Nonlinear-optical effects in semiconductor lasers based on InGaAs/GaAs/AlGaAs quantum-confinement heterostructures
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ICS OF SEMICONDUCTOR DEVICES
Nonlinear-Optical Effects in Semiconductor Lasers Based on InGaAs/GaAs/AlGaAs Quantum-Confinement Heterostructures N. S. Averkiev, S. O. Slipchenko^, Z. N. Sokolova, N. A. Pikhtin, and I. S. Tarasov Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia ^e-mail: [email protected] Submitted September 4, 2006; accepted for publication September 5, 2006
Abstract—Generation of a difference-frequency wave by two electromagnetic waves propagating in a heterolaser is analyzed theoretically. Calculations are carried out for InGaAs/GaAs/AlGaAs heterostructures of design optimized to attain maximum lasing power. It is shown that phase matching between the primary waves and the difference-frequency wave may persist over a distance of ~1 mm, comparable to the cavity length (2−3 mm), and the conversion coefficient can be as large as several percent. PACS numbers: 42.55.Px, 78.67.De, 78.66.Fd DOI: 10.1134/S1063782607030220
Although studies of nonlinear effects in solids have a long history [1], semiconductor materials undeservedly dropped out of the list of nonlinear crystals being investigated. This is despite the fact that single crystals of III–V compounds represent efficient nonlinear media, and their nonlinear susceptibility exceeds that of well-studied materials such as lithium niobate [2]. Recently, there has been growing interest in studies of the nonlinear properties of III–V semiconductors [3, 4], inspired by the possibility of combining the functionality of injection and parametric generators of radiation into a single device [5–9]. In this study, we analyze the efficiency of the conversion of two electromagnetic waves of frequencies ω1 and ω2 propagating in a multilayer dielectric waveguide in a difference-frequency wave. We consider a waveguide structure whose parameters are optimized for the fabrication of high-power semiconductor lasers [10–14]. 1. III–V compounds possess a face-centered cubic crystal lattice whose symmetry is characterized by the cubic-crystal system, class Td ( 43 m). For a fairly intense optical wave propagating through the crystal, the refractive index becomes significantly dependent on the wave intensity. The relationship between the external field intensity E and the polarization P of a nonlinear medium is described by the following nonlinear material equation: Pi =
∑α
ik E k
∑∑∑θ k
j
∑∑χ k
k
+
+
m
ikj E k E j
j
ikjm E k E j E m
(1) + …;
here, αik is the linear susceptibility (a second-rank tensor), χikj is the quadratic nonlinear susceptibility (a third-rank tensor), and θikjm is the cubic nonlinear susceptibility (a fourth-rank tensor). The first term in (1) describes the components of the linear polarization vector, and the other terms describe the components of the nonlinear polarization vector (with the second and third terms representing the quadratic and cubic polarization, respectively). It should be noted that, in III–V compounds, components of the χikj tensor do not vanish only if i ≠ j ≠ k, and a
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