Chapter 16: Advanced Semiconductor Lasers

Source: Amnon Yariv and Pochi Yeh, Photonics: Optical Electronics in Modern Communications, sixth edition (2007), Chapter 16. Use each problem number with the book; the original prompts are not reproduced. Each entry supplies the governing model, a decisive solution route, and an independent consistency check.

End-of-chapter problems

Problem 16.1 — quantum-well confinement and scaling: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Solve the piecewise one-dimensional Schrödinger equation and match wavefunction and mass-weighted derivative at interfaces. Combine the resulting confinement with mirror loss and differential efficiency when scaling cavity length. Bound-state energies must lie inside the well and approach the infinite-well values as the barrier grows.

Problem 16.2 — quantum-well confinement and scaling: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Solve the piecewise one-dimensional Schrödinger equation and match wavefunction and mass-weighted derivative at interfaces. Combine the resulting confinement with mirror loss and differential efficiency when scaling cavity length. Bound-state energies must lie inside the well and approach the infinite-well values as the barrier grows.

Problem 16.3 — quantum-well confinement and scaling: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Solve the piecewise one-dimensional Schrödinger equation and match wavefunction and mass-weighted derivative at interfaces. Combine the resulting confinement with mirror loss and differential efficiency when scaling cavity length. Bound-state energies must lie inside the well and approach the infinite-well values as the barrier grows.

Problem 16.4 — distributed-feedback coupling and oscillation phase: calculation

Convert the supplied data to one unit system, isolate the requested quantity symbolically, and retain guard digits until the final numerical evaluation. Solve the forward/backward coupled-mode equations with detuning, coupling \(\kappa\), and gain or loss. Apply both facet conditions; oscillation requires both the magnitude condition and a round-trip phase equal to an integer multiple of \(2\pi\). With \(\kappa o0\) the distributed stop band must disappear, and passive reciprocal reflection must satisfy the expected symmetry.

Problem 16.5 — distributed-feedback coupling and oscillation phase: plot

Derive a dimensionless plotting expression first, evaluate the limiting values and resonance or cutoff points, and then sample densely enough to resolve the narrowest feature. Solve the forward/backward coupled-mode equations with detuning, coupling \(\kappa\), and gain or loss. Apply both facet conditions; oscillation requires both the magnitude condition and a round-trip phase equal to an integer multiple of \(2\pi\). With \(\kappa o0\) the distributed stop band must disappear, and passive reciprocal reflection must satisfy the expected symmetry.

Problem 16.6 — distributed-feedback coupling and oscillation phase: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Solve the forward/backward coupled-mode equations with detuning, coupling \(\kappa\), and gain or loss. Apply both facet conditions; oscillation requires both the magnitude condition and a round-trip phase equal to an integer multiple of \(2\pi\). With \(\kappa o0\) the distributed stop band must disappear, and passive reciprocal reflection must satisfy the expected symmetry.

Problem 16.7 — distributed-feedback coupling and oscillation phase: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Solve the forward/backward coupled-mode equations with detuning, coupling \(\kappa\), and gain or loss. Apply both facet conditions; oscillation requires both the magnitude condition and a round-trip phase equal to an integer multiple of \(2\pi\). With \(\kappa o0\) the distributed stop band must disappear, and passive reciprocal reflection must satisfy the expected symmetry.

Problem 16.8 — distributed-feedback coupling and oscillation phase: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Solve the forward/backward coupled-mode equations with detuning, coupling \(\kappa\), and gain or loss. Apply both facet conditions; oscillation requires both the magnitude condition and a round-trip phase equal to an integer multiple of \(2\pi\). With \(\kappa o0\) the distributed stop band must disappear, and passive reciprocal reflection must satisfy the expected symmetry.