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[Editors Pick] Current Optics and Photonics Vol. 5 no. 1 (2021 February)

한국광학회 hit 209 date 2021-04-05

Shannon Entropy as an Indicator of the Spatial Resolutions of the Morphologies of the Mode Patterns in an Optical Resonator
Kyu-Won Park1 *, Jinuk Kim1, and Songky Moon2

1 Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
2 Faculty of Liberal Education, Seoul National University, Seoul 08826, Korea

 

 

 

Current Optics and Photonics  Vol. 5 No.1 (2021 February) pp. 16-22
DOI: https://doi.org/10.3807/COPP.2021.5.1.016

 


 


Fig. 1  The eigenvalue trajectories and their corresponding Shannon entropies. (a) Real part of eigenvalues kR as the eccentricity ε is varied. (b) Imaginary part of eigenvalues kR as ε is varied. The Shannon entropies for N = 98, 212, 398, 596, 810, and 1040 are shown in (c), (d), (e), (f), (g), and (h), respectively.

 

 

Abstract

We present the Shannon entropy as an indicator of the spatial resolutions of the morphologies of the resonance mode patterns in an optical resonator. We obtain each optimized number of mesh points, one of minimum size and the other of maximum one. The optimized mesh-point number of minimum size is determined by the identifiable quantum number through a chi-squared test, whereas the saturation of the difference between Shannon entropies corresponds to the other mesh-point number of maximum size. We also show that the optimized minimum mesh-point increases as the (real) wave number increases and approximates the proportionality constant between them.