Effect of defect structure on light extraction from a photonic crystal slab nanocavity

TH1

C-(I

6)-I

EFFECT

OF

DEFECT STRUCTURE

ON

LIGHT EXTRACTION FROM

A PHOTONIC CRYSTAL SLAB NANOCAVITY

Jyh-Yang

Wang,

Yean-Woei Kiang,

and

C. C. Yang

Graduate Institute

of

Communication Engineering, Graduate Institute of Electro-Optical

Engineering, and Department

of

Electrical Engineering, National Taiwan University,

I ,

Roosevelt Road, Section 4,

Taipei,

Taiwan

(phone) 886-2-2363525 1

(fax)

886-2-23652637 (e-mail) [email protected]

Abstract

--

Radiation characteristics of photonic crystal slab nanocavities are numerically studied.

The radiation rate and extraction efficiency are calculated for diflerent defect structures.

In this paper, we numerically calculate the effective extraction rate for photonic crystal slab

nanocavities with different defect structures and compare the differences among them. The s t r u e r e

we considered is shown schematically in Fig. 1. It is a dielectric slab standing in the air, penetrated

with a 7x7 square lattice of air holes. The air hole at the center is specially processed (by varying the

depth d, or radius rJ to form a single defect

as

a nanocavity. The radius r of other holes is fixed to be

0.35a and the thickness d of the slab to be 0 . 4 q where a is the lattice constant. The refractive index of

the slab is set to be 3.4. For simulations, the three-dimensional finite-difference time-domain (3-D

FDTD) method is used. By discretizing in space and time with appropriate boundary conditions, the

Maxwell's equations can be solved iteratively for whole computation domain at each time step. The excitation is chosen to be a ydirectional oscillating dipole located at the center of the slab to excite the TE-like modes, simulating the light emission from a quantum well structure. An important measure of an LED is the extraction efficiency, which is defined here as the fraction of emitted flux through the top surface of the slab to the total emitted flux. We also calculate the radiation rate defined

as the ratio of the total radiated'power of a dipole in a nanocavity to the total radiated power of the

same dipole in the free space. By multiplying the radiation rate and the extraction efficiency, a more practical quantity, the effective extraction rate, can be defined. After Fourier transforming the field

evolution in time, we can compute all these derived quantities over a frequency range in a single

simulation run. Figure 2 shows the effective extraction rate versus the normalized frequency (a/

A)

for

the cavity without a central air hole (d,=r,=O, denoted by the solid curve) and for the cavity with a

central air hole (d,=O. l a and rC=0.35a, denoted by the dashed curve). It is found that the peak effective

extraction rate is enhanced by about 33% at normalized frequency around 0.3, if the central air hole is

properly introduced. 30 ...

,1

~,

I

. . . I , . I i i . ~ ~ ~ ...

.,

L,/

..

..

... $, .I' ~ /' . ,

Normalized Irquency

(an)

~ i1 Schematic diagram ~ . of a

nanocavity (only half shown). clysml

slab Fig. 2 The effective extraction rate versus the

normalized frequency. The solid curve is for the

cavity without a central air hole (d,=r,=O) and the

dashed curve for the cavity with a central air hole

(d,=O.la andrC=0.35a). 0-7803-7766-4103/617.00 02003 IEEE