Professor A. E. Siegman: Current Research Interests

This page provides links to most of my current and a few of my past research interests and projects. For additional information see also the Publications section on my home page.

Past research projects (1990-2000)

Research projects and topics I've been involved with or completed during the decade from 1990 to 2000.

Research problems

A list of research problems and ideas concerned with beams, resonators, beam quality, and lasers generally, which students and others are welcome to attack,or which I might get around to myself some day.

Evanescent gain, Fresnel reflection, and TIR greater than unity?

Significant changes in classical optics phenomena such as wave guiding, Fresnel reflection, and total internal reflection (TIR) can occur when one adds even a small amount of active gain to the dielectric media contained in an optical structure.

Significant controversy over these changes also persists in the literature, centered around such questions as, "Can one have Fresnel reflection with reflection coefficient greater than unity at an interface looking into a gainy semi-infinite half space under TIR conditions?", and also "Does something that can properly be called 'evanescent gain' actually exist?".

The seminar presentation linked to a few paragraphs above provides what are believed to be the correct answers to these questions; additional links will be added to this section in the near future.

FM fiber lasers

"FM laser operation" is a rather unusual type of laser operation discovered by Steve Harris in the early 1960s in which an intracavity phase modulator that is tuned a small amount away from the exact axial mode spacing of the laser causes the laser to operate in a purely frequency modulated (FM) manner, with the axial modes locked together in a classic Bessel-function frequency modulated spectrum.

FM laser operation is thus quite different in character from the better known "FM mode-locked" type of operation which produces short mode-locked output pulses, although FM laser operation can easily be converted into FM mode locked (i.e., pulsed) operation in the same laser simply by tuning the intracavity phase modulation frequency more or less exactly to the axial mode spacing frequency.

FM laser operation can be of some interest and possibly even some practical application in situations -- such as perhaps in broadband fiber lasers -- where one wants to create a very wide "comb" spectrum with known and coherent phases between the individual spectral components of the comb, while at the same time avoiding nonlinear or other problems that may be associated with a short-pulse type of mode-locked operation.

Unfortunately, recent experiments seem to show that although a very broadband type of FM laser operation can easily be achieved in a fiber laser, the resulting oscillation spectrum can also be quite noisy. The noise fluctuations in this case are associated with the fact that the oscillation spectrum in an FM laser only converges quite slowly to the desired FM-laser steady-state spectrum when the phase modulator is first turned on, or only slowly converges back to steady-state following any transient disturbances in the laser.

An unpublished memo for file derives this slow transient behavior, and also illustrates its character with three associated animations [movie-1 : movie-2 : movie-3] (space bar to stop and start; arrow keys to step). Further work on this behavior is planned.

Nonnormal (i.e., nonhermitian or nonorthogonal) optical systems

"Normal mode expansions" are a basic analytical tool in physics, especially in optics and in quantum theory. Many laser resonators, optical waveguides, and other simple physical systems, however, have resonant or propagating eigenmodes that are nonnormal, i.e., nonorthogonal or non-Hermitian in character.

This in turn leads to some quite unusual mathematical, physical and quantum properties of these systems, including the concept of "adjoint" rather than "matched" coupling into these systems, fundamental changes in eigenmode expansion procedures, and large and measurable excess quantum noise effects in lasers using such resonators.

This topic has now become fairly well understood theoretically and confirmed experimentally, but there are still a few aspects of the subject that remain unpublished, including a generalized Nyquist theorem for linear but nonnormal systems. Links to a number of recent and pending publications on the general subject of nonnormal optical systems will be added to this page shortly.

Small-scale self focusing in tapered optical beams

The basic process of small-scale self focusing due to optical Kerr effects or saturable gain in collimated optical beams, and the possibility of exponential growth leading to filamentation and beam break up, is well understood theoretically and experimentally.

This memo for file and a longer and more up to date seminar presentation describe an unpublished analysis of the same phenomena in strongly diverging or converging optical beams, using a model involving a combination of Newtons' rings and nonlinearly induced Fresnel zone plates. No exponential growth is predicted because of the lack of any Talbot effects in a strongly tapered optical beams.

Virtual source model for unstable resonators

A memo for file describing an alternative, more physically meaningful version of the "virtual source model" for interpreting and calculating the resonant modes of unstable optical resonators based on Sommerfeld or Keller edge waves scattered from the mirror edges.