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Kerr nonlinear switch based on ultra-compact photonic crystal directional coupler
Optik 122 (2011) 502–505
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Kerr nonlinear switch based on ultra-compact photonic crystal directional coupler Azadeh Taher Rahmati, Nosrat Granpayeh ∗ Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 18 September 2009 Accepted 26 March 2010
Keywords: Optical directional coupler All optical switches Nonlinear Kerr effect Nonlinear photonic crystal
a b s t r a c t In this paper, an all optical switch based on nonlinear photonic crystal directional coupler has been simulated and analyzed by the finite difference time domain (FDTD) method. The lunched pump signal increases the refractive indices of the central row of the coupler, due to nonlinear Kerr effect, hence the coupler works in the nonlinear conditions and lightwave guides to the other output port. We have tried to increase the coupling efficiency and reduce the required power in the nonlinear status by optimizing the bends structure and increasing the interaction between dielectric and lightwave signal. Therefore, the input signal beam can be controlled to be exchanged between two output ports to earn the highest output power ratio and the smallest amount of power required for nonlinear performance, the physical length of the coupler is determined to be 20a, where a is the structure lattice constant. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction All optical switches have been under intensive study in recent years due to their potential abilities for optical system and network applications. Several methods have been reported to control the propagation properties of optical devices, employing nonlinear materials and effects. Nonlinear photonic crystal structures are the best candidates for these devices [1–3]. An all optical switch fabricated by nonlinear waveguide directional coupler was primarily proposed by Jensen [4]. These devices which made of nonlinear dielectric were operating as linear directional couplers at low input power. However, at higher input powers, optical nonlinearities modify the phase matching of both waveguides and thus by selecting proper coupling length and appropriate power, input signal energy is transferred to a different output port [5,6]. Furthermore, one of the most important applications of photonic crystal structure is their ability to make compact optical devices, which would be an important factor in integrated optical circuits [7–9]. Photonic crystal directional couplers have attracted many researchers due to their small size, especially short coupling length and high extinction ratio [10,11]. These devices perform various functions in optical circuits, including power splitting and combining [12–15], wavelength-selective coupling, optical filters [16], resonators [17] and switching [18,19]. By using nonlinear pho-
∗ Corresponding author. E-mail addresses: [email protected] (A.T. Rahmati), [email protected] (N. Granpayeh). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.04.004
tonic crystal in these structures, the refractive index of dielectric materials depends on the light intensity, thus the tunable optical devices such as filters and switches can be designed [20–23]. In this paper, an all optical switch based on nonlinear directional coupler is simulated and its different parameters are modified. The bend structure is changed to decrease the required power in nonlinear status and to confine the pump signal. Also, by increasing the interaction of nonlinear material and lightwave signal, the required power and the output power for nonlinear status are optimized. 2. Photonic crystal directional couplers The proposed optical switch structure based on photonic crystal (PC) directional coupler is shown in Fig. 1. The device is made of two dimensional hexagonal PC structure. The AlGaAs rods have high refractive index of 3.4 and radius of 0.2a, where a is the structure lattice constant, implanted in a substrate with lower refractive index of 1.44. The central rods acting as the nonlinear defects in nonlinear regime have the refractive index of 3.4. The six ports of the coupler are tagged in Fig. 1. The TM band gap of the structure, as depicted in Fig. 2, is in the range of 0.2735 ≤ a/ ≤ 0.3833, where denotes the optical wavelength in free space. The directional coupler can be obtained by creating two single line defect waveguides next to each other in the K direction, separated by the single row of decreased radius rods. Central row radii have important roll on the nonlinearity effect caused by high power pump signal. Reducing the radius of the central rods leads to generation of a low frequency mode in dispersion diagram which is calculated by using supercell in plane wave expansion (PWE)
A.T. Rahmati, N. Granpayeh / Optik 122 (2011) 502–505
503
Fig. 1. Schematic view of the proposed directional coupler switch. It consists of three regions of input, coupling and output. Total length of the coupling region is L.
method. In spite of this special characteristic in band diagram, the optimum radius of the rods must be considered, because it has significant effect on required power of pump signal for inducing nonlinearity. In our proposed structure the central rods radius (rc ) is determined to be 0.14a. Different types of directional couplers with different applications and dispersion properties can be designed by variation of the number and radius of the central row rods. The coupling mechanism for all couplers depends on the frequency-dependent parameter of propagation constant (ˇ). Each isolated waveguide guides only a single mode, but the two waveguides near each other, interact and generate supermodes splitting into two odd and even modes, according to their symmetry with respect to the mirror plane between the guides. Therefore, the input power will couple to the other waveguide and exchange between them periodically The coupling length (Lc ) is the distance over which the phase difference between two modes is 180◦ , and depends on the difference between propagation constants of the odd and even modes, Lc =
|ˇodd − ˇeven |
(1)
The coupling region can be separated from input and output region by bending the waveguide [18]. The bend is considered to be 60◦ to avoid the coupling and mixing of the output fields. In addition, the waveguides bends have significant role in confinement of the control pump signal in the central row rods, as will be shown later. Due to the Kerr nonlinearity, the nonlinear dielectric constant of the central row can be written as εNL = εL + (3) |E|2
(2)
where E is the electric field vector and (3) = 4.4 × 10−19 m2 /V2 is the Kerr nonlinear coefficient of AlGaAs. The effect of two-photon absorption has been ignored [20].
Fig. 2. Band diagram for TM polarization in a triangular lattice of AlGaAs rods (ε = 11.56) in substrate (ε = 2.1).
Fig. 3. Normalized frequency of switching. The frequencies are selected in the range of TM band gap in which the lightwave from upper input is coupled to the upper output.
3. All optical switches In order to demonstrate the switching performance of the device, we have simulated the linear state, which the refractive index of the central row is unchanged during the guidance of the lightwave. For linear case, as depicted in Fig. 4(a), which no pump signal is induced to the central row, the coupler is expected to operate in bar state; it means that the input lightwave, I1 , with the proper frequency is guided to port O1 . In selecting the accurate frequency, we have considered the shortest coupling length and also the optimal output powers ratio, which both of them are important factors in evaluating the coupling efficiency. The FDTD method has been applied for simulation of the structure. The nonlinear perfectly matched layers (PMLs) are located around the structure as the absorbing boundary condition. The number of layers of PMLs is set to be 20. To derive the frequencies in which the input signal guides to a special output, a Gaussian pulse is launched into the input port (I1 ), then the electric and magnetic fields of the lightwave signals, of the output ports are measured. The proper frequencies are determined by taking the fast Fourier transform (FFT) of the electric and magnetic fields and integrating the Poynting vector over the cells of the output ports, the results of which are depicted in Fig. 3. In this paper, we have used the visual studio software and our codes are in C++. We have run the code for 60,000 time steps of 0.67 ps for finding proper frequency and 200,000 time steps for simulation and analysis of the linear and nonlinear effects. By selecting the optimal length for coupling region, in the linear regime the input light exits from the direct output port, as depicted in Fig. 4(a). But when high intensity pump signal is launched to the nonlinear rods in the central row, the refractive index is increased
Fig. 4. Electric field distributions of the coupler for normalized frequency of f = 0.3031 in (a) linear state, (b) pump signal is launched to the central rods with normalized frequency of fc = 0.2755 and (c) nonlinear state.
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A.T. Rahmati, N. Granpayeh / Optik 122 (2011) 502–505
Fig. 5. Electric field intensity of the pump signal for our two first proposed structures. The second structure pump signal is more confined than the first one, where 2d is the width of the coupler of Fig. 1.
as a result of the Kerr effect, thus the even mode propagation constant varies. According to Eq. (1), this will induce a slight shift in the coupling length. So, in this nonlinear regime, the input lightwave signal is switched to other waveguide and exits from that port. Therefore, the state of the directional coupler is inverted from the bar to the cross state, as illustrated in Fig. 4(c). The pump signal, as shown in Fig. 5, has even symmetry and is strongly confined to the central row rods. This can be figure out by electric field distribution obtained by FDTD shown in Fig. 4(b) for the normalized frequency of 0.2755. Therefore, the central row between the waveguides in the coupling region behaves as another waveguide to guide the pump lightwave signal of the switch. 4. Nonlinear light coupling in different structures There are some factors to improve the switching performance and the device efficiency. In this paper, the power output ratio, called extinction ratio, and required power for the nonlinear status are concerned. The former is for evaluation of directional coupler efficiency and the latter is an important factor of all optical nonlinear switches. Confining the pump lightwave in the central row is an important factor for reducing the required power for nonlinear switching performance, thus we have changed the waveguides bend structure, in which, the number of rod rows between central nonlinear row and the input and output ports is increased. By this method the light coupling between the central waveguide and the input port is reduced and the amount of energy loss during pump injection is reduced. By this modified bend, the output power ratio is improved due to more isolation between output ports. The electric field distribution of the pump signal is shown in Fig. 5. It is clear that the pump signal in the nonlinear row, in the second structure is more confined than the first one. The coupler has acted as a splitter when the output power ratio is 0 dB, as shown in Fig. 6. By increasing the power of the pump signal, Po2 /Po1 is increased slowly due to the Kerr nonlinear effect. The maximum output power ratio is achieved for special value of pump signal, so increasing pump power over that cause to decrease the output power ratio. Also, we have increased the number of rods in the central row, which has increased the interaction of waves and material, thus the required power for inducing nonlinearity and also switching is less than that of the previous structures and also the output power ratio is increased. The schematic and required pump powers for these three structures to obtain maximum output power ratios are illustrated in Fig. 6. The required switching pump power for the second and third structures are respectively less than half and one sixth of that of the first one.
Fig. 6. Output power ratio vs. required pump power for three different structures, (a) original structure, (b) second structure with 4 rows of rods between the central and the input and output ports, and (c) the structure of (b) with higher number of central row rods.
The essential standpoint of propagation in a nonlinear coupler, at a specified input power, is identical to that of a linear coupler with a specified index fluctuation along the central row. Thus reducing the required input power in nonlinear status is an important factor to have better qualifications. Therefore, the required power for the third structure which extra rods are added to the central row is much less than that of the other two structures. 5. Conclusion In this paper, an all optical switch based on nonlinear photonic crystal directional coupler with nonlinear central rods has been proposed. The switching frequency is selected to have the most output power ratio and the shortest coupling length in the linear and nonlinear states. A pump signal is used to induce the nonlinearity to the coupler and invert the switching from bar to cross state. The required power for switching is modified by confining the pump signal in the central row and also increasing the nonlinear material in that area to enhance the interaction of the lightwave and material. The required switching powers for our three proposed structures have been compared and it is shown that the second structure with farther ports at input and output and higher number of central row rods, and third structure, with farther ports at input and output and higher number of central row rods, require pump powers for nonlinear switching respectively less than half and one sixth of that of the first one. Acknowledgement The authors wish to thank Iran Telecommunication Research Center for the financial support of this project.
A.T. Rahmati, N. Granpayeh / Optik 122 (2011) 502–505
References [1] S.W. Leonard, J.P. Mondia, H.M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gosele, V. Lehmann, Tunable two-dimensional photonic crystals using liquid-crystal infiltration, Phys. Rev. B 61 (4) (2000) 2389–2392. [2] A. Sharkawy, S. Shi, D.W. Prather, R.A. Soref, Electro-optical switching using coupled photonic crystal waveguides, Opt. Express 10 (20) (2002) 1048–1059. [3] T. Yasuda, Y. Tsuji, M. Koshiba, Tunable light propagation in photonic crystal coupler filled with liquid crystal, IEEE Photon. Technol. Lett. 17 (1) (2005) 55–57. [4] S.M. Jensen, The nonlinear coherent coupler, IEEE J. Quantum Electron. 18 (2) (1982) 1580–1583. [5] P.R. Berger, P.K. Bhattacharya, S. Gupta, A waveguide directional coupler with a nonlinear coupling medium, IEEE J. Quantum Electron. 27 (3) (1991) 288–295. [6] S. Ha, A.A. Sukhorukov, Nonlinear switching and reshaping of slow-light pulses in Bragg-grating couplers, J. Opt. Soc. Am. B (JOSA-B) 25 (12) (2008) 15–22. [7] T. Liu, A.R. Zakharian, M. Fallahi, J.V. Moloney, M. Mansuripur, Design of a compact photonic-crystal-based polarizing beam splitter, IEEE Photon. Technol. Lett. 17 (7) (2005) 1435–1437. [8] T. Fujisawa, M. Koshiba, Finite-element modeling of nonlinear Mach–Zehnder interferometers based on photonic-crystal waveguides for all-optical signal processing, IEEE J. Lightwave Technol. 24 (1) (2006) 617–623. [9] I.V. Guryev, I.A. Sukhoivanov, E.A. Mendez, R.R. Laguna, J.E. Ayala, J.A.A. Lucio, Theoretical study of optical processes in nonlinear photonic crystal devices, in: Optoelectron. Phys. Technol. Int. Workshop, 2007, pp. 25–28. [10] T. Kamalakis, T. Sphicopoulos, Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory, IEEE J. Quantum Electron. 41 (6) (2005) 863–871. [11] C.H. Huang, W.F. Hsieh, S.C. Cheng, Tuning the decoupling point of a photoniccrystal directional coupler, J. Opt. Soc. Am. B (JOSA-B) 26 (2) (2009) 203–209. [12] M. Djavid, A. Ghaffari, F. Monify, M.S. Abrishamian, Photonic crystal power dividers using L-shaped bend based on ring resonators, J. Opt. Soc. Am. B (JOSAB) 25 (8) (2008) 1231–1235.
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[13] Y. Wang, Nonlinear optical limiter and digital optical switch by cascaded nonlinear couplers: analysis, IEEE J. Lightwave Technol. 17 (2) (1999) 292–297. [14] A. Ferreras, F. Rodriguez, E. Gomez-Salas, J.L. de Miguel, F. Hernandez-Gil, Useful formulas for multimode interference power splitter/combiner design, IEEE Photon. Technol. Lett. 5 (10) (1993) 1224–1227. [15] J.N. Roy, Mach–Zehnder interferometer-based tree architecture for all-optical logic and arithmetic operations, Optik 120 (7) (2009) 318–324. [16] J. Zimmermann, M. Kamp, A. Forchel, R. Marz, Photonic crystal waveguide directional couplers as wavelength selective optical filters, Opt. Commun. 230 (4) (2004) 387–392. [17] S.H. Jeong, N. Yamamoto, J. Sugisaka, M. Okano, K. Komori, GaAs-based twodimensional photonic crystal slab ring resonator consisting of a directional coupler and bent waveguides, J. Opt Soc. Am. B (JOSA-B) 24 (8) (2007) 1951–1959. [18] A. Martinez, F. Cuesta, J. Marti, Ultra short 2-D photonic crystal directional couplers, IEEE Photon. Technol. Lett. 15 (5) (2003) 694–696. [19] F. Cuesta-Soto, A. Martinez, B. Garcia-Banos, J. Marti, Numerical analysis of alloptical switching based on a 2-D nonlinear photonic crystal directional coupler, IEEE Select. Top. Quantum Electron. 10 (5) (2004) 1101–1106. [20] I.S. Maksymov, L.F. Marsal, J. Pallares, An FDTD analysis of nonlinear photonic crystal waveguides, Opt. Quantum Electron. 38 (1) (2006) 149–160. [21] C.M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, R.K. Lee, Nonlinear finite-difference time-domain method for the simulation of anisotropic, (2), and (3) optical effects, IEEE J. Lightwave Technol. 24 (1) (2006) 624–634. [22] A.T. Rahmati, N. Granpayeh, Design and simulation of a switch based on nonlinear directional coupler, Optik (in press). [23] M.S. Saremi, M.M. Mirsalehi, Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference timedomain method, Optik 116 (10) (2005) 486–492.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Kerr nonlinear switch based on ultra-compact photonic crystal directional coupler Azadeh Taher Rahmati, Nosrat Granpayeh ∗ Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 18 September 2009 Accepted 26 March 2010
Keywords: Optical directional coupler All optical switches Nonlinear Kerr effect Nonlinear photonic crystal
a b s t r a c t In this paper, an all optical switch based on nonlinear photonic crystal directional coupler has been simulated and analyzed by the finite difference time domain (FDTD) method. The lunched pump signal increases the refractive indices of the central row of the coupler, due to nonlinear Kerr effect, hence the coupler works in the nonlinear conditions and lightwave guides to the other output port. We have tried to increase the coupling efficiency and reduce the required power in the nonlinear status by optimizing the bends structure and increasing the interaction between dielectric and lightwave signal. Therefore, the input signal beam can be controlled to be exchanged between two output ports to earn the highest output power ratio and the smallest amount of power required for nonlinear performance, the physical length of the coupler is determined to be 20a, where a is the structure lattice constant. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction All optical switches have been under intensive study in recent years due to their potential abilities for optical system and network applications. Several methods have been reported to control the propagation properties of optical devices, employing nonlinear materials and effects. Nonlinear photonic crystal structures are the best candidates for these devices [1–3]. An all optical switch fabricated by nonlinear waveguide directional coupler was primarily proposed by Jensen [4]. These devices which made of nonlinear dielectric were operating as linear directional couplers at low input power. However, at higher input powers, optical nonlinearities modify the phase matching of both waveguides and thus by selecting proper coupling length and appropriate power, input signal energy is transferred to a different output port [5,6]. Furthermore, one of the most important applications of photonic crystal structure is their ability to make compact optical devices, which would be an important factor in integrated optical circuits [7–9]. Photonic crystal directional couplers have attracted many researchers due to their small size, especially short coupling length and high extinction ratio [10,11]. These devices perform various functions in optical circuits, including power splitting and combining [12–15], wavelength-selective coupling, optical filters [16], resonators [17] and switching [18,19]. By using nonlinear pho-
∗ Corresponding author. E-mail addresses: [email protected] (A.T. Rahmati), [email protected] (N. Granpayeh). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.04.004
tonic crystal in these structures, the refractive index of dielectric materials depends on the light intensity, thus the tunable optical devices such as filters and switches can be designed [20–23]. In this paper, an all optical switch based on nonlinear directional coupler is simulated and its different parameters are modified. The bend structure is changed to decrease the required power in nonlinear status and to confine the pump signal. Also, by increasing the interaction of nonlinear material and lightwave signal, the required power and the output power for nonlinear status are optimized. 2. Photonic crystal directional couplers The proposed optical switch structure based on photonic crystal (PC) directional coupler is shown in Fig. 1. The device is made of two dimensional hexagonal PC structure. The AlGaAs rods have high refractive index of 3.4 and radius of 0.2a, where a is the structure lattice constant, implanted in a substrate with lower refractive index of 1.44. The central rods acting as the nonlinear defects in nonlinear regime have the refractive index of 3.4. The six ports of the coupler are tagged in Fig. 1. The TM band gap of the structure, as depicted in Fig. 2, is in the range of 0.2735 ≤ a/ ≤ 0.3833, where denotes the optical wavelength in free space. The directional coupler can be obtained by creating two single line defect waveguides next to each other in the K direction, separated by the single row of decreased radius rods. Central row radii have important roll on the nonlinearity effect caused by high power pump signal. Reducing the radius of the central rods leads to generation of a low frequency mode in dispersion diagram which is calculated by using supercell in plane wave expansion (PWE)
A.T. Rahmati, N. Granpayeh / Optik 122 (2011) 502–505
503
Fig. 1. Schematic view of the proposed directional coupler switch. It consists of three regions of input, coupling and output. Total length of the coupling region is L.
method. In spite of this special characteristic in band diagram, the optimum radius of the rods must be considered, because it has significant effect on required power of pump signal for inducing nonlinearity. In our proposed structure the central rods radius (rc ) is determined to be 0.14a. Different types of directional couplers with different applications and dispersion properties can be designed by variation of the number and radius of the central row rods. The coupling mechanism for all couplers depends on the frequency-dependent parameter of propagation constant (ˇ). Each isolated waveguide guides only a single mode, but the two waveguides near each other, interact and generate supermodes splitting into two odd and even modes, according to their symmetry with respect to the mirror plane between the guides. Therefore, the input power will couple to the other waveguide and exchange between them periodically The coupling length (Lc ) is the distance over which the phase difference between two modes is 180◦ , and depends on the difference between propagation constants of the odd and even modes, Lc =
|ˇodd − ˇeven |
(1)
The coupling region can be separated from input and output region by bending the waveguide [18]. The bend is considered to be 60◦ to avoid the coupling and mixing of the output fields. In addition, the waveguides bends have significant role in confinement of the control pump signal in the central row rods, as will be shown later. Due to the Kerr nonlinearity, the nonlinear dielectric constant of the central row can be written as εNL = εL + (3) |E|2
(2)
where E is the electric field vector and (3) = 4.4 × 10−19 m2 /V2 is the Kerr nonlinear coefficient of AlGaAs. The effect of two-photon absorption has been ignored [20].
Fig. 2. Band diagram for TM polarization in a triangular lattice of AlGaAs rods (ε = 11.56) in substrate (ε = 2.1).
Fig. 3. Normalized frequency of switching. The frequencies are selected in the range of TM band gap in which the lightwave from upper input is coupled to the upper output.
3. All optical switches In order to demonstrate the switching performance of the device, we have simulated the linear state, which the refractive index of the central row is unchanged during the guidance of the lightwave. For linear case, as depicted in Fig. 4(a), which no pump signal is induced to the central row, the coupler is expected to operate in bar state; it means that the input lightwave, I1 , with the proper frequency is guided to port O1 . In selecting the accurate frequency, we have considered the shortest coupling length and also the optimal output powers ratio, which both of them are important factors in evaluating the coupling efficiency. The FDTD method has been applied for simulation of the structure. The nonlinear perfectly matched layers (PMLs) are located around the structure as the absorbing boundary condition. The number of layers of PMLs is set to be 20. To derive the frequencies in which the input signal guides to a special output, a Gaussian pulse is launched into the input port (I1 ), then the electric and magnetic fields of the lightwave signals, of the output ports are measured. The proper frequencies are determined by taking the fast Fourier transform (FFT) of the electric and magnetic fields and integrating the Poynting vector over the cells of the output ports, the results of which are depicted in Fig. 3. In this paper, we have used the visual studio software and our codes are in C++. We have run the code for 60,000 time steps of 0.67 ps for finding proper frequency and 200,000 time steps for simulation and analysis of the linear and nonlinear effects. By selecting the optimal length for coupling region, in the linear regime the input light exits from the direct output port, as depicted in Fig. 4(a). But when high intensity pump signal is launched to the nonlinear rods in the central row, the refractive index is increased
Fig. 4. Electric field distributions of the coupler for normalized frequency of f = 0.3031 in (a) linear state, (b) pump signal is launched to the central rods with normalized frequency of fc = 0.2755 and (c) nonlinear state.
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A.T. Rahmati, N. Granpayeh / Optik 122 (2011) 502–505
Fig. 5. Electric field intensity of the pump signal for our two first proposed structures. The second structure pump signal is more confined than the first one, where 2d is the width of the coupler of Fig. 1.
as a result of the Kerr effect, thus the even mode propagation constant varies. According to Eq. (1), this will induce a slight shift in the coupling length. So, in this nonlinear regime, the input lightwave signal is switched to other waveguide and exits from that port. Therefore, the state of the directional coupler is inverted from the bar to the cross state, as illustrated in Fig. 4(c). The pump signal, as shown in Fig. 5, has even symmetry and is strongly confined to the central row rods. This can be figure out by electric field distribution obtained by FDTD shown in Fig. 4(b) for the normalized frequency of 0.2755. Therefore, the central row between the waveguides in the coupling region behaves as another waveguide to guide the pump lightwave signal of the switch. 4. Nonlinear light coupling in different structures There are some factors to improve the switching performance and the device efficiency. In this paper, the power output ratio, called extinction ratio, and required power for the nonlinear status are concerned. The former is for evaluation of directional coupler efficiency and the latter is an important factor of all optical nonlinear switches. Confining the pump lightwave in the central row is an important factor for reducing the required power for nonlinear switching performance, thus we have changed the waveguides bend structure, in which, the number of rod rows between central nonlinear row and the input and output ports is increased. By this method the light coupling between the central waveguide and the input port is reduced and the amount of energy loss during pump injection is reduced. By this modified bend, the output power ratio is improved due to more isolation between output ports. The electric field distribution of the pump signal is shown in Fig. 5. It is clear that the pump signal in the nonlinear row, in the second structure is more confined than the first one. The coupler has acted as a splitter when the output power ratio is 0 dB, as shown in Fig. 6. By increasing the power of the pump signal, Po2 /Po1 is increased slowly due to the Kerr nonlinear effect. The maximum output power ratio is achieved for special value of pump signal, so increasing pump power over that cause to decrease the output power ratio. Also, we have increased the number of rods in the central row, which has increased the interaction of waves and material, thus the required power for inducing nonlinearity and also switching is less than that of the previous structures and also the output power ratio is increased. The schematic and required pump powers for these three structures to obtain maximum output power ratios are illustrated in Fig. 6. The required switching pump power for the second and third structures are respectively less than half and one sixth of that of the first one.
Fig. 6. Output power ratio vs. required pump power for three different structures, (a) original structure, (b) second structure with 4 rows of rods between the central and the input and output ports, and (c) the structure of (b) with higher number of central row rods.
The essential standpoint of propagation in a nonlinear coupler, at a specified input power, is identical to that of a linear coupler with a specified index fluctuation along the central row. Thus reducing the required input power in nonlinear status is an important factor to have better qualifications. Therefore, the required power for the third structure which extra rods are added to the central row is much less than that of the other two structures. 5. Conclusion In this paper, an all optical switch based on nonlinear photonic crystal directional coupler with nonlinear central rods has been proposed. The switching frequency is selected to have the most output power ratio and the shortest coupling length in the linear and nonlinear states. A pump signal is used to induce the nonlinearity to the coupler and invert the switching from bar to cross state. The required power for switching is modified by confining the pump signal in the central row and also increasing the nonlinear material in that area to enhance the interaction of the lightwave and material. The required switching powers for our three proposed structures have been compared and it is shown that the second structure with farther ports at input and output and higher number of central row rods, and third structure, with farther ports at input and output and higher number of central row rods, require pump powers for nonlinear switching respectively less than half and one sixth of that of the first one. Acknowledgement The authors wish to thank Iran Telecommunication Research Center for the financial support of this project.
A.T. Rahmati, N. Granpayeh / Optik 122 (2011) 502–505
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