KOUSIK MUKHERJEE Faculty, PG and UG Departments of Physics B. B. College, Asansol , West Bengal, India

Optics and Photonics Letters Vol. 4, No. 1 (2011) 25 34 c World Scientific Publishing Company DOI: 10.1142/S1793528811000159 ON THE METHOD OF IMPLEMENTATION OF FREQUENCY ENCODED ALL OPTICAL RECONFIGURABLE LOGIC GATES BASED ON TOTAL REFLECTIONAL OPTICAL SWITCH AT THE INTERFACE KOUSIK MUKHERJEE Faculty, PG and UG Departments of Physics B. B. College, Asansol 713303, West Bengal, India lipton007@indiatimes.com Received 8 February 2011 A novel method of implementation of frequency encoded reconfigurable logic gates NOT, OR, AND, NOR, NAND, X-OR, X-NOR is discussed. The frequency sources and physical requirements for the implementation are also discussed. The non-linear material (liquid) suitable for these operations to be performed should be of large non-linear coefficient, high reverse saturation absorption, large thermo optic coefficient and low viscosity to get transformed into gas quickly when illuminated with a controlling beam of suitable intensity. The input controlling beams used to induce non-linearity in the switch are either of frequency υ 1 or υ 2 and the probe beam is a mixed signal of frequencies υ 1 and υ 2. The controlling inputs decide the output conditions of the probe to get different logic gates. The gates are reconfigurable in the sense that we can get one gate from another gate by just changing the filters used in the output ports or tuning the filters. Keywords: All optical; logic gates; non-linear total reflectional switch; frequency encoding. 1. Introduction Optical processors have proved their potential and strong role in signal processing, computation, image processing and communication due to several advantages over electronic processing in the high speed domain. A photon is a suitable information carrier in many ways and a variety of information processors have been proposed in the last few decades using photon as carrier. 1 4 All optical parallel computation is the key technology for all optical networks and all optical logic gates are the essential parts of the optical computer. Recently, quantum information and computation has emerged as a growing field of research, but has many difficulties to overcome, among them decoherence is an important one, 5,6 so research on high speed classical optical computation is still an active area using non-linear effects. 7 15 In a large amount of these works, the states of information are represented by intensity encoding technique or polarization encoding technique. In intensity encoding, the state 1 is represented by the presence of a photon whereas 0 is represented by the absence of photon. This technique has many drawbacks namely, intensity loss dependent problems 25

26 K. Mukherjee in non-linear medium. In intensity encoding, a particular value of the signal intensity level must be maintained to properly encode the state of information, otherwise distinguishing the different bits becomes difficult due to degradation in extinction ratio. So mechanism for adjustment of a prefixed intensity level is required. This makes the system complex. In transmission, reflection or refraction, the intensity of the signals changes and problems are created in the channel selection. This is because a non-linear medium directs signals of different intensities in different directions. As an alternative technique, one can mention polarization encoding 16 18 but this scheme also has drawback of changing state of polarization on reflection, refraction or transmission. So some polarization control mechanism is also required, making the system complex. Recently, frequency encoding 19 21 and hybrid encoding 22 24 techniques free from intensity loss dependent problem and polarization dependent problem are proposed. The signal itself maintains its frequency and no frequency maintaining mechanism is required if we encode information in terms of frequencies. Most of the proposals proposed so far are not truly all-optical also, so there is electronic speed latency and some use non-linear processes of very low efficiency. Using the total reflectional switch, all optical frequency encoded logic gates are proposed by the author. 25 However these logic gates are not reconfigurable but implemented separately. In this communication, the frequency encoding technique is utilized to implement different reconfigurable logic gates using total reflectional optical switches. The possibility of reconfiguration of the gates makes it possible to use the same module for different logic gates by simply changing the filters in the different paths. If tunable filters are used, then the changing of the filtering frequencies can give rise to a different logic gate. 2. The Principle of the Scheme The working of the proposed logic gates are based on the frequency encoding and optical routing based on total reflectional switches. 18,25 2.1. Frequency encoding In the frequency encoding scheme, the states of information 0 and 1 are represented by signals of frequencies υ 1 and υ 2 respectively. Using this encoding technique, the truth table of different all optical logic gates are shown in Table 1 (NOT gate) and Table 2 (other gates) below. Table 1. Truth table of the NOT gate. Input A Output à υ 1 (0) υ 2 (1) υ 1 (1) υ 1 (0)

Total Reflectional OS at Interface 27 Table 2. Truth table of OR, AND, NOR, NAND, X-OR, X-NOR gates. Inputs Outputs A B OR AND NOR NAND X-OR X-NOR 0(υ 1 ) 0(υ 1 ) 0(υ 1 ) 0(υ 1 ) 1(υ 2 ) 1(υ 2 ) 0(υ 1 ) 1(υ 2 ) 0(υ 1 ) 1(υ 2 ) 1(υ 2 ) 0(υ 1 ) 0(υ 1 ) 1(υ 2 ) 1(υ 2 ) 0(υ 1 ) 1(υ 2 ) 0(υ 1 ) 1(υ 2 ) 0(υ 1 ) 0(υ 1 ) 1(υ 2 ) 1(υ 2 ) 0(υ 1 ) 1(υ 2 ) 1(υ 2 ) 1(υ 2 ) 1(υ 2 ) 0(υ 1 ) 0(υ 1 ) 0(υ 1 ) 1(υ 2 ) Thus it is clear from Tables 1 and 2 that the information coded in terms of frequencies is an efficient way to represent different digital input and output conditions. In addition, a mixed signal of two frequencies υ 1 and υ 2 is used as the probe beams. 2.2. Optical switching and routing The optical switching and routing is based on the non-linearity induced by the input control beams, depending on the variation in the propagation of the probe beams in a 1 2 total internal reflectional switch, 18 shown in Fig. 1 and described below. It consists of a pair of rectangular prisms with a non-linear medium (NLM) between them. As a non-linear medium, a liquid of refractive index n l can be used. The refractive index of the material of the prism n p is chosen such that in normal conditions, n p = n l. If a controlling signal is made incident on the liquid, the liquid should be converted into gas such that the refractive index of the NLM decreases. If n l = n p sin θ input is maintained, then the probe signal will be total internally reflected from the non-linear medium (NLM) prism interface and changes its path. So the control signals induce a non-linearity and controls the path of propagation of the probe beam. The simplest way to achieve this type of non-linearity is to use Kerr effect, 26,27 but the effect is too weak. So alternatively, one can use quartz as optical refractive media and fullerenes as the non-linear medium. 18 When there is no controlling signal signing on the non-linear medium n fullerenes = n quartz = 1.46, which can be obtained by properly adjusting the proportion of fullerenes and toluene, the probe signal will be transmitted without changing the path of propagation. Now shining controlling signal on the non-linear medium converts it into a liquid, and the refractive index of the non-linear medium becomes n fullerenes = n quartz sin 45 =1.03. NLM Fig. 1. Optical switch.

28 K. Mukherjee X Beam splitter F 1 L 1 S 1 NM Y Coupler NM F 2 L 2 S 2 Fig. 2. Optical router. In this condition, the probe signal will be reflected at the interface and the propagation direction will be changed. The structure of the optical router is shown in Fig. 2. The router consists of a pair of total internal reflectional switches. The controlling signals (X, Y) are first coupled and then divided equally. One part is passed through the filter F 1 (υ 1 pass) and focusing lens L 1 and another part through filter F 2 (υ 2 pass) and focusing lens L 2.The routing of the probe signal depends on the conditions of the input controlling signals. This type of optical switches are independently realized by Li et al. 18 and Lawson et al. 28 and a similar one using Kerr effect by Deshazer et al. 29 The input controlling signal may interfere with the input probe signals if they are simultaneously present. This can be avoided by using these two types of signals in two different planes. For example, if the controlling signals are used on the plane of the paper, then the probe signal will be used in the plane perpendicular to the plane of the paper. Another way to avoid this problem of interference is to use probe and controlling signal one by one, which may cause the system to be a little bit slower but also reduces the possibility of probe induced refractive index change, although it is very small compared to that due to controlling signals. This technique can be improved by adjusting the time between injection of control signal and probe signal in such a way that as soon as the control signals make the liquid convert into gas, the probe signal is injected into the gas. 3. Scheme of Generation of Different Logic Gates The scheme of generation of different logic gates is based on frequency encoding and frequency routing by the total reflectional switches. 25 In the scheme, the input controlling beams are passed through two filters F 1 (υ 1 pass) and F 2 (υ 2 pass) corresponding to switches S 1 and S 2 respectively. So the non-linearity is induced in the switch S 1 by signal of frequency υ 1 andintheswitchs 2,signaloffrequencyυ 2 induces the non-linearity. Depending on the condition of the controlling beam, the path of the probe beams are shown in Fig. 3. In Fig. 3, there are three different paths A, B and C of the probe beams depending on the conditions of the input controlling beams. When both the controlling inputs X and Y are signals of frequency υ 1, the non-linearity is only induced in the switch S 1 and the corresponding path of the probe beam is A due to total internal reflection at S 1 (Fig. 3a).

Total Reflectional OS at Interface 29 S 1 S 2 A S 1 S 2 C S 1 S 2 B Fig. 3. The optical router. Similarly, when the inputs are signals of frequency υ 1 and υ 2 (either X = υ 1 and Y = υ 2 or X = υ 2 and Y = υ 1 ), the non-linearity is induced on both the switches S 1 and S 2. The corresponding path of the probe light is B due to total internal reflection on both the switches S 1 and S 2 (Fig. 3b). When both the controlling inputs X and Y are signals of frequency υ 2, the non-linearity is only induced in the switch S 2 and the corresponding path of the probe beam is C due to transmission through the switch S 1 (Fig. 3c). The basic design of the reconfigurable logic gates based on the optical router is shown in Fig. 4. Here A, B, and C are different paths corresponding to the different input controlling beams as described above. F 1,F 2 and F 3 are three filters which can be properly utilized to generate different logic gates. 3.1. Implementation of the NOT gate A NOT gate is a single input gate, and the output is the inverted version of the input. Thus if the controlling beam is of frequency υ 1, then the output will be a signal of frequency υ 2, which will be extracted from the probe beam. Similarly for input controlling beam of frequency υ 2, the output should be a signal of frequency υ 1, extracted from the probe. In Fig. 4, for a NOT gate, there will be no light in the path B because the path of the probe light is along A or C, depending on the condition whether the input controlling beam is a signal of frequency υ 1 or a signal of frequency υ 2 respectively. If we select the filter F 1, C S1 F 3 S 2 F 1 A Output Probe signal B F 2 Fig. 4. Reconfigurable logic gates.

30 K. Mukherjee a υ 1 pass filter and F 2,aυ 2 pass filter, then it becomes a NOT gate. Let us explain the operation of the NOT gate. In this configuration, when the controlling input is a signal of frequency υ 1 (i.e. LOW), then the path of the probe signal will be along A, and in the path A, a υ 2 pass filter is used to extract output signal at frequency υ 2 (i.e. HIGH) from the probe signal of mixed frequency. This is the NOT operation corresponding to 0(υ 1 ) 1(υ 2 ) Again when the input control beam is a signal of frequency υ 2 (i.e. HIGH), then the path of the probe signal will be along C and in the path C, a υ 1 pass filter is used to extract the output signal at frequency υ 1 (i.e. LOW) from the probe signal. This is the NOT operation corresponding to 1(υ 2 ) 0(υ 1 ). Thus the switches S 1 and S 2 along with filters υ 1 pass and υ 2 pass operate like a NOT gate. 3.2. Implementation of the OR, AND, NOR, NAND, X-OR, X-NOR gates The implementation of different reconfigurable logic gates are described below. 3.2.1. OR gate An OR gate gives high output when any one of the input is high and low only when both the inputs are low. In the module describing the propagation of probe beam and extraction of different outputs corresponding to the OR gate, the filters F 1 is a υ 1 pass, F 2 and F 3 are υ 2 pass. When both the input controlling beams are of frequency υ 1 (LOW), the path of the probe beam is A. The use of υ 1 pass filter in the path A makes the output a signal of frequency υ 1 (LOW). So the operation, 0(υ 1 )OR0(υ 1 ) 0(υ 1 )isachieved. Similarly, when the inputs are signals of frequency υ 1 and υ 2 (either X = υ 1 and Y = υ 2 or X = υ 2 and Y = υ 1 ), the path of the probe beam is along B. The corresponding outputs are signals of frequency υ 2 (HIGH) through the υ 2 pass filter placed in the path B, so the OR operations 0(υ 1 )OR1(υ 2 ) (υ 2 )and1(υ 2 )OR0(υ 1 ) 1(υ 2 ) are achieved. Now when the input controlling beams are both signals of frequency υ 2, the corresponding path of the probe signal is along C. The υ 2 pass filter in the path C generates an output signal at frequency υ 2. So the operation 1(υ 2 )OR1(υ 2 ) (υ 2 ) is achieved. So the OR gate can be achieved using the optical router and three filters only. 3.2.2. AND gate The output of an AND gate is high only when both the inputs are high. In the module of the AND gate, the filters (F 1 and F 2 ) in the paths A and B are υ 1 pass and in the path C

Total Reflectional OS at Interface 31 is a υ 2 pass filter (F 3 ). The action of the AND gate is clear from Table 2. When any one of the inputs is low i.e. signal of frequency υ 1, the path of the probe light is either A or B in which υ 1 pass filters (F 1 and F 2 ) are present. So the output is low or signal of frequency υ 2. For both the inputs being υ 2, the path of the probe signal is C in which υ 2 pass filter is present. This results in a high output at frequency υ 2. 3.2.3. NOR gate and NAND gate The NOR gate has high output only when both the inputs are low, otherwise the output is low. This can be achieved by using filter F 1 a υ 2 pass and F 2 and F 3 υ 1 pass in the module shown in Fig. 4. The working of the NOR gate is exactly complementary to that of OR gate as shown in Table 2. It is also clear from the fact that the υ 1 pass filters are replaced in the OR gate by υ 2 pass filters and vice versa to get NOR gate. Similarly, to get the performance of the NAND gate which is complementary to that of AND gate, one has to just interchange the filters (υ 1 pass in place of υ 2 pass and vice versa) in the AND gate as mentioned above. 3.2.4. X-OR gate The X-OR gate gives output when the inputs are different and gives low when the inputs are the same as clearly shown in Table 2. For the implementation of the X-OR gate, the filters F 1 and F 3 are υ 1 pass and the filter F 2 is υ 2 pass. The operation is described below. In the paths A and C of the probe beams corresponding to the conditions when both the controlling inputs are signals of frequency υ 1 or υ 2 respectively, υ 1 pass filters are used. So in these conditions, signal of frequency υ 1 (LOW) is detected in the output. So the operations 0(υ 1 )X-OR0(υ 1 ) 0(υ 1 ). 1(υ 2 )X-OR1(υ 2 ) (υ 1 ) are achieved. Now when the controlling inputs are signals of two different frequencies υ 1 and υ 2,the path of the probe beam is along B in which a υ 2 pass filter is used. This gives rise to the output signal at frequency υ 2 i.e. high. So the X-OR operations 0(υ 1 )X-OR1(υ 2 ) 1(υ 2 ). 1(υ 2 )X-OR0(υ 1 ) 1(υ 2 ) are achieved. 3.2.5. X-NOR gate The output of an X-NOR gate is high only when both the inputs are either low or high, otherwise the outputs are low. For the implementation of the X-NOR gate, the filters F 1 and F 3 are υ 2 pass and the filter F 2 is υ 1 pass. So the operation is exactly complementary to that of X-NOR gate.

32 K. Mukherjee 4. Discussion and Conclusions The all optical reconfigurable logic gates NOT, OR, AND, NOR, NAND, X-OR, X-NOR are implemented in a single optical routing system using total reflectional switches for the first time in frequency encoded format. The basic physical requirement for the logic gates are discussed below. (1) Sources of two frequencies υ 1 and υ 2, preferably in the C band suitable for all optical communication for both probe and controlling inputs. The maximum power density is 1 10 6 W/cm 2 for controlling inputs and for probe light, the maximum power density should be 5 10 2 W/cm 2. 18 (2) Filters which can pass frequencies υ 1 and υ 2. (3) Non-linear optical switches. (4) Focusing lenses. (5) Coupler and beam splitters. The non-linear material suitable for the implementation of the gates should have the following properties: 18 (1) Large non-linear coefficient to focus large optical signal, (2) High reverse saturation absorption to ensure high light energy absorption, (3) Large thermo-optic coefficient to enhance Kerr effect, and (4) Low viscosity for maintaining initial condition when no light is present. Actually, the first three properties of the liquid makes the switching speed as fast as possible. The input controlling beams can be taken to be of wavelengths 1,540 nm and 1,550 nm in the C band corresponding to the frequencies υ 1 and υ 2 respectively. These signals can be extracted from a mode locked fiber laser (MLFL) by spectral slicing method. 30,31 The probe beam is a mixer of signals of frequency υ 1 and υ 2. The intensity of the controlling signals is adjusted so that they can cause pronounced non-linearity in the optical switches. The speed of operation of the gates is limited by the time taken in transmission of the signal and the time of conversion of the liquid into gas. The gates can show ultrafast speed of operation if proper material having suitable properties mentioned above is used. Among the implemented gates, NAND and NOR gates are universal and one can generate any logical and functional device by cascading these gates. The X-OR gate is an integral part of a binary half adder, comparator and also finds application in header recognition scheme. Use of frequency encoding reduces the drawback of intensity loss dependent problems or polarization sensitiveness. For these reasons, the hardware becomes simpler. The main challenge for the scheme to be realizable is to find an appropriate liquid, which gets converted into gas when illuminated by controlling signals. So further research in this field is necessary to find a suitable non-linear material, and the author believes that the technique and device has the potential of becoming the essential part of future all optical computation and communication network. 25 Since the logic gates proposed are reconfigurable and it is due to the use of frequency encoding, one can only use tunable filters to achieve the desired logic operations.

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