Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method

Lucio Claudio Andreani and Dario Gerace
Phys. Rev. B 73, 235114 – Published 19 June 2006

Abstract

According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow us to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we present a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction losses of quasiguided modes are calculated for the periodic lattice as well as for line and point defects defined therein. The main results are summarized as follows: (i) The triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode, but the useful region is generally limited by the presence of second-order waveguide modes; (ii) the lattice may support the usual photonic band gap for even modes (quasi-TE polarization) and several band gaps for odd modes (quasi-TM polarization), which could be tuned in order to achieve doubly resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second-harmonic frequency; (iii) diffraction losses of quasiguided modes in the triangular lattices with circular and triangular holes, and in line-defect waveguides or point-defect cavities based on these geometries, are comparable. The results point to the interest of the triangular lattice of triangular holes for nonlinear optics, and show the usefulness of the guided-mode expansion method for calculating photonic band dispersion and diffraction losses, especially for higher-lying photonic modes.

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  • Received 22 March 2006

DOI:https://doi.org/10.1103/PhysRevB.73.235114

©2006 American Physical Society

Authors & Affiliations

Lucio Claudio Andreani and Dario Gerace*

  • Dipartimento di Fisica “A. Volta,” Università degli Studi di Pavia, via Bassi 6, I-27100 Pavia, Italy

  • *Present address: Institute of Quantum Electronics, ETH-Hönggerberg, CH-8093 Zürich, Switzerland.

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Issue

Vol. 73, Iss. 23 — 15 June 2006

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