Analysis of energy-band structure of 1D and 2D photonic crystals

Hanna Laba; Volodymyr Fitio; Yaroslav Bobitski

doi:10.1117/12.596669

3 June 2005 Analysis of energy-band structure of 1D and 2D photonic crystals by the method of coupled waves

Hanna Laba, Volodymyr Fitio, Yaroslav Bobitski

Proceedings Volume 5825, Opto-Ireland 2005: Optoelectronics, Photonic Devices, and Optical Networks; (2005) https://doi.org/10.1117/12.596669
Event: OPTO-Ireland, 2005, Dublin, Ireland

Abstract

In the classic method for calculation of energy-band structure of photonic crystal the electromagnetic field of wave that propagates in crystal is expanded in plane waves. The determination task of the allowed frequencies at certain wave vector in the first Brillouin zone leads to the finding of eigenvalues and eigenvectors of the corresponding matrix equation with dimension, which provides the necessary precision of determination of the allowed frequencies. Because of slow convergence of expansion in plane waves, it is necessary to solve the matrix equation of high dimension that requires considerable computation time. The proposed method of determination of the allowed frequencies is based on the coupled wave method (CWM) at the corresponding definition of boundary periodic conditions. Especially, this method is simple for 1D photonic crystals, that comes to the eigenvalue problem of the matrix equation of 2x2 dimension. For 2D photonic crystals the solution also leads to the eigenvalue problem, but of 2Nx2N matrix, where N is number of the coupled waves. Frequency will be allowed, if absolute value of eigenvalue is equal to one. In the proposed method the 2Nx2N dimension of the matrix equation is equivalent to the dimension of N²xN² of classic method. The stable S-algorithm of computation is developed. The computations of energy-band structure of 1D and 2D photonic crystals of the simplest structure are conducted. The dependencies of computation precision on the number of coupled waves at change of N from 1 to 29 are obtained.

Citation Download Citation

Hanna Laba, Volodymyr Fitio, and Yaroslav Bobitski "Analysis of energy-band structure of 1D and 2D photonic crystals by the method of coupled waves", Proc. SPIE 5825, Opto-Ireland 2005: Optoelectronics, Photonic Devices, and Optical Networks, (3 June 2005); https://doi.org/10.1117/12.596669

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
11 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Photonic crystals

Diffraction

Crystals

Polarization

Radio propagation

Differential equations

Electromagnetism

Show All Keywords

Keywords/Phrases

Search In:

Publication Years