Alexander Cerjan

In this thesis we generalize and extend the steady-state ab initio laser theory (SALT), first developed by Tureci and Stone, and apply it problems in laser design. SALT as first formulated modeled the gain medium as identical two-level atoms, leading to the well-known Maxwell Bloch laser equations. The result is a set of coupled non-linear wave equations that treats the openness of the cavity exactly and the non-linear modal interactions to infinite order. Most gain media have more than two atomic levels, and in this thesis we generalize the SALT equations to treat realistic and complex gain media, specifically N-level atomic media with a single lasing transition, N-level atomic media with multiple lasing transitions and semiconductor gain media with particle-hole band excitations. The extension to multiple transitions requires fundamentally enlarging the set of SALT equations, by adding a set of population equations that must be solved self-consistently with the non-linear wave equations for the lasing modes in standard SALT. In addition, the population equation can be generalized to treat gain diffusion, an important problem in a number of laser systems, not treated in SALT or in most earlier laser theories. The semiconductor version (Semi-SALT) includes the continuum of particle-hole transitions and the effect of Pauli blocking of transitions, but is only developed and applied in the free-carrier approximation. The resulting theory is termed complex SALT (C-SALT). We also demonstrate how to incorporate amplification and injected signals naturally within the SALT framework, yielding injection SALT (I-SALT). The generalization to I-SALT leads to a larger set of self-consistent coupled non-linear wave equations, a set for the lasing modes and a set for the injected and amplified fields, coupled through cross gain saturation. It clearly distinguishes the lasing modes, which correspond to poles of the scattering matrix, from the injected fields, which do not; in this limit the locking of a lasing mode corresponds to the injected signal forcing the lasing pole off the real axis, reducing its amplitude to zero. I-SALT is shown to reduce to a version of the standard Adler theory of injection-locked lasing in a certain limit (the single pole approximation).

We apply SALT to design a highly multimode cavity for use as a spatially incoherent light source for applications to imaging and microscopy. Laser illumination typically leads to coherent artifacts that degrade optical images; this can be alleviated by having a very large number of modes (~ 500) which are spatially independent and average out such artifacts. We used SALT to model a D-shaped laser cavity with chaotic ray dynamics and showed that a certain shape greatly increases the number of lasing modes for the same cavity size and pump strength, due to a flat distribution of Q-values and reduced mode competition. An on-chip electrically-pumped semiconductor laser was realized using this cavity design and showed negligible coherent artifacts in imaging, as well as much better efficiency and power per mode than traditional incoherent light sources such as LEDs.

The thesis also goes beyond semiclassical laser theory to treat quantum noise and the laser linewidth in a SALT-based approach. We demonstrate that SALT solutions can be used in conjunction with a temporal coupled mode theory (TCMT) to derive an analytic formula for the quantum limited laser linewidth in terms of integrals over SALT solutions. This linewidth formula is a substantial generalization of the well-known Schawlow-Townes result and includes all previously known corrections: the Petermann factor, Henry alpha factor, incomplete inversion factor and the “bad cavity factor”. However, unlike previous theories these corrections are not simply multiplicative and are not separable in general. The predictions of TCMT linewidth theory are tested quantitatively by means of an FDTD algorithm that includes the Langevin noise as a source term.