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A proposal for optical WDM using embedded photonic crystal ring resonator with distributed coupling
Physica E 79 (2016) 173–179
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
A proposal for optical WDM using embedded photonic crystal ring resonator with distributed coupling Mohammad Reza Almasian, Kambiz Abedi n Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University, G.C. 1983963113, Tehran, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 20 November 2015 Accepted 4 January 2016 Available online 4 January 2016
In this paper, an ultra-narrow band channel drop filter (CDF) based on embedded photonic crystal ring resonator with distributed coupling for optical wavelength division multiplexing is proposed and designed in which silicon rods arranged as square lattice. For this purpose, the influences of variation of the central ring radius, on the operating wavelength have been investigated. Calculation results show that the efficiency of 88% with quality factor of 5740, 98% with quality factor of 4889 and 98% with quality factor of 4798 at operating wavelength of 1550 nm can be achieved. Consequently the channel band width and channel spacing are reduced to 270 pm and 600 pm respectively, which will be suitable for dense wavelength division multiplexing (DWDM) optical network systems with 600 pm channel spacing. Simulations have been performed using 2-D finite difference time-domain (2D FDTD) calculations. & 2016 Elsevier B.V. All rights reserved.
Keywords: Embedded photonic crystal ring resonator FDTD Quality factor Channel drop filter
1. Introduction Photonic crystals (PhCs) have ability to control propagation light waves, which have many applications in optical integrated circuits and optical telecommunications. Foundation of the design and manufacturing of the majority of optical devices such as waveguides, high quality factor resonant cavities, optical switches and channel drop filters (CDFs) are photonic crystals [1]. Recently, channel drop filters based on 2D photonic crystals with square and hexagonal lattices have attracted much attention [2–6]. In this regard, several kinds of CDF based on 2D photonic crystal ring resonator (PCRR) have been presented by using the square PCRR, dual square PCRR [7], quasi-square PCRR [8–10], dual curved PCRR [11], hexagonal PCRR [12], 45° PCRR [13], circular PCRR [3,4], X-shaped PCRR [5], improvement X-shaped PCRR [18] and elliptical PCRR [14]. The wavelength division multiplexing (WDM) devices are fundamental components for improving bandwidth of optical communication. In fact, the wavelength division multiplexer is a device that merges the multiple light signals of a set of wavelengths into compound signal, which are directed from several fibers to inputs and conversely the wavelength division de-multiplexer is a device that separates the received compound signal into multiple light signals of a set of wavelengths, which are directed to several fibers for outputs. However, researchers have tremendous interests in developing device that is more compact n
Corresponding author. E-mail address: [email protected] (K. Abedi).
http://dx.doi.org/10.1016/j.physe.2016.01.001 1386-9477/& 2016 Elsevier B.V. All rights reserved.
[15,16]. In this paper, a new scheme of CDF based on 2D PCRR with three types of drop-waveguide is proposed and designed. The performance of filters with square lattice of silicon rods in air background are investigated by using two-dimensional finite-difference time-domain (2D FDTD) numerical method. The proposed filter can be used as either multiplexer or de-multiplexer. Considering that the band width and channel spacing are very small, so this filter will be very suitable for DWDM systems. In continuation, this paper is arranged as follows. In Section 2.1, the description of the structure and its photonic band structure with creating line defect for designing the CDF based on 2D-PhC are discussed and then a CDF with straight horizontal drop-waveguide dropping is designed. Design of MUX/ DEMUX for WDM systems with oblique horizontal drop-waveguide is described in Section 2.2 and MUX/DEMUX for DWDM systems with straight vertical drop-waveguide is described in Section 2.3. Eventually, Section 3 will conclude the paper.
2. Design and numerical results 2.1. Design The proposed structure consists of 2D photonic crystal with square lattice which consists of silicon dielectric rods with refractive index of 3.46 and radius of 0.2a (110 nm) that are embedded in the air background with refractive index of 1. Fig. 1(a) shows the line defect (waveguide) that has been created by removing a row of dielectric rods along the ΓX direction. The approximation of two-dimensional
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Fig. 2. Earlier work that had been presented with a very low quality factor [17].
Fig. 3. The proposed CDF based on embedded PCRR with straight horizontal drop waveguide.
Fig. 1. (a) PhC waveguide created with line defect, (b) 2D super-cells with a defect, and (c) dispersion curves for TM polarization, waveguide transmission components are marked as dashed red line which located in the photonic band gap. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
super-cell is shown in Fig. 1(b). According to Fig. 1(c), waveguide supports single-mode frequency in range of a/λ ¼0.304–0.413, where “λ” is the wavelength of light in free space and “a” is lattice constant (the distance between two adjoining rods). The lattice constant is 552 nm and 526 nm for Sections 2.2 and 2.3 respectively for optical communication systems (1550 nm). In fact, by adjusting the lattice constant of this structure, waveguide has the capability of propagating the wavelengths of 1341–1822 nm that behaves as a single mode waveguide. This structure is the evolved form of earlier works that had been presented with a very low quality factor (Fig. 2) [17]. For achieving high quality factor, several rods have been added around the central rod. So that, around rods and central rod act as
Fig. 4. Resonance frequency as a function of radius of central rod.
embedded photonic crystal ring resonator with distributed coupling. As can be seen in Fig. 3, the rings have been embedded in the background of diamond shape cavity. Diamond shaped arrangement improves the coupling of light from the waveguide into ring and vice versa (coupling of light from the ring into waveguide). Two coupling regions in Fig. 3 show that these regions
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Fig. 6. Electric field distribution of CDF (a) at the resonance wavelength of 1550 nm and (b) at the wavelength of 1549 nm. Fig. 5. Normalized transmission spectrum of the output ports (a) for Rc ¼ 0.742a and a ¼554 nm and (b) for Rc ¼0.748a and a ¼552 nm.
have the highest coupling coefficient. The proposed structure consists of two waveguide and a diamond embedded PCRR which has been placed between two waveguides. Considering Fig. 3, the upper waveguide is called bus waveguide and lower waveguide is called drop-waveguide (or dropping waveguide). The input port is labeled with “A”, forward transmission output port with “B” and the forward and backward dropping output ports are labeled with “C” and “D” respectively. The transmission characteristics of proposed CDF are calculated with FDTD method. A light source of Gaussian distribution with TM polarization is applied to the input port and time monitors records the transmitted power spectral density. Time monitors are placed in each of the B, C and D output ports. All the transmitted power densities are normalized to the light power density of input port. Influence of the radius of central rod on the resonance frequency is shown in Fig. 4. According to Fig. 4, decreasing radius reduces the resonance wavelength of CDF. Simulations show that the resonance wavelength changes as a function of Rc (radius of central rod) in the range of 0.724a–0.754a is linear. So in this range it can be concluded:
Fig. 7. The proposed CDF based on embedded PCRR with oblique horizontal drop waveguide for WDM systems (with properly bending the drop waveguide with lossless bends).
λ ∝ Rc
(1)
On the other hand according to Fig. 4 lattice constant “a” for the desired wavelength it can be achieved. For example, for Rc ¼ 0.748a, if we want to resonance wavelength be 1550 nm, so “a” should be 551.93 nm.
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Fig. 8. Normalized transmission spectrum of the output ports related to the proposed structure with oblique horizontal drop waveguide (suitable for WDM systems).
Normalized transmission spectrum of the output ports of B, C and D for Rc1 ¼0.742a and Rc2 ¼ 0.748a are shown in Fig. 5(a) and (b) respectively. There is no forward-dropping at resonance state while the dropping path has the high backward transmission (as can be seen in Fig. 5). In other words, all the power of bus waveguide is completely transmitted through the port-D by the resonant-tunneling process of ring resonator. Electric field distribution of the CDF at the resonance wavelength is shown in Fig. 6(a) and (b) which are obtained by applying a continuous light source to the port A. According to Fig. 6, PCRR acts as embedded PCRRs. Propagation mode in the both rings is anti-clockwise which leads to a backward-dropping. Interestingly, the main difference between this filter and traditional filters is the opposite propagation direction of the ring and waveguide (traditionally, clockwise propagation in a single ring leads to backwarddropping). 2.2. MUX/DEMUX design for WDM systems with oblique horizontal drop waveguide Given that the straight drop-waveguide is not suitable for the design of WDM systems, thus for design of DEMUX we consider the prior structure as seen in Fig. 7. By properly bending the dropwaveguide (as Fig. 7), the dropping efficiency and quality factor of the CDF (with oblique horizontal drop-waveguide) will be 98% and 4889 respectively. Normalized transmission spectrum of the
Fig. 10. Normalized transmission spectrum of the multi-channel drop-filter with 3-channel: (a) 2 nm channel spacing and (b) 3 nm channel spacing. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
output ports related to the proposed structure has been shown in Fig. 8 which is suitable for WDM systems. According to these results, a multi-channel drop-filter can be designed and different wavelengths can be extracted from a multiwavelength source. To design this filter, we consider the three
Fig. 9. The structure of multi-channel drop-filter with three channel (suitable for WDM systems).
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Fig. 11. The proposed CDF based on embedded PCRR with vertical drop waveguide (suitable for DWDM systems).
Fig. 13. Electric field distribution of CDF (a) at the resonance wavelength of 1550 nm and (b) at the wavelength of 1549.7 nm.
Fig. 12. Normalized transmission spectrum of the output ports related to the proposed structure with vertical drop waveguide (suitable for DWDM systems).
embedded PCRR which are tandem-connected to the bus waveguide. Filter consists of three parts with different refractive indexes that the resonance wavelength can be adjusted for each region. As seen in Fig. 9, the radius of rods for the each region is same and the refractive index of region 1, 2 and 3 are 3.4655, 3.46 and 3.4547 respectively. Input port is named as “A” and the output ports are named as B, C, D and E. A multi-wavelength light source is applied to the input and the wavelengths of the corresponding any embedded PCRRs are de-multiplexed from the separate drop channels. The system can also act as a multiplexer if we change the sides of input and output ports. In this case, the signals with different wavelengths will be applied into the input ports C, D and E and a single signal with combination of three different wavelengths will exit from the output port A. The normalized transmission spectrum of the output ports B, C, D and E are displayed in Fig. 10 as dash–dot (blue line), solid (black line), dashed (violet line) and short dashed (red line) styles respectively. As can be observed, the wavelengths of 1.548 mm, 1.55 mm and 1.552 mm with spacing of 2 nm in Fig. 10(a) and wavelengths of 1.547 mm, 1.55 mm and 1.553 mm with spacing of 3 nm in Fig. 10(b) are selected. On the other hand, Fig. 10 shows the resonance wavelength increases
with increasing refractive index of the dielectric rods ( λ ∝ Δn ). The resonance characteristics can be precisely adjusted by adjusting the radius and refractive index of the main dielectric rods and central rod. 2.3. MUX/DEMUX design for DWDM systems with vertical drop waveguide The proposed structure can be considered as a CDF with vertical drop-waveguide. Fig. 11 is the proposed CDF structure that has a vertical drop-waveguide. In the best case, the radius of central rod is 3.7a (a ¼526 nm) that choosing this value causes the quality factor improves to 5740 whereas the drop efficiency is 88%. Normalized transmission spectrum of the output ports related to the proposed structure with vertical drop waveguide is shown in Fig. 12 which is suitable for DWDM systems. Electric field distribution of the CDF at the resonance wavelength is shown in Fig. 13(a) and (b) which is obtained by applying a continuous light source to the port A. As can be seen, resonance occurs at the wavelength of 1550 nm and at the 1549.5 embedded PCRR has no resonance. Now a multichannel drop-filter can be designed and different wavelengths can be extracted from a Multi-wavelength source (Fig. 14). The refractive index of region 1, 2 and 3 are 3.46145, 3.46 and 3.45854 respectively. Input port is named as “A” and the output ports are named as B, C, D and E. A multi-wavelength light source is applied
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Fig. 14. The structure of multi-channel drop-filter with three channel and 600 pm channel spacing (suitable for DWDM systems).
line), dashed (violet line) and short dashed (red line) styles respectively. As can be observed, the wavelengths of 1549.4 nm, 1550 nm and 1550.6 nm with spacing of 600 pm have been selected. According to comparing the new design of CDF and the similar articles, the different features of this filter are higher quality factor and higher spectral selectivity. This comparison is done in Table 1, which the drop efficiency of the proposed structure is acceptable and the quality factor of vertical drop waveguide is 5740 at the wavelength of 1550 nm.
3. Conclusions
Fig. 15. Normalized transmission spectrum of the multi-channel drop-filter with 3-channel and 600 pm channel spacing. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
to the input and the wavelengths of the corresponding any region are de-multiplexed from the separate drop channels. The system can also act as a multiplexer if we change the sides of input and output ports. The normalized transmission spectrum of the output ports B, C, D and E are shown in Fig. 15 as dash–dot (blue line), solid (black
In this paper, three kinds of CDF based on two-dimensional photonic crystal with square lattice of silicon rods in air background were proposed and designed. Influence of variation of the central rod radius on the operating wavelength was investigated. Forward dropping efficiency of 88% with the quality factor of 5740, 98% with quality factor of 4889 and 98% with quality factor of 4798 at the wavelength of 1550 nm were achieved and the quality factor was improved, so that the channel bandwidth and channel spacing were reduced to 270 pm and 600 pm respectively. As a result, the proposed multi-channel drop-filter, due to having the high quality factor is suitable for DWDM systems (ITU-T grid-32 wavelengths in each band).
Table 1 Comparing devices based on PCRRs available in variety of papers. Reference This paper. This paper. This paper. Alipour-Banaei et al. [14]. Almasian et al. [18]. Youcef Mahmoud et al [5]. Robinson and Nakkeeran [3,4]. Ma and Ogusu [6]. Bai et al. [13]. Hsiao and Lee [12]. Andalib and Granpayeh [11]. Djavid et al. [8-10]. Qiang et al. [7].
Dropping efficiency (%) 98 98 88 100 100 100 100 95 90 55 68 99 498
Quality factor of dropping waveguide
PCRR type
4798 4889 5740 1559 1500 1000 114.6 775 840 423 153.6 52.7 160–1000
Embedded (with straight horizontal drop waveguide) Embedded (with oblique horizontal drop waveguide) Embedded (with vertical drop waveguide) Elliptical (with triple ring configuration) X-shaped (improvement) X-shaped (with double ring configuration) Circular Diamond 45° Hexagonal Dual curved Quasi-square Quasi-square
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References [1] J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press (2008), pp. 229–238. [2] K.M. Ho, C.T. Chan, C.M. Soukoulis, Existence of a photonic gap in periodic dielectric structures, Phys. Rev. Lett. 65 (25) (1990) 3152–3155. [3] S. Robinson, R. Nakkeeran, Performance evaluation of PCRR based add drop filter with different rod shapes, Optoelectron. Electromagn. Appl. 11 (1) (2012). [4] S. Robinson, R. Nakkeeran, “Investigation on parameters affecting the performance of two dimensional photonic crystal based bandpass filter, Opt. Quantum Electron. 43 (6–10) (2012) 69–82. [5] M. Youcef Mahmoud, G. Bassou, F. Fornel, A. Taalbi, Channel drop filter for CWDM systems, Opt. Commun. 306 (2013) 179–184. [6] Z. Ma, K. Ogusu, Channel drop filters using photonic crystal Fabry–Perot resonators, Opt. Commun. 284 (5) (2011) 1192–1196. [7] Z. Qiang, W. Zhou, R.A. Soref, Optical add-drop filters based on photonic crystal ring resonators, Opt. Express 15 (4) (2007) 1823–1831. [8] A. Ghaffari, F. Monifi, M. Djavid, M.S. Abrishamian, Photonic crystal bends and power splitters based on ring resonators, Opt. Commun. 281 (2008) 5929–5934. [9] M. Djavid, A. Ghaffari, F. Monifi, M.S. Abrishamian, T-Shaped channel-drop filters using photonic crystal ring resonators, in: Integrated Photonics and Nanophotonics Research and Applications, Optical Society of America, 2008. [10] M. Djavid, F. Monifi, A. Ghaffari, M.S. Abrishamian, Heterostructure
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wavelength division demultiplexers using photonic crystal ring resonators, Opt. Commun. 281 (2008) 4028–4032. P. Andalib, N. Granpayeh, Optical add/drop filter based on dual curved photonic crystal resonator, in: Proceedings of the International Conference on Optical MEMs and Nanophotonics, Freiburg, 2008, pp. 170–171. F.L. Hsiao, C..Lee, A nano-ring resonator based on 2-D hexagonal-lattice photonic crystals, in: Proceedings of the International Conference on Optical MEMs and Nanophotonics, Clearwater, FL, 2009, pp. 107–108. J.B. Bai, J.Q. Wang, X.Y. Chen, J.Z. Jiang, L. Hui, Y.S. Qiu, Z.X. Qiang, Characteristics of 45° photonic crystal ring resonators based on square-lattice silicon rods, Optoelectron. Lett. 6 (3) (2010) 203–206. H. Alipour-Banaei, F. Mehdizadeh, M. Hassangholizadeh-Kashtiban, A new proposal for PCRR-based channel drop filter using elliptical rings, Physica E 56 (2014) 211–215. F. Mehdizadeh, H. Alipour-Banaei, S. Serajmohammadi, Channel-drop filter based on a photonic crystal ring resonator, J. Opt. 15 (7) (2013). X. Zhang, Q. Liao, T. Yu, N. Liu, Y. Huang, Novel ultracompact wavelength division demultiplexer based on photonic band gap, Opt. Commun. 285 (2012) 274–276. S. Fan, P.R. Villeneuve, J.D. Joannopoulos, H.A. Haus, Channel drop filters in photonic crystals, Opt. Express 3 (1) (1998) 4–11. M.R. Almasian, K. Abedi, Performance improvement of wavelength division multiplexing based on photonic crystal ring resonator, Optik 126 (20) (2015) 2612–2615.
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
A proposal for optical WDM using embedded photonic crystal ring resonator with distributed coupling Mohammad Reza Almasian, Kambiz Abedi n Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University, G.C. 1983963113, Tehran, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 20 November 2015 Accepted 4 January 2016 Available online 4 January 2016
In this paper, an ultra-narrow band channel drop filter (CDF) based on embedded photonic crystal ring resonator with distributed coupling for optical wavelength division multiplexing is proposed and designed in which silicon rods arranged as square lattice. For this purpose, the influences of variation of the central ring radius, on the operating wavelength have been investigated. Calculation results show that the efficiency of 88% with quality factor of 5740, 98% with quality factor of 4889 and 98% with quality factor of 4798 at operating wavelength of 1550 nm can be achieved. Consequently the channel band width and channel spacing are reduced to 270 pm and 600 pm respectively, which will be suitable for dense wavelength division multiplexing (DWDM) optical network systems with 600 pm channel spacing. Simulations have been performed using 2-D finite difference time-domain (2D FDTD) calculations. & 2016 Elsevier B.V. All rights reserved.
Keywords: Embedded photonic crystal ring resonator FDTD Quality factor Channel drop filter
1. Introduction Photonic crystals (PhCs) have ability to control propagation light waves, which have many applications in optical integrated circuits and optical telecommunications. Foundation of the design and manufacturing of the majority of optical devices such as waveguides, high quality factor resonant cavities, optical switches and channel drop filters (CDFs) are photonic crystals [1]. Recently, channel drop filters based on 2D photonic crystals with square and hexagonal lattices have attracted much attention [2–6]. In this regard, several kinds of CDF based on 2D photonic crystal ring resonator (PCRR) have been presented by using the square PCRR, dual square PCRR [7], quasi-square PCRR [8–10], dual curved PCRR [11], hexagonal PCRR [12], 45° PCRR [13], circular PCRR [3,4], X-shaped PCRR [5], improvement X-shaped PCRR [18] and elliptical PCRR [14]. The wavelength division multiplexing (WDM) devices are fundamental components for improving bandwidth of optical communication. In fact, the wavelength division multiplexer is a device that merges the multiple light signals of a set of wavelengths into compound signal, which are directed from several fibers to inputs and conversely the wavelength division de-multiplexer is a device that separates the received compound signal into multiple light signals of a set of wavelengths, which are directed to several fibers for outputs. However, researchers have tremendous interests in developing device that is more compact n
Corresponding author. E-mail address: [email protected] (K. Abedi).
http://dx.doi.org/10.1016/j.physe.2016.01.001 1386-9477/& 2016 Elsevier B.V. All rights reserved.
[15,16]. In this paper, a new scheme of CDF based on 2D PCRR with three types of drop-waveguide is proposed and designed. The performance of filters with square lattice of silicon rods in air background are investigated by using two-dimensional finite-difference time-domain (2D FDTD) numerical method. The proposed filter can be used as either multiplexer or de-multiplexer. Considering that the band width and channel spacing are very small, so this filter will be very suitable for DWDM systems. In continuation, this paper is arranged as follows. In Section 2.1, the description of the structure and its photonic band structure with creating line defect for designing the CDF based on 2D-PhC are discussed and then a CDF with straight horizontal drop-waveguide dropping is designed. Design of MUX/ DEMUX for WDM systems with oblique horizontal drop-waveguide is described in Section 2.2 and MUX/DEMUX for DWDM systems with straight vertical drop-waveguide is described in Section 2.3. Eventually, Section 3 will conclude the paper.
2. Design and numerical results 2.1. Design The proposed structure consists of 2D photonic crystal with square lattice which consists of silicon dielectric rods with refractive index of 3.46 and radius of 0.2a (110 nm) that are embedded in the air background with refractive index of 1. Fig. 1(a) shows the line defect (waveguide) that has been created by removing a row of dielectric rods along the ΓX direction. The approximation of two-dimensional
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Fig. 2. Earlier work that had been presented with a very low quality factor [17].
Fig. 3. The proposed CDF based on embedded PCRR with straight horizontal drop waveguide.
Fig. 1. (a) PhC waveguide created with line defect, (b) 2D super-cells with a defect, and (c) dispersion curves for TM polarization, waveguide transmission components are marked as dashed red line which located in the photonic band gap. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
super-cell is shown in Fig. 1(b). According to Fig. 1(c), waveguide supports single-mode frequency in range of a/λ ¼0.304–0.413, where “λ” is the wavelength of light in free space and “a” is lattice constant (the distance between two adjoining rods). The lattice constant is 552 nm and 526 nm for Sections 2.2 and 2.3 respectively for optical communication systems (1550 nm). In fact, by adjusting the lattice constant of this structure, waveguide has the capability of propagating the wavelengths of 1341–1822 nm that behaves as a single mode waveguide. This structure is the evolved form of earlier works that had been presented with a very low quality factor (Fig. 2) [17]. For achieving high quality factor, several rods have been added around the central rod. So that, around rods and central rod act as
Fig. 4. Resonance frequency as a function of radius of central rod.
embedded photonic crystal ring resonator with distributed coupling. As can be seen in Fig. 3, the rings have been embedded in the background of diamond shape cavity. Diamond shaped arrangement improves the coupling of light from the waveguide into ring and vice versa (coupling of light from the ring into waveguide). Two coupling regions in Fig. 3 show that these regions
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Fig. 6. Electric field distribution of CDF (a) at the resonance wavelength of 1550 nm and (b) at the wavelength of 1549 nm. Fig. 5. Normalized transmission spectrum of the output ports (a) for Rc ¼ 0.742a and a ¼554 nm and (b) for Rc ¼0.748a and a ¼552 nm.
have the highest coupling coefficient. The proposed structure consists of two waveguide and a diamond embedded PCRR which has been placed between two waveguides. Considering Fig. 3, the upper waveguide is called bus waveguide and lower waveguide is called drop-waveguide (or dropping waveguide). The input port is labeled with “A”, forward transmission output port with “B” and the forward and backward dropping output ports are labeled with “C” and “D” respectively. The transmission characteristics of proposed CDF are calculated with FDTD method. A light source of Gaussian distribution with TM polarization is applied to the input port and time monitors records the transmitted power spectral density. Time monitors are placed in each of the B, C and D output ports. All the transmitted power densities are normalized to the light power density of input port. Influence of the radius of central rod on the resonance frequency is shown in Fig. 4. According to Fig. 4, decreasing radius reduces the resonance wavelength of CDF. Simulations show that the resonance wavelength changes as a function of Rc (radius of central rod) in the range of 0.724a–0.754a is linear. So in this range it can be concluded:
Fig. 7. The proposed CDF based on embedded PCRR with oblique horizontal drop waveguide for WDM systems (with properly bending the drop waveguide with lossless bends).
λ ∝ Rc
(1)
On the other hand according to Fig. 4 lattice constant “a” for the desired wavelength it can be achieved. For example, for Rc ¼ 0.748a, if we want to resonance wavelength be 1550 nm, so “a” should be 551.93 nm.
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Fig. 8. Normalized transmission spectrum of the output ports related to the proposed structure with oblique horizontal drop waveguide (suitable for WDM systems).
Normalized transmission spectrum of the output ports of B, C and D for Rc1 ¼0.742a and Rc2 ¼ 0.748a are shown in Fig. 5(a) and (b) respectively. There is no forward-dropping at resonance state while the dropping path has the high backward transmission (as can be seen in Fig. 5). In other words, all the power of bus waveguide is completely transmitted through the port-D by the resonant-tunneling process of ring resonator. Electric field distribution of the CDF at the resonance wavelength is shown in Fig. 6(a) and (b) which are obtained by applying a continuous light source to the port A. According to Fig. 6, PCRR acts as embedded PCRRs. Propagation mode in the both rings is anti-clockwise which leads to a backward-dropping. Interestingly, the main difference between this filter and traditional filters is the opposite propagation direction of the ring and waveguide (traditionally, clockwise propagation in a single ring leads to backwarddropping). 2.2. MUX/DEMUX design for WDM systems with oblique horizontal drop waveguide Given that the straight drop-waveguide is not suitable for the design of WDM systems, thus for design of DEMUX we consider the prior structure as seen in Fig. 7. By properly bending the dropwaveguide (as Fig. 7), the dropping efficiency and quality factor of the CDF (with oblique horizontal drop-waveguide) will be 98% and 4889 respectively. Normalized transmission spectrum of the
Fig. 10. Normalized transmission spectrum of the multi-channel drop-filter with 3-channel: (a) 2 nm channel spacing and (b) 3 nm channel spacing. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
output ports related to the proposed structure has been shown in Fig. 8 which is suitable for WDM systems. According to these results, a multi-channel drop-filter can be designed and different wavelengths can be extracted from a multiwavelength source. To design this filter, we consider the three
Fig. 9. The structure of multi-channel drop-filter with three channel (suitable for WDM systems).
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Fig. 11. The proposed CDF based on embedded PCRR with vertical drop waveguide (suitable for DWDM systems).
Fig. 13. Electric field distribution of CDF (a) at the resonance wavelength of 1550 nm and (b) at the wavelength of 1549.7 nm.
Fig. 12. Normalized transmission spectrum of the output ports related to the proposed structure with vertical drop waveguide (suitable for DWDM systems).
embedded PCRR which are tandem-connected to the bus waveguide. Filter consists of three parts with different refractive indexes that the resonance wavelength can be adjusted for each region. As seen in Fig. 9, the radius of rods for the each region is same and the refractive index of region 1, 2 and 3 are 3.4655, 3.46 and 3.4547 respectively. Input port is named as “A” and the output ports are named as B, C, D and E. A multi-wavelength light source is applied to the input and the wavelengths of the corresponding any embedded PCRRs are de-multiplexed from the separate drop channels. The system can also act as a multiplexer if we change the sides of input and output ports. In this case, the signals with different wavelengths will be applied into the input ports C, D and E and a single signal with combination of three different wavelengths will exit from the output port A. The normalized transmission spectrum of the output ports B, C, D and E are displayed in Fig. 10 as dash–dot (blue line), solid (black line), dashed (violet line) and short dashed (red line) styles respectively. As can be observed, the wavelengths of 1.548 mm, 1.55 mm and 1.552 mm with spacing of 2 nm in Fig. 10(a) and wavelengths of 1.547 mm, 1.55 mm and 1.553 mm with spacing of 3 nm in Fig. 10(b) are selected. On the other hand, Fig. 10 shows the resonance wavelength increases
with increasing refractive index of the dielectric rods ( λ ∝ Δn ). The resonance characteristics can be precisely adjusted by adjusting the radius and refractive index of the main dielectric rods and central rod. 2.3. MUX/DEMUX design for DWDM systems with vertical drop waveguide The proposed structure can be considered as a CDF with vertical drop-waveguide. Fig. 11 is the proposed CDF structure that has a vertical drop-waveguide. In the best case, the radius of central rod is 3.7a (a ¼526 nm) that choosing this value causes the quality factor improves to 5740 whereas the drop efficiency is 88%. Normalized transmission spectrum of the output ports related to the proposed structure with vertical drop waveguide is shown in Fig. 12 which is suitable for DWDM systems. Electric field distribution of the CDF at the resonance wavelength is shown in Fig. 13(a) and (b) which is obtained by applying a continuous light source to the port A. As can be seen, resonance occurs at the wavelength of 1550 nm and at the 1549.5 embedded PCRR has no resonance. Now a multichannel drop-filter can be designed and different wavelengths can be extracted from a Multi-wavelength source (Fig. 14). The refractive index of region 1, 2 and 3 are 3.46145, 3.46 and 3.45854 respectively. Input port is named as “A” and the output ports are named as B, C, D and E. A multi-wavelength light source is applied
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Fig. 14. The structure of multi-channel drop-filter with three channel and 600 pm channel spacing (suitable for DWDM systems).
line), dashed (violet line) and short dashed (red line) styles respectively. As can be observed, the wavelengths of 1549.4 nm, 1550 nm and 1550.6 nm with spacing of 600 pm have been selected. According to comparing the new design of CDF and the similar articles, the different features of this filter are higher quality factor and higher spectral selectivity. This comparison is done in Table 1, which the drop efficiency of the proposed structure is acceptable and the quality factor of vertical drop waveguide is 5740 at the wavelength of 1550 nm.
3. Conclusions
Fig. 15. Normalized transmission spectrum of the multi-channel drop-filter with 3-channel and 600 pm channel spacing. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
to the input and the wavelengths of the corresponding any region are de-multiplexed from the separate drop channels. The system can also act as a multiplexer if we change the sides of input and output ports. The normalized transmission spectrum of the output ports B, C, D and E are shown in Fig. 15 as dash–dot (blue line), solid (black
In this paper, three kinds of CDF based on two-dimensional photonic crystal with square lattice of silicon rods in air background were proposed and designed. Influence of variation of the central rod radius on the operating wavelength was investigated. Forward dropping efficiency of 88% with the quality factor of 5740, 98% with quality factor of 4889 and 98% with quality factor of 4798 at the wavelength of 1550 nm were achieved and the quality factor was improved, so that the channel bandwidth and channel spacing were reduced to 270 pm and 600 pm respectively. As a result, the proposed multi-channel drop-filter, due to having the high quality factor is suitable for DWDM systems (ITU-T grid-32 wavelengths in each band).
Table 1 Comparing devices based on PCRRs available in variety of papers. Reference This paper. This paper. This paper. Alipour-Banaei et al. [14]. Almasian et al. [18]. Youcef Mahmoud et al [5]. Robinson and Nakkeeran [3,4]. Ma and Ogusu [6]. Bai et al. [13]. Hsiao and Lee [12]. Andalib and Granpayeh [11]. Djavid et al. [8-10]. Qiang et al. [7].
Dropping efficiency (%) 98 98 88 100 100 100 100 95 90 55 68 99 498
Quality factor of dropping waveguide
PCRR type
4798 4889 5740 1559 1500 1000 114.6 775 840 423 153.6 52.7 160–1000
Embedded (with straight horizontal drop waveguide) Embedded (with oblique horizontal drop waveguide) Embedded (with vertical drop waveguide) Elliptical (with triple ring configuration) X-shaped (improvement) X-shaped (with double ring configuration) Circular Diamond 45° Hexagonal Dual curved Quasi-square Quasi-square
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