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 :math:`\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 :math:`2\pi`.
With :math:`\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 :math:`\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 :math:`2\pi`.
With :math:`\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 :math:`\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 :math:`2\pi`.
With :math:`\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 :math:`\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 :math:`2\pi`.
With :math:`\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 :math:`\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 :math:`2\pi`.
With :math:`\kappa	o0` the distributed stop band must disappear, and passive reciprocal reflection must satisfy the expected symmetry.