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Designing whispering gallery modes via transformation optics

Nature Photonics volume 10, pages 647–652 (2016)Cite this article

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Abstract

In dielectric cavities with a rotational symmetry, whispering gallery modes (WGMs) with an extremely long lifetime (that is, a very high Q factor) can be formed by total internal reflection of light around the rim of the cavities. The ultrahigh Q factor of WGMs has enabled a variety of impressive photonic systems, such as ultralow threshold microlasers1,2,3, bio-sensors with unprecedented sensitivity4,5 and cavity optomechanical devices6. However, the isotropic emission of WGMs, which is due to the rotational symmetry, is a serious drawback in applications that require directional light sources. Considerable efforts have thus been devoted to achieving directional emission by intentionally breaking the rotational symmetry7,8,9. However, all of the methods proposed so far have suffered from substantial Q-spoiling. Here, we show how the mode properties of dielectric whispering gallery cavities, such as the Q factor and emission directionality, can be tailored at will using transformation optics. The proposed scheme will open a new horizon of applications beyond the conventional WGMs.

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Figure 1: A homogeneous disk cavity versus a limaçon-shaped transformation cavity.
Figure 2: Comparison of a transformation cavity and a homogeneous cavity with limaçon shapes.
Figure 3: Bidirectional and unidirectional far-field emission of the cWGMs of a limaçon-shaped transformation cavity and a triangular transformation cavity.
Figure 4: Numerical verification of WGMs and cWGMs in the cavities implemented by holes and posts.
Figure 5: Experimental implementation of a triangular transformation cavity.

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Acknowledgements

This research at KNU (S.-Y.L, J.-W.R., I.K, J.-H.H and M.C) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2013R1A1A2065357). J.-W.R was supported by Project Code (IBS-R024-D1). H.-S.T was supported by the NRF funded by the Ministry of Education (2013R1A1A4A03008577). KAIST (Y.K and B.M) was supported by Nano·Material Technology Development Program (2015036205), the World Class Institute Program (No. WCI 2011-001) and the Pioneer Research Center Program (2014M3C1A3052537) through the NRF as funded by the Ministry of Science, ICT and Future Planning (No. 2012R1A2A1A03670391 and No. 2015001948). This work was supported by the Center for Advanced Meta-Materials funded by the Ministry of Science, ICT and Future Planning as Global Frontier Project (CAMM-2014M3A6B3063709).

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  1. Yushin Kim, Soo-Young Lee and Jung-Wan Ryu: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Republic of Korea

    Yushin Kim & Bumki Min

  2. School of Electronics Engineering, Kyungpook National University, Daegu, 41566, Republic of Korea

    Soo-Young Lee, Jung-Wan Ryu, Inbo Kim, Jae-Hyung Han, Heung-Sik Tae & Muhan Choi

  3. Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, 34051, Republic of Korea

    Jung-Wan Ryu

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Contributions

Y.K., S.-Y.L., J.-W.R., I.K., M.C. and B.M. conceived the original idea. S.-Y.L., I.K. and M.C. performed theoretical calculations. Y.K., S.-Y.L. and J.-W.R. performed numerical simulations. Y.K. prepared the experimental set-up and performed the experiments. Y.K., S.-Y.L., J.-W.R., I.K., M.C. and B.M. analysed the data. Y.K., S.-Y.L., J.-W.R., I.K., J.-H.H., H.-S.T., M.C. and B.M. discussed the results. Y.K., S.-Y.L., J.-W.R., I.K., M.C. and B.M. wrote the manuscript, and all authors provided feedback.

Corresponding authors

Correspondence to Muhan Choi or Bumki Min.

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Kim, Y., Lee, SY., Ryu, JW. et al. Designing whispering gallery modes via transformation optics. Nature Photon 10, 647–652 (2016). https://doi.org/10.1038/nphoton.2016.184

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