Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response

Yoshihiro Akahane, Takashi Asano, Hitomichi Takano, Bong-Shik Song, Yoshinori Takana, and Susumu Noda

Open Access Open Access

Abstract

We report a theoretical and experimental study of a channel drop filter with two cascaded point-defects between two line-defects in a two-dimensional photonic-crystal slab. Using coupled-mode analysis and a three-dimensional finite-difference time-domain method, we design a filter to engineer the line shape of the drop spectrum. A flat-top and sharp roll-off response is theoretically and experimentally achieved by the designed and fabricated filters. Furthermore, we theoretically demonstrate that drop efficiency is increased dramatically, up to 93%, by introducing hetero-photonic crystals. We also describe a method to modify the bandwidth of the spectrum.

©2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs

Ziyang Zhang and Min Qiu
Opt. Express 13(7) 2596-2604 (2005)

Channel drop filter in two-dimensional triangular lattice photonic crystals

Hongliang Ren, Chun Jiang, Weisheng Hu, Mingyi Gao, Yang Qu, and Fanghua Wang
J. Opt. Soc. Am. A 24(10) A7-A11 (2007)

Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal

Hitomichi Takano, Bong-Shik Song, Takashi Asano, and Susumu Noda
Opt. Express 14(8) 3491-3496 (2006)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)
Fig. 1.
Fig. 1. (a) Schematic of channel drop filter consisting of two cascaded point-defect cavities between two line-defect waveguides in a 2D PC slab and (b) its simplified model.

Download Full Size | PDF

Fig. 2.
Fig. 2. A schematic diagram showing distances g and h between two cavities and the cavity structure used in Sec. 2 and Sec. 3, where the displacement of air holes at the cavity edges is set to 0.15a.

Download Full Size | PDF

Fig. 3.
Fig. 3. Plot of (a) the in-plane Q (Q in), the vertical Q (Q v), and (b) 1/τ v+1/τ in calculated for the filter including the point-defect cavity shown in Fig. 2 as a function of the distance d 0 between the cavity and waveguide.

Download Full Size | PDF

Fig. 4.
Fig. 4. Calculated drop spectra from CMT analysis (solid line) and 3D-FDTD simulation (open circles). Lorentzian curve with the same FWHM as the solid line is also shown as dashed line for comparison.

Download Full Size | PDF

Fig. 5.
Fig. 5. SEM image near the point-defect cavities of the fabricated sample and magnified image of the cavity.

Download Full Size | PDF

Fig. 6.
Fig. 6. Experimental results observed from the outgoing waveguide-facet side of ports 2 and 4 by infrared camera. (a) Near-field image in the on-resonant case. The dropped and transmitted light spots are observed. (b) Near-field image in the off-resonant case. Only the transmitted light is observed.

Download Full Size | PDF

Fig. 7.
Fig. 7. (a) Measured drop spectrum of the fabricated filter (open circles) and its fitted curve by CMT analysis (solid line). Lorentzian curve with the same FWHM as the measured spectrum is also shown as a dashed line for comparison. (b) Measured drop spectrum of a filter consisting of one cavity and one waveguide in a 2D PC slab (open circles) and Lorentzian curve with the same FWHM as the spectrum (dashed line).

Download Full Size | PDF

Fig. 8.
Fig. 8. (a) Schematic of channel drop filter with both flat-top response and high drop efficiency. IP-HPC is introduced into a filter consisting of two cascaded point-defect cavities between two line-defect waveguides in a 2D PC slab. (b) Simplified model of (a).

Download Full Size | PDF

Fig. 9.
Fig. 9. Plot of drop efficiency calculated for the filter with the cavity for each Qv as a function of (1/τ v+1/τinsystem)/µ.

Download Full Size | PDF

Fig. 10.
Fig. 10. A schematic diagram showing distances g and h between two cavities and the cavity structure used in Sec. 4, where the displacements of air holes at the nearest neighbors and the second and third nearest neighbors near the cavity edges are set to 0.20a, 0.025a, and 0.20a, respectively.

Download Full Size | PDF

Fig. 11.
Fig. 11. Plot of 1/τ v+1/τinsystem calculated for the filter for each distance d 0 between the cavity and waveguide as a function of the distance d 2 between the cavity and the hetero-interface.

Download Full Size | PDF

Fig. 12.
Fig. 12. Calculated drop spectra (open circles) from 3D-FDTD simulation of the filters with the following distances (d 0, d 2): (a) (5 rows, 11a 1), (b) (6 rows, 7a 1), and (c) (6 rows, 9a 1). Lorentzian curves with the same FWHM as the spectra are also shown as dashed lines for comparison.

Download Full Size | PDF

Fig. 13.
Fig. 13. Plot of absolute values of µ calculated for the 2D PC slab in which the radius of some air holes located in the center between two cavities is different from that of the surroundings (0.29a), as a function of their radius.

Download Full Size | PDF

Fig. 14.
Fig. 14. Calculated drop spectra (open circles) from 3D-FDTD simulation of the filter in which the radius of two holes located in the center between two cavities and the distance (d 0, d 2) are set to 0.49a 1 and (6 rows, 8a 1), respectively. Lorentzian curve with the same FWHM as the spectrum is also shown as a dashed line for comparison.

Download Full Size | PDF

Tables (2)

Tables Icon

Table 1. The mutual coupling coefficient between the two point-defect cavities over the angular resonant frequency, µ/ω 0, as a function of the distance between the cavities, as shown in Fig. 2. It is calculated for the cavity where the displacement of air holes at the cavity edges is set to 0.15a.

View Table | View all tables in this article
Tables Icon

Table 2. The mutual coupling coefficient between the two point-defect cavities over the angular resonant frequency, µ/ω0, as a function of the distance between the cavities, as shown in Fig. 10. It is calculated for the cavity where the displacements of air holes at the nearest neighbors and at the second and third nearest neighbors near the cavity edges are set to 0.20a, 0.025a, and 0.20a, respectively.

View Table | View all tables in this article

Equations (44)

Equations on this page are rendered with MathJax. Learn more.

d a 1 d t = ( j ω 0 − 1 τ v − 1 τ in ) a 1 + 1 τ in e − j β d 1 S + 1 − j μ a 2
d a 2 d t = ( j ω 0 − 1 τ v − 1 τ in ) a 2 − j μ a 1
S − 1 = − 1 τ in e − j β d 1 a 1
S − 2 = e − j β ( d 1 + d 2 ) ( S + 1 − 1 τ in e j β d 1 a 1 )
S − 3 = − 1 τ in e − j β d 3 a 2
S − 4 = − 1 τ in e − j β d 4 a 2
η = ∣ S − 3 S + 1 ∣ 2 = ∣ S − 4 S + 1 ∣ 2
= 1 τ in 2 μ 2 [ ( ω − ω 0 ) 4 + 2 { ( 1 τ v + 1 τ in ) 2 − μ 2 } ( ω − ω 0 ) 2 + { ( 1 τ v + 1 τ in ) 2 + μ 2 } 2 ]
μ 2 = ( 1 τ v + 1 τ in ) 2
Δ ω = 2 2 ∣ μ ∣
η = ∣ S − 3 S + 1 ∣ 2 = ∣ S − 4 S + 1 ∣ 2 = 1 4 ( 1 + τ in τ v ) 2
μ = ω 0 ∫ ∫ ∫ e 2 * ( ε − ε 1 ) e 1 dxdydz 2 ∫ ∫ ∫ e 2 * ε e 2 dxdydz
d a 1 d t = ( j ω 0 − 1 τ v − 1 τ in ) a 1 + 1 τ in e − j β d 1 S + 1 + 1 τ in e − j β d 2 S + 2 − j μ a 2
d a 2 d t = ( j ω 0 − 1 τ v − 1 τ in ) a 2 + 1 τ in e − j β d 2 S + 4 − j μ a 1
S − 1 = e − j β ( d 1 + d 2 ) ( S + 2 − 1 τ in e j β d 2 a 1 )
S − 2 = e − j β ( d 1 + d 2 ) ( S + 1 − 1 τ in e j β d 1 a 1 )
S − 3 = e − j β ( d 1 + d 2 ) ( S + 4 − 1 τ in e j β d 2 a 2 )
S − 4 = − 1 τ in e − j β d 2 a 2
S + 2 = S − 2 e − j Δ
S + 4 = S − 4 e − j Δ
η = ∣ S − 3 S + 1 ∣ 2
= 4 τ in system 2 μ 2 [ ( ω − ω 0 system ) 4 + 2 { ( 1 τ v + 1 τ in system ) 2 − μ 2 } ( ω − ω 0 system ) 2 + { ( 1 τ v + 1 τ in system ) 2 + μ 2 } 2 ]
τ in system = τ in 1 + cos θ
ω 0 system = ω 0 + sin θ τ in
θ = Δ + 2 β d 2
η = ∣ S − 3 S + 1 ∣ 2 = 4 { 1 μ τ in system ( 1 + τ in system τ v ) 2 + μ τ in system } 2
η = ∣ S − 3 S + 1 ∣ 2 = 4 { 1 μ τ in system + μ τ in system } 2
μ 2 = ( 1 τ v + 1 τ in system ) 2 = 1 ( τ in system ) 2 ( τ in system τ v + 1 ) 2
∇ × ∇ × e 1 + μ 0 ε 1 ∂ 2 e 1 ∂ t 2 = 0
∇ × ∇ × e 2 + μ 0 ε 2 ∂ 2 e 2 ∂ t 2 = 0
∇ × ∇ × E + μ 0 ε ∂ 2 E ∂ t 2 = 0
j ω 2 ( ε − ε 1 ) e 1 a ̂ 1 + j ω 2 ( ε − ε 2 ) e 2 a ̂ 2 + 2 ω ε e 1 d a ̂ 1 d t + 2 ω ε e 2 d a ̂ 2 d t − j ε e 1 d 2 a ̂ 1 d t 2 − j ω e 2 d 2 a ̂ 2 d t 2
= 0
A ≡ ∫ ∫ ∫ e 1 * ( ε − ε 1 ) e 1 dxdydz = ∫ ∫ ∫ e 2 * ( ε − ε 2 ) e 2 dxdydz
B ≡ ∫ ∫ ∫ e 1 * ( ε − ε 2 ) e 2 dxdydz = ∫ ∫ ∫ e 2 * ( ε − ε 1 ) e 1 dxdydz
C ≡ ∫ ∫ ∫ e 1 * ε e 1 dxdydz = ∫ ∫ ∫ e 2 * ε e 2 dxdydz
A ≡ ∫ ∫ ∫ e 1 * ε e 2 dxdydz = ∫ ∫ ∫ e 2 * ε e 1 dxdydz
j ω 2 A a ̂ 1 + j ω 2 B a ̂ 2 + C ( 2 ω d a ̂ 1 d t − j d 2 a ̂ 1 d t 2 ) + D ( 2 ω d a ̂ 2 d t − j d 2 a ̂ 2 d t 2 ) = 0
j ω 2 B a ̂ 1 + j ω 2 A a ̂ 2 + D ( 2 ω d a ̂ 1 d t − j d 2 a ̂ 1 d t 2 ) + C ( 2 ω d a ̂ 2 d t − j d 2 a ̂ 2 d t 2 ) = 0
a 1 = a ̂ 1 exp ( j ω t )
a 2 = a ̂ 2 exp ( j ω t )
d a 1 d t = j ω 0 a 1 − j ω 0 B C − A D 2 ( C 2 − D 2 ) B D − A C a 2
ω 0 ≡ ω { 1 + B D − A C 2 ( C 2 − D 2 ) }
μ = ω 0 B C − A D 2 ( C 2 − D 2 ) + B D − A C ≈ ω 0 B 2 C
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use