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High Q-factor optical filter with high refractive index sensitivity based on hourglass-shaped photonic crystal ring resonator
Journal Pre-proof High Q-factor optical filter with high refractive index sensitivity based on Hourglass-shaped photonic crystal ring resonator Sana Rebhi, Monia Najjar
PII:
S0030-4026(19)31561-X
DOI:
https://doi.org/10.1016/j.ijleo.2019.163663
Reference:
IJLEO 163663
To appear in:
Optik
Received Date:
17 December 2018
Revised Date:
29 August 2019
Accepted Date:
16 October 2019
Please cite this article as: Rebhi S, Najjar M, High Q-factor optical filter with high refractive index sensitivity based on Hourglass-shaped photonic crystal ring resonator, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163663
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
High Q-factor optical filter with high refractive index sensitivity based on Hourglass-shaped photonic crystal ring resonator Sana Rebhi1, Monia Najjar1,2
1
University of Tunis El Manar, National Engineering School of Tunis Communications Systems LR-99-ES21(LRSys’Com-ENIT), 1002, Tunisia 2 University of Tunis El Manar, Higher Institute of Computer2080, Ariana, Tunisia
Abstract: In this paper, a novel hourglass-shaped ring resonator based on square lattice of GaAs in air
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is proposed for the design of a high sensitive all optical filter. The proposed structure guarantees a transmission efficiency of 100% and a high Q-factor of 2578.5. Moreover, some parameters variation such as refractive index , rods radius and lattice constant are investigated in order to show their effects on the transmission efficiency, the Q-factor, the central wavelength and the bandwidth. The results demonstrate that the proposed structure is very sensitive upon the refractive index variation of the total structure, such that the refractive index sensitivity to the refractive index of total structure is ∆λ/∆n = 3.9nm /0.02 . Keywords: Photonic crystal, ring resonator, hourglass, sensitivity, Q-factor, optical filter, GaAs.
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1 Introduction
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Nowadays, photonic crystal based optical devices are gaining remarkable attention since their characteristics are intriguing such as photonic band gap, flexibility, negligeable loss in micrometer scale, reduced size and simplicity of integration in photonic integrated circuits (PICs) [1]. Photonic crystal ring resonators, a resonators located between two parallel waveguides called as bus and drop waveguides, are favorable structures for all optical devices design since they provide high Q-factor, high transmission efficiency and appropriate wavelength tuning [2-6]. Its working mechanism is that in a specific wavelength, optical waves propagating in bus waveguide will be droped to the drop waveguide. Thus, PhCRRs can be employed as wavelength selector for designing various optical components.
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Considering the ever increasing trend toward optical communication networks based on fiber optics communications, we understand the significant importance of all optical devices. The optimum goal for optics and photonics engineers is having a complete all optical network. Reaching this goal needs all optical devices such as optical add/drop filters [24-26], sensors [27,28], logic gates and switches [29], analog to digital converters [30-33], digital to analog converters [34], encoders [35,36], and adders [37-38] . The most common devices designed using PhCRRs are channel drop filters (CDFs). Optical filters are crucial in all optical communication networks. They can be utilized to remove noise and unwanted waves from the channel and to separate narrowed spaced optical channels in wavelength division multiplexing (WDM) systems. In this context, divers optical photonic crystal based filters are reported. The recently presented types are hexagonal [7], X-shaped [8,19] with a quality factor and a refractive index sensitivity of 196 and ∆λ/∆n = 1.4 nm/ 0.01 respectively, H-shaped with quality factor and refractive index sensitivity were 224 and ∆λ/∆n = 1nm/ 0.01 [9] , plus-shaped [10], quasi-shaped [11] and egg-shaped [12].
Other types of ring resonator coupled into waveguides are proposed in the design of such components as logic gates [13,14], optical switches [15], modulators and demultiplexers [16,17] In this paper, we propose a novel hourglass-shaped PhCRR working as an optical filter. Compared with previously reported structures, our designed PhCRR is characterized by its high sensitivity, simplicity of design and its capacity of filtering the desired wavelength with both ultra-high transmission efficiency and Q-factor. The rest of the paper is structured as follows: in section 2, we present the design procedure of the proposed optical filter. Simulations and results analysis are shown in section 3 and finally, conclusion is drown in section 4.
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2 Design procedure of the proposed optical filter The basic structure employed for the PhCRR design consists of a 35*29 square lattice of In0,53Ga0,47As rods immersed in air. The effective refractive index of dielectric rods is 3.59 and its radius is R = 0.181a, where a is the period of the PhC structure. The Plane Wave Expansion (PWE) method is explored to extract the photonic bandgap before proceeding the PhCRR design. The proposed structure exihibits only two photonic bandgaps in TE mode. Only the first bandgap can be considered (0.28< a/λ<0.43) which is corresponding to wavelength range 1.279 µm <λ<1.964. For operating wavelength equals to λ=1.55µm, the obtained period is a=0.586 µm.
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The proposed PhCRR based filter structure is designed by creating required defects in appropriate places inside the basic PhC structure. We start by creating two parallel PhC waveguides separated by 13 rows of dielectric rods. Then, a resonant ring is obtained by removing an 11∗9 array of dielectric rods and put an hourglass shaped structure at the center as a resonant ring core. The radius of the core rods is defined to be R1 = 0.152*a. Four scattering rods are introduced at the corners of the square to improve transmission efficiency of the resonant ring by cancelling backward reflections from the corners of the designed structure. The radius of these scattering rods is adjusted to R2=0.187*a. The final sketch of the proposed PhC-based ring resonator is shown in Fig. 1.
Port B
Input
Port C
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Port D
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Fig. 1 Sketch of proposed structure
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3 Simulations and results analysis
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Simulations and calculations are conducted using the Finite difference time domaine (FDTD) method which require careful meshing and time calculations. The use of 2D FDTD method offers the possibility to find solutions of Maxwell’s equations with a reduced computational time and without affecting accuracy. Also perfectly matched layers (PML) boundary condition surrounding our structure are used; the width of the PML is 500 nm [18]. The normalized transmission spectra of the proposed PhCRR at port B, C and D are depicted in Fig. 2 with blue, red and green curves. All signal wavelengths will travel toward port B except the wavelength λ = 15471 nm will drop to the drop waveguide and propagate toward port D with a drop efficiency of 100%, and the bandwidth is 0.6 nm. Therefore, the calculated quality factor is equal to 2578.5.
1.0
Port D
Normalized Transmission (a.u.)
0.9
Port C
0.8 Port B
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.540
1.542
1.544
1.546
1.548
1.550
1.552
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Wavelength (m)
Fig.2 Output spectrum of the proposed PhCRR
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For better understanding the functionality of the device, the distribution of the optical wave inside the structure for two different wavelengths is shown in Fig. 3. The latter shows that light is coupled into the ring resonator at λ = 15471nm and dropped into the ring reaching output port D. whereas, the wavelength λ = 1551 nm can’t resonate and can’t coupled into the PhCRR. So, the light at this wavelength will travel toward port B.
(a)
(b)
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Fig.3 Optical intensity propagation for (a) λ = 15471 nm (b) λ = 1551 nm Besides the importance of achieving high drop efficiency and high quality factor, the tunability is also greatly desired in designing filters. Therefore, the effect of different parameters on the filtering behavior of the proposed filter is investigated. To filter and separate different wavelengths at a specific frequency range, an altering of the central wavelength is conducted by varying the refractive index of the total structure, the refractive index of adjacent and core rods, the lattice constant and the resonator core rods radius. Firstly, we have investigated the refractive index change of the hole structure, adjacent rods (blue rods), The core rods (yellow color) and both adjacent and core rods with steps of Δn = 0.02, Δn1 = 0.005 , Δn2 = 0.005, Δn3 = 0.005 respectively. Fig. 4 shows the structure output
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spectra at port D for different refractive index values. It is noted that the increase of the refractive index results a shift of output wavelengths toward higher values. However, the transmission efficiency and the Q-factor didn’t considerably change. The detailed specifications of the output spectra for different refractive index values are resumed in Table 1, Table 2, Table 3 and Table 4 respectively. It can be concluded that when the rods refractive index changes, the light coupled to the resonator section encounters a reflecting medium which cannot pass through. Therefore, lights don’t couple to the resonator and the peak wavelength would be shifted. In this case, the sensitivity of the resonant wavelength upon the refractive index is ∆λ/n = 3.9 nm / 0.02=1.95/0.01, ∆λ/n1 = 1.2nm / 0.01, ∆λ/n2 =0.6 nm /0.01, ∆λ/n3 = 1.8nm /0.01 respectively. It is noticed that despite the small variation of refractive index, there will be a shift of 3.9 nm, 1.2 nm, 0.6nm and 1.8nm respectively in the resonant wavelength which confirms the high sensitivity of the proposed filter. Table 1. Parameters of the proposed filter for different values of n. ∆λ (nm) 0.6 0.6 0.5 0.6
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0.8
0.6
0.2
n=3.61 n=3.63 n=3.65
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0.3
n=3.59
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0.7
T.M (%) 100 99.7 90 78.7
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Normalized Transmission (a.u.)
0.9
0.4
Q-factor 2578.5 2580.6 3099.4 2585
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λ (nm) 1547.1 1548.4 1549.7 1551
n 3.59 3.61 3.63 3.65
0.1 0.0
1.544
1.546
1.548
1.550
Wavelength (m)
(a)
1.552
1.554
n1=3.59
0.9
n1=3.595
0.8
n1=3.6
0.7 n1=3.605
0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.545
1.546
1.547
1.548
(b)
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1.0
0.7
0.5
n2=3.605
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0.4
0.2
n2=3.6
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0.6
0.1 0.0
1.545
1.546
1.547
Wavelength (m)
(c)
n2=3.59 n2=3.59
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0.8
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Normalized Transmission(a.u.)
0.9
0.3
1.549
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Wavelength (m)
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Normalized Transmission (a.u.)
1.0
1.548
1.549
1.0
n3=3.59 n3=3.595
0.8 n3=3.6
0.7 n3=3.605
0.6 0.5 0.4 0.3 0.2
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Normalized Transmission(a.u.)
0.9
0.1 0.0 1.544
1.546
1.548
1.550
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Wavelength (m)
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(d) Fig.4 Output spectra of the proposed filter for different refractive indices of: a) Hole structure refractive index (n) b) Adjacent rods refractive index (n1) c) Core rods refractive index d) Adjacent and core rods (n3)
λ (nm) 1547.1 1547.3 1547.5 1547.7
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n1 3.59 3.595 3.6 3.605
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Table 2. Parameters of the proposed filter for different values of n1. ∆λ (nm) 0.6 0.4 0.4 0.45
Q-factor 2578.5 3868.25 3868.75 3439.33
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Table 3. Parameters of the proposed filter for different values of n2. n2 λ (nm) ∆λ (nm) Q-factor 3.59 1547.1 0.6 2578.5 3.595 1547.2 0.5 3094.4 3.6 1547.3 0.4 3868.25 3.605 1547.4 0.5 3094,8
T.M (%) 100 99.8 99.2 98
T.M (%) 100 99.6 99 98.8
(n2)
Table 4. Parameters of the proposed filter for different values of n3. λ (nm) 1547.1 1547.4 1547.7 1548
n3 3.59 3.595 3.6 3.605
∆λ (nm) 0.6 0.5 0.4 0.4
Q-factor 2578.5 3094.8 3869.25 3870
T.M (%) 100 99.4 97.5 96.4
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Another parameter which can influence the filter operation is core rods radius (R1) of the PhCRR. An investigation of the core rods radius variation with ΔR1 = 3 nm is conducted and the output spectrum is investigated. The output spectrum for different radius R1 values is shown in Figure 5. According to the figure, by increasing R1, the resonant wavelength moves up to higher wavelengths, while the transmission and the quality factor don’t change significantly. Detailed specifications are presented in Table 5. The sensitivity of the resonant wavelength upon the core radius is ∆λ/∆R1 = 0.28nm /1. Table 5. Parameters of the proposed filter for different values of R1. ∆λ (nm) 0. 6 0.4 0.5 0.4
1.0
0.6
R1=0.154*a R1=0.156*a R1=0.158*a
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0.5
0.3
R1=0.152*a
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0.7
0.4
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0.8
T.M (%) 100 95.5 94.2 90
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Normalized Transmission (a.u.)
0.9
Q-factor 2578.5 3870 3098 3874
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λ (nm) 1547.1 1548 1549 1549.6
R1 0.152*a 0.154*a 0.156*a 0.158*a
0.2 0.1 0.0
1.536
1.539
1.542
1.545
1.548
1.551
1.554
Wavelength (m)
Fig.5 Output spectra of the proposed filter for different core rods radius R1
Moreover we investigated, in this study, the lattice constant change of the structure with Δa = 2 nm upon the output spectrum. The output spectrum for different lattice constant values is shown in Figure 6. According to the figure, the resonant wavelength shifts to higher values while increasing the lattice constant. The quality factor and the transmission increase with increasing wavelength. Detailed information is listed in Table 6 from which the calculated sensitivity upon the lattice constant is ∆λ/∆a = 2.57nm/1. Table 6. Parameters of the proposed filter for different values of a. ∆λ (nm) 0.4 0.45 0.6 0.4
Q-factor 3842 3854.75 2578.5 3880.5
1.0
a=582 nm
0.9
a=584 nm
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0.8 0.7
a=586 nm a=588 nm
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0.6 0.5
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0.4 0.3 0.2 0.1 0.0
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1.53
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Normalized Transmission (a.u.)
T.M (%) 86 100 100 96
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λ (nm) 1536.8 1541.9 1547.1 1552.2
a 582 584 586 588
1.54
1.55
Wavelength (m)
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Fig.6 Output spectra of the proposed optical filter for different lattice constant As comparison with published results of proposed filters using PCRRs, our designed has a higher quality factor which is an important requirement for such devices. In addition, the simplicity of the design and its reduced size, its high dropping efficiency and the high sensitivity of the resonant wavelength upon different parameters makes this kind of device a promising choice for the implementation of PICs. The functional characteristics of the newly designed filter are compared with the reported CDFs which are listed in Table 7.
Table 7. Comparison between different parameters of the proposed optical filter with other optical filters
[21] Rakhshani et al.
[23] Moradi et al.
[22] Daghooghi et al.
Our work
100
1000
Quasishaped Egg-shaped
90
387
100
647
H-shaped Plus-shaped hexagonal
100 99 95
221 1011 1290
Single resonator Racetrack resonator Squareshaped Hexagoneshaped Hourglassshaped
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Q-factor
71 96
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Transmission
25-30 -
1065
95
-
100
2578.5
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Youcef Mahmoud et al. [8] Alipour-Banaei et al. [11] Alipour-Banaei et al. [12] Rezaee et al. [9] Bendjelloul et al. [10] Mahmood Seifouri et al. [7] [20] Danaie et al.
Ring resonator type X-shaped
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Structure
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In this study, we propose an optical filter based on a novel shape of photonic crystal ring resonator. The filter has a resonance peak at the wavelength of 15471 nm, with a transmission efficiency of 100% and a high-quality factor of 2578.5. The effects of altering different parameters of the structure are studied, and no noticeable change is observed in the transmission coefficient. The advantages of this design are its high sensitivity upon the refractive index and also the fact that its output spectrum does not change by varying different structural parameters. Consequently, this makes our device very suitable to be used as a building block for photonic crystal-based devices.
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PII:
S0030-4026(19)31561-X
DOI:
https://doi.org/10.1016/j.ijleo.2019.163663
Reference:
IJLEO 163663
To appear in:
Optik
Received Date:
17 December 2018
Revised Date:
29 August 2019
Accepted Date:
16 October 2019
Please cite this article as: Rebhi S, Najjar M, High Q-factor optical filter with high refractive index sensitivity based on Hourglass-shaped photonic crystal ring resonator, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163663
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
High Q-factor optical filter with high refractive index sensitivity based on Hourglass-shaped photonic crystal ring resonator Sana Rebhi1, Monia Najjar1,2
1
University of Tunis El Manar, National Engineering School of Tunis Communications Systems LR-99-ES21(LRSys’Com-ENIT), 1002, Tunisia 2 University of Tunis El Manar, Higher Institute of Computer2080, Ariana, Tunisia
Abstract: In this paper, a novel hourglass-shaped ring resonator based on square lattice of GaAs in air
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is proposed for the design of a high sensitive all optical filter. The proposed structure guarantees a transmission efficiency of 100% and a high Q-factor of 2578.5. Moreover, some parameters variation such as refractive index , rods radius and lattice constant are investigated in order to show their effects on the transmission efficiency, the Q-factor, the central wavelength and the bandwidth. The results demonstrate that the proposed structure is very sensitive upon the refractive index variation of the total structure, such that the refractive index sensitivity to the refractive index of total structure is ∆λ/∆n = 3.9nm /0.02 . Keywords: Photonic crystal, ring resonator, hourglass, sensitivity, Q-factor, optical filter, GaAs.
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1 Introduction
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Nowadays, photonic crystal based optical devices are gaining remarkable attention since their characteristics are intriguing such as photonic band gap, flexibility, negligeable loss in micrometer scale, reduced size and simplicity of integration in photonic integrated circuits (PICs) [1]. Photonic crystal ring resonators, a resonators located between two parallel waveguides called as bus and drop waveguides, are favorable structures for all optical devices design since they provide high Q-factor, high transmission efficiency and appropriate wavelength tuning [2-6]. Its working mechanism is that in a specific wavelength, optical waves propagating in bus waveguide will be droped to the drop waveguide. Thus, PhCRRs can be employed as wavelength selector for designing various optical components.
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Considering the ever increasing trend toward optical communication networks based on fiber optics communications, we understand the significant importance of all optical devices. The optimum goal for optics and photonics engineers is having a complete all optical network. Reaching this goal needs all optical devices such as optical add/drop filters [24-26], sensors [27,28], logic gates and switches [29], analog to digital converters [30-33], digital to analog converters [34], encoders [35,36], and adders [37-38] . The most common devices designed using PhCRRs are channel drop filters (CDFs). Optical filters are crucial in all optical communication networks. They can be utilized to remove noise and unwanted waves from the channel and to separate narrowed spaced optical channels in wavelength division multiplexing (WDM) systems. In this context, divers optical photonic crystal based filters are reported. The recently presented types are hexagonal [7], X-shaped [8,19] with a quality factor and a refractive index sensitivity of 196 and ∆λ/∆n = 1.4 nm/ 0.01 respectively, H-shaped with quality factor and refractive index sensitivity were 224 and ∆λ/∆n = 1nm/ 0.01 [9] , plus-shaped [10], quasi-shaped [11] and egg-shaped [12].
Other types of ring resonator coupled into waveguides are proposed in the design of such components as logic gates [13,14], optical switches [15], modulators and demultiplexers [16,17] In this paper, we propose a novel hourglass-shaped PhCRR working as an optical filter. Compared with previously reported structures, our designed PhCRR is characterized by its high sensitivity, simplicity of design and its capacity of filtering the desired wavelength with both ultra-high transmission efficiency and Q-factor. The rest of the paper is structured as follows: in section 2, we present the design procedure of the proposed optical filter. Simulations and results analysis are shown in section 3 and finally, conclusion is drown in section 4.
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2 Design procedure of the proposed optical filter The basic structure employed for the PhCRR design consists of a 35*29 square lattice of In0,53Ga0,47As rods immersed in air. The effective refractive index of dielectric rods is 3.59 and its radius is R = 0.181a, where a is the period of the PhC structure. The Plane Wave Expansion (PWE) method is explored to extract the photonic bandgap before proceeding the PhCRR design. The proposed structure exihibits only two photonic bandgaps in TE mode. Only the first bandgap can be considered (0.28< a/λ<0.43) which is corresponding to wavelength range 1.279 µm <λ<1.964. For operating wavelength equals to λ=1.55µm, the obtained period is a=0.586 µm.
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The proposed PhCRR based filter structure is designed by creating required defects in appropriate places inside the basic PhC structure. We start by creating two parallel PhC waveguides separated by 13 rows of dielectric rods. Then, a resonant ring is obtained by removing an 11∗9 array of dielectric rods and put an hourglass shaped structure at the center as a resonant ring core. The radius of the core rods is defined to be R1 = 0.152*a. Four scattering rods are introduced at the corners of the square to improve transmission efficiency of the resonant ring by cancelling backward reflections from the corners of the designed structure. The radius of these scattering rods is adjusted to R2=0.187*a. The final sketch of the proposed PhC-based ring resonator is shown in Fig. 1.
Port B
Input
Port C
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Port D
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Fig. 1 Sketch of proposed structure
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3 Simulations and results analysis
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Simulations and calculations are conducted using the Finite difference time domaine (FDTD) method which require careful meshing and time calculations. The use of 2D FDTD method offers the possibility to find solutions of Maxwell’s equations with a reduced computational time and without affecting accuracy. Also perfectly matched layers (PML) boundary condition surrounding our structure are used; the width of the PML is 500 nm [18]. The normalized transmission spectra of the proposed PhCRR at port B, C and D are depicted in Fig. 2 with blue, red and green curves. All signal wavelengths will travel toward port B except the wavelength λ = 15471 nm will drop to the drop waveguide and propagate toward port D with a drop efficiency of 100%, and the bandwidth is 0.6 nm. Therefore, the calculated quality factor is equal to 2578.5.
1.0
Port D
Normalized Transmission (a.u.)
0.9
Port C
0.8 Port B
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.540
1.542
1.544
1.546
1.548
1.550
1.552
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Wavelength (m)
Fig.2 Output spectrum of the proposed PhCRR
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For better understanding the functionality of the device, the distribution of the optical wave inside the structure for two different wavelengths is shown in Fig. 3. The latter shows that light is coupled into the ring resonator at λ = 15471nm and dropped into the ring reaching output port D. whereas, the wavelength λ = 1551 nm can’t resonate and can’t coupled into the PhCRR. So, the light at this wavelength will travel toward port B.
(a)
(b)
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Fig.3 Optical intensity propagation for (a) λ = 15471 nm (b) λ = 1551 nm Besides the importance of achieving high drop efficiency and high quality factor, the tunability is also greatly desired in designing filters. Therefore, the effect of different parameters on the filtering behavior of the proposed filter is investigated. To filter and separate different wavelengths at a specific frequency range, an altering of the central wavelength is conducted by varying the refractive index of the total structure, the refractive index of adjacent and core rods, the lattice constant and the resonator core rods radius. Firstly, we have investigated the refractive index change of the hole structure, adjacent rods (blue rods), The core rods (yellow color) and both adjacent and core rods with steps of Δn = 0.02, Δn1 = 0.005 , Δn2 = 0.005, Δn3 = 0.005 respectively. Fig. 4 shows the structure output
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spectra at port D for different refractive index values. It is noted that the increase of the refractive index results a shift of output wavelengths toward higher values. However, the transmission efficiency and the Q-factor didn’t considerably change. The detailed specifications of the output spectra for different refractive index values are resumed in Table 1, Table 2, Table 3 and Table 4 respectively. It can be concluded that when the rods refractive index changes, the light coupled to the resonator section encounters a reflecting medium which cannot pass through. Therefore, lights don’t couple to the resonator and the peak wavelength would be shifted. In this case, the sensitivity of the resonant wavelength upon the refractive index is ∆λ/n = 3.9 nm / 0.02=1.95/0.01, ∆λ/n1 = 1.2nm / 0.01, ∆λ/n2 =0.6 nm /0.01, ∆λ/n3 = 1.8nm /0.01 respectively. It is noticed that despite the small variation of refractive index, there will be a shift of 3.9 nm, 1.2 nm, 0.6nm and 1.8nm respectively in the resonant wavelength which confirms the high sensitivity of the proposed filter. Table 1. Parameters of the proposed filter for different values of n. ∆λ (nm) 0.6 0.6 0.5 0.6
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0.6
0.2
n=3.61 n=3.63 n=3.65
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0.3
n=3.59
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T.M (%) 100 99.7 90 78.7
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Normalized Transmission (a.u.)
0.9
0.4
Q-factor 2578.5 2580.6 3099.4 2585
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λ (nm) 1547.1 1548.4 1549.7 1551
n 3.59 3.61 3.63 3.65
0.1 0.0
1.544
1.546
1.548
1.550
Wavelength (m)
(a)
1.552
1.554
n1=3.59
0.9
n1=3.595
0.8
n1=3.6
0.7 n1=3.605
0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.545
1.546
1.547
1.548
(b)
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0.7
0.5
n2=3.605
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0.2
n2=3.6
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1.546
1.547
Wavelength (m)
(c)
n2=3.59 n2=3.59
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Normalized Transmission(a.u.)
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0.3
1.549
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1.548
1.549
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n3=3.59 n3=3.595
0.8 n3=3.6
0.7 n3=3.605
0.6 0.5 0.4 0.3 0.2
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Normalized Transmission(a.u.)
0.9
0.1 0.0 1.544
1.546
1.548
1.550
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(d) Fig.4 Output spectra of the proposed filter for different refractive indices of: a) Hole structure refractive index (n) b) Adjacent rods refractive index (n1) c) Core rods refractive index d) Adjacent and core rods (n3)
λ (nm) 1547.1 1547.3 1547.5 1547.7
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n1 3.59 3.595 3.6 3.605
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Table 2. Parameters of the proposed filter for different values of n1. ∆λ (nm) 0.6 0.4 0.4 0.45
Q-factor 2578.5 3868.25 3868.75 3439.33
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Table 3. Parameters of the proposed filter for different values of n2. n2 λ (nm) ∆λ (nm) Q-factor 3.59 1547.1 0.6 2578.5 3.595 1547.2 0.5 3094.4 3.6 1547.3 0.4 3868.25 3.605 1547.4 0.5 3094,8
T.M (%) 100 99.8 99.2 98
T.M (%) 100 99.6 99 98.8
(n2)
Table 4. Parameters of the proposed filter for different values of n3. λ (nm) 1547.1 1547.4 1547.7 1548
n3 3.59 3.595 3.6 3.605
∆λ (nm) 0.6 0.5 0.4 0.4
Q-factor 2578.5 3094.8 3869.25 3870
T.M (%) 100 99.4 97.5 96.4
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Another parameter which can influence the filter operation is core rods radius (R1) of the PhCRR. An investigation of the core rods radius variation with ΔR1 = 3 nm is conducted and the output spectrum is investigated. The output spectrum for different radius R1 values is shown in Figure 5. According to the figure, by increasing R1, the resonant wavelength moves up to higher wavelengths, while the transmission and the quality factor don’t change significantly. Detailed specifications are presented in Table 5. The sensitivity of the resonant wavelength upon the core radius is ∆λ/∆R1 = 0.28nm /1. Table 5. Parameters of the proposed filter for different values of R1. ∆λ (nm) 0. 6 0.4 0.5 0.4
1.0
0.6
R1=0.154*a R1=0.156*a R1=0.158*a
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0.3
R1=0.152*a
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0.4
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T.M (%) 100 95.5 94.2 90
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Normalized Transmission (a.u.)
0.9
Q-factor 2578.5 3870 3098 3874
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λ (nm) 1547.1 1548 1549 1549.6
R1 0.152*a 0.154*a 0.156*a 0.158*a
0.2 0.1 0.0
1.536
1.539
1.542
1.545
1.548
1.551
1.554
Wavelength (m)
Fig.5 Output spectra of the proposed filter for different core rods radius R1
Moreover we investigated, in this study, the lattice constant change of the structure with Δa = 2 nm upon the output spectrum. The output spectrum for different lattice constant values is shown in Figure 6. According to the figure, the resonant wavelength shifts to higher values while increasing the lattice constant. The quality factor and the transmission increase with increasing wavelength. Detailed information is listed in Table 6 from which the calculated sensitivity upon the lattice constant is ∆λ/∆a = 2.57nm/1. Table 6. Parameters of the proposed filter for different values of a. ∆λ (nm) 0.4 0.45 0.6 0.4
Q-factor 3842 3854.75 2578.5 3880.5
1.0
a=582 nm
0.9
a=584 nm
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0.8 0.7
a=586 nm a=588 nm
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0.6 0.5
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0.4 0.3 0.2 0.1 0.0
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1.53
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Normalized Transmission (a.u.)
T.M (%) 86 100 100 96
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λ (nm) 1536.8 1541.9 1547.1 1552.2
a 582 584 586 588
1.54
1.55
Wavelength (m)
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Fig.6 Output spectra of the proposed optical filter for different lattice constant As comparison with published results of proposed filters using PCRRs, our designed has a higher quality factor which is an important requirement for such devices. In addition, the simplicity of the design and its reduced size, its high dropping efficiency and the high sensitivity of the resonant wavelength upon different parameters makes this kind of device a promising choice for the implementation of PICs. The functional characteristics of the newly designed filter are compared with the reported CDFs which are listed in Table 7.
Table 7. Comparison between different parameters of the proposed optical filter with other optical filters
[21] Rakhshani et al.
[23] Moradi et al.
[22] Daghooghi et al.
Our work
100
1000
Quasishaped Egg-shaped
90
387
100
647
H-shaped Plus-shaped hexagonal
100 99 95
221 1011 1290
Single resonator Racetrack resonator Squareshaped Hexagoneshaped Hourglassshaped
97
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Q-factor
71 96
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Transmission
25-30 -
1065
95
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100
2578.5
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Youcef Mahmoud et al. [8] Alipour-Banaei et al. [11] Alipour-Banaei et al. [12] Rezaee et al. [9] Bendjelloul et al. [10] Mahmood Seifouri et al. [7] [20] Danaie et al.
Ring resonator type X-shaped
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Structure
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In this study, we propose an optical filter based on a novel shape of photonic crystal ring resonator. The filter has a resonance peak at the wavelength of 15471 nm, with a transmission efficiency of 100% and a high-quality factor of 2578.5. The effects of altering different parameters of the structure are studied, and no noticeable change is observed in the transmission coefficient. The advantages of this design are its high sensitivity upon the refractive index and also the fact that its output spectrum does not change by varying different structural parameters. Consequently, this makes our device very suitable to be used as a building block for photonic crystal-based devices.
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