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Design of A Two-Dimensional Chalcogenide Photonic Crystal for Application as A Band Pass Filter

Rajpal Singh1, a) A. Bhargava2

1Department of Physics, Govt. College, Khetri, India

2Nanophysics Laboratory, Department of Physics, Govt. Dungar College, Bikaner-334001 India.

a) Corresponding author’s Email: rajubkn@gmail.com

Abstract. In this paper, we have designed a two- dimensional (2D) photonic crystal structure using chalcogenide glass for band pass filter application. A two dimensional square lattice structure is taken with chalcogenide rods in air. The filter is formed by creating two linear waveguides on both side of a point defect. The resonant mode is then coupled between the waveguide and point defect, which allows the requisite frequencies to pass. The effect of size of defect on the transmission and electric field distribution is also studied.

Introduction

Photonic crystals (PhCs) have attracted great attention of the researchers due to their tremendous control over the propagation of electromagnetic wave in it [1, 2]. The periodic arrangement of alternatively high and low dielectric materials causes the photonic bandgap (PBG) region, in which light doesn’t allow to propagate in certain frequencies. Therefore, PhCs find many potential applications as photonic devices in optical communications [2-10].

Optical filters selectively transmit light in a particular range of wavelengths. The optical properties of filters are completely described by their frequency response, which specifies how the magnitude and phase of each frequency component of an incoming signal is modified by the filter [8, 9]. In photonic crystal waveguides, light of certain frequencies is forced to propagate along the linear defect, since the photonic band gap prohibits propagation in other directions. PCW filters exhibiting wavelength selectivity can be realized by coupling a point defect to a linear waveguide [8-10].

Chalcogenide glasses have properties of infrared transmitting, which contain materials as chalcogen elements S, Se or Te, combined with others such as As, Si and Ge. Chalcogenides have a great advantage because of their attractive properties as glasses can be formed over a wide range of compositions; the refractive index is high, typically between 2.4 and 3, linear absorption losses are low over a wide wavelength range and a large χ(3) nonlinearity (much larger than Si) [2]. Thus, the chalcogenide glass PC platform is a promising architecture for confining and guiding light [11].

In present paper, we propose a simple band pass filter design using line defect waveguide coupled with point defect in a chalcogenide photonic crystal of square lattice. The field distribution patterns are also studied.

Theoretical Method and Structure

We have used the well-known FDTD method with a computational domain of 31x21 lattice constants (total 651 unit cells) [12]. The waveguides are along the direction of the longer side of the computational domain. The computation domain is surrounded by PML. The total number of time steps is 10,000 with each time step Δt = 0.99/c(Δx2+Δy2), where c is the speed of light, Δx and Δy are space intervals [5]. The source is placed at the input port waveguide to insert signal. Moreover, one can easily normalize the transmission spectra, by comparing the energy flow (Poynting vector) through the output port with that without PhC waveguide in between.

We have taken a square lattice of 2-D photonic crystal of chalcogenide As2S3 rods in air to design a band pass filter. A cavity is formed by removing of rods and coupled with two waveguides, each of which is formed by the absence of a row of rods as shown in figure 1. The radius of As2S3 rod is r = 0.2a and the refractive index is 2.405 at a wavelength λ = 1.55μm [13]. The band gap for chalcogenide As2S3/air PBG system in the frequency range is from 0.38456 to 0.4641 (in unit: ωa/2πc) for TM-mode [14,15].

FIGURE 1: The geometrical structure for band pass filter with defect cavity dimension h X w.

The band pass filter is designed with different point defect cavity having different horizontal dimension but similar vertical dimension for the studied structure, as shown in figure 2. As can be seen, in figure 2(a), a single rod of dielectric material is removed, in figure 2(b), two rods are removed, in figure 2(c), three rods are removed and in figure 2(d), four rods are removed.

(a)

(b)

(c)

(d)

FIGURE 2: Geometrical structure for Band Pass Filter with point defect for (a) 1X1 defect, (b) 1X2 defect, (c) 1X3 defect, (d) 1X4 defect.

Result and discussion

The output transmission obtained using FDTD method for the proposed structure of band pass filter device is shown in figure 3.

FIGURE 3: The transmission spectra at output port for band pass filter.

The narrow band is found at different frequencies for different defect structures as outlined in table 1.

Table 1: Frequency that are allowed through band pass filter.

Point Defect size

Peak I

Normalized Frequency

Peak II

Normalized Frequency

1x1

0.431

1x2

0.3926

0.4598

1x3

0.4182

1x4

0.3972

0.4382

Sharp peak can be seen inside PBG at particular frequencies which are related to transmission frequencies allowed by the device. However, when the cavity is excited from one of the waveguides, the desired frequency can be obtained by choosing the size of the defect and the number of defects coupled to the waveguide [9].

The important qualitative performance index of an optical device is quality factor (Q), which is defined as the ratio of central wavelength and wavelength difference at full-width half maximum (FWHM) [4]

Q = Central wavelength / FWHM = λ / Δλ

For the band pass filter device consisting of 1X1 defect cavity, the pass normalized frequency is 0.431. At this frequency the transmission is 37%. The quality factor Q for this structure is 86. For the device with 1X2 defect cavity, two sharp peaks can be seen in transmission spectra at frequencies 0.3926 and 0.4598 on normalized scale (ωa/2πc). The transmission on the both frequencies is about 35% and 47 % with quality factor Q = 98 and 92 respectively. For the band pass filter device having 1X3 defect cavity, the pass frequency is 0.4182 on normalized scale (ωa/2πc). At this frequency the transmission is about 42%. The quality factor Q for this structure is 110. For the device with 1X4 defect cavity, two symmetric narrow bands are found in transmission spectra at frequencies 0.3972 and 0.4382 on normalized scale (ωa/2πc). The transmission on the both frequencies is about 24% with quality factor Q = 113.

The light is transmitted for frequencies near the resonant frequency of the cavity, and is reflected for lower or higher frequencies. The existence of the resonance peak conforms to intuition: near the resonant frequency, light from the input waveguide can couple into the cavity, and the cavity in turn can couple into the output waveguide.

The field distribution for band pass filter for different cavity structure is as shown in figure 4 and 5.

(a)

(b)

(c)

(d)

FIGURE 4: Electric field Ez distribution for a band pass filter for (a) ON resonance at ωa/2πc = 0.431 for defect 1X1 (b) ON resonance at ωa/2πc = 0.4598 for defect 1X2 (c) ON resonance at ωa/2πc = 0.4182 for defect 1X3 (d) ON resonance at ωa/2πc = 0.4382 for defect 1X4.

FIGURE 5: Electric field Ez distribution for a band pass filter for OFF resonance at ωa/2πc = 0.405 for all structures.

The field pattern indicates transmission corresponding to ON resonance at ωa/2πc = 0.431 for defect 1X1, ON resonance at ωa/2πc = 0.4598 for defect 1X2, ON resonance at ωa/2πc = 0.4182 for defect 1X3 and ON resonance at ωa/2πc = 0.4382 for defect 1X4 as shown in figure 4(a-d). The field pattern for transmission corresponding to OFF resonance frequency ωa/2πc = 0.405 is shown in Figure 5.

Thus, a frequency shift by only 1% from the resonance frequency of the cavity, results in transmission to dropv almost half of initial value, corresponding to the fields in the middle of resonant peak. The fractional width ∆ω/ω0 at half-maximum (maximum transmission) is precisely equal to 1/Q, where Q is the quality factor of the cavity mode when excited internally.

From figure 3, it is also seen that the resonant frequency can be tuned by changing the size of the defect cavity and refractive index of cavity [8]. The oscillations at high and low frequencies correspond to frequencies outside the band gap, where energy propagates through the crystal instead of being confined to the waveguide and cavity. In a truly infinite system, light outside the gap would escape, but because we simulate this structure within a finite computational box, some light returns to the output waveguide where interference results in an oscillating spectrum.

Conclusions

In the present paper, 2D PhC is used to investigate band pass filter application. A point defect is placed between two linear waveguide to design the filter device. The resonant mode coupled from input to point defect than output waveguide. This resonant mode is affected with the size of defect. It is found that the horizontal dimension of defect cavity increases quality factor value with it. The resonant peak shows blue shift with the horizontal dimension of the defect cavity. Such device is useful for use as band pass filter.

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