M.Sc Thesis | |

M.Sc Student | Shlafman Michael |
---|---|

Subject | Complex Frequency Perturbation Treatment of Optical Resonances with Radiation Loss |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROFESSOR EMERITUS Yosef Salzman |

Full Thesis text |

This work is an extension of perturbation treatment to the case of 3D
vector electromagnetic resonant modes in cavities experiencing radiation loss.
Mathematically, such resonances have complex eigen-frequencies, the imaginary
part of which is responsible for the decay rate, (the reciprocal of the *Q-factor*
of the cavity). A small change in the cavity results in changes in the
frequency real and imaginary parts, thus, it affects the photon lifetime as
well.

Present perturbation treatment is inspired in quantum mechanics
perturbation theory in which modulation of the system's structure leads to changes
in the eigen-mode and eigen-value predictable by the theory. It was then
reformulated for the equivalent electromagnetic case. Former perturbation
theories in electromagnetics are inadequate for estimating changes in the *Q-factor*
because they address only stationary modes (of infinite lifetime)*.*

In a previous work, the perturbation treatment using complex
eigen-frequency scalar leaky-cavity modes in 1D was developed. We augment this
formalism to higher dimensions, and treat vector electromagnetic fields, by
establishing the normalisable leaky-cavity mode (NLM) framework. Based on it a
new perturbation treatment in the complex domain was derived. It is capable to
treat finite lifetime resonances (the loss of which is attributed to radiation
to the outer world) and accurately predict the changes in frequency and *Q*.

The NLM semi-analytical model was tested against an analytical solution
in 1D and a Finite Difference Time Domain (FDTD) simulation in 2D. It was found
that the extent of *Q* switching ability is mainly characterized by square
of the imaginary part of the (newly) normalized complex electric field
[Shlafman, Bayn and Salzman, Opt. Exp. 18, 15907 19 July 2010]. In addition,
the limitations of the prediction capability of the new formalism were explored.
It was found that the theory's accuracy is better correlated to the *Q*
change extent rather than to the material modulation strength. [Shlafman and Salzman, Photon. Nanostruct.?Fund. Appl.-
submitted].

An interesting insight regarding modes anti-crossing revealed how minor
material modulations may cause major *Q* changes (*Q*- Switching).
This was exemplified in 2D where a relative material modulation of 7x10^{-4}
resulted in a change in *Q* of nearly 50%.