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Random stack of resonant dielectric layers as a laser system

Yan Feng and Ken-ichi Ueda

Open Access Open Access

Abstract

We propose a random stack of resonant dielectric layers as a system for random-laser study. Owing to the Fabry–Perot resonance of the dielectric layers, the propagation of light in such systems is frequency dependent (a band structure). As a consequence, if the system is designed such that pump light is in passband while optical gain is in stop band, the laser threshold can be reduced dramatically compared with those of completely disordered systems.

©2004 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. Transmission spectra for systems with number of layers N=15. In (a) the system is completely random; in (b) it contains 10 identical layers of 1-µm thickness and a transmission spectrum for a single dielectric layer of 1-µm thickness; in (c) all dielectric layers are identical but the spacing remains random; in (d) the dielectric layers and the spacing are identical.

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Fig. 2.
Fig. 2. Transmission spectra averaged over 5000 realizations and the variance for systems formed by dielectric layers of thickness with normal distribution. System length N=15; ε=9; variance σ=0.01, 0.03, 0.09.

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Fig. 3.
Fig. 3. Simulation results for systems with σ=0.1, 0.01, and random system. Top, the reciprocal of localization length as a function of wave number; bottom, the threshold of laser at 0.325π µm-1, which is near the best-localized wavelength, for a system of 60-µm length, as a function of wave number of pump light.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

g ( x ) = GA ( x ) exp ( − x ξ p ) .
I ( x , x 0 ) = B ( x , x 0 ) exp ( − ∣ x − x 0 ∣ ξ l ) ,
δ ∼ exp ( − x 0 ξ l ) + exp ( − L − x 0 ξ l ) + δ 0 ,
∫ 0 L g ( x ) I ( x , x 0 ) d x = ∫ 0 L G t A ( x ) B ( x , x 0 ) exp ( − x ξ p − ∣ x − x 0 ∣ ξ l ) d x
= G t C ∫ 0 L exp ( − x ξ p − ∣ x − x 0 ∣ ξ l ) d x
= δ .
− L ⁄ ξ ( λ ) = < ln T ( λ , L ) > .
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