course: Physics of Quantum Cascade Lasers

teaching methods:
lecture with tutorials
computer based presentation, black board and chalk
responsible person:
Dr. Nathan Jukam
Dr. Nathan Jukam (Physik)
offered in:
winter term


Die Angaben zu den Prüfungsmodalitäten (im WiSe 2020/2021 | SoSe 2021) erfolgen vorbehaltlich der aktuellen Situation. Notwendige Änderungen aufgrund universitärer Vorgaben werden zeitnah bekanntgegeben.

Date according to prior agreement with lecturer.

Form of exam:oral
Registration for exam:FlexNow


This course will cover the physics necessary to understand quantum cascade lasers. Quantum cascade lasers are a new class of semiconductor lasers that are based on intersubband transitions. They emit radiation at mid-infrared and far-infrared wavelengths. This is in contrast to conventional diode semiconductor lasers which are based on interband transitions and emit radiation at visible and near-infrared wavelengths. The active region of a quantum cascade laser consists of repeating series (cascades) of quantum wells and barriers that are grown in Molecular Beam Epitaxy (MBE) or Metal Organic Vapor Deposition (MOCVD) machines. In order to achieve lasing, wavefunctions and levels should be designed to maximize / (minimize) the lifetime of the upper / (lower) laser level, reduce parasitic scattering, maximize injection into the upper laser level, and minimize losses. This requires a thorough understanding of the optical properties of twodimensional semiconductors, and electron transport and scattering in semiconductor heterostructures.

In addition to these topics, the course will review basic laser theory, survey different types of waveguides, and give an introduction to interband diode lasers.


Basic Laser theory spontaneous emission, stimulated emission, absorption, Einstein A and B coefficients, Rate equations, 3 and 4 level laser systems, laser threshold, gain clamping / saturation, homogeneous and inhomogeneous broadening, multi-mode and single mode lasers, spatial hole burning, longitudinal and transverse modes, spontaneous emission noise and laser line width, frequency pulling, Q-switching, mode-locking line width, different types of lasers.

Wave functions and effective mass: Review of tight binding model, nearly free-electron model, and the formation of bands. Bloch’s theorem, envelope approximation, effective mass approximation, hetero-structure effective mass theory - modifications of the continuity conditions and the kinetic operator in the envelope approximation

Idealized potentials parabolic well, infinite square well, finite square well, finite hetero-structure square well, superlattices and minibands, Bloch oscillations, coupled quantum wells, Stark effect

Refinements of effective mass theory: k dot p method, Kane 2 and 3 band models, non-parabolicity, Luttinger parameters

Optical properties of quantum wells: Interband, and intraband transitions, absorption in quantum wells, selection rules, oscillator strength – sum rules, depolarization shift, gain and loss, modification of sum rules and transition dipole moments from non-parabolicity

QCL design strategies: two-dimensional rate equations, slope efficiency, importance of lifetimes, parasitic scattering, Bragg confinement, resonant tunneling (qualitative treatment), backfilling and self-heating, bound-to-continuum designs, LO-phonon designs, chirped supper-lattice and phase space designs.

Resonant tunneling injection and extraction: coupled quantum wells, resonant tunneling diodes, density matrix - two and three-level models, coherent and incoherent transport regimes, scattering assisted injection, electric field domains

Carrier scattering: phonon scattering, electron-electron scattering, impurity scattering, interface roughness, elevated electron temperatures

Conventional diode lasers: pn junction injection, electron-hole recombination, quasi -fermi levels, quantum well laser, quantum dot lasers, VCSELs, DFB lasers, diode laser rate equations, relaxation oscillations and frequency chirp, line-width enhancement factor

Waveguides / mode confinement: TE and TM modes, dielectric slab waveguides, surface plasmon waveguides, photonic crystals, distributed brag reflectors, mode coupling, orthogonality / completeness of modes, mode overlap factor

Applications/methods: vibrational spectroscopy, mode control, frequency locking, wavelength tuning in a Littrow configuration, injection seeding and locking



recommended knowledge

A course in Quantum Mechanics (at the level of Shankar) and Electromagnetism is required. An introductory course in solid state physics is highly desirable, but is not required.