Analysis of rectangular ring resonator sensor with photonic crystal microcavity

Hong-Seung Kim*a, Doo-Gun Kim b, Geum-Yoon Oh a, and Young-Wan Choi a

a School of Electrical and Electronics Engineering, Chung-Ang University, 221 Heuksuk-dong, Dongjak-ku, Seoul, 156-756, Korea,

bPhotonics Device Team, Korea Photonics Technology Institute, Gwangju, 500-460, Korea Tel: +82-2-820-5326, Fax: +82-2-822-5326, e-mail:ychoi@cau.ac.kr

ABSTRACT

In this paper, we propose a novel sensor structure based on the rectangular ring resonator with the photonic crystal microcavity (PCM), and optimize the structure using finite-difference time-domain (FDTD) method. This sensor consists of the rectangular resonator with total internal reflection mirror and the PCM, which can be placed at the nearby optical waveguide of the rectangular ring resonator. The PCM is composed of a defect cavity with different holes on the center of it. The Q-factor of the PCM can be significantly enhanced when the PCM has the resonance wavelength. The PCM can be evanescently coupled to a side waveguide arm of the rectangular ring resonator. The sensitivity of the ring resonator in the presence of gas or biomolecules composition was calculated using the FDTD method. When the injected gas or biomolecules pass through the PCM, the variation of effective index due to their concentration affects the resonance condition of the rectangular ring resonator. We have investigated how the shift of the resonance peak in the resonance wavelengths depends on the gas or biomolecules concentration. We also have optimized the sensor structure for the waveguide width and length, the hole radius, and the number of hole on the PCM. The optimum lattice constants, hole radius, and cavity length are 370, 100, and 580 nm, respectively. The rectangular ring resonator sensor with microcavity significantly enhances the quality factor and the sensitivity compared to the directional coupler sensor with PCM. The change of normalized output power in rectangular ring resonator with PCM is approximately twice larger than the change in directional coupler with PCM.

Keywords: Finite-difference time-domain (FDTD), Microcavity, Optical waveguide, Photonic bandgap, Rectangular ring resonator, Biosensor.

1. INTRODUCTION Recently, bio-chemical sensors using photonic device are actively studied. Though numerous different architectures

have been developed (micro resonator sensors [1], surface plasmon resonance sensors [2], Interferometric sensors [3] and photonic crystals sensors) in nearly all cases detection is based on measuring the change in refractive index that results when solution phase targets bind with complimentary probes that have been predeposited on the surface. Small size photonic crystals sensor is focused by many researchers, because it can make sure of large contact area of bio-material for detection and has high sensitivity. Generally, the primary advantages of optical techniques over analogous mechanical or electrical label free methods [4] are : the relative ease with which devices can be fabricated and the broad range of fluids and environments in which they can be used (e.g. gas, water and serum).

The photonic bandgap theory is suggested by Yablonobich at 1987 [5]. Using the theory, filter characteristic of 1D photonic crystals waveguide are reported [6]. The drawback of these designs is that the large photonic bandgap restricts high sensitivity sensing along the 1D photonic crystals sensor. Nanoscale optofluidic sensor arrays of directional coupler structure using the 1D photonic crystals is suggested [7]. Here, we propose a new scheme to overcome this limitation as using a rectangular ring resonator sensor with photonic crystal microcavity (PCM) for optofluidic sensing. This technique has the high sensitivity without the need for target labeling using the ring resonator

Physics and Simulation of Optoelectronic Devices XVII, edited by Marek Osinski, Bernd Witzigmann, Fritz Henneberger, Yasuhiko Arakawa, Proc. of SPIE Vol. 7211,

72110V · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.808902

Proc. of SPIE Vol. 7211 72110V-1

having high quality factor. The PCM is located around the ring resonator. Therefore, the Q-factor of the rectangular resonator can be significantly enhanced when the PCM has the resonant wavelength. As such our device can detect rarer targets in a given sample size since a smaller number of them are required to impart a measurable change.

In this paper, we theoretically analyze and design a rectangular ring resonator with PCM. We determine the sensitivity of our devices by observing the shift in the resonant wavelength of the resonators as a function of the change in refractive index of the fluid.

2. THEORETICAL ANALYSIS Photonic crystal is a structure, in which the atoms or molecules are replaced by macroscopic media with differing

dielectric constants, and the periodic potential is replaced by a dielectric function (or, equivalent, a periodic index of refraction). If the dielectric constants of the materials in the crystal are sufficiently different and if the absorption of light by the materials is minimal, then the refractions and reflections of light from all of the various interfaces can produce many of the same phenomena for photons (light modes) that the atomic potential produces for electrons. One solution to the problem of optical control and manipulation is thus a photonic crystal, a low-loss periodic dielectric medium. In particular, we can design and construct photonic crystals with photonic band gaps, preventing light from propagating in certain directions with specified frequencies.

Photonic band gap structures are calculated by transfer matrix method [6]. Assume that the transfer matrix functions M is given by

(1)

Tracking the complex amplitudes of the forward and backward waves through the boundary of a multilayered medium is facilitated by use of matrix method. Consider two arbitrary planes within a given optical system, denoted plane 1 and plane 2. The amplitudes of the forward and backward collected waves at plane 1, U1

(+) and U1(-) , respectively, are

represented by a column matrix of dimension 2, and similarly for plane 2. These two column matrices are related by matrix equation (1). The matrix M, whose elements are A, B, C, and D, is called the wave-transfer matrix (or transmission matrix). It depends on the optical properties of the layered medium between the two planes.

A multilayered medium is conveniently divided into a concatenation of basic elements described by known wave-transfer matrices, say M1, M2, …, MN. The amplitudes of the forward and backward collected waves at the two ends of the overall medium are then related by a single matrix that is the matrix product,

M= M1M2 … MN (2)

where the elements 1, 2, …, N are number of medium.

Consider a grating comprising a stack of N identical generic segments, each described by a unimodular wave-transfer matrix Mx satisfying the conservation relations for a lossless, reciprocal system, so that

1/ * /* / * 1/x

t r tM

r t t⎡ ⎤

= ⎢ ⎥⎣ ⎦

(3)

2 2 1, / ( / )*, arg{ } arg{ } / 2t r t r t r t r π+ = = − − = ± (4)

( ) ( ) ( )2 1 1

( ) ( ) ( )2 1 1

U U UA BM

C DU U U

+ + +

− − −

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤= =⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

Proc. of SPIE Vol. 7211 72110V-2

rLatticeConstal

Cavitylngth /

its

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WITH PCM

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e

Proc. of SPIE Vol. 7211 72110V-3

substrate. The silicon waveguide locates on the SiO2 layer. These holes symmetrically locate on the silicon waveguide. The defect mode of cavity exist middle of holes. The lattice constant (a) is the period of holes. The cavity length is the central defect size.

(a) (b)

(c)

Fig. 2 Transmittance for changes of hole radius, lattice constants, and cavity length

These results are calculated by the finite difference time domain (FDTD) method. The resonance is occurred at central defect state by Fabry-Perot mode. The figure 2 (a) shows simulation results of transmittance by the change of hole radius. As the hole radius changed +0.01 μm, resonance wavelength is -40 nm shifted. The sensitivity, ∆λ/∆R (Radius) results are very linear. The figure 2 (b) shows simulation results of transmittance by the change of lattice constants. As lattice constants is changed +0.01 μm, resonance wavelength is +32.5 nm shifted. The figure 2 (c) illustrates simulation results of transmittance by the change of cavity length. When cavity length is changed +0.01 μm, resonance wavelength is +18.3 nm shifted. ∆λ/∆x (cavity length) variation is also very linear. These phenomena can be explained by equation (5) and (6). As the lattice constant is increased, center frequency of photonic bandgap is decreased. So, resonant wavelength is red shifted. As the hole radius is increased, resonant frequency is increased. Because the cavity length is decreased by hole radius increase in fitted the lattice constants.

As a result, the optimized result of optical waveguide with PCM for 1550 nm wavelength is shown in Fig. 3(a). The waveguide width, hole radius, lattice constants, and cavity length are 470, 100, 370, and 580 nm, respectively. The wavelength to satisfied resonance condition propagates during traveling the waveguide, because other frequencies belong to the photonic bandgap region of hole arrays. The table 1 shows the summary for various parameter changes.

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.800.0

0.2

0.4

0.6

0.8

1.0

Nom

alliz

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ansm

issi

on p

ower

[a.u

.]

Wavelength [μm]

Hole radius [μm] 0.08 0.1 0.12 0.14 0.16

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.800.0

0.2

0.4

0.6

0.8

1.0

Nom

alliz

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ansm

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ower

[a.u

.]

Wavelength [μm]

Lattice constants [μm] 0.37 0.39 0.41

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.800.0

0.2

0.4

0.6

0.8

1.0

Nom

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ansm

issi

on p

ower

[a.u

.]

Wavelength [μm]

Cavity length [μm] 0.15 0.18 0.21 0.24

Proc. of SPIE Vol. 7211 72110V-4

Table 1 Summary for various parameter changes

Parameter Shift by the increase of the parameters ∆λ/∆x (nm/nm)

Hole radius Blue shift - 40 / 10

Lattice constants Red shift + 32.5 / 10

Cavity length Red shift +18.5 / 10 The 1550 nm wavelength can propagate in the medium but 1500 nm wave cannot propagate, because the normalized

transmission power is nearly zero shown in Fig. 3 (a).

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.800.0

0.2

0.4

0.6

0.8

1.0

Nom

alliz

ed tr

ansm

issi

on p

ower

[a.u

]

Wavelength [μm]

Number of holes 2 4 6 8 10 12 14 16

(a) (b)

Fig. 3 (a) Simulation results of optimized waveguide with PCM at 1500 nm wavelength (b) Simulation results of number of hole change

The sharpness is the very important parameter for high quality factor. The sharpness of resonance peak is determined by number of holes. These results are shown in Fig. 3 (b). As the number of hole is increased, sharpness is increased. This is because the hole in the waveguide roles as a mirror. The normalized transmission power is decreased because many holes cause high loss. The optimized number of hole for low loss and high transmission power is 8 at 1550 nm wavelength.

3.2. Directional coupler with PCM

Fig. 4 Structure of directional coupler with PCM

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.800.0

0.2

0.4

0.6

0.8

1.0

Nom

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[a.u

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Wavelength [μm]

Proc. of SPIE Vol. 7211 72110V-5

I reflected wavehR mlrrc

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4

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Proc. of SPIE Vol. 7211 72110V-6

2.0

0

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-4

-6

-8

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-12

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16-020 -0.15 -0.

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1.48 1.490.0

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arp peak. Ththe structure o

out PCM. Thd characteristicget the sharp pPCM is enhan

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(b)

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1.50

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he PCM is addof rectangular

he figure 8 (b)c curve of rectpeak than peak

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x change

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aveguide of or. The figureomparison of resonator withal coupler.

d r, s r s n d s s

h

Proc. of SPIE Vol. 7211 72110V-7

-4 -3 -2

X(um)-1

*-3 -2

x (lAm)

)molecule,lecule binder

=00C===0C=

F-4

Bk

The biosensmicro-cavity pass through rectangular ribiomolecules

Figure 10 sh

resonance at proposed in FPCM structur

4. BIOSE

sor proposed ithat lies adjacthe PCM, the

ing resonator. s concentration

Fig. 10

hows light wa1510 nm wav

Fig. 9 by the rire, because PC

ENSOR USI

Fig. 9 Stru

in this study iscent to the wavvariation of e The shift of

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on results. Tght of 1510 nmand PCM struonly had the r

ANGULAR

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g. 9. It consictangular ringx due to their ce peak in the

(a) 1490 nm w

The rectangulam wavelength ucture. Lightesonance con

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ONATOR W

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tor and PCM ha double resonwavelength d1510 nm wav

WITH PCM

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avelength

have the charanance in the stoesn’t couple velength.

M

otonic crystal iomolecules dition of the gas or

acteristic of tructure with the

Proc. of SPIE Vol. 7211 72110V-8

1.00 1.01 1.02 1.03 1.04 1.050.000

0.005

0.010

0.015

0.020

0.025

0.030

Cha

nge

of n

orm

aliz

ed p

ower

[|Δ

p|]

Effective index in holes [RI]

Directional coupler with PCM Rectangular ring resonator with PCM

Fig. 11 Change of output power by the effective index change

The change of refractive index can be confirmed by detection of output power variation as Fig. 11. These results are shown for the comparison of directional coupler with PCM and rectangular ring resonator with PCM. Figure 11 present that the rectangular ring resonator with PCM is more sensitive than directional coupler with PCM. The change of normalized output power in rectangular ring resonator with PCM is larger than the change in directional coupler with PCM, because the structure rectangular ring resonator with PCM had additional resonance by PCM structure. The broad filter characteristic of directional coupler is advanced by using the sharp filter characteristic of rectangular ring resonator with PCM. Therefore, the sensitivity for detection of biomolecules is improved compared to the directional coupler with PCM. Here, if we use the array of PCM resonator, the sensitivity can be significantly increased [7].

5. CONCLUSION

In this paper, a new biosensor structure, which we refer to as rectangular resonator with PCM, has been optimized and

characterized. This device comprise of a waveguide with evanescently coupled defect mode on the side waveguide. The broad filter characteristic of directional waveguides with microcavity is improved by sharp filter characteristic of rectangular resonator. The rectangular ring resonator sensor with microcavity enhanced quality factor and sensitivity for using sensor than directional coupler sensor with PCM. The change of normalized output power in rectangular ring resonator with PCM is approximately twice larger than change in directional coupler with PCM. The sensitivity of directional coupler with PCM is 0.003 output power change, but the sensitivity of rectangular resonator with PCM is 0.006 output power change. These with values can be significantly enhanced by using the array of PCM resonator. Single TIR mirror in rectangular resonator is designed 0.57 dB loss using the mirror offset by Goos-Hänchen shift. The offset depth is – 0.09 μm. Such optimization of rectangular resonator with PCM enables bio sensor with small size portable modules with very high sensitivity.

6. ACKNOWLEDGEMENT

This work was supported by “Seoul R&BD program (10544)”

Proc. of SPIE Vol. 7211 72110V-9

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Kimerling, Henry I. Smith, and E. P. Ippen., “Photonic-bandgap microcavities in optical waveguides,” Nature, 390(13), 1997

[7] Sudeep Mandal and David Erickson, “Nanoscale optofluidic sensor arrays,” Optics Express, 16(3), 2008 [8] Saleh and Teich, [Fundamental of photonics], Wiley-interscience, 243-279, 2007 [9] John D. Joannopoulos, Steven G. Johnson, Hoshua N. Winn, and Robert D. Meade., [Photonic crystals :

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1947

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