is given in Section 4. Section 5 reviews a more ambitious and challenging first principles design of an optically-pumped vertical external cavity semiconductor laser (VECSEL) structure. The complexity here comes in designing an active semiconductor sub-cavity mirror that can be pumped by one or more external high power diode bars. The microscopic inputs must furnish accurate absorption values for the pump laser and gain at the signal wavelength. These devices are highly susceptible to thermal shut-off requiring a combination of microscopic inputs and full-scale device simulation. We end this section by highlighting a time domain VECSEL simulator based on a spatial digital filter that allows us to accurately resolve the broad bandwidth dynamical interactions within the VEC- SEL device. A time domain application to a synchronouslypumped mode-locked VECSEL will be discussed. Section 6 addresses issues relating to modeling high power edge emitting semiconductor lasers. Here filamentation instabilities dominate and the full spatiotemporal evolution of the internal field (optical, carrier and temperature) must be quantified. The role of microscopic inputs will again be vital as realistic gain saturation and recombination losses will prove vital in providing a predictive capability. We briefly summarize the paper in Section 7 and point to future outlooks and prospects for this bottom-up approach. 2. Microscopic gain calculations for diverse material systems As the central part for any predictive modeling of semiconductor laser systems one needs a reliable model for the gain materials [7,20]. Such a model should not only be able to describe the absorption and gain spectra as functions of carrier density and temperature, but also yield the refractive index, the luminescence and the nonradiative (Auger)

3 26 J.V. Moloney et al.: Quantum design of semiconductor materials Figure 1 Computed bandstructure for a 6 nm wide In 0.9Ga 0.1As 0.53P 0.47 well between 10 nm wide In 0.88Ga 0.12As 0.26P 0.74 barriers and InP cladding layers. Black: Electron-bands. Red: Heavy hole bands. Blue: Light hole bands; Green: Split-off hole bands. Solid: Subbands confined in the well; Dashed: Bulk bands of the barrier material. losses. Ideally, the results of this model should be directly validated by detailed comparisons with quantitative experiments. All this can be achieved on the basis of a quantummechanical theory for the electron-hole system in the active semiconductor material. In order to base the calculations on as little empirical input as possible, we evaluate in a first step the relevant part of the material s bandstructure. This can be done at the level of the well-established k.p theory where only few input quantities, such as the Luttinger parameters and the band-offsets are needed [2,3,5,7]. In many cases, these inputs are known from independent investigations, allowing one to have a high level of confidence in the resulting bandstructure calculations. These calculations not only yield a detailed description of the relevant valence and conduction bands of the gain material, but one also obtains the corresponding electronic wavefunctions needed e.g. to evaluate the transition-dipole matrix elements that determine the relative strengths of the optically allowed interband transitions. An example for such a computed bandstructure for InGaPAs is shown in Fig. 1. Despite the great success of these bandstructure calculations for a wide range of material systems, one has to remember, however, that often for less well-studied and novel materials important input parameters may not be known with high precision. For example, in a quantum-well heterostructure the alignment between the conduction-band minima and valence-band maxima of quantum-well and barrier material can be uncertain. Sometimes the possibilities range even from the standard type-i alignment, where the conduction-band minimum is lower and the valenceband maximum is higher in the quantum well than in the barrier, to a type-ii alignment where the conduction-band minimum may be higher in the well than in the barrier. In such a situation, one needs feedback from independent experiments to reduce the level of uncertainty. The microscopically correct description of the interaction and dephasing processes lead to significant deviations from the Lorentzian lineshape that is well known from atomic systems. As one can see in the example in Fig. 2 (Left) the fully microscopic theory (solid lines) agrees very well with the experimental results (dots). On the other hand, the identical calculation, using the same bandstructure, carrier densities and Coulomb effects like excitonic resonances, Coulomb enhancement of the continuum absorption and bandgap renormalisation, and however, using a phenomenological dephasing time instead of the explicit calculation of the underlying microscopic scattering processes, shows characteristic deviations (see Fig. 2 Right). Not only does the gain lineshape, amplitude and spectral position not agree with the experiment, but the phenomenological dephasing approximation leads to the well-know artifact that absorption (negative gain) is predicted energetically below the true gain spectrum. This semiconductorlaser lineshape problem is well known in the literature and could be eliminated by the microscopic approach. On this basis it became possible for the first time to predict semiconductor laser gain spectra without ad hoc empirical fit parameters. After the bandstructure and the matrix elements are known, the next important step is to compute the optical material response. For this purpose, it is crucially important to correctly deal with the Coulomb interactions in the system of charge carriers. Furthermore, one has to keep in mind that electrons and holes are Fermionic quasi-particles, for which the Pauli exclusion principle states that each quantum state can be occupied at most by a single particle. This Pauli exclusion principle and the other many-body interaction effects are correctly included in the Semiconductor Bloch Equations [20, 31], which in a multi-band generalized form are by now the basis for most microscopic gain theories. For all optical systems, and in particular for semiconductor lasers it is crucial to properly model the phase destroying processes since these are responsible for the loss of optical coherence and for the spectral lineshapes. Based on the fundamentally new concept of excitation induced dephasing (EID) [20, 23] it became possible for the first time to systematically compute the temporal decay of the optical polarization for the relevant densities and excitation conditions. The EID concept replaces the old dogma of constant dephasing times through a microscopic theory that allows us to compute the density-, temperature-, and frequency-dependent decoherence rates.

4 Laser & Photon. Rev. 1, No. 1 (2007) 27 Figure 2 Left: Comparison of microscopically computed and experimentally measured gain spectra for an GaInAs QW as a function of increasing carrier density (bottom to top curves). Right: Same experimental data but using phenomenological dephasing times InGaAs/AlGas material system Semiconductor lasers based on InGaAs quantum wells sandwiched between AlGaAs barriers are well established and widely used commercially for emission in the range of 980 nm. All the relevant material and bandstructure parameters are well known. Figure 3 shows measured gain spectra for an InGaAs/AlGaAs material system in comparison with our theoretical analysis yielding very good agreement [13]. Encouraged by this good agreement, we felt confident to propose using our microscopic theory as a diagnostic tool for wafer testing Wafer-level diagnostics: from photoluminescence to gain After the epitaxial growth of semiconductor wafers, it is desirable to perform quantitative tests before the structure is moved on to further processing steps. In particular it would be helpful to know already at this wafer level, if and to which degree the amplification and gain characteristics of the structure satisfy the specified requirements. For this purpose, it is useful to employ photoluminescence measurements taken at relatively low excitation intensities which corresponds to low internal carrier densities in the excited semiconductor structure. Because of the low density, the luminescence does not provide direct information about the preferred wavelength at which the strongly pumped, inverted semiconductor material will lase. Here, the usual recipe is to assume that the laser wavelength will generally be shifted 6 10 nm down from the low density PL peak! However, such guesses are uncertain at best, often they are incorrect. To overcome this problem, we propose to use the fully microscopic theory which straightforwardly allows us to extract the high density material gain from Figure 3 Calculated gain spectra (red lines) for a structure with a 10 nm wide In 0.2Ga 0.8As quantum well between 85 nm wide Al xga 1 xas graded index barriers where the Aluminium concentration rises linearly from x =0.1 to x =0.6 with distance from the well. [13]. the same calculation as the low density luminescence. The first validation of the connection between low carrier density PL and high density inverted semiconductor gain was made possible via a collaboration between a semiconductor growth team at AFRL, the University of Arizona ACMS research group and an experimental group at the University of Bochum in Germany in 2002 [14]. The sequence of steps involved in this validation procedure provide the first demonstration of a closed-loop wafer level diagnostic coupled to gain measurement on the processed sample.

5 28 J.V. Moloney et al.: Quantum design of semiconductor materials Figure 4 Experimentally measured photoluminescence spectra (blue curves) at different low level illumination intensities and corresponding microscopically computed PL spectra for a series of increasing carrier densities. The latter were computed for the nominal In 20Ga 80As QW structure believed to have been grown by the experimentalists. Step 1. A structure with three InGaAs wells between GaAs barriers was grown by MBE. The measured photoluminescence spectra were provided at five excitation pump levels together with the nominal growth parameters i.e the well widths of 5 nm and Indium concentrations of 20%. The measured PL spectra are shown in blue in Fig. 4. Step 2. The photoluminescence spectra were then computed for the ideal semiconductor crystal using the microscopic theory and the nominal growth parameters supplied. The corresponding PL spectra are shown in red in Fig. 5. There is a clear misalignment between the theory and calculated PL spectra and, moreover, the theoretical spectra are somewhat narrower. The 6 nm shift in PL spectral peaks can be accounted for by changing the In concentration from the nominal value of 20% to about 19% or reducing the well width by about 1 nm. As the former is more likely, the Indium concentration was adjusted to 19% and the PL spectra re-calculated. Additionally, inevitable growth fluctuations during the MBE deposition lead to an inhomogeneous broadening of the PL peaks. By applying an inhomogeneous broadening of 16 mev (FWHM) we obtained the PL spectra shown in Fig. 5. The PL peaks are perfectly aligned and the relatively small degree of inhomogeneous broadening indicates a very high quality MBE growth. We emphasize that the Indium concentration adjustment and inhomogeneous spectral broadening are related to growth and not, theory uncertainties! Another issue that needs to be addressed here is the conversion from external pump laser intensity to internal sample carrier density. With this approach this relationship can be unambiguously tied down if PL measurements are provided for a few close by illumination intensities. If the ex- Figure 5 New comparison of the experimentally measured and microscopically calculated PL spectra when the nominal structure was adjusted to account for growth uncertainty. perimental PL is known only for one excitation density (in the low excitation regime), the approach can still be used to determine possible deviations from the nominal structural parameters and determine the inhomogeneous broadening. Only the exact correspondence between excitation power and intrinsic carrier density can no longer be established. This is due to the fact that in the limit of low excitation densities the PL-lineshape and spectral position become excitation independent and only the amplitude changes. It should be noted however, that in the experiment the excitation density has to be chosen high enough such that the measured PL is not dominated by the emission from defect states below the bandgap. Step 3. Now that we have verified the actual growth structure, we simply compute the inverted material gain for this structure. Importantly, it is vital to compute the gain for the homogeneously broadened epi structure and apply the calculated inhomogeneous broadening to the calculated gain spectra. To test the level of accuracy of the theoretical predictions, an experimental measurement of the gain from the exact same wafer was performed. The experimental gain curves (blue with dots) were found to lie on top of the theoretically computed gain spectra (see Fig. 6). This to our knowledge was the first time that an experimental measurement verified a prior theoretical calculation! The above sequence of steps provides a systematic predictive and adjustable-parameter-free methodology for characterization semiconductor wafer growth InGaPAs/InP material system There is sustained interest in suitable laser materials for the so-called telecommunication wavelengths, defined

6 Laser & Photon. Rev. 1, No. 1 (2007) 29 Figure 6 Comparison of microscopically computed gain spectra after adjustment for the offset in the structure with the experimentally measured gain spectra. The gain spectra were calculated prior to the experimental measurement. by the dispersion and absorption minima of silica fibers at 1.3 µm and 1.55 µm, respectively. Currently, the In- GaPAs/InP material system is the standard semiconductor laser telecoms source. High power broad area devices and diode bars emitting at these wavelengths are also being developed for eye-safe atmospheric communications. The difficulty of growing distributed Bragg reflectors (DBR) with these material systems has limited their application to surface emitting VCSEL structures. Both PL and gain spectra measurements were recently carried out on a4qw1.3µm InGaPAs sample cleaved from a wafer designed using the microscopic approach discussed above [16]. The end device was a low power ridge laser employed to demonstrate the first closed-loop design of a semiconductor laser that is free of fit parameters. The actual structure consisted of four 6 nm wide In 0.9 Ga 0.1 P 0.53 As 0.47 QWs separated by 10 nm wide barriers and surrounded by 40 nm wide cladding layers of In 0.88 Ga 0.12 P 0.26 As This active region is embedded in p- and n-doped InP layers. The internal electric field across the QWs due to the dopant layers had to be calculated as this modifies the PL spectra. PL spectra at different illumination intensities were measured on a sample cleaved from the wafer. Two modes of measurement were employed. In the first, the PL was measured using CW excitation and the corresponding spectra are shown on the left in Fig. 7. These measured data represent low quality PL but yet they were sufficient to validate wafer growth accuracy and quality. The theoretical PL extracted from this data are shown by the solid black curves in the figure. The second measurement with the femtosecond pulsed source show much cleaner measured PL spectra. The primary difference between the two measurement procedures is that CW illumination continually excites hot Figure 7 PL spectra measured with a CW illumination (Left picture) and a femtosecond pulsed laser source (Right picture). Once the wafer growth was validated, we easily obtain the gain from the same pre-generated database by simply extracting the data at carrier densities corresponding to the inverted semiconductor and applying the inhomogeneous broadening to these. These gain data are shown in Fig. 8. Here we did not proceed to measure gain spectra as we were confident in the robustness of our microscopic approach. In other words, measured low intensity PL are all we need to proceed to the end laser device performance prediction as we show in Section 4 below. carriers on the high-energy side the latter are evidenced by the long tails on the short wavelength side in the left picture. The pulsed data shown in Fig. 7 (Right) have no such tails as thermally excited carriers have relaxed and consequently this data is much cleaner. The nominal structure parameters were fed into the microscopic calculations and the latter had to be shifted by 23 nm corresponding to slightly smaller In or As composition in the grown sample. An inhomogeneous broadening of 14 mev (FWHM) was applied to the theoretical spectra to account for growth fluctuations. Overall these adjustments confirmed that the MBE grown wafer was of high quality Antimonide based material systems There is sustained interest in additional laser materials for 1.3 µm and 1.55 µm emission wavelengths. Also longer-wavelengths systems are important for eye-safe remote sensing and infra-red countermeasures applications. Promising candidates for this spectral range are the Antimonide containing material systems, such GaAsSb/GaAs as well as GaInAsSb and GaInSb heterostructures. Whereas light emission and lasing in the desired spectral ranges has been demonstrated, even though partially only under restricted conditions such as low temperatures, knowledge of the detailed material characteristics is still rather spotty. For example, for GaAs (1 x) Sb x embedded between GaAs for 0.3 <x<0.4 which is the relevant Sb content for emission at telecommunication wavelengths, the

7 30 J.V. Moloney et al.: Quantum design of semiconductor materials Figure 8 Microscopically computed gain spectra based on the InGaPAs PL measurement data of Fig. 7. The gain spectra are for increasing carrier density from bottom to top. band alignment between quantum well and barrier material could be determined only recently through detailed theoryexperiment comparisons [4]. Whereas there is little doubt that the holes are confined in the Ga(AsSb) layer, the electrons may or may not be, making the structure spatially direct (type I) or spatially indirect (type II), respectively. Through a detailed analysis of the lineshape of the modulation spectra in the full region of the confined interband transitions it could be concluded that the GaAsSb/GaAs system indeed shows a type II offset of approximately 40 mev in the conduction band. Using the extracted parameters then allows for a good agreement between experimentally measured and theoretically computed PL, as shown in Fig. 9 for the example of a7nmgaas 0.64 Sb 0.36 quantum well between Al 0.25 Ga 0.75 As barriers. This example shows the importance of the combination of a variety of different experimental techniques, here electroabsorption and PL, with detailed microscopic theory in order to arrive at reliable conclusions. More studies of this kind will be done in the future to fully explore the potential of the Sb-containing material system Metastable GaInNAs/GaAs material systems Progress in modern epitaxy makes it possible to grow material systems outside the range of thermodynamically stable compositions. Examples are the Nitrogen-containing In- GaAs/GaAs heterostructures where only a few percent of Nitrogen are incorporated. Besides its interesting growth aspects, these materials are promising candidates for laser applications since their unusual bandstructure allows for added design flexibility. The bandstructure peculiarities result form the fact that the Nitrogen in these material leads Figure 9 Experimentally measured photo luminescence spectra (signs) and calculated spectra (solid lines) at various temperatures (300 K, 250 K, 200 K, 150 K from left to right) for a structure witha7nmwide GaAs 0.64Sb 0.36 well between Al 0.25Ga 0.75Asbarriers (experimental results from G. Blume, P.J. Klar and G. Weiser, Department of Physics, Philipps University Marburg, Germany). Figure 10 Comparision of experimentally measured and microscopically computed gain spectra as a function of increasing carrier density (bottom to top). to an atomic like discrete state that anti-crosses with the conduction band [33]. This anti-crossing leads to a reduction in the bandgap of GaInNAs/GaAs in comparison to InGaAs/GaAs instead of the bandgap increase normally expected for the group-iii nitrides (see Section 2.5). As a consequence, the GaInNAs/GaAs material system is another promising candidate for a GaAs-based active material emitting at the telecommunication wavelengths. It is

8 Laser & Photon. Rev. 1, No. 1 (2007) 31 has been found particularly promising for applications in vertical cavity surface emitting devices. One reason for that is that the DBR-mirrors can be made from AlGaAs/GaAs layer stacks, avoiding the problems with low index contrast and high thermal resistivity that would be associated with InP-based DBR mirrors that have to be used for InGaAsPbased devices. Also, the anti-crossing mechanism leads to a reduced temperature dependence of the bandgap in this material, allowing for operation over a wider temperature range [22]. Detailed theory-experiment comparisons for different GaInNAs/GaAs systems have been done in the past few years. An example of a successful gain analysis is shown in Fig. 10. Despite these successes, there remain a number of unresolved problems concerning in particular the material properties of GaInNAs/GaAs. For example, there have been reports on Nitrogen clustering and other spatially inhomogeneous growth of these materials. Furthermore, it is not clear to which degree and in which range of parameters the anti-crossing model accurately describes all of the relevant bandstructure properties for the different possible material compositions. Clearly, it is expected to fail for very high Nitrogen concentrations, but no well-defined limits of the model s validity are currently available Wide gap group III nitrides For many laser applications, such as optical displays, optical data storage etc., it is desirable to extend the semiconductor laser frequency all the way across the optical region of the electromagnetic spectrum, also well into the UV. A material system of interest in this context are the so-called group-iii nitrides, such as InGaN/GaN quantum well systems [35 37]. Even though blue lasers and LEDs based on these materials are already commercially available, many other wavelengths are desirable and many material and growth issues of these systems are still unresolved. A number of theses problems are related to the fact, that basically no lattice matching substrates are commercially available so that the wide-gap nitride materials are often grown on materials like sapphire with the consequence that the large lattice mismatch results in significant strain and piezoelectric field effects. Furthermore, due to their relative novelty and restricted availability, very few reliable spectroscopic data are available for these materials, making it difficult to anchor our quantitative microscopic approach. A notable exception in this respect is a recent publication, [44], where the authors not only presented experimentally measured gain spectra for a wide bandgap InGaN/GaN quantum well laser but also included all the relevant structural information. On this basis, we attempted a microscopic modeling of the gain and, thus, to test our code for these materials [17]. Fig. 11 shows the resulting comparison between theoretical spectra and experimental data extracted from the pictures of the publication. The very good agreement is particularly remarkable, Figure 11 Red: Computed gain spectra for a structure containing 2 nm wide InGaN QWs between 6 nm wide GaN barriers. Black dots: Experimental data. Experimental data from [44], Theory from [17]. since the experimental data is given in absolute numbers. Thus, the match is not only with respect to the density dependent line shapes and shifts of the spectra, but also to the absolute heights, indicating that our theoretical model seems to be well capable of describing these wide-bandgap Nitride materials. The obtained theory-experiment agreement is encouraging given the fact that at the level used here, the theory doesn t include excitonic populations and strong phonon correlations, which could be expected to become important in these wide-gap materials. In order to obtain the agreement shown above, the theoretical spectra had to be broadened by a typical inhomogeneous broadening of 80 mev (FWHM). An overall spectral shift of ev had to be applied to all spectra. The most plausible reason for the latter is that the formula used for the bulk bandgap of In- GaN is not exactly correct. Although the band-gap formula nominally should describe the interaction free bandgap, it has probably not been corrected for the strong bandgap shift induced by electron-phonon interaction. Here we find that shift to virtually coincide with the value of 110 mev by which we have to shift our spectra in order to agree with the experiment. Published values for the bandgap parameter still adhere to a rather large uncertainty. All in all, it will be necessary to do more systematic work with detailed theory-experiment comparisons to increase the level of confidence in the modeling of these materials. 3. Radiative and nonradiative losses The microscopically computed photoluminescence and gain spectra discussed in Section 2 provide the critical foundation for designing a semiconductor active region for a

9 32 J.V. Moloney et al.: Quantum design of semiconductor materials targeted wavelength. At this level, they provide invaluable wafer analysis tools and direct feedback to the semiconductor laser designer and wafer grower on the accuracy and quality of the actual grown wafer. However to move to the next step and design a final semiconductor laser device we need to know the sources of current losses in the device law [1,8,9,11,43,45,48]. The widely accepted model for such losses is the well-known ABC whereby carrier density dependent current losses at a fixed temperature are represented by the formula: J Loss =AN+BN 2 +CN 3 The individual terms appearing on the right hand side of this equation have the following physical interpretation. The first term, linearly proportional to the carrier density N, accounts for defect recombination losses. Generally in high quality material growth, this term is not a significant player. The second term, quadratically dependent on carrier density N, accounts to radiative or spontaneous recombination losses. The last term, proportional to the carrier density cubed, accounts for nonradiative Auger losses. The following schematic provides a pictorial representation of these individual loss terms as well as some additional sources of loss. The non-capture, escape losses are even negligible in electrically-pumped semiconductor lasers except possibly for the case of shallow wells with weak carrier confinement. This law for current loss is globally accepted in the literature and the assumptions contained in it, have a profound influence of almost all operating characteristics of a semiconductor amplifier or laser. For example, such loss rates determine static properties such as laser threshold, slope efficiency, thermal rollover etc and intrinsic dynamic properties such as modulation rate/bandwidth, gain switching, mode-locking, feedback instabilities, intensity filaments in broad area emitters etc. The usual prescription in using this formula in laser modeling is to extract the A,B,C coefficients from fits to experimental measurements on known semiconductor samples. Usually, such measurements are carried out under low excitation conditions where the carrier (electrons and holes) approximately obey Boltzmann statistics. Moreover, these ABC coefficient values are then taken as fixed parameters for the semiconductor material system in question and are then applied to other lasers in the same material class. Microscopic calculations carried out at the same level of sophistication as the gain measurements, have demonstrated unequivocally that the empirical ABC formula becomes invalid for inverted semiconductor laser media [15]. This should not be too surprising given the fact that for high densities the Boltzmann approximation for the carrier distributions becomes invalid and one has to use the correct Fermi-Dirac statistics. However, the situation is even more complex however since the loss mechanisms additionally exhibit sensitive dependencies on the many-body interactions in the electron-hole plasma, on the QW widths etc. The end result is that the carrier dependencies assumed for spontaneous and Auger losses differ dramatically from the assumed dependence in the ABC law. Fig. 12 shows plots of the spontaneous current loss as a function of carrier density for three temperatures in a 6.4 nm GaInNAs quantum well laser emitting at 1.3 µm. At low carrier densities one observes the expected quadratic dependence of the spontaneous loss (linear in the normalized plot). At densities near and beyond the transparency one begins to see a strong deviation from the expected quadratic behavior and the current loss becomes approximately linearly dependent on carrier density beyond this point. The Schematic view of the dominant carrier loss processes in semiconductor laser structures. In the traditional semiconductor laser literature, the loss current J loss is often parametrized into a simple power law, where the linear term describes defect recombination, the quadratic term mimics spontaneous emission losses, the cubic term represents Auger losses and the term J rest accounts for carriers that are not trapped into the quantum wells, escape from the wells etc. The microscopic theory shows that these simple power-law approximations often often misrepresent the situation under typical laser conditions.

10 Laser & Photon. Rev. 1, No. 1 (2007) 33 Figure 12 Log-log plot of the microscopically computed spontaneous current losses scaled inversely with carrier density as a function of carrier density at three temperature. The normalization to carrier density ensures that the spontaneous current loss term in the ABC law is a linear function of carrier density as shown. The phenomenological BN 2 dependence is shown as a series of straight lines. Figure 13 Log-log plots of microscopically computed normalized Auger current losses at three different temperatures for a 6.4 nm GaInNAs QW at 1.3 µmanda4 2.5 nm InGaPAs QW at 1.5 µm. The Auger loss rates are divided by N 2 to yield a linear plot for the phenomenological CN 3 loss rates. phenomenological loss rates are extrapolated from the lowdensity values where they and the microscopic calculations show the expected quadratic density dependence. The lasing threshold density is indicated by open circles in the plots. The extrapolated BN 2 relation is way off for the inverted semiconductor medium. We note here that the often used Kubo-Martin-Schwinger (KMS) relation, which provides a simple integral-conversion of absorption/gain spectra, only gives good agreement for lineshapes at low densities but not too low temperatures. Usually KMS fails for densities near transparency and above (lasing threshold and above) and can be off by a factor or more than two or more. A proper microscopic calculation of spontaneous losses additionally requires quantization of the light field which then leads us to the evaluation of the Semiconductor Luminescence Equations [25,26]. The microscopic calculation of Auger processes is even more involved and has only recently been achieved. Details of the calculations are provided in [15]. Here we present microscopic calculations of both spontaneous and Auger process for three different material systems and show that these agree quantitatively with measured data, again without using adjustable fit-parameters. Fig. 13 shows log-log plots of the Auger loss rates for two material systems, a 1.3 µm 6.4 nm GaInNAs QW and a 1.5 µm nm InGaPAs material. The calculations are shown for three different temperatures. The phenomenological loss rates are again extrapolated from the microscopic low-density values. Strong deviations from the microscopically computed loss rates are again evident at and beyond transparency density. The data in Fig. 13 show the density dependent radiative spontaneous and non-radiative Auger loss rates at a given temperature. The temperature dependence of these rates is depicted in Fig. 14 [38] together with microscopic calculations for a 1.3 µm and a 1.5 µm InGaPAs laser. The theory-experiment comparison in Fig. 14 shows that the combined spontaneous and Auger currents agree quantitatively with the measured data over the broad temperature range indicated. The slight deviations at high temperature are probably due to internal heating of the device beyond the heat sink temperature The final result in this section provides added confirmation of the quantitative accuracy of the microscopic calculations. The laser system investigated is the 6.4 nm GaInNAs QW structure discussed above. Fig. 15 shows that the microscopically computed spontaneous and Auger rates [15] and their total contribution to the threshold current are again in excellent agreement with the measured data [12]. In this low N-concentration metastable semiconductor system it turns out that the defect recombination is significant. However, because the experiment was able to independently measure the spontaneous and Auger contributions, this could be subtracted from the experimental data. 4. Closed-loop design of a low power edge emitter The microscopically computed gain and refractive index, spectra, radiative and non-radiative recombination rates

11 34 J.V. Moloney et al.: Quantum design of semiconductor materials Figure 14 Plot of experimentally measure threshold currents (black dots) as a function of temperature for a 1.3 µm (Left) and a 1.5 µm InGaPAs laser. The microscopically computed spontaneous (red) and Auger (blue) and their sum (black solid) are graphed on the same plot for each laser. discussed in the previous sections are the critical inputs in a bottom-up approach to designing an final semiconductor amplifier or laser device. As an example, we will review in this section the first ever closed-loop design of an end electrically-pumped semiconductor laser L-I curve without having to use adjustable fit parameters [16]. The L-I characteristic (predicted solid line) and measured (dots) for the 4-QW InGaPAs ridge waveguide laser structure discussed earlier is shown at two temperatures in Fig. 16. The remarkable feature here is that the calculation preceded the wafer growth and device packaging, so that there was no prior access to experimentally measured data! No parameters were needed to be adjusted to get this remarkable agreement the cavity losses extracted from cut-back experiments were used to close the loop. Using the known input bandstructure parameters such as band offsets and Luttinger parameters for this specific structure, photoluminescence spectra were calculated for different carrier densities and temperatures. Fig. 16 shows the measured PL spectra (dots) for the above device grown according to the design prescription. A gain database, pre-computed for the designed epi structure, was used to establish the accuracy and quality of the actual wafer growth. The measured PL peaks show an offset of 23 nm from the design, indicating that the actual growth was off by 1 2% in Indium- or Arsenic-concentration. The pre-computed PL peaks were inhomogeneously broadened by 14 mev to account for inevitable growth fluctuations from the ideal single crystal spectra. The comparison between predicted and measured PL is remarkable. Once the PL spectra had unambiguously established the reliability of the growth, the gain spectra were immediately accessible from the pre-computed gain databases (see Fig. 17 Left picture). The next step involved computing both spontaneous and Auger recombination rates at the same level of sophistication. Defect recombination is Figure 15 Threshold current measured (black dots) as a function of temperature for a GaInNAs 6.4 nm QW device lasing at 1.3 µm. The separately measured spontaneous (green dots) and Auger (blue dots) data are also shown in this figure. Corresponding microscopically computed spontaneous and Auger contributions are shown as solid lines. not a significant player in determining the optical properties of these high quality grown semiconductor crystals. Fig. 17 (Right picture) shows the pre-computed spontaneous and Auger rates over a range of internal carrier densities ranging from below to above the transparency point at a fixed temperature. Note the radical departure from the usual phenomenological spontaneous and Auger carrier density dependence at and above transparency density. Combining the above inputs generated the fitparameter-free L-I curves in Fig. 16 at two different

12 Laser & Photon. Rev. 1, No. 1 (2007) Designing high power vertical external cavity semiconductor lasers Figure 16 Input-output characteristic for a 1.3 µm InGaPAs ridge laser at two temperatures. Predicted L-I characteristic from the microscopic inputs and cut-back measured losses are shown by solid lines. The experimental data is shown as dots. temperatures. Considering the critical role of the above recombination processes in not only, determining gain and slope efficiency but, also all dynamic properties (modulation rates, gain switching, injection locking etc) of SOAs and SLs, it is clear that the impact of this work reaches well beyond the accurate prediction of an L-I characteristic. The application of these powerful results obviously extends beyond this particular material system and carries over to the broad class of semiconductor material systems generating light from the UV/Visible (GaN for example) to the far-infrared (InGaSb 2 10 µm). Optically-pumped vertical external cavity surface emitting lasers (VECSELs) or equivalently, optically pumped semiconductor lasers (OPSLs) provide a new class of high power, high brightness semiconductor laser sources. In contrast to broad area devices where the output beam suffers strong astigmatism due to differing beam divergence along the fast and slow axis, the VECSEL output can be confined to a clean TEM 00 beam. Moreover, broad area emitters undergo strong dynamic filamentation along the slow axis leading to broad far-field outputs well in excess of the expected far-field divergence of a stable beam. The VECSEL is akin to a mini-disk-solid state laser but with many advantages over the latter. Solid-state mini-disk lasers typically require narrow wavelength pumps and multiple passes back and forth through the structure to achieve sufficient pump absorption. Barrier pumped VECSELs can absorb all of the pump light in either a single or double pass through an extremely thin (5 10 µm) active layer and can use offthe-shelf low cost pumps requiring no temperature stabilization. Because VECSELs are based on semiconductor QW materials, they provide wavelength agile systems and have already been demonstrated to operate around 675 nm (InGaP) [19], 850 nm (GaAs) [18], 980 nm (InGaAs) [30], 1500 nm (InGaPAs) [32] and 2400 nm (GaSb) [42]. The key design principles of a VECSEL structure resemble that of the more common low-power vertical cavity surface emitting lasers (VCSELs). The key difference with VCSELs lies in the fact that the top high reflectivity DBR mirror is removed and replaced by a lower reflectivity external cavity curved mirror. The external cavity mirror re- Figure 17 Left: Computed PL spectra at increasing illumination intensities (bottom to top) for the nominal InGaPAs design adjusted for growth offset and fluctuations (solid black curves) is plotted along with measured PL data (black dots) using femtosecond pulsed excitation. The solid red curves represent the corresponding gain spectra as a function of increasing carrier density for the same structure. Right: Spontaneous (dashed) andauger loss currents (solid) for the InGaPAs structure at the two different temperatures of the experiment. The straight lines are the ABC power law fits to the full calculations at low densities.

13 36 J.V. Moloney et al.: Quantum design of semiconductor materials Figure 18 Schematic of a vertical external cavity semiconductor laser. The active semiconductor chip consists of a MQW resonantperiodic gain stack grown on a high reflectivity DBR mirror. Typically the structure is optimized with QWs in the RPG stack. The active chip is mounted on a high thermal conductivity CVD diamond heat spreader and the latter is typically mounted on a copper heat sink. The incoherent pump light from the diode bars is incident at close to a 45 angle and an external curved reflector at a distance of between cm provides external feedback of light to the active semiconductor mirror. Figure 20 Reflectivity (R) and absorption (A) spectra of the active semiconductor mirror as a function of incident pump power. Low pump levels show an absorption dip in the photonic stopband at the central resonance of the MQW RPG stack (solid black and dashed red curves). The corresponding absorption spectra are shown in green for the same conditions. At higher pump levels (carrier sheet density of cm 2 )and at the elevated temperature of the running hot cavity (blue dashed curve) the mirror exhibits a narrow gain peak superimposed on the stop-band. Figure 19 Top: Detailed refractive index profile of the active RPG region with 14 InGaAs QWs and the passive DBR stack with 30 repeats. The blue curves represent the refractive index along the active mirror chip and the red curves the standing wave intensity distribution along the structure. flectivity can range from 90% to 98% requiring the addition of many QWs to provide enough single pass gain to offset these relatively large losses. The lower external mirror loss facilitates greater power extraction from the optically pumped spot on the VECSEL chip and power scaling is achieved by increasing the pumped area on the chip. With this particular geometry, Coherent Inc of Santa Clara, California [6] have demonstrated up to 50 Watts output from a single 900 µm pump spot at 1050 nm. A schematic of the VECSEL structure is shown in Fig. 18. The active semiconductor chip consists of a resonant periodic gain (RPG) structure consisting of multiple QWs arranged to coincide with the anti-nodes of the standing wave optical field within the semiconductor sub-cavity. The QWs are grown on a high reflectivity DBR stack containing on the order of repeats of, for example, Al- GaAs/AlAs pairs (see Fig. 19). The active chip consisting of the RPG and DBR stack is mounted on a high thermal conductivity heat spreader such as CVD diamond so as to efficiently extract the heat from the hot active RPG layer. The VECSEL cavity is completed by adding an external reflector typically places around cm from the active chip as shown in Fig. 18. Finally the pump light (at 808 nm for example) is incident on the active chip at an angle close to 45. The VECSEL cavity can be viewed as a classical twomirror resonator but with the important provison that the reflectivity of one mirror (the active semiconductor chip) can be actively controlled via the external diode bar pumps. The reflectivity of this active mirror as a function of coupled pump power is shown in Fig. 20. At low external pump powers (internal sheet carrier density of cm 2 solid black curve in the figure) the active chip reflectivity spectrum shows a pronounced absorption dip within its photonic stop-band due to strong absorption of the pump light by the QWs. The absorption of the QW stack is precomputed using our many-body microscopic approach and

14 Laser & Photon. Rev. 1, No. 1 (2007) 37 Figure 21 Input power density versus output power density for four different VECSEL structures (see captions). represents a critical input to thevecsel design. Increasing the pump power to the point where the QWs are inverted (internal sheet carrier density of cm 2 solid green curve in the figure) leads to a narrow gain peak (reflectivity > 1) superimposed on the sub-cavity stop-band. Note that the gain peak is shifter to longer wavelengths relative to the absorption dip due to the internal heating of the chip (now 360 K versus the cold-cavity 300 K temperature at low pump levels). The strong shift in material gain peak with increasing pump intensity (carrier density and temperature) must be allowed for in the VECSEL cavity design. Additionally the internal active chip resonance due to the DBR stack and semiconductor air interface shifts to longer wavelength with increasing temperature but this shift is much less than the gain peak shift. Our cold-cavity design takes accounts of these relative shifts and optimizes the structure to avoid early shut-off due to thermal rollover. Designing a high power VECSEL structure optimized to extract maximum power at, say 975 nm when pumped by an 808 nm diode bar, requires optimization at many levels. The underlying semiconductor active sub-cavity has to be designed to exhibit the maximum gain at the internal temperature of the running laser. The latter depends sensitively on thermal management. As we mentioned earlier, the gain peak can shift rapidly as a function of increasing temperature in the active layer. Typically an internal temperature elevation relative to ambient of about 100 K can be tolerated before the device shuts off. Efficient heat removal from the active layer is key to maximizing the power extraction the latter depends on a number of factors including high thermal conductivity heat spreaders as close as possible to the active RPG layer. The most effective design to date has involved growing the VECSEL chip (DBR+RPG) on a substrate with the DBR layer on top. In this setup, the chip is typically mounted on a CVD diamond heat spreader and the entire GaAs substrate has to be removed by chemical etching. These processing steps are extremely critical as Figure 22 Input vs output power for a VECSEL chip with a 400 µm pump spot diameter. The lower left black curve corresponds to the case where the substrate is completely removed and the device in mounted on a CVD diamond heat spreader. The green curve is when additionally a transparent intracavity diamond heat spreader is capillary bonded to the top RPG stack end of the device. The red curve is a conventional structure with 50 µmofthe GaAs substrate remaining for mechanical support and an additional intracavity transparent diamond heat spreader boned to the top of the RPG stack. the end active mirror is only 6 10 µms thick! If the chip is grown in the conventional manner, the thermal impedance through the DBR and GaAs substrate is too high and the chip heats up rapidly never achieving lasing threshold. The only option here is to partially remove the GaAs substrate to get the heat spreader closer to the active region. Fig. 21 shows a comparison of the situation above with the entire substrate removed against a conventional grown structure with 5 µm and 7.5 µm of substrate remaining after etching. The numbers on each curve indicate the internal temperature along each characteristic input-output characteristic. Both cases with a finite thickness of substrate remaining show a rapid heating in the active layer and a sharp shut-off in the device with increasing pump level. The device with the entire substrate removed shows a much more gradual temperature increase and no evidence of thermal shut-off with increasing pump power. In practice, this device will ultimately shut-off but at much higher output power levels. An interesting optimization strategy is to remove the heat directly from the top of the chip by capillary bonding a transparent single crystal diamond heat spreader on top and actively water cooling the intracavity heat spreader. This approach has been shown to work for conventionally grown VECSELs by providing a much lower thermal impedance pathway via the high thermal conductivity diamond. However, extracting the heat simultaneously from top and bottom of the chip offers even greater power scaling possibilities. Fig. 22 contrasts a the extracted output power for three cases with different cooling setups. In each

15 38 J.V. Moloney et al.: Quantum design of semiconductor materials Figure 23 3D temperature profile computed for a 980 nm InGaAs semiconductor VECSEL chip pumped by an 808 nm multi-watt diode bar. The hot part of the chip (bright red) is at the top where the MQW RPG stack is located. case the pump spot is 400 µm. The leftmost black curve corresponds to the power extracted from our first device when the heat extraction is through the DBR to the CVD diamond heat spreader i.e no top heat spreader. By adding a transparent diamond heat spreader to the top of this device, a dramatic improvement in extracted power is predicted as shown by the red curve. Even keeping the conventional device with 50 µm of GaAs remaining but with a top and bottom heat spreader gives significantly improved extracted power as shown by the green curve. These VECSEL structures offer enormous flexibility as regards wavelength selectivity, high power, high brightness operation, wavelength generation in the visible through intra-cavity SHG (red at the fundamental, blue, green and yellow at the second harmonic have been generated). The near TEM 00 fundamental mode operation can be achieved by carefully matching the incident pump spot to the laser signal spot. The RPG and DBR structure also offer the possibility of implementing novel slow-light gain enhancement by modifying the basic RPG design Time domain VECSEL simulator A realistic simulation of the VECSEL device shown in Fig. 18 requires a proper model of the complex semiconductor sub-cavity and the propagation of light back and forth from the active mirror to the external curved reflector. The active mirror is itself a spectrally selective sub-cavity that must see the correct physical response of the semiconductor material. The latter is provided by the pre-computed gain databases and recombination rates discussed in Sections 2 and 3. The databases contain the physically correct absorption at the pump wavelength (808 nm) and the laser signal gain at the emission wavelength (980 nm) as well as heat generating losses due to spontaneous and Auger recombination. As the device heats up with increased optical pumping level, proper account must be taken of the internal temperature. Therefore the gain databases must contain a complete mapping of the semiconductor response over a broad carrier density and temperature landscape. Two approaches have been developed to model the VECSEL cavity. The first assumes a quasi-cw behavior and tracks the slow thermal evolution of the internal optical field within the device [46]. Full details of the internal optical and thermal fields under CW optical pumping are tracked within the semiconductor sub-cavity using an extended vectorial BPM method combined with thermal transport through the entire device, including heat spreaders and heat sinks. This approach was employed to generate Figures 21 and 22 above and played a central role in the overall device optimization. Fig. 23 shows the computed 3D thermal profile on the semiconductor chip mounted on a In solder bonded CVD diamond heat spreader and mounted on a copper heat sink. The key goal in designing the VECSEL chip for high power extraction is to minimize the temperature elevation

16 Laser & Photon. Rev. 1, No. 1 (2007) 39 Figure 25 Schematic layout of the VECSEL cavity to simulate synchronously-pumped mode-locking with an external Ti:Sapphire pulse train. Figure 24 Three typical active mirror responses obtained from an extensive gain-database spanning the range of accessible carrier densities and temperatures in a VECSEL device. The carrier densities are scaled to a reference sheet carrier density of cm 2. in the active layer at high pump levels. The cooling of the device due to heat transport through the DBR stack and down to the CVD diamond heat spreader and copper submount is evident in this picture. Because of the poor thermal conductivity of the semiconductor materials making up the DBR, this remains a high thermal impedance pathway. By capillary bonding an intra-cavity transparent single crystal diamond heat spreader to the top of the structure, its performance can be dramatically improved as shown in Fig. 22. Again the microscopic inputs are key to designing an optimized structure. A broadband simulator proposed by Kolesik et al. in 2001 for edge emitting lasers has recently been adapted to the special case of the VECSEL [29]. The idea here is to adopt the active VECSEL chip reflectivity calculations from the above quasi-cw approach and incorporate these as a look-up table spanning the full carrier density and temperature range of the running device the latter are determined from the quasi-cw calculation. Now these active mirror reflectivities are input to a full broadband simulation of the device. The active mirror response to an incident light field is shown in Fig. 24 at different carried densities and temperatures. The location of the absorption dip at low density and room temperature and the gain peaks at room temperature and at the elevated temperature show the strong excursion of these nonlinear responses within the active mirror stopband. The numerical approach must capture the full details of this response over the large spectral bandwidth shown in this figure. The spectral nature of the VECSEL propagator makes it straightforward to incorporate other frequency selective elements such as a birefringent filter or second harmonic crystal in the external cavity. The spatial digital filter implementation is illustrated in the next section. As an illustrative example of the simulation capability, we present a study of a synchronously-pumped mode-locking of the VECSEL cavity. A recent experimental demonstration of synchronously-pumped mode-locking was carried out by a group at Strathclyde University [47]. A quantitative study of such dynamical behavior requires both accurate microscopic inputs and accurate broadband simulation. Fig. 25 shows the cavity layout for the simulation where the VECSEL chip is optimized to lase around 975 nm. Stable mode-locking requires very fine adjustment of the VECSEL cavity length to tune to the Ti:Sapphire pulse train repetition rate [24]. This tuning is nontrivial nonlinear due to nonlinear length changes caused by induced refractive index changes in the active semiconductor mirror. Fig. 26a shows that there is a very strong wavelength shift in the device prior to the establishment of modelocking in the cavity. Even after mode-locking is established at around 40 microseconds, the wavelength continues to fluctuate randomly indicating that stable modelocking cannot be achieved. This behavior is observed around the optimized detuning setting of the cavity. The observation is consistent with the experimental observations of the Strathclyde group. We can understand these fluctuations from Fig. 26b where instantaneous temporal snapshots of the pulse spectrum are shown. The figure shows that the pulse train is never stable but fluctuates strongly with time. This is not a surprising observation as the semiconductor active chip exhibits strong nonlinear dispersion as the carrier density is rapidly swept out as a pulse propagates in the semiconductor sub-cavity. The pulses themselves in the cavity are of about 20 picoseconds duration and exhibit strong temporal distortion [29]. This observation suggests a route to stabilization the modelocked pulse train by incorporating some intra-cavity active dispersion element. This VECSEL time-domain simulator can be used to study mode-locking with a SESAM mirror, gain switching of the cavity or second harmonic generation to produce multi-watt visible lasers.

17 40 J.V. Moloney et al.: Quantum design of semiconductor materials 6. Device simulation with microscopic inputs The two examples of a low power edge and high power, optically-pumped VECSEL were chosen to illustrate the predictive power of a bottom up approach to semiconductor amplifier and laser design. It should be evident to the reader that this simply represents the tip-of-the-iceberg! For example, every device that relies on semiconductor components for light amplification, can benefit greatly from such a systematic closed loop approach. Modeling real devices is generally very complicated and requires proper description of macroscopic carrier and heat transport within a 3D structure. This in itself is a daunting task and most state-of-theart device simulators usually break such transport problems down to quasi-2d simulations. Optical confinement within the 3D amplifier of laser structure is vitally important but in most instances this confinement is sufficiently strong in one Figure 27 Schematic of a planar broad area semiconductor emitter with lateral index confinement via a ridge structure. The active layer typically consists of 1-3 QWs and a wide current stripe on top. Electrical injection occurs through the top (blue) p- and bottom (purple) n-dope layers. Figure 26a Dynamical wavelength shifts in the cavity during and subsequent to the establishment of the synchronously-pumped mode-locked train for two initial cavity detunings. Figure 26b Temporal snapshots of the pulse spectrum showing that the spectrum shifts back and forth between roughly 966 nm and 970 nm during the post transient mode-locking. (broad area planar) or two (conventional low power single transverse mode devices) dimensions. Most semiconductor amplifier or laser structures are intrinsically dynamical by nature and this additional degree of freedom needs to be accounted for. Most optical solvers within sophisticated 3D laser solvers treat the optics in a steady state via either a BPM propagator or a Helmholtz solver approach. Broad area semiconductor lasers are a case in point where spatio-temporal effects predominate. These lasers cannot be described by a steady state approach although this is the current method of choice. Broad area emitters are the basic building blocks of high power diode bar development. Understanding intensity filamentation and possible light induced short or long term degradation of these devices will require the development of future simulation capabilities that integrate the complex spatio-temporal dynamics with microscopically computed semiconductor material responses. A schematic of a broad area semiconductor laser is shown in Fig. 27. This device has strong optical confinement in the vertical growth direction (fast axis) but weak index confinement in the lateral (slow axis) direction. Consequently the light emitted from the output facets diverges strongly along the fast axis. The weak optical confinement along the slow axis leads to strong dynamic intensity filamentation within the device in that dimension. The complex interplay between dynamic, lateral and longitudinal spatial degrees is manifest in some early measurements of the far-field spectrally resolved outputs of these devices at various levels of pumping. Fig. 28 shows three cases where the laser is run just above threshold, at three and at six times threshold. The horizontal axis depicts wavelength and the vertical off-axis emission. The individual features approximately repeating along the pictures depict individual longitudinal cavity modes. Spectral features extending above and below the center line repc 2007 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

18 Laser & Photon. Rev. 1, No. 1 (2007) 41 Figure 28 Experimentally measured spectrally resolved far-field output from a broad area semiconductor laser with a 100 µm output aperture. Top: Output 10% above lasing threshold. Middle: Output at three times laser threshold. Bottom: Output at six times laser threshold. [Data courtesy of D. Bossert]. resent off-axis emission. Just above lasing threshold, the device emits in a near lowest order Gaussian mode but this randomly steers left and right dynamically. Most of the energy is confined in a diffused central spot in the far-field due to dynamic beam steering. Increasing the injected current to six time threshold shows a dramatic extension of the far-field emission angle. Individual parabolic shapes associated with each longitudinal mode are randomly filled as the broad area device undergoes chaotic internal filamentation. These signify internal waves traveling to the left and right at relatively large angles. It is hard to imagine how a steady state beam propagation or Helmholtz solver approach could possibly capture the complex spatio-temporal dynamics intrinsic to real broad area emitters as shown in Fig. 28. A proper modeling approach entails implementing an ultra-broadband spatiotemporal simulator that captures the details exhibited by the above experimental pictures. A simulation approach introduced by Kolesik et al. in 2001 [27], based on a highly efficient spatial-digital filter algorithm, is designed to capture the full spectral bandwidth (gain and refractive index) of the light coupling to the semiconductor material. This simulator takes as input pre-calculated microscopic gain tables but as yet has not been updated to include the important microscopic radiative and non-radiative recombination rates. These rates are being implemented in the simulator at the writing of this paper. Fig. 29 shows a typical gain and refractive index curve at a fixed carrier density derived from the microscopic gain tables described in Section 2. The spatial digital filter approximation to the gain curve is shown by blue dots and to the refractive index by red dots. The digital filter faithfully captures the full dynamic response of the semiconductor material over a huge spectral bandwidth it only begins to deviate in the wings well outside the window that the real laser dynamics experiences. The extent of the spatial digital mapping to the real dispersion dictates the time step required in the propagator. This accurate mapping is achieved by the algorithm in the full (k,ω) space of the simulation. Figure 29 Broadband spatial digital filter maps the numerical algorithm dispersion to the real material dispersion (gain and refractive index) over the physically relevant material bandwidth accessible in the running laser. This approach should be contrasted with a classical BPM or finite difference approach that are necessarily spectrally local In other words artificial numerical dispersion misrepresents the physical response of the light field outside a narrow spectral window centered at the optical carrier frequency. Results from this broad area emitter simulator can be viewed as a movie at the web page under the movies section. The movie called BALSIM shows the behavior of the spectrally resolved far-field corresponding to the experimental pictures shown in Fig. 28 above. In the movie, the drive current is continuously ramped up from below to six times threshold. One observes qualitatively similar features as in the experiment by freezing the movie frame at different current ramp levels. The data in the movie were only accumulated over a 50 nanosecond window while the above experimental data were gathered over seconds hence the much thicker experimental curves due to long detection times. 7. Summary and future outlook We have presented a comprehensive overview of the powerful capabilities of a quantum mechanical microscopic many-body approach to design semiconductor QW material systems as the basic building blocks for semiconductor amplifier and laser design. The approach is truly predictive and its predictive power has been demonstrated by applications to the closed-loop design of a low-power

19 42 J.V. Moloney et al.: Quantum design of semiconductor materials InGaPAs 1.3 µm ridge laser and a complex high-power, high-brightness optically-pumped 980 nm VECSEL. This predictive approach is completely general and applies to any semiconductor material system where the bulk bandstructure parameters and band offsets are known. Quantitative comparisons with experimental gain data have been made for material systems wit wavelengths spanning the UV through mid-ir. Our bottom up approach of integrating the microscopic many body results into laser design are explicitly demonstrated for the optically-pumped VECSEL structure. However the impact of this approach reaches far beyond this specific example and applies equally well to electricallypumped edge and surface emitting amplifiers and lasers of all sorts. We are in the process of incorporating microscopic gain databases and recombination rate tables into low power edge emitter broadband optical system simulators (OSS) [28, 34] and high-power broad area broadband simulators [29]. The latter fully resolve the spatiotemporal degrees of freedom within a structure longitudinal modes for low power and longitudinal/lateral modes for high power. The approach outlined here can also interface to existing top-down semiconductor device simulation tools [10, 21, 39 41] by replacing the phenomenological models by pre-computed microscopic look-up tables. In this sense, the sophisticated thermal and electrical transport capabilities of the latter can be married with the quantitative semiconductor optical response reviewed in this paper. Acknowledgements The authors acknowledge the support of colleagues Armis Zakharian and Miroslav Kolesik of the College of Optical Sciences, University of Arizona. This work was supported by grants from the U.S Air Force Office of Scientific Research: an STTR grant FA C-0069 and a grant AFOSR F JVM acknowledges support through a senior scientist award of the Alexander von Humboldt Foundation. J. Hader received his M.S. degree in physics from the Friedrich-Alexander University, Erlangen-Nurnberg, Germany, in 1994, and his Ph.D. degree in physics from the Phillips-University, Marburg, Germany, in He is currently working as an Assistant Research Professor at the College of Optical Sciences at the University of Arizona, Tucson and as Senior Scientist at Nonlinear Control Strategies Inc., Tucson. Currently his main focus is on the microscopic modeling of equlibrium and non-equilibrium optical and electronical properties of semiconductor heterostructures. Jerome V. Moloney is a Professor of Mathematics and Optical Sciences at the University of Arizona and is Director of the Arizona Center for Mathematical Sciences, an internationally recognized research center in applied mathematics. He is a fellow of the Optical Society of America and a recent recipient of the Alexander von Humboldt Prize in physics. Research interests span a wide range of photonics and nonlinear optics fields including ultrashort, high power femtosecond pulse propagation; computational nanophotonics, fiber laser modeling, many-body physics of semiconductor optical properties and modeling semiconductor passive and active devices. He has published more than 200 papers in peer-reviewed journals and has given over one hundred invited papers at national and international conferences. Stephan W. Koch has been a professor of Physics at Philipps-University Marburg (Germany), and a research professor at the Optical Sciences Center, Univerity of Arizona, Tucson/USA, since He spent eight years, first as associate professor, then as professor of Physics and Optical Sciences at the University of Arizona, was a Heisenberg Fellow at the University Frankfurt/Germany in 1985, and a visiting scientist at IBM Reserach in 1981 and Prof. Dr. Koch received his MS and PhD in Physics from the Goethe-University Frankfurt (Germany) in 1977 and 1979, respectively. His fields of major current interests include condensed matter theory, optical and electronic properties of semiconductors, many-body interactions, disorder effects, quantum confinement in solids, coherent and ultrafast phenomena, semiconductor laser theory, microcavity effects, and optical instabilities and nonlinearities. He received the 1999 Max-Planck Research Prize, the 1997 Leibniz Prize of the Deutsche Forschungsgemeinschaft, was a DivisionalAssociate Editor of Physical Review Letters , and a Topical Editor of the European Physics Journal , is a Fellow of the Optical Society of America, and a member of the German Physical Society (DPG). Prof. Dr. Koch is the author or co-author of 7 books, editor of 1 book, and author or co-author of more than 500 publications in refereed scientific journals.