Semiconductor Laser Rate Equation Pdf

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Quantum-mechanical rate equations are derived for semiconductor lasers (SL). Fluctuation operators with shot-noise character describe the quantum nature of the transitions. These equations are treated in the high-temperature limit for pure and highly doped III-V compound semiconductors. Numerical calculations are carried out for GaAs. From the mean rate equations we determine (a) the temperature dependence of the threshold pump rate for pure bulk SL and the threshold current for SL junctions and (b) the temperature and pump dependences of the mean light intensity and of the mean quasi-Fermi-level. By linearizing the fluctuations around the mean values, the noise spectrum for the light intensity is obtained. The general form of the noise spectrum is the same as that obtained by McCumber for a four-level laser system. Above threshold a sharp resonance is found in the GHz region. The temperature and pump dependences of the spectrum and especially of the resonance frequency are calculated in detail. The results from the mean equations and from the noise calculations which are obtained for highly doped GaAs are compared with experimental results for junction lasers, and good agreement is found. For pure SL the present numerical results are in good agreement with former analytical results of Haug and Haken for the mean intensity and for the low-frequency part of the noise spectrum, which have been found for the regions below and above threshold. The results for pure bulk SL are applicable to experiments with optical or electron-beam excitation.

To integrate a semiconductor laser and solid-state laser monolithically, a vertical-cavity surface-emitting laser (VCSEL) is more attractive compared to an edge-emitting laser as a pumping laser source because it can emit a laser beam perpendicular to its surface, making it suitable for vertical integration. However, as the volume of the active region of the single-emitter VCSEL is small, the laser output is substantially limited. Therefore, the following problems occur when a solid-state laser is externally pumped. First, it is necessary to use an optical lens to focus the pumping laser beam, which complicates the system configuration and makes vertical integration difficult. Second, as the pumping laser passes through the solid-state laser medium only once or at most twice, the thickness of the solid-state laser medium should be of the same order as the absorption length, which is undesirable from the viewpoint of manufacturing via vertical integration.

To solve these problems, we employ a vertical-external-cavity surface-emitting laser (VECSEL) as an intra-cavity pumping source. Figure 1 illustrates a schematic of our proposed chip-scale semiconductor/solid-state vertically integrated laser, in which two cavities are optically coupled at the solid-state laser gain medium. The first cavity is a VECSEL for intra-pumping of Yb:YAG, with an electrically driven InGaAs quantum well, and the second cavity is for passive Q-switching that comprises Yb:YAG and Cr:YAG. This configuration provides the following advantages. First, as the pumping laser beam is focused via the thermal lens generated at the GaAs substrate and Yb:YAG, the optical lens necessary for external pumping configuration is not required. Second, via intra-pumping, even when the single-pass absorption rate of the Yb:YAG is low, the pumping laser can be efficiently absorbed and the thickness of the Yb:YAG can be reduced. Thus, vertical integration is possible in the proposed configuration.

Some differences exist between the result of the mechanically assembled laser and that of the fully integrated chip-scale laser. In addition to the cavity configuration, these differences might arise from the VECSEL cavity length (air gap), the thermal diffusion effect between the semiconductor element and Yb:YAG, and individual differences among the elements (VECSEL, Yb:YAG, and Cr:YAG). Interaction among these factors should affect the coupled laser oscillation parameters such as pumping laser power, mode matching, absorption cross section, and stimulated emission cross-section of the Yb:YAG and Cr:YAG.

This laser can be applied to several applications. Compact high-peak-power lasers are very promising in the field of light detection and ranging (LiDAR) applications for autonomous driving cars, drones, and robots. The use of such lasers in LiDAR applications is necessary to meet the potential demands of a high-peak-power laser source on the size scale of semiconductor lasers, but no laser source currently meets this market demand.

where Pcav is the sum of the laser output power and absorbed power in the VECSEL cavity, which is referred to as the potential pumping power. An external cavity can be treated as one effective layer23, and then, Reff, Teff, and Aeff are introduced as the effective reflectivity, effective transmissivity, and effective absorption rate of the external cavity part, respectively. They are calculated using Fabry-Perot resonance theory24 under the maximum reflection condition (i.e., antiresonance condition) with parameters R2, R940, and AGaAs. Pcav is obtained for each R940 condition in the experiment (Fig. 2b) and is defined as a function of Reff by interpolating the obtained data. As a next step, the pumping-power absorption PYb is derived. It is assumed that the same power of Pcav is obtained at the same effective reflectivity at steady state; therefore, PYb can be calculated by considering the absorbed portion by the Yb:YAG in the external cavity part when the effective parameters (Reff1, Teff1, and Aeff1) are changed according to the external cavity parameters (R2, R3, AGaAs, and AYb). In addition to the major external cavity parameters, which are taken into account in this model, further consideration of other factors, such as diffraction and scattering losses, will contribute to realizing more accurate cavity design.

All authors contributed extensively to the work presented in this paper. M.K. conceived the original concept. M.K., G.H., J.Y., K.T., R.K., and Y.H. designed the basic chip-scale laser structure. G.H. and H.W. designed the VECSEL devices. G.H. fabricated and tested the VECSEL devices. M.S., G.Y., H.T., and Y.I. fabricated the chip-scale laser and performed the measurements. K.T. and J.Y. performed the theoretical analysis and the rate equation simulation. J.Y., K.T., G.H., G.Y., and M.K. wrote the paper. M.K. supervised the project with K.Y.

This paper presents a number of models for semiconductor laser diodes. The models are divided into different categories, according to the independent variables they include. The use of these different models is critically investigated and the advantages of these models are compared and discussed. A number of models are elaborated into mathematical detail and some examples are discussed. 2b1af7f3a8