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Ultra compact and fast All Optical Flip Flop design in photonic crystal platform
Optics Communications 285 (2012) 5073–5078
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Ultra compact and fast All Optical Flip Flop design in photonic crystal platform Amin Abbasi a, Morteza Noshad a,b, Reza Ranjbar a, Reza Kheradmand a,n a b
Photonics Group, Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
a r t i c l e i n f o
abstract
Article history: Received 5 March 2012 Received in revised form 12 June 2012 Accepted 13 June 2012 Available online 23 August 2012
In this work we present a heterostructure All Optical Flip-Flop configuration based on all optical switching with Kerr nonlinear photonic crystal. In this square-hexagonal structure, we propose three different schemes for the cavities in order to show the trade-off between switching time and triggering power. Loss in the system is reasonably low because of the perfect band gap matching at bending points where two lattices join. The proposed RS-Flip Flop has exceptional features, which make it one of the well optimized and most practical structures to be used in the all optical integrated circuits. The novel design has a fast switching action (on the order of a few picoseconds), and low input power (on the order of 100 mW). Furthermore, high contrast of the output signals for ON and OFF states, can help the easy detection or its coupling to the other devices. The structure is fascinatingly uncomplicated, which results in ultra small dimensions which make it suitable to be placed in an all optical integrated circuit. Besides, we provide a profound analytical view on the functioning of the system, as analyzed by the finite difference time domain (FDTD) method. & 2012 Published by Elsevier B.V.
Keywords: Nonlinear integrated optics Photonic crystals Flip Flop All optical switching Waveguide
1. Introduction Nowadays the demand for high speed telecommunication systems has increased intensively. An all optical switching takes its position as a remarkable candidate by representing dramatically fast and extremely low energy switching operation [1–7]. All optical logic gates are the key elements of optical network systems. In recent years so many studies have been done on basic logic gates, AND, NAND, OR, and XOR [8–12]. Combining and constructing more complex structures with these basic elements are common in electronic circuits. Flip Flops are one of those highly practical and useful circuits for data processing in the communication networks. All Optical Flip-Flops (AOFFs) will be the most important circuits in the future compact optically-switched communication systems [13–18]. They temporarily memorize past input–output information and process it with the present input signals. Many of the AOFF structures which have been proposed so far, are based on different nonlinear optical fields: silicon-on-insulator (SOI) microdisk laser [13], semiconductor ring laser [14], coupled laser diodes [15,16], multimode interferometers [17], Semiconductor Optical Amplifier (SOA) [18,19] and Photonic Crystal (PhC) based circuits [20–22]. Former solutions for All-Optical Flip-Flops have been involved with
n
Corresponding author. E-mail address: [email protected] (R. Kheradmand).
0030-4018/$ - see front matter & 2012 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.optcom.2012.06.095
some problems that prevent them to be practically used in all optical integrated circuits. Some of them have been demonstrated exploiting discrete devices [8], which lead to the large scale dimensions of the whole structure. Most of them suffer from slow switching times and high Set/Reset input powers. In [21,22] a symmetry breaking solution in coupled nonlinear micro-cavities using photonic crystal structure is proposed. This solution offers a certain number of advantages: it can provide small power loss due to the use of photonic crystal platform. In addition, there is no need for any external light or electrical current for biasing. The simple structure also allows it to be designed in an ultra small scale. However, the proposed structures suffer low contrast ratios between states. Moreover, they require high input powers to trigger output between the states (about 10 W). Also, the same ports are used for both the input and output signals. These disadvantages prevent it from being practically used in the optical integrated circuits. In this work, a structure based on symmetry breaking principal with double resonant micro-cavities is proposed. Use of double resonant cavities allows us to design different ports for inputs and outputs. The input powers are considerably decreased due to the frequency matched input powers and cavity resonances. Also, the high contrast between the states allows it to be easily detected by detector. Although the proposed structure in [20] may have some of these advantages (For example, it needs the switching power of 60 mW), it is basically a D-Flip Flop, which is fundamentally different from our RS-Flip Flop structure, in function.
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A flip-flop circuit has two outputs, one for the normal value (Q) and one for the complement value of the stored bit (Q0 ). Binary information can enter a flip-flop by separate ways and this gives rise to the different types of flip-flops. RS-latch is a basic flip flop in which two input ports of ‘Set’ and ‘Reset’ have been inserted. Applying a pulse to each of the inputs changes the state of the outputs. These types of flip flops are the most basic devices used in all optical memories. The other kinds of flip flops can be made by using RS-Flip Flop. Photonic crystals offered new platform for all optical switching networks due to low energy loss and small structure dimension, comparable to a few wavelengths [22–25]. It is common to use heterostructure photonic crystal lattice to increase the coupling efficiency between waveguides in photonic crystal devices. Especially, heterostructure lattices have been designed for increasing the transmission in Y-branches and bends [26–31]. In our design, in order to reach a highly perfect structure with the lowest amount of loss we used optimized heterostructure squarehexagonal lattice configuration, which is introduced and studied in [26]. This structure is considered to have less power loss and higher coupling efficiency in comparison with the simple unistructure square or hexagonal configurations for using as a Ysplitter or in the bending points. In this paper, we adopt AlGaAs as a nonlinear material in air background. We have showed the
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Fig. 1. (a) State table and (b) negative pulse shape for RS-Flip Flop.
trade-off relation between switching time and driving power for designing an optimum flip flop.
2. Design and optimization The fundamental structure for flip-flop circuit in electronics consists of only two input signals, which are named as Set–Reset ports, and two output ports that usually are in opposite logical states. Fig. 1 shows the binary-state table of RS-Flip Flop and input negative pulse shapes schematically. Similar to the NAND based RS Flip Flops; the proposed structure uses negative pulses for input signals. Fig. 2 shows the designed structure of the heterostructure flipflop based on 2D-PhC. As shown in Fig. 2, the structure is constructed by mixing of five different regions of both hexagonal and square lattices. There are also five waveguides (L1–L5) and two elliptical defect cavities (C1, C2). The lattice constant a, is 575 nm, and radius of the rods are 0.2a and 0.22a for the square and hexagonal lattices, respectively. The Set signal enters the system from L1 with wavelength of l2 which corresponds to the second resonance frequency of cavity C1. Also the Reset signal with wavelength l1 enters to cavity C2 through the waveguide L5. The rods are AlGaAs material with the refractive index of n¼3.5, and the central elliptical rod’s Kerr nonlinear coefficient is considered to be n2 ¼ 1.5 10 17 m2/W. AlGaAs is one wellstudied ultrafast nonlinear material for C-band operation. Unlike silicon, chalcogenide glasses and bismuth oxide, III–V semiconductor devices can be easily integrated with lasers and optical amplifiers. AlGaAs has a nonlinear coefficient which is 500 times larger than that of silica, five times larger that of the As2S3chalcogenide glass and three times larger than that of silicon at telecommunication wavelengths. Its negligible two-photon absorption (TPA) within C-band makes it more attractive than silicon, the As2Se3-chalcogenide glass and GaAs [34,35]. As the predicted network power consumption will grow tremendously [32,33], becoming the major concern in terms of operational costs, AlGaAs’s intrinsic high nonlinearity as well as low-TPA over C-band [34] would rekindle commercial interest, despite its relatively high material cost. The background material is also supposed to be air with the refractive index of n ¼1. The structure has a band gap for TM modes. Simultaneously using of the mixed structure of square and hexagonal lattices defines new configuration expected to have low loss. However, discontinuity in the band gap where two
Fig. 2. The schematic heterostructure configuration of flip-flop circuit consisting five waveguides and two cavities. The cavities have been rotated by 451 to satisfy high coupling efficiency. The rods are nonlinear AlGaAs material which are embedded in air background.
A. Abbasi et al. / Optics Communications 285 (2012) 5073–5078
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Fig. 4. (a) The rotation angle around z axis (z axis is the axis along rods length) and (b) coupling efficiency versus rotation angle of elliptical cavity rod around z axis. According to this figure, it is obvious that in order to keep the symmetry and efficient matching between the both couple of waveguides, the rotation angle should be 451.
Fig. 3. Band gap diagrams for (a) square lattice and (b) hexagonal lattice with the rod radii of 0.2a and 0.22a respectively. It can be seen from this figure that hexagonal lattice provides wide band gap in comparison with square one. Furthermore, the band gaps overlap each other perfectly.
lattices join causes new internal mismatch. In order to solve the problem of mismatching between the band gaps, the optimized geometry and radius of rods have been evaluated and selected precisely (rod radii of 0.2a and 0.22a for square and hexagonal lattices, respectively). So the band gaps of two lattices find an appropriate overlap as it can be seen in Fig. 3. In the proposed structure, utilizing elliptical cavity with the diameters of ‘0.64a’ and ‘0.54a’ allows us to have it as a nonlinear switcher between the waveguides. As shown in Fig. 4, we investigate the optimum angle for the elliptical cavity by rotating it to obtain the maximum coupling between two pairs of the waveguides (L1, L3) and (L2, L3). The results of the coupling between the waveguides are shown in Fig. 4. It is obvious that in order to keep the symmetry and efficient coupling between both pairs of waveguides, the rotation angle should be 451. The cavities in the system have the same resonance frequencies along their major and minor axes as l1¼1.6565 mm and l2¼1.5565 mm, respectively. Also, the corresponding quality factors for l1 and l2 are respectively Q1¼1559 and Q2¼1132.
3. Realization of flip-flop circuit and results As discussed before in the introduction section, our proposed Flip Flop is based on the symmetry breaking principal. Similar to [21,22]
the coupled mode theory have been used for this structure. In this section we describe the system’s performance and give the results of the proposed structure. The dynamical mechanism of the system regarding the time intervals has been illustrated schematically in Fig. 5. Suppose that in time t1 at which both the Set and Reset signals are in high level, the output Q is in ON state. In this state, the Reset signal has passed through both the cavities C1 and C2, and it has reached output Q. In addition, existence of Reset signal with wavelength l1 inside the cavity C1, has resulted in changing the resonance frequency of this cavity away from l2 because of the nonlinearity. The resonance wavelength changing is represented in Fig. 6. This phenomenon prevents the Set signal from passing through cavity C1 and reaching output Q0 . Therefore, output Q0 is in the OFF state. The electric field pattern is shown for this situation in Fig. 7(a). In this case, no changes in the Set signal can alter the state of outputs. In time t2 we give a negative pulse to the Reset signal. By bringing the Reset signal to the low level, and after an small delay time, cavity C1 becomes devoid of l1, and Set signal finds the opportunity to pass through the cavities C1 and C2, and reach output Q0 . In this case, the state of outputs Q and Q0 change to OFF and ON, respectively. The electric field pattern of this behavior is shown in Fig. 7(b). Changing the state of Reset signal back to the high level in time t3, makes no variation in the state of the outputs due to the altered resonance wavelength of cavity C2. Existence of the light with wavelength l2 inside the cavity C2 prevents the Set signal from passing through cavity C2 and reaching output Q. Fig. 7(c) depicts the electric field pattern in this case. Similarly, making a negative pulse in the Set signal in time t4 causes outputs Q and Q0 to turn to ON and OFF respectively. The corresponding electric pattern for this case is presented in Fig. 7(d).
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Fig. 5. Time chart of the states of input and output signals. Indicated times on horizontal axis show critical times when logical state of the system change.
Fig. 6. The solid line shows the transmission spectrum of the cavity C1 from waveguide L2–L3 with the resonance wavelength of l1 ¼ 1:6565 mm, and the dashed-line shows the considered transmission spectrum of l1 in the case of existence of light l2 in the cavity.
Proper operation of the system mainly depends on Set–Reset negative pulse duration. If this delay time adjusts adequately, system’s function would be successful. Firstly, we mention the fundamental trade-off property in the operation of nonlinear photonic crystal optical switching devices based on microcavity. For reaching a low triggering signal intensity required for switching, the quality factor should be high so that the needed resonance shift for this operation becomes smaller. For deriving the minimum signal power it is important to consider the minimum resonance frequency shift required for switching. If this value is taken 3DoT =2 it would correspond to the output transmission of below 10% [7]. Here, DoT denotes the FWHM (full width at half maximum) for transmission spectrum of cavity which can be achieved by DoT ¼ o0 =Q where o0 is the cavity resonance frequency. The uncertainty relation between cavity decay time and cavity spectral width is as follows [7]: DoT T Cavity ¼ 1 ð1Þ 2 The switching time of the structure is usually on the order of cavity decay time [7]. Lower quality factor of the cavities leads to shorter decay times. So in a system with lower minimum required power of signals the switching time will be longer, and vice-versa. Here we investigate three cavity structures to optimize the
Fig. 7. Electric field patterns for different states of inputs in the proposed Flip Flop.
switching time and minimum input power. The cavities are built by inserting extra rods joined to the main elliptical cavities in the intersection of three waveguides. The structures of these cavities are given in Fig. 8. Table 1 presents the characteristics of three different cavities. An appropriate cavity for the Flip Flop structure should have low working power with fast switching ability. Transmission efficiency is also important since the output power of the Flip Flop should be detectable. Cavity (a) structure presents high transmission efficiency and fast switching time (lower than 1 ps), but it requires high input powers for Set and Reset signals. Cavity (c) in contrast, provides a low needed input power for switching, but the transmission efficiency is too low to be detected. In Cavity (b) all the mentioned parameters are suitable. In this structure, the system has a fast switching performance due to small cavity decay time, and the required triggering power is also low. Furthermore, it has appropriate transmission efficiency. It may also be useful to discuss more about the input power dimension. Actually in practice, the vertical confinement of the light in the 2D photonic crystals (PC) is realized by the refractiveindex difference caused by the cladding layer. Since numerically modeling the exact 3D PC waveguides is hardly realistic due to an
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Fig. 8. Three different types of cavity geometries that considered in presented flip flop circuit.
Table 1 Characteristics of three proposed structures for the cavities.
First resonance l1 (mm) Second resonance l2 (mm) Q factor of l1 Q factor of l2 Transmission l1 (%) Transmission l2 (%) Cavity decay time of l1 (ps) Cavity decay time of l2 (ps) Switching power l1 (mW/mm2) Switching power l2 (mW/mm2)
Cavity (a)
Cavity (b)
Cavity (c)
1.6636 1.5565 518 82 93 95 0.85 0.14 5460 5890
1.6565 1.5565 1559 1132 85 87 2.74 1.86 260 280
1.6585 1.5552 4570 3887 15 2 5.70 3.64 50 55
logically ‘1’, and output Q is logically ‘0’. In section (b), the Set signal changes its value to ‘0’ and output Q reaches ‘1’ in a transient interval, the system switches to the opposite state. Interestingly, recovering of the Set signal to the ‘1’ state in period (c) has no effect on the output intensity, which is what we expected from a flip flop circuit. As mentioned before, the negative pulse duration is a critical issue. It must be equal or larger than minimum switching time. The transient switching time for this flip flop is about 10 ps for Set input, and 6 ps for Reset input.
4. Conclusion We proposed a 2D-PhC based All-Optical Rs-Flip Flop using two nonlinear micro-cavities connected via a waveguides. The dynamical behavior of the structure is simulated by using the numerical FDTD method. Our design has the benefit of compactness and fastness in comparison to other previously proposed flip flops. In addition, no external signal is needed to supply the output power, and the output power is provided by the either Set of Reset signals. Also, like the electronic circuits of flip flops, our proposed flip flop has two outputs Q and Q0 with opposite status. This ultra compact optimized flip flop configuration has the capability of being used in fundamental all optical signal processors and all optical communication based on photonic crystal structures. References
Fig. 9. The time dependent output power of the flip flop system when Set signal experiences negative pulse. Here the pulse duration is taken almost 20 ps which is larger than minimum switching time. Three steps have been illustrated on curve. (a) when Set signal logical value is 1, system output is 0 but (b) as it collapses to 0 logical state, the output value starts to grow and reaches steady state amount at the end. (c) Now the Set signal existence has no effect on the system output value.
exorbitant amount of memory and computational demand, an alternative approach is required [36]. So usually investigations of 3D PC waveguides are simplified with its 2D cross section along the propagation direction. Here, because our focus is not on the modal pattern of the input light (which is dependent on the type of cladding layer for confining the light) we have given the powers in Table 1 in the general form of mW/mm2. However, because the results of some of the previous works are given in mW, we can also approximate our results in mW. For example, by considering the high degree confinement of the input light in a photonic crystal slab with the thickness of 1.5a, the switching power for l1 and l2 in a flip flop with cavity (b) in Table 1 can be approximated as 80 mW and 85 mW respectively. Time dependent dynamics of the system output intensity when Set signal experiences a short negative pulse, is shown in Fig. 9. As presented in this figure, in period (a) Set signal is
[1] H. Kawaguchi, Proceedings of the International Conference on Transparent Optical Networks, We A2 1, 2005. [2] F. Prati, M. Travagnin, L.A. Lugiato, Physical Review A 55 (1997) 690. [3] N. Pleros, D. Apostolopoulos, D. Petrantonakis, C. Stamatiadis, H. Avramopoulos, IEEE Photonics Technology Letters 21 (2009) 73. [4] K. Gallo, G. Assanto, Journal of the Optical Society B 16 (1999) 267. [5] M.T. Hill, H.J.S. Dorren, T. de Vries, X.J.M. Leijtens, J.H. den Besten, B. Smalbrugge, Y.S. Oei, H. Binsma, G.D. Khoe, M.K. Smit, Nature 432 (2004) 206. [6] G. Yuan, Z. Wang, S. Yu, IEEE Photonics Technology Letters 20 (2008) 785. [7] D. Vujic, S. John, Physical Review A 72 (2005) 013807. [8] Y. Liu, F. Qin, Z. Meng, F. Zhou, Q. Mao, Z. Li, Optics Express 19 (3) (2011) 1945. [9] P. Andalib, N. Granpayeh, Journal of the Optical Society of America B 26 (1) (2009). [10] P. Andalib, N. Granpayeh, Journal of Optics A: Pure and Applied Optics 11 (2009) 085203. [11] K. Lee, J. Lin, Y. Yang, Y. Yang, J. Wu, Y. Huang, Y. Lin, K. Lin, and W. Lee, Proceedings on Optoelectronic Materials and Devices III, vol. 7135, 2008, pp. 71353Y. [12] B.M. Isfahani, T.A. Tameh, N. Granpayeh, A.M. Javan, Journal of the Optical Society of America B 26 (5) (2009) 097. [13] L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D.V. Thourhout, R. Baets, G. Morthier, Nature Photonics 4 (2010) 82. ¨ [14] A. Trita, G. Mezosi, F. Bragheri, J. Yu, S. Furst,W. Elsasser, I. Cristiani, M. Sorel, G. Giuliani, Proceedings of the European Conference on Optical Communication, Paper We2C3, 2008. [15] M.T. Hill, H. de Waardt, G.D. Khoe, H.J.S. Dorren, Journal of Quantum Electronics 37 (2001) 405.
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[16] M.T. Hill, H.J.S. Dorren, T. de Vries, X.J.M. Leijtens, J.H. den Besten, B. Smalbrugge, Y.S. Oei, H. Binsma, G.D. Khoe, M.K. Smit, Nature 432 (2004) 206. [17] M. Takenaka, M. Raburn, Y. Nakano, Photonics Technology Letters 17 (2005) 968. [18] D. Apostolopoulos, P. Zakynthinos, L. Stampoulidis, E. Kehayas, R. McDougall, R. Harmon, A. Poustie, G. Maxwell, R. Van Caenegem, D. Colle, M. Pickavet, E. Tangdiongga, H.J.S. Dorren, H. Avramopoulos, IEEE Photonics Technology Letters (2008) 2024. [19] R. Clavero, F. Ramos, J.M. Martinez, J. Marti, Photonics Technology Letters 17 (2005) 843. [20] A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, S. Kawanishi, Optics Express 14 (3) (2006) 1230. [21] B. Maes, M. Soljacic, J. Joannopoulos, P. Bienstman, R. Baets, S. Gorza, M. Haelterman, Optics Express 14 (22) (2006) 10678. [22] S.H. Li, X.H. Cai, Journal of Applied Physics 106 (2009) 083105. [23] K. Srinivasan, P.E. Barclay, O. Painter, J. Chen, A.Y. Cho, C. Gmachl, Applied Physics Letters 83 (2003) 1915. [24] Y. Akahane, T. Asano, B.-S. Song, S. Noda, Nature 425 (2003) 944. [25] E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, L. Ramunno, Physical Review B 72 (2005) 161318.
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Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Ultra compact and fast All Optical Flip Flop design in photonic crystal platform Amin Abbasi a, Morteza Noshad a,b, Reza Ranjbar a, Reza Kheradmand a,n a b
Photonics Group, Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
a r t i c l e i n f o
abstract
Article history: Received 5 March 2012 Received in revised form 12 June 2012 Accepted 13 June 2012 Available online 23 August 2012
In this work we present a heterostructure All Optical Flip-Flop configuration based on all optical switching with Kerr nonlinear photonic crystal. In this square-hexagonal structure, we propose three different schemes for the cavities in order to show the trade-off between switching time and triggering power. Loss in the system is reasonably low because of the perfect band gap matching at bending points where two lattices join. The proposed RS-Flip Flop has exceptional features, which make it one of the well optimized and most practical structures to be used in the all optical integrated circuits. The novel design has a fast switching action (on the order of a few picoseconds), and low input power (on the order of 100 mW). Furthermore, high contrast of the output signals for ON and OFF states, can help the easy detection or its coupling to the other devices. The structure is fascinatingly uncomplicated, which results in ultra small dimensions which make it suitable to be placed in an all optical integrated circuit. Besides, we provide a profound analytical view on the functioning of the system, as analyzed by the finite difference time domain (FDTD) method. & 2012 Published by Elsevier B.V.
Keywords: Nonlinear integrated optics Photonic crystals Flip Flop All optical switching Waveguide
1. Introduction Nowadays the demand for high speed telecommunication systems has increased intensively. An all optical switching takes its position as a remarkable candidate by representing dramatically fast and extremely low energy switching operation [1–7]. All optical logic gates are the key elements of optical network systems. In recent years so many studies have been done on basic logic gates, AND, NAND, OR, and XOR [8–12]. Combining and constructing more complex structures with these basic elements are common in electronic circuits. Flip Flops are one of those highly practical and useful circuits for data processing in the communication networks. All Optical Flip-Flops (AOFFs) will be the most important circuits in the future compact optically-switched communication systems [13–18]. They temporarily memorize past input–output information and process it with the present input signals. Many of the AOFF structures which have been proposed so far, are based on different nonlinear optical fields: silicon-on-insulator (SOI) microdisk laser [13], semiconductor ring laser [14], coupled laser diodes [15,16], multimode interferometers [17], Semiconductor Optical Amplifier (SOA) [18,19] and Photonic Crystal (PhC) based circuits [20–22]. Former solutions for All-Optical Flip-Flops have been involved with
n
Corresponding author. E-mail address: [email protected] (R. Kheradmand).
0030-4018/$ - see front matter & 2012 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.optcom.2012.06.095
some problems that prevent them to be practically used in all optical integrated circuits. Some of them have been demonstrated exploiting discrete devices [8], which lead to the large scale dimensions of the whole structure. Most of them suffer from slow switching times and high Set/Reset input powers. In [21,22] a symmetry breaking solution in coupled nonlinear micro-cavities using photonic crystal structure is proposed. This solution offers a certain number of advantages: it can provide small power loss due to the use of photonic crystal platform. In addition, there is no need for any external light or electrical current for biasing. The simple structure also allows it to be designed in an ultra small scale. However, the proposed structures suffer low contrast ratios between states. Moreover, they require high input powers to trigger output between the states (about 10 W). Also, the same ports are used for both the input and output signals. These disadvantages prevent it from being practically used in the optical integrated circuits. In this work, a structure based on symmetry breaking principal with double resonant micro-cavities is proposed. Use of double resonant cavities allows us to design different ports for inputs and outputs. The input powers are considerably decreased due to the frequency matched input powers and cavity resonances. Also, the high contrast between the states allows it to be easily detected by detector. Although the proposed structure in [20] may have some of these advantages (For example, it needs the switching power of 60 mW), it is basically a D-Flip Flop, which is fundamentally different from our RS-Flip Flop structure, in function.
5074
A. Abbasi et al. / Optics Communications 285 (2012) 5073–5078
A flip-flop circuit has two outputs, one for the normal value (Q) and one for the complement value of the stored bit (Q0 ). Binary information can enter a flip-flop by separate ways and this gives rise to the different types of flip-flops. RS-latch is a basic flip flop in which two input ports of ‘Set’ and ‘Reset’ have been inserted. Applying a pulse to each of the inputs changes the state of the outputs. These types of flip flops are the most basic devices used in all optical memories. The other kinds of flip flops can be made by using RS-Flip Flop. Photonic crystals offered new platform for all optical switching networks due to low energy loss and small structure dimension, comparable to a few wavelengths [22–25]. It is common to use heterostructure photonic crystal lattice to increase the coupling efficiency between waveguides in photonic crystal devices. Especially, heterostructure lattices have been designed for increasing the transmission in Y-branches and bends [26–31]. In our design, in order to reach a highly perfect structure with the lowest amount of loss we used optimized heterostructure squarehexagonal lattice configuration, which is introduced and studied in [26]. This structure is considered to have less power loss and higher coupling efficiency in comparison with the simple unistructure square or hexagonal configurations for using as a Ysplitter or in the bending points. In this paper, we adopt AlGaAs as a nonlinear material in air background. We have showed the
S
R
Q
Q'
1
1
Last Q
Last Q'
0
1
1
0
1
0
0
1
0
0
X
X
Fig. 1. (a) State table and (b) negative pulse shape for RS-Flip Flop.
trade-off relation between switching time and driving power for designing an optimum flip flop.
2. Design and optimization The fundamental structure for flip-flop circuit in electronics consists of only two input signals, which are named as Set–Reset ports, and two output ports that usually are in opposite logical states. Fig. 1 shows the binary-state table of RS-Flip Flop and input negative pulse shapes schematically. Similar to the NAND based RS Flip Flops; the proposed structure uses negative pulses for input signals. Fig. 2 shows the designed structure of the heterostructure flipflop based on 2D-PhC. As shown in Fig. 2, the structure is constructed by mixing of five different regions of both hexagonal and square lattices. There are also five waveguides (L1–L5) and two elliptical defect cavities (C1, C2). The lattice constant a, is 575 nm, and radius of the rods are 0.2a and 0.22a for the square and hexagonal lattices, respectively. The Set signal enters the system from L1 with wavelength of l2 which corresponds to the second resonance frequency of cavity C1. Also the Reset signal with wavelength l1 enters to cavity C2 through the waveguide L5. The rods are AlGaAs material with the refractive index of n¼3.5, and the central elliptical rod’s Kerr nonlinear coefficient is considered to be n2 ¼ 1.5 10 17 m2/W. AlGaAs is one wellstudied ultrafast nonlinear material for C-band operation. Unlike silicon, chalcogenide glasses and bismuth oxide, III–V semiconductor devices can be easily integrated with lasers and optical amplifiers. AlGaAs has a nonlinear coefficient which is 500 times larger than that of silica, five times larger that of the As2S3chalcogenide glass and three times larger than that of silicon at telecommunication wavelengths. Its negligible two-photon absorption (TPA) within C-band makes it more attractive than silicon, the As2Se3-chalcogenide glass and GaAs [34,35]. As the predicted network power consumption will grow tremendously [32,33], becoming the major concern in terms of operational costs, AlGaAs’s intrinsic high nonlinearity as well as low-TPA over C-band [34] would rekindle commercial interest, despite its relatively high material cost. The background material is also supposed to be air with the refractive index of n ¼1. The structure has a band gap for TM modes. Simultaneously using of the mixed structure of square and hexagonal lattices defines new configuration expected to have low loss. However, discontinuity in the band gap where two
Fig. 2. The schematic heterostructure configuration of flip-flop circuit consisting five waveguides and two cavities. The cavities have been rotated by 451 to satisfy high coupling efficiency. The rods are nonlinear AlGaAs material which are embedded in air background.
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Fig. 4. (a) The rotation angle around z axis (z axis is the axis along rods length) and (b) coupling efficiency versus rotation angle of elliptical cavity rod around z axis. According to this figure, it is obvious that in order to keep the symmetry and efficient matching between the both couple of waveguides, the rotation angle should be 451.
Fig. 3. Band gap diagrams for (a) square lattice and (b) hexagonal lattice with the rod radii of 0.2a and 0.22a respectively. It can be seen from this figure that hexagonal lattice provides wide band gap in comparison with square one. Furthermore, the band gaps overlap each other perfectly.
lattices join causes new internal mismatch. In order to solve the problem of mismatching between the band gaps, the optimized geometry and radius of rods have been evaluated and selected precisely (rod radii of 0.2a and 0.22a for square and hexagonal lattices, respectively). So the band gaps of two lattices find an appropriate overlap as it can be seen in Fig. 3. In the proposed structure, utilizing elliptical cavity with the diameters of ‘0.64a’ and ‘0.54a’ allows us to have it as a nonlinear switcher between the waveguides. As shown in Fig. 4, we investigate the optimum angle for the elliptical cavity by rotating it to obtain the maximum coupling between two pairs of the waveguides (L1, L3) and (L2, L3). The results of the coupling between the waveguides are shown in Fig. 4. It is obvious that in order to keep the symmetry and efficient coupling between both pairs of waveguides, the rotation angle should be 451. The cavities in the system have the same resonance frequencies along their major and minor axes as l1¼1.6565 mm and l2¼1.5565 mm, respectively. Also, the corresponding quality factors for l1 and l2 are respectively Q1¼1559 and Q2¼1132.
3. Realization of flip-flop circuit and results As discussed before in the introduction section, our proposed Flip Flop is based on the symmetry breaking principal. Similar to [21,22]
the coupled mode theory have been used for this structure. In this section we describe the system’s performance and give the results of the proposed structure. The dynamical mechanism of the system regarding the time intervals has been illustrated schematically in Fig. 5. Suppose that in time t1 at which both the Set and Reset signals are in high level, the output Q is in ON state. In this state, the Reset signal has passed through both the cavities C1 and C2, and it has reached output Q. In addition, existence of Reset signal with wavelength l1 inside the cavity C1, has resulted in changing the resonance frequency of this cavity away from l2 because of the nonlinearity. The resonance wavelength changing is represented in Fig. 6. This phenomenon prevents the Set signal from passing through cavity C1 and reaching output Q0 . Therefore, output Q0 is in the OFF state. The electric field pattern is shown for this situation in Fig. 7(a). In this case, no changes in the Set signal can alter the state of outputs. In time t2 we give a negative pulse to the Reset signal. By bringing the Reset signal to the low level, and after an small delay time, cavity C1 becomes devoid of l1, and Set signal finds the opportunity to pass through the cavities C1 and C2, and reach output Q0 . In this case, the state of outputs Q and Q0 change to OFF and ON, respectively. The electric field pattern of this behavior is shown in Fig. 7(b). Changing the state of Reset signal back to the high level in time t3, makes no variation in the state of the outputs due to the altered resonance wavelength of cavity C2. Existence of the light with wavelength l2 inside the cavity C2 prevents the Set signal from passing through cavity C2 and reaching output Q. Fig. 7(c) depicts the electric field pattern in this case. Similarly, making a negative pulse in the Set signal in time t4 causes outputs Q and Q0 to turn to ON and OFF respectively. The corresponding electric pattern for this case is presented in Fig. 7(d).
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Fig. 5. Time chart of the states of input and output signals. Indicated times on horizontal axis show critical times when logical state of the system change.
Fig. 6. The solid line shows the transmission spectrum of the cavity C1 from waveguide L2–L3 with the resonance wavelength of l1 ¼ 1:6565 mm, and the dashed-line shows the considered transmission spectrum of l1 in the case of existence of light l2 in the cavity.
Proper operation of the system mainly depends on Set–Reset negative pulse duration. If this delay time adjusts adequately, system’s function would be successful. Firstly, we mention the fundamental trade-off property in the operation of nonlinear photonic crystal optical switching devices based on microcavity. For reaching a low triggering signal intensity required for switching, the quality factor should be high so that the needed resonance shift for this operation becomes smaller. For deriving the minimum signal power it is important to consider the minimum resonance frequency shift required for switching. If this value is taken 3DoT =2 it would correspond to the output transmission of below 10% [7]. Here, DoT denotes the FWHM (full width at half maximum) for transmission spectrum of cavity which can be achieved by DoT ¼ o0 =Q where o0 is the cavity resonance frequency. The uncertainty relation between cavity decay time and cavity spectral width is as follows [7]: DoT T Cavity ¼ 1 ð1Þ 2 The switching time of the structure is usually on the order of cavity decay time [7]. Lower quality factor of the cavities leads to shorter decay times. So in a system with lower minimum required power of signals the switching time will be longer, and vice-versa. Here we investigate three cavity structures to optimize the
Fig. 7. Electric field patterns for different states of inputs in the proposed Flip Flop.
switching time and minimum input power. The cavities are built by inserting extra rods joined to the main elliptical cavities in the intersection of three waveguides. The structures of these cavities are given in Fig. 8. Table 1 presents the characteristics of three different cavities. An appropriate cavity for the Flip Flop structure should have low working power with fast switching ability. Transmission efficiency is also important since the output power of the Flip Flop should be detectable. Cavity (a) structure presents high transmission efficiency and fast switching time (lower than 1 ps), but it requires high input powers for Set and Reset signals. Cavity (c) in contrast, provides a low needed input power for switching, but the transmission efficiency is too low to be detected. In Cavity (b) all the mentioned parameters are suitable. In this structure, the system has a fast switching performance due to small cavity decay time, and the required triggering power is also low. Furthermore, it has appropriate transmission efficiency. It may also be useful to discuss more about the input power dimension. Actually in practice, the vertical confinement of the light in the 2D photonic crystals (PC) is realized by the refractiveindex difference caused by the cladding layer. Since numerically modeling the exact 3D PC waveguides is hardly realistic due to an
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Fig. 8. Three different types of cavity geometries that considered in presented flip flop circuit.
Table 1 Characteristics of three proposed structures for the cavities.
First resonance l1 (mm) Second resonance l2 (mm) Q factor of l1 Q factor of l2 Transmission l1 (%) Transmission l2 (%) Cavity decay time of l1 (ps) Cavity decay time of l2 (ps) Switching power l1 (mW/mm2) Switching power l2 (mW/mm2)
Cavity (a)
Cavity (b)
Cavity (c)
1.6636 1.5565 518 82 93 95 0.85 0.14 5460 5890
1.6565 1.5565 1559 1132 85 87 2.74 1.86 260 280
1.6585 1.5552 4570 3887 15 2 5.70 3.64 50 55
logically ‘1’, and output Q is logically ‘0’. In section (b), the Set signal changes its value to ‘0’ and output Q reaches ‘1’ in a transient interval, the system switches to the opposite state. Interestingly, recovering of the Set signal to the ‘1’ state in period (c) has no effect on the output intensity, which is what we expected from a flip flop circuit. As mentioned before, the negative pulse duration is a critical issue. It must be equal or larger than minimum switching time. The transient switching time for this flip flop is about 10 ps for Set input, and 6 ps for Reset input.
4. Conclusion We proposed a 2D-PhC based All-Optical Rs-Flip Flop using two nonlinear micro-cavities connected via a waveguides. The dynamical behavior of the structure is simulated by using the numerical FDTD method. Our design has the benefit of compactness and fastness in comparison to other previously proposed flip flops. In addition, no external signal is needed to supply the output power, and the output power is provided by the either Set of Reset signals. Also, like the electronic circuits of flip flops, our proposed flip flop has two outputs Q and Q0 with opposite status. This ultra compact optimized flip flop configuration has the capability of being used in fundamental all optical signal processors and all optical communication based on photonic crystal structures. References
Fig. 9. The time dependent output power of the flip flop system when Set signal experiences negative pulse. Here the pulse duration is taken almost 20 ps which is larger than minimum switching time. Three steps have been illustrated on curve. (a) when Set signal logical value is 1, system output is 0 but (b) as it collapses to 0 logical state, the output value starts to grow and reaches steady state amount at the end. (c) Now the Set signal existence has no effect on the system output value.
exorbitant amount of memory and computational demand, an alternative approach is required [36]. So usually investigations of 3D PC waveguides are simplified with its 2D cross section along the propagation direction. Here, because our focus is not on the modal pattern of the input light (which is dependent on the type of cladding layer for confining the light) we have given the powers in Table 1 in the general form of mW/mm2. However, because the results of some of the previous works are given in mW, we can also approximate our results in mW. For example, by considering the high degree confinement of the input light in a photonic crystal slab with the thickness of 1.5a, the switching power for l1 and l2 in a flip flop with cavity (b) in Table 1 can be approximated as 80 mW and 85 mW respectively. Time dependent dynamics of the system output intensity when Set signal experiences a short negative pulse, is shown in Fig. 9. As presented in this figure, in period (a) Set signal is
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