- Email: [email protected]
Periodic dielectric waveguide-based cross- and T-connections with a resonant cavity at the junctions
Optics Communications 284 (2011) 2292–2297
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Periodic dielectric waveguide-based cross- and T-connections with a resonant cavity at the junctions Hongtao Guo, Yao Zhang, Baojun Li ⁎ State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
a r t i c l e
i n f o
Article history: Received 10 September 2010 Accepted 6 January 2011 Available online 18 January 2011
a b s t r a c t We propose a cross-connection and a T-connection in periodic dielectric waveguides (PDWs) with ultrasmall size and high transmission efficiency at λ = 1.55 μm. The cross-connection was formed by introducing a 3 × 3 square dielectric resonant cavity at the cross-junction with a crosstalk of less than 0.8% (about − 21 dB) and a transmission of larger than 93% at the desired output port. The T-connection was formed by introducing a 3 × 5 dielectric resonant cavity with modifications at the T-junction. The total transmission is up to 95%. In addition, different power splitting ratios were also achieved by moving the input waveguide of the Tconnection with different displacements. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Waveguide based optical cross- and T-connections are extremely important structures in photonic integrated circuits (PICs) to connect functional devices [1,2]. Ideal waveguide-based cross-connection must ensure that the incident lightwave from the input port of the waveguides are totally transmitted to the output port along the same direction with negligible crosstalk, reflection, and radiation loss. For a high-performance T-connection, incident lightwave should be totally transmitted into the two output ports with a desired power ratio. In the past several years, cross- and T-connections based on conventional dielectric waveguides (CDW) and photonic crystal (PC) waveguides have been designed and demonstrated with different structures [3–14], which exhibited good transmission performances. However, CDW-based devices usually have a relatively large size (up to tens of micrometers), while PC-based devices have an intrinsic disadvantage that the device structures must follow the PC lattice orientation, which is difficult to achieve the flexible control of lightwaves. Furthermore, a wide PC background area (at least several lattice constants) is required for device applications. These may cause inconvenience for highly integrated PICs. Periodic dielectric waveguides (PDWs) [15], which are good waveguide structures for building ultracompact devices, have the ability to afford both high transmission and small size [16]. Today, many functional PDW-based devices have been designed including power splitter [17], wavelength and polarization splitter [18,19], demultiplexer/filter [20], Fabry–Pérot microcavities [21], and optical logic gates [22]. However, as basic components, ultrasmall size and high performance PDW-based optical
⁎ Corresponding author. E-mail address: [email protected] (B. Li). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.01.008
cross- and T-connections are desirable to be designed and optimized for highly efficient optical connection within limited spaces. Therefore, in this work, we propose PDW-based cross- and T-connections with a resonant cavity at the junctions to achieve high transmission performance. The design of the devices has been conducted using a plane wave expansion (PWE) method, and the performances have been evaluated using a finite-difference time-domain (FDTD) method. The results show that more than 93% transmission was obtained for both the cross- and T-connections structures with ultrasmall resonant cavity size (less than 1 μm × 1 μm). 2. Cross-connection in PDWs 2.1. Simple cross-connection PDWs can be formed by dielectric cylinder array in air or air-hole array in a dielectric [23,24]. Here, the considered single-row PDW is a dielectric cylinder array with a refractive index of n = 3.45 (Si). The radius of the cylinders is set to be r = 0.4a, where a is the center-tocenter spacing between two adjacent cylinders. A simple crossconnection is directly formed by arranging two PDWs perpendicularly (Fig. 1a). The enlarged view of the junction is shown in Fig. 1b. For optical communication wavelength application, a is specified as a = 232.5 nm. From the FDTD simulated steady-state field distribution (Fig. 2), it can be seen that, for the simple cross-connection, when a λ = 1.55 μm was launched into the input 1, only 62.8% optical power was output from the straight waveguide. 14.3% optical power was reflected to the input waveguide while 21.6% was coupled into the cross waveguide. If launched, the λ = 1.55 μm into the input 2 (Fig. 1a), same simulated distribution can be obtained. Obviously, the performance of the simple structure without optimization is not satisfactory. Therefore,
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
Fig. 1. (a) Schematic of a simple PDW-based cross-connection. (b) Enlarged view of the junction.
Fig. 2. FDTD simulated steady-state field distribution in the simple PDW-based crossconnection.
an optimization will be done in the following subsection to improve the transmission performance of the PDW-based cross-connection. 2.2. Optimized cross-connection To improve the performance of the PDW-based cross-connection, a model of resonant cavity was applied at the junction (Fig. 3). In such a model of the cavity, to achieve desirable performances (high transmission, low crosstalk and reflection), the cavity must have fourfold symmetry with planes coinciding with the waveguide axes. Besides, the cavity has to support only two resonant modes in the frequency range of interest. One of the resonant modes has an odd symmetry with respect to the horizontal waveguide and an even symmetry with respect to the vertical waveguide axis, while the other has opposite symmetries. Under these conditions, one resonant mode
Fig. 3. Scheme of the transmission process through a cross-connection with a model of the cavity.
2293
Fig. 4. (a) Schematic of a PDW-based cross-connection with a 3 × 3 square dielectric resonant cavity. (b) Enlarged view of the waveguide. (c) Enlarged view of the cavity.
will be coupled into the straight waveguide and be outputted as a transmission, while the other mode will be resonated in the cavity and finally also be coupled into the straight waveguide and be outputted as a transmission. As a result, the transmission performance of the structure with the cavity will be improved while the crosstalk and the reflection will be reduced. With the implementation of the cavity model described above, an optimized cross-connection can be obtained by introducing a 3 × 3 square dielectric resonant cavity at the cross-junction (Fig. 4). In the 3 × 3 square dielectric resonant cavity, the row-to-row space between adjacent cylinders is a1 and the radius of the cylinders is r1. Fig. 5a is the calculated band structure for a single PDW by the PWE method. The inset (solid frame) of Fig. 5a is an a × 9a supercell for PWE calculation. The parameters a1 and r1 greatly affect the performance of the resonant cavity and determine whether the cavity can satisfy the requirement of supporting two resonant modes in a wide resonant frequency range. By calculations, a1 = 0.8a and r1 = 0.4a1 are chosen to make the cavity hold two resonant modes with resonant frequencies in the range from 0.125 to 0.165(a/λ), corresponding to 1.41 to 1.86 μm. Fig. 5b depicts the profiles of the two resonant modes at λ = 1.55 μm in the square cavity, in which the two modes exhibit opposite symmetries with respect to the waveguide axes x and y. Since a = 232.5 nm, the center-to-center distance between two adjacent cylinders in the cavity is a1 = 186 nm. The distance between the waveguide and the cavity is L = a.
Fig. 5. Calculations for the PDWs and the square cavity based on the PWE method. (a) Band structure for TM mode in a single PDW. (b) Profiles of the two resonant modes at λ = 1.55 μm in the square cavity with opposite symmetries with respect to the waveguide axes x and y.
2294
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
Fig. 6. FDTD simulated steady-state field distribution in the optimized cross-connection with a 3 × 3 square dielectric resonant cavity.
To evaluate the performance of the optimized cross-connection, steady-state field distribution was simulated by FDTD method with λ = 1.55 μm launched from the input 1 (Fig. 6). Compared with the simulation of simple PDW-based cross-connection showed in Fig. 2, total crosstalk has been reduced from 21.6% to 1.6% and the reflection reduced from 14.3% to 3.9%. A 93.1% transmission has been obtained in the desired straight output port. By taking FDTD simulations with wavelengths range at around 1.55 μm (e.g., 1.48 to 1.62 μm), the transmission and crosstalk spectra for the simple and the optimized cross-connections are obtained (Fig. 7). It can be seen from Fig. 7 that, by adding a 3 × 3 square dielectric resonant cavity at the cross junction, the transmission is increased and the crosstalk is significantly reduced. The size of the resonant cavity is 520.8 nm × 520.8 nm, which is smaller than those reported in conventional dielectric waveguides [2] (about 1.16 μm × 1.16 μm) and photonic crystal waveguides [10] (about 3.74 μm × 2.16 μm).
Fig. 7. Comparison of the normalized transmission (a) and total crosstalk (b) for the simple and the optimized cross-connections in a wavelength range of 1.48 to 1.62 μm.
Fig. 8. (a) Schematic of a simple PDW-based T-connection. (b) Enlarged view of the junction.
3. T-connection in PDWs 3.1. Simple T-connection In this section, we use the dielectric resonant cavity to optimize the PDW-based T-connection. Before the optimization, a simple PDW-based T-connection (Fig. 8a) and an enlarged view of its junction (Fig. 8b) will be discussed. The center-to-center spacing between the two adjacent cylinders is a′ and the radius of the cylinders is set to be r′ = 0.42a′. By band structure calculation, a′ is specified as a′ = 201.6 nm for the λ = 1.55 μm operation. Fig. 9 shows the simulated steady-state field distribution by the FDTD method. For the simple T-connection, the calculated transmission is rather low (45.2% in total at the two outputs). 35.1% optical power was reflected back to the input waveguide. The radiation is also large (19.7%).
Fig. 9. FDTD simulated steady-state field distribution in the simple PDW-based Tconnection.
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
2295
Fig. 10. Scheme of a T-connection with a cavity at the junction.
3.2. Optimized T-connection To improve the performance of the PDW-based T-connection, a resonant cavity was also applied at the junction (Fig. 10). The optical powers inputted, reflected, outputted to port 1, and port 2 are denoted by Pin, Pr, Pout−1, and Pout−2, respectively. Therefore, the coefficients of reflection R, left transmission TL and right TR can be expressed as R = Pr/Pin, TL = Pout−1/Pin, and TR = Pout−2/Pin. To transfer the input optical power as much as possible to ports 1 and 2, in the following design, the resonant frequency will be chosen to match the wavelength of the inputted light by adjusting the shape of the cavity. Similar to the optimization for the PDW-based cross-connection discussed in Section 2.2, a 3 × 5 dielectric resonant cavity was firstly introduced at the junction of the T-connection (Fig. 11a). According to the steady-state field distribution (Fig. 11b) simulated by the FDTD method, the reflection has been reduced from 35.1% to 15.4%, but the radiation at the cavity is still very large (up to 67.2%) and the transmission decreased to 17.4%. Therefore, further optimization was done by removing four dielectric cylinders at the junction (Fig. 12). The calculation and the simulation (Fig. 13) shows that the reflection has been reduced to 1.2% while the radiation is less than 1% and the total transmission increased to 97.8%.
Fig. 12. (a) Schematic of the PDW-based T-connection with an optimized dielectric resonant cavity. (b) Enlarged view of the optimized cavity.
By comparing the normalized transmission and reflection spectra of the simple and the optimized T-connections (Fig. 14), for the optimized T-connection, the total transmission is over 95% and the reflection is less than 4%. The size of the cavity is b × 2c = 572.5 nm× 975.8 nm, which is much smaller than those reported in Ref. [7] (about 1.1 μm × 2.2 μm) and Ref. [8] (multimode waveguide-based, 13 μm × 134.7 μm). 3.3. Output optical power splitting ratios In this section, output optical power splitting ratios were investigated by shifting the input waveguide. Fig. 15 schematically shows that the input waveguide was shifted to the left with a displacement (d). d can be varied from 0 to 201.6 nm (0 to a′). Fig. 16 depicts the normalized optical power outputted at ports 1 and 2 for different d in the wavelength range of 1.48 to 1.62 μm. Fig. 17 shows the calculated output optical power splitting ratio (Pout−1/Pout−2). It can be seen that, with the shift of the input waveguide to the left, the output optical power splitting ratio Pout−1/Pout−2 increased from 1 to 1.82 for λ = 1.55 μm. If the input waveguide shifts to the right, same results can be obtained.
Fig. 11. (a) T-connection with a 3 × 5 resonant cavity at the junction. (b) Simulated steady-state electric field distribution at a wavelength of 1550 nm.
2296
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
Fig. 15. Schematic of the optimized T-junction with the input waveguide shifted to the left with a displacement d.
Fig. 13. Simulated steady-state electric field distribution in the optimized T-connection at 1550 nm.
4. Conclusion Ultrasmall cross- and T-connections have been proposed in periodic dielectric waveguides by adding a resonant cavity at the junctions for optical communication wavelengths. For the crossconnection, by adding a cavity with a size of 520.8 nm × 520.8 nm, over 93% optical power can be transmitted to the desired output port
Fig. 16. Normalized output optical power for different displacement d. (a) Output port 1. (b) Output port 2.
in the large wavelength region of 1.48 to 1.62 μm. For the Tconnection, over 95% optical power can be equally split and transmitted to the two output ports in the wavelength region of 1.48 to 1.62 μm by adding an optimized cavity with a small size of 572.5 nm × 975.8 nm. Moreover, the output power splitting ratios of
Fig. 14. Comparison of the normalized transmission (a) and reflection (b) for the simple and the optimized T-connections in a wavelength region of 1.48 to 1.62 μm.
Fig. 17. The calculated output optical power splitting ratio versus the displacement of the input waveguide shifted.
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
the T-connection can be changed by shifting the input waveguide from 0 to 201.6 nm. Compared with those reported in conventional dielectric waveguides and photonic crystal waveguides, the structures proposed in this work are much simpler and more compact, which would be desirable for highly integrated PICs. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grants 60625404 and 10974261). References [1] D.N. Christodoulides, F. Lederer, Y. Silberberg, Nature 424 (2003) 817. [2] C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, J.D. Joannopoulos, J. Lightwave. Technol. 17 (1999) 1682. [3] Y.G. Roh, S. Yoon, H. Jeon, S.H. Han, Q.H. Park, Appl. Phys. Lett. 85 (2004) 3351. [4] F. Xu, A.W. Poon, Opt. Express 16 (2008) 8649. [5] J. Li, D.A. Fattal, R.G. Beausoleil, Opt. Express 17 (2009) 7717. [6] Y. Zhang, W. Huang, B. Li, J. Opt. A: Pure Appl. Opt. 10 (2008) 095302.
2297
[7] R.U. Ahmad, F. Pizzuto, G.S. Camarda, R.L. Espinola, H. Rao, R.M. Osgood Jr., IEEE Photon. Technol. Lett. 14 (2002) 65. [8] Q. Wang, S. He, L. Wang, IEEE Photon. Technol. Lett. 14 (2002) 1124. [9] S. Lan, H. Ishikawa, Opt. Lett. 27 (2002) 1567. [10] Y. Watanabe, Y. Sugimoto, N. Ikeda, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, K. Asakawa, Opt. Express 14 (2006) 9502. [11] L. Worschech, H.Q. Xu, A. Forchel, L. Samuelson, Appl. Phys. Lett. 79 (2001) 3287. [12] H.P. Chan, S.Y. Cheng, P.S. Chung, Microwave Opt. Technol. Lett. 11 (1996) 87. [13] M.H. Hu, J.Z. Huang, R. Scarmozzino, M. Levy, R.M. Osgood Jr., IEEE Photon. Technol. Lett. 9 (1997) 203. [14] H. Lin, J. Su, R. Cheng, W. Wang, IEEE J. Quantum Electron. 35 (1999) 1092. [15] S. Fan, J.D. Joannopoulos, J.N. Winn, A. Devenyi, J.C. Chen, R.D. Meade, J. Opt. Soc. Am. B 12 (1995) 1267. [16] P. Luan, K. Chang, Opt. Express 14 (2006) 3263. [17] P. Luan, K. Chang, Opt. Express 15 (2007) 4536. [18] W. Huang, Y. Zhang, B. Li, Opt. Express 16 (2008) 1600. [19] Y. Zhang, H. Lei, B. Li, Opt. Commun. 283 (2010) 2140. [20] S. Zeng, Y. Zhang, B. Li, Opt. Express 17 (2009) 365. [21] Y. Zhang, W. Huang, B. Li, Appl. Phys. Lett. 93 (2008) 031110. [22] S. Zeng, Y. Zhang, B. Li, E.Y. Pun, Photon. Nanostruct. Fundam. Appl. 8 (2010) 32. [23] D.N. Chigrin, A.V. Lavrinenko, C.M.S. Torres, Opt. Quantum Electron. 37 (2005) 331. [24] W. Zhang, J. Liu, W. Huang, W. Zhao, Proc. SPIE 7609 (2010) 76091H.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Periodic dielectric waveguide-based cross- and T-connections with a resonant cavity at the junctions Hongtao Guo, Yao Zhang, Baojun Li ⁎ State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
a r t i c l e
i n f o
Article history: Received 10 September 2010 Accepted 6 January 2011 Available online 18 January 2011
a b s t r a c t We propose a cross-connection and a T-connection in periodic dielectric waveguides (PDWs) with ultrasmall size and high transmission efficiency at λ = 1.55 μm. The cross-connection was formed by introducing a 3 × 3 square dielectric resonant cavity at the cross-junction with a crosstalk of less than 0.8% (about − 21 dB) and a transmission of larger than 93% at the desired output port. The T-connection was formed by introducing a 3 × 5 dielectric resonant cavity with modifications at the T-junction. The total transmission is up to 95%. In addition, different power splitting ratios were also achieved by moving the input waveguide of the Tconnection with different displacements. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Waveguide based optical cross- and T-connections are extremely important structures in photonic integrated circuits (PICs) to connect functional devices [1,2]. Ideal waveguide-based cross-connection must ensure that the incident lightwave from the input port of the waveguides are totally transmitted to the output port along the same direction with negligible crosstalk, reflection, and radiation loss. For a high-performance T-connection, incident lightwave should be totally transmitted into the two output ports with a desired power ratio. In the past several years, cross- and T-connections based on conventional dielectric waveguides (CDW) and photonic crystal (PC) waveguides have been designed and demonstrated with different structures [3–14], which exhibited good transmission performances. However, CDW-based devices usually have a relatively large size (up to tens of micrometers), while PC-based devices have an intrinsic disadvantage that the device structures must follow the PC lattice orientation, which is difficult to achieve the flexible control of lightwaves. Furthermore, a wide PC background area (at least several lattice constants) is required for device applications. These may cause inconvenience for highly integrated PICs. Periodic dielectric waveguides (PDWs) [15], which are good waveguide structures for building ultracompact devices, have the ability to afford both high transmission and small size [16]. Today, many functional PDW-based devices have been designed including power splitter [17], wavelength and polarization splitter [18,19], demultiplexer/filter [20], Fabry–Pérot microcavities [21], and optical logic gates [22]. However, as basic components, ultrasmall size and high performance PDW-based optical
⁎ Corresponding author. E-mail address: [email protected] (B. Li). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.01.008
cross- and T-connections are desirable to be designed and optimized for highly efficient optical connection within limited spaces. Therefore, in this work, we propose PDW-based cross- and T-connections with a resonant cavity at the junctions to achieve high transmission performance. The design of the devices has been conducted using a plane wave expansion (PWE) method, and the performances have been evaluated using a finite-difference time-domain (FDTD) method. The results show that more than 93% transmission was obtained for both the cross- and T-connections structures with ultrasmall resonant cavity size (less than 1 μm × 1 μm). 2. Cross-connection in PDWs 2.1. Simple cross-connection PDWs can be formed by dielectric cylinder array in air or air-hole array in a dielectric [23,24]. Here, the considered single-row PDW is a dielectric cylinder array with a refractive index of n = 3.45 (Si). The radius of the cylinders is set to be r = 0.4a, where a is the center-tocenter spacing between two adjacent cylinders. A simple crossconnection is directly formed by arranging two PDWs perpendicularly (Fig. 1a). The enlarged view of the junction is shown in Fig. 1b. For optical communication wavelength application, a is specified as a = 232.5 nm. From the FDTD simulated steady-state field distribution (Fig. 2), it can be seen that, for the simple cross-connection, when a λ = 1.55 μm was launched into the input 1, only 62.8% optical power was output from the straight waveguide. 14.3% optical power was reflected to the input waveguide while 21.6% was coupled into the cross waveguide. If launched, the λ = 1.55 μm into the input 2 (Fig. 1a), same simulated distribution can be obtained. Obviously, the performance of the simple structure without optimization is not satisfactory. Therefore,
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
Fig. 1. (a) Schematic of a simple PDW-based cross-connection. (b) Enlarged view of the junction.
Fig. 2. FDTD simulated steady-state field distribution in the simple PDW-based crossconnection.
an optimization will be done in the following subsection to improve the transmission performance of the PDW-based cross-connection. 2.2. Optimized cross-connection To improve the performance of the PDW-based cross-connection, a model of resonant cavity was applied at the junction (Fig. 3). In such a model of the cavity, to achieve desirable performances (high transmission, low crosstalk and reflection), the cavity must have fourfold symmetry with planes coinciding with the waveguide axes. Besides, the cavity has to support only two resonant modes in the frequency range of interest. One of the resonant modes has an odd symmetry with respect to the horizontal waveguide and an even symmetry with respect to the vertical waveguide axis, while the other has opposite symmetries. Under these conditions, one resonant mode
Fig. 3. Scheme of the transmission process through a cross-connection with a model of the cavity.
2293
Fig. 4. (a) Schematic of a PDW-based cross-connection with a 3 × 3 square dielectric resonant cavity. (b) Enlarged view of the waveguide. (c) Enlarged view of the cavity.
will be coupled into the straight waveguide and be outputted as a transmission, while the other mode will be resonated in the cavity and finally also be coupled into the straight waveguide and be outputted as a transmission. As a result, the transmission performance of the structure with the cavity will be improved while the crosstalk and the reflection will be reduced. With the implementation of the cavity model described above, an optimized cross-connection can be obtained by introducing a 3 × 3 square dielectric resonant cavity at the cross-junction (Fig. 4). In the 3 × 3 square dielectric resonant cavity, the row-to-row space between adjacent cylinders is a1 and the radius of the cylinders is r1. Fig. 5a is the calculated band structure for a single PDW by the PWE method. The inset (solid frame) of Fig. 5a is an a × 9a supercell for PWE calculation. The parameters a1 and r1 greatly affect the performance of the resonant cavity and determine whether the cavity can satisfy the requirement of supporting two resonant modes in a wide resonant frequency range. By calculations, a1 = 0.8a and r1 = 0.4a1 are chosen to make the cavity hold two resonant modes with resonant frequencies in the range from 0.125 to 0.165(a/λ), corresponding to 1.41 to 1.86 μm. Fig. 5b depicts the profiles of the two resonant modes at λ = 1.55 μm in the square cavity, in which the two modes exhibit opposite symmetries with respect to the waveguide axes x and y. Since a = 232.5 nm, the center-to-center distance between two adjacent cylinders in the cavity is a1 = 186 nm. The distance between the waveguide and the cavity is L = a.
Fig. 5. Calculations for the PDWs and the square cavity based on the PWE method. (a) Band structure for TM mode in a single PDW. (b) Profiles of the two resonant modes at λ = 1.55 μm in the square cavity with opposite symmetries with respect to the waveguide axes x and y.
2294
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
Fig. 6. FDTD simulated steady-state field distribution in the optimized cross-connection with a 3 × 3 square dielectric resonant cavity.
To evaluate the performance of the optimized cross-connection, steady-state field distribution was simulated by FDTD method with λ = 1.55 μm launched from the input 1 (Fig. 6). Compared with the simulation of simple PDW-based cross-connection showed in Fig. 2, total crosstalk has been reduced from 21.6% to 1.6% and the reflection reduced from 14.3% to 3.9%. A 93.1% transmission has been obtained in the desired straight output port. By taking FDTD simulations with wavelengths range at around 1.55 μm (e.g., 1.48 to 1.62 μm), the transmission and crosstalk spectra for the simple and the optimized cross-connections are obtained (Fig. 7). It can be seen from Fig. 7 that, by adding a 3 × 3 square dielectric resonant cavity at the cross junction, the transmission is increased and the crosstalk is significantly reduced. The size of the resonant cavity is 520.8 nm × 520.8 nm, which is smaller than those reported in conventional dielectric waveguides [2] (about 1.16 μm × 1.16 μm) and photonic crystal waveguides [10] (about 3.74 μm × 2.16 μm).
Fig. 7. Comparison of the normalized transmission (a) and total crosstalk (b) for the simple and the optimized cross-connections in a wavelength range of 1.48 to 1.62 μm.
Fig. 8. (a) Schematic of a simple PDW-based T-connection. (b) Enlarged view of the junction.
3. T-connection in PDWs 3.1. Simple T-connection In this section, we use the dielectric resonant cavity to optimize the PDW-based T-connection. Before the optimization, a simple PDW-based T-connection (Fig. 8a) and an enlarged view of its junction (Fig. 8b) will be discussed. The center-to-center spacing between the two adjacent cylinders is a′ and the radius of the cylinders is set to be r′ = 0.42a′. By band structure calculation, a′ is specified as a′ = 201.6 nm for the λ = 1.55 μm operation. Fig. 9 shows the simulated steady-state field distribution by the FDTD method. For the simple T-connection, the calculated transmission is rather low (45.2% in total at the two outputs). 35.1% optical power was reflected back to the input waveguide. The radiation is also large (19.7%).
Fig. 9. FDTD simulated steady-state field distribution in the simple PDW-based Tconnection.
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
2295
Fig. 10. Scheme of a T-connection with a cavity at the junction.
3.2. Optimized T-connection To improve the performance of the PDW-based T-connection, a resonant cavity was also applied at the junction (Fig. 10). The optical powers inputted, reflected, outputted to port 1, and port 2 are denoted by Pin, Pr, Pout−1, and Pout−2, respectively. Therefore, the coefficients of reflection R, left transmission TL and right TR can be expressed as R = Pr/Pin, TL = Pout−1/Pin, and TR = Pout−2/Pin. To transfer the input optical power as much as possible to ports 1 and 2, in the following design, the resonant frequency will be chosen to match the wavelength of the inputted light by adjusting the shape of the cavity. Similar to the optimization for the PDW-based cross-connection discussed in Section 2.2, a 3 × 5 dielectric resonant cavity was firstly introduced at the junction of the T-connection (Fig. 11a). According to the steady-state field distribution (Fig. 11b) simulated by the FDTD method, the reflection has been reduced from 35.1% to 15.4%, but the radiation at the cavity is still very large (up to 67.2%) and the transmission decreased to 17.4%. Therefore, further optimization was done by removing four dielectric cylinders at the junction (Fig. 12). The calculation and the simulation (Fig. 13) shows that the reflection has been reduced to 1.2% while the radiation is less than 1% and the total transmission increased to 97.8%.
Fig. 12. (a) Schematic of the PDW-based T-connection with an optimized dielectric resonant cavity. (b) Enlarged view of the optimized cavity.
By comparing the normalized transmission and reflection spectra of the simple and the optimized T-connections (Fig. 14), for the optimized T-connection, the total transmission is over 95% and the reflection is less than 4%. The size of the cavity is b × 2c = 572.5 nm× 975.8 nm, which is much smaller than those reported in Ref. [7] (about 1.1 μm × 2.2 μm) and Ref. [8] (multimode waveguide-based, 13 μm × 134.7 μm). 3.3. Output optical power splitting ratios In this section, output optical power splitting ratios were investigated by shifting the input waveguide. Fig. 15 schematically shows that the input waveguide was shifted to the left with a displacement (d). d can be varied from 0 to 201.6 nm (0 to a′). Fig. 16 depicts the normalized optical power outputted at ports 1 and 2 for different d in the wavelength range of 1.48 to 1.62 μm. Fig. 17 shows the calculated output optical power splitting ratio (Pout−1/Pout−2). It can be seen that, with the shift of the input waveguide to the left, the output optical power splitting ratio Pout−1/Pout−2 increased from 1 to 1.82 for λ = 1.55 μm. If the input waveguide shifts to the right, same results can be obtained.
Fig. 11. (a) T-connection with a 3 × 5 resonant cavity at the junction. (b) Simulated steady-state electric field distribution at a wavelength of 1550 nm.
2296
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
Fig. 15. Schematic of the optimized T-junction with the input waveguide shifted to the left with a displacement d.
Fig. 13. Simulated steady-state electric field distribution in the optimized T-connection at 1550 nm.
4. Conclusion Ultrasmall cross- and T-connections have been proposed in periodic dielectric waveguides by adding a resonant cavity at the junctions for optical communication wavelengths. For the crossconnection, by adding a cavity with a size of 520.8 nm × 520.8 nm, over 93% optical power can be transmitted to the desired output port
Fig. 16. Normalized output optical power for different displacement d. (a) Output port 1. (b) Output port 2.
in the large wavelength region of 1.48 to 1.62 μm. For the Tconnection, over 95% optical power can be equally split and transmitted to the two output ports in the wavelength region of 1.48 to 1.62 μm by adding an optimized cavity with a small size of 572.5 nm × 975.8 nm. Moreover, the output power splitting ratios of
Fig. 14. Comparison of the normalized transmission (a) and reflection (b) for the simple and the optimized T-connections in a wavelength region of 1.48 to 1.62 μm.
Fig. 17. The calculated output optical power splitting ratio versus the displacement of the input waveguide shifted.
H. Guo et al. / Optics Communications 284 (2011) 2292–2297
the T-connection can be changed by shifting the input waveguide from 0 to 201.6 nm. Compared with those reported in conventional dielectric waveguides and photonic crystal waveguides, the structures proposed in this work are much simpler and more compact, which would be desirable for highly integrated PICs. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grants 60625404 and 10974261). References [1] D.N. Christodoulides, F. Lederer, Y. Silberberg, Nature 424 (2003) 817. [2] C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, J.D. Joannopoulos, J. Lightwave. Technol. 17 (1999) 1682. [3] Y.G. Roh, S. Yoon, H. Jeon, S.H. Han, Q.H. Park, Appl. Phys. Lett. 85 (2004) 3351. [4] F. Xu, A.W. Poon, Opt. Express 16 (2008) 8649. [5] J. Li, D.A. Fattal, R.G. Beausoleil, Opt. Express 17 (2009) 7717. [6] Y. Zhang, W. Huang, B. Li, J. Opt. A: Pure Appl. Opt. 10 (2008) 095302.
2297
[7] R.U. Ahmad, F. Pizzuto, G.S. Camarda, R.L. Espinola, H. Rao, R.M. Osgood Jr., IEEE Photon. Technol. Lett. 14 (2002) 65. [8] Q. Wang, S. He, L. Wang, IEEE Photon. Technol. Lett. 14 (2002) 1124. [9] S. Lan, H. Ishikawa, Opt. Lett. 27 (2002) 1567. [10] Y. Watanabe, Y. Sugimoto, N. Ikeda, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, K. Asakawa, Opt. Express 14 (2006) 9502. [11] L. Worschech, H.Q. Xu, A. Forchel, L. Samuelson, Appl. Phys. Lett. 79 (2001) 3287. [12] H.P. Chan, S.Y. Cheng, P.S. Chung, Microwave Opt. Technol. Lett. 11 (1996) 87. [13] M.H. Hu, J.Z. Huang, R. Scarmozzino, M. Levy, R.M. Osgood Jr., IEEE Photon. Technol. Lett. 9 (1997) 203. [14] H. Lin, J. Su, R. Cheng, W. Wang, IEEE J. Quantum Electron. 35 (1999) 1092. [15] S. Fan, J.D. Joannopoulos, J.N. Winn, A. Devenyi, J.C. Chen, R.D. Meade, J. Opt. Soc. Am. B 12 (1995) 1267. [16] P. Luan, K. Chang, Opt. Express 14 (2006) 3263. [17] P. Luan, K. Chang, Opt. Express 15 (2007) 4536. [18] W. Huang, Y. Zhang, B. Li, Opt. Express 16 (2008) 1600. [19] Y. Zhang, H. Lei, B. Li, Opt. Commun. 283 (2010) 2140. [20] S. Zeng, Y. Zhang, B. Li, Opt. Express 17 (2009) 365. [21] Y. Zhang, W. Huang, B. Li, Appl. Phys. Lett. 93 (2008) 031110. [22] S. Zeng, Y. Zhang, B. Li, E.Y. Pun, Photon. Nanostruct. Fundam. Appl. 8 (2010) 32. [23] D.N. Chigrin, A.V. Lavrinenko, C.M.S. Torres, Opt. Quantum Electron. 37 (2005) 331. [24] W. Zhang, J. Liu, W. Huang, W. Zhao, Proc. SPIE 7609 (2010) 76091H.