Unidirectional emission from whispering gallery modes via transformation optics

Yushin Kim; Soo-Young Lee; Jung-Wan Ryu; Inbo Kim; Jae-hyung Han; Heung-Sik Tae; Muhan Choi; Bumki Min

doi:10.1117/12.2061850

12 September 2014 Unidirectional emission from whispering gallery modes via transformation optics

Yushin Kim, Soo-Young Lee, Jung-Wan Ryu, Inbo Kim, Jae-hyung Han, Heung-Sik Tae, Muhan Choi, Bumki Min

Proceedings Volume 9193, Novel Optical Systems Design and Optimization XVII; 919310 (2014) https://doi.org/10.1117/12.2061850
Event: SPIE Optical Engineering + Applications, 2014, San Diego, California, United States

Abstract

It is well known from transformation optics that a light pathway can be designed with artificial materials. When a coordinate transform technique is applied to optically resonating dielectric structures, interesting phenomena can be observed as well. Generally, a long-lived whispering gallery mode (WGM) has no preferential direction of radiation because of its rotationally symmetric structure. However, if the space inside the resonator is transformed so that the discontinuity of coordinates exists, it becomes possible to reconcile directional emission with WGMs. Here, we transform only the inner space of a deformed optical cavity, e.g., the Limaçon cavity into a virtual perfect disk via a conformal mapping and show these two seemingly incompatible behaviors can be observed simultaneously. The refractive index profiles that realize the transformed space can be obtained from the conformal space transformation. The resonant mode calculated with a transformed boundary element method shows that the WGMs can restore for the deformed cavity. The Husimi function calculated for this transformed cavity shows a weighted band-like profile, which implies that the optical rays inside the cavity is maintaining its reflecting angle as is for the original cavity. However, the far-field pattern shows anisotropic emission of radiation because it is determined by tunneling through the rotationally asymmetric boundary. For example, the conformal WGMs in Limaçon and center-shifted triangular cavities exhibit bidirectional and uni-directional emission patterns in the far-field, respectively. These conformal WGM cavities with both the ultra-high quality factor and the directional light emission may be used in the realization of efficient directional light sources.

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Yushin Kim, Soo-Young Lee, Jung-Wan Ryu, Inbo Kim, Jae-hyung Han, Heung-Sik Tae, Muhan Choi, and Bumki Min "Unidirectional emission from whispering gallery modes via transformation optics", Proc. SPIE 9193, Novel Optical Systems Design and Optimization XVII, 919310 (12 September 2014); https://doi.org/10.1117/12.2061850

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KEYWORDS

Refractive index

Optical resonators

Dielectrics

Near field

Light

Light sources

Resonators

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