Modeling of All-Optical Even and Odd Parity Generator Circuits Using Metal-Insulator-Metal Plasmonic Waveguides

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1 PHOTONI SENSORS / Vol. 7, No., 7: 8 9 Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides Lokendra SINGH, na BEDI, and Santosh KUMR * Photonics Lab, Departent of Electronics and ounication Engineering, DIT University, Dehradun-489, India * orresponding author: Santosh KUMR E-ail: santoshrus@yahoo.co bstract: Plasonic etal-insulator-etal (MIM) waveguides sustain excellent property of confining the surface plasons up to a deep subwavelength scale. In this paper, linear and S-shaped MIM waveguides are cascaded together to design the odel of Mach-Zehnder interferoeter (MZI). Nonlinear aterial has been used for switching of light across its output ports. The structures of even and odd parity generators are projected by cascading the MZIs. Parity generator and checker circuit are used for error correction and detection in an optical counication syste. Study and analysis of proposed designs are carried out by using the MTLB siulation and finite-differencetie-doain (FDTD) ethod. Keywords: Plasonics; MIM waveguides; Mach-Zehnder interferoeter; nonlinear process; FDTD ethod itation: Lokendra SINGH, na BEDI, and Santosh KUMR, Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides, Photonic Sensors, 7, 7(): Introduction In today s scenario of photonic industry, the ajor challenge is the iniaturization of optical coponents for wavelength division ultiplexing []. Despite the deep subwavelength confineent of surface plason polaritons (SPPs) with respect to other nanophotonic waveguides such as photonic crystals, SPP waveguides work well beyond the diffraction liit [ 4]. Plasonics is one of the proising fields of integrated photonics due to its nuerous applications in optical clocking, cancer therapy, nano-lithography, solar cells, etc. In designing of building blocks for future generation of integrated optical coponents and devices, plasonic waveguides play a significant role. Recently, several types of waveguides were discovered such as slots [5, 6], plasonic wedge waveguide [7], and dielectric ridge on the etal surface [8], but aong all these waveguides the etal-insulator-etal (MIM) waveguide is generally preferred due to its their exceptional property of confining the surface plasons to a deep subwavelength scale [9 3]. In these waveguides, propagation is achieved by using even odes due to their low-loss confineent profile. onsidering the photonic device altogether, directional couplers (Ds) are serves as a prie coponent to design the eleentary part of optical circuits. Recently, several designs of directional couplers have been proposed by using plasonic waveguides [4 7]. The ajor phenoenon of coupling of light within the D is beating of even-odd odes. s the equal splitting of power through the directional coupler is wavelength dependent, for broadband response either wavelength dependency should be reoved by Received: July 6 / Revised: 6 Noveber 6 The uthor(s) 7. This article is published with open access at Springerlink.co DOI:.7/s rticle type: Regular

2 Lokendra SINGH et al.: Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides 83 aking coupler adiabtic, or input power with its coupling length should be controlled. In the proposed structure of D connected in the Mach-Zehnder interferoeter (MZI), equal splitting of power is attained with coupling length and propagation length of and., respectively. Hence, by adjoining the two Ds using two linear MIM waveguides, a design of MZI has been designed within the footprints of (6.4). lthough interferoetric circuit using Fabry-Perot interferoeter is also used in various applications, the need of too any sources will lead to an increase in the cost and coplexity of devices [8]. One of the ars of MZI is filled with an active aterial. Here, MEH-PPV [poly (-ethoxy-5- (8-ethylexyloxy)-PPV)] is used as an active aterial with refractive index and response tie of n=.65 and =.le 5 s, respectively [9]. The presence of active aterials in the structure of MZI is used to switch the light across its output ports by changing the refractive index of waveguide with respect to power of input signals. The changes in phase canceling out or adding each other depend on nonlinear processes. If phase of both the signals cancels out each other then it crosses phase odulation (XPM), and if it adds then it is self phase odulation (SPM). Due to XPM, the optical signal arrives at through port and SPM thrives the signal at cross port of MZI. Thus, by cascading plasonic Ds and MZIs, all-optical structures of even and odd parity generators are odeled within the footprints of (5) and (5), respectively. Recently, soe switching circuits have been proposed by using LiNbO 3 -based MZI, which work on the principle of electro-optic effect []. lthough the work is excellent, it still lacks advanced applications in ters of device iniaturization up to a deep subwavelength scale (hence overall design of device reains in thousand of icroeters), and due to the presence of electrical signals for altering the refractive index of waveguides, it liits the speed of device. Soe switching circuits were also proposed by using seiconductor optical aplifier (SO) but they were backsitted due to the phenoenon of gain saturation []. ll optical logic gates were also proposed using photonic crystal but being lack of the nonlinear aterial inside the structure will enable the switching of optical signals for coplex circuits []. The proposed design of parity generators are verified by using the finite difference tie doain (FDTD) ethod [3] and MTLB siulation. Section presents the odels of even and odd parity generators with their atheatical forulations. In Section 3, the propagation of light through proposed structures is projected. Finally, the conclusions of coplete work are presented in Section 4.. Design of parity generator circuits The cobinational circuits are useful in designing various integrated circuits which are very useful in icro-controlling and central processing units. In this work, for designing the all optical circuits of parity generators, MIM plasonic waveguides are used. To create the MIM geoetry, a etal (SiON) having high refractive index of n. with perittivity of +j.9 is deposited over a low index substrate having refractive index of n.44, and air is considered as dielectric between the. The thickness of dielectric is taken as.5 for the propagation of surface plasons with a propagation length of.. Thus by using these MIM waveguides, the structure of MZI is designed as shown in Fig., whose second linear ar is filled with nonlinear Kerr or active aterial. When the optical signals with power of E in =.4 W/ (considered as digital logic ) are given at the first input port, then by obeying the phenoenon of SPM, signals are obtained at the second output port of MZI as shown in Fig. (a). When signals with the power E in =.8W/ (considered as digital logic ) are incident at the first input port of MZI, then

3 84 Photonic Sensors due to XPM optical signals arrive at the first output port of it as shown in Fig. (b). The extinction ratio (ER) of single MZI is about 6 db at output power difference of.7 db and.8 db. The analyzed value of ER for single MZI is quite useful and enough for designing the all-optical logic gates [4]. Fig. Scheatic of single Mach-Zehnder interferoeter. Input signal (a) Output port l Output port (b) Fig. Propagation of light through single MZI: (a) for low intensity signals and (b) for high intensity signals. Thus, this toggling of optical signals across output ports of MZI with respect to input power of source is atheatically written as [5 8] Tout sin atein.4 W/μ () T out cos ate in.8 W/μ () where is the total change in phase in two linear ars of MZI. Equations () and () represent the atheatical expressions for outputs of MZI when input is fed with high and low powers, respectively.. Even parity generator Figure 3 shows the digital circuit and K-ap of three bit even parity generators, and Table presents the truth table of the even parity generator. The circuit of the even parity generator is designed by cascading six MZIs and four directional couplers as shown in Fig. 4. For the proper functioning of device, three optical sources are placed in front of the second input ports of MZI, MZI, and MZI3. Three directional couplers D, D, and D3 for splitting the optical energy into two equal parts are connected at the second output port of all three MZIs, respectively. The second output ports of D and D are cobined together with the first output port of D3 to feed the MZI5. While the first output ports of D and D are cobined together to feed the MZI4 at the second input port D4 is connected at the second output port of sae MZI. Then the second output ports of D3 and D4 are cobined together to feed MZI6 at its first input port. Finally, the second and first output ports of MZI5 and MZI6 are cobined together to get the required output of even parity generator. Fig. 3 Digital circuit and K-ap of three bit even parity generator circuit.

4 Lokendra SINGH et al.: Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides 85 Fig. 4 Scheatic diagra of even parity generator. Table Truth table of even parity generator. Min-ters Input signals Output signals B P E In Fig., the power at the output of directional coupler towards the input side can be written as [4] sin L P PB cos L (3) where is the attenuation constant of D towards input side, and L is its coupling length which is. Thus, by using () (3), atheatical expressions for the output of even parity generator circuit can be written as MZI MZI MZI3 cos cos cos (4) MZI MZI cos cos MZI3 MZI5 sin sin LD3 cos cos sin cos MZI5 MZI3 cos cos MZI 4 cos MZI MZI 3 D L (5) (6) MZI sin cos D L MZI5 sin MZI3 (7) sin sin LD3 MZI MZI5 5 sin cos LD cos cos cos MZI MZI3 MZI sin cos LD MZI5 6 sin MZI3 sin sin LD3 cos MZI (8) (9) MZI sin cos D L MZI5 7 sin MZI sin cos LD MZI3 cos () MZI sin sin D L 8 MZI sin sin LD MZI4 sin cos D L MZI6 sin MZI3. sin cos LD3 Thus, overall output of even parity generator (EPG)

5 86 Photonic Sensors can be written as OUTEPG 3 5 8, since there is no signal at output ports for the rest of in-ters. The tiing diagra of even parity generator through MTLB is presented in Fig. 5, which is verified by its truth table given in Table. Fig. 5 Tiing diagra of even parity generator through MTLB. In Fig. 5, the first three rows present the tiing sequence for input optical signals, and the fourth row presents the tiing signals for the output of parity generator. In the tiing diagra, signals in the fourth row with higher agnitudes represent the presence of signal at output, while signals with lower agnitude show absence of signal.. Odd parity generator Figure 6 shows a digital circuit and K-ap of a three-bit-odd-parity generator, and Table presents the truth table of odd parity generator. The design of an odd-parity generator is obtained by cascading seven MZIs and five Ds as shown in Fig. 7. Fig. 6 Digital circuit and K-ap of a three-bit-odd-parity generator. Fig. 7 Block diagra of odd parity generator. Input optical signals are given at the second, first and second input ports of MZI, MZI, and MZI3, respectively. D and D are connected at the second and first output ports of MZI and MZI,

6 Lokendra SINGH et al.: Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides 87 respectively. The second and first output ports of MZI and MZI3 are cobbled together to feed the MZI4 with optical signals at its second input port, while the second and first output ports of D and MZI4 are cobined together to feed MZI5 at its second input port. To feed MZI6 at its first input port, the first output ports of MZI and D5 (which is connected at the second output port of MZI4) are cobined together. The second and first output ports of D and D3 (which is connected at the second output port of MZI3) are cobined together to feed D4, whose first output port is cobined with the second output port of MZI6 to feed the MZI7. Finally, to get the output of odd parity generator, the first output ports of MZI6 and MZI7 are cobined together with the second output port of MZI5. The atheatical expression for outputs of odd parity generator circuit using () (3) can be written as MZI cos MZI cos MZI3 MZI6 cos sin MZI4 sin sin LD5 MZI MZI6 cos cos MZI3 sin sin D3 sin MZI7 MZI cos cos MZI4 MZI5 cos cos L L MZI MZI6 cos cos 3 MZI sin sin D sin MZI7 MZI3 cos cos MZI4 MZI5 cos cos D4 L L D4 MZI MZI6 cos cos MZI sin sin LD MZI7 4 sin MZI3 sin sin LD3 sin LD4 MZI MZI5 5 sin cos LD cos MZI MZI3 cos cos MZI4 sin sin LD5 MZI6 MZI7 cos cos sin cos L 6 MZI MZI4 cos cos MZI3 sin sin LD3 MZI7 sin LD4 cos MZI sin cos LD 7 MZI3 MZI4 cos cos MZI5 MZI sin sin sin LD MZI7 sin LD4 cos MZI MZI5 8 sin cos LD cos MZI D MZI5 sin MZI sin sin LD sin L MZI3 sin sin LD3 MZI7 MZI cos sin sin L MZI7 sin LD4 cos D3 D

7 88 Photonic Sensors Table Truth table of odd parity generator. Min-ters Input signals Output signals B P O Thus, the overall output of odd parity generator (OPG) is written as OUTOPG 4 6 7, since there is no optical signal at the output port for the rest of in-ters. The tiing diagra of the odd parity generator through MTLB is presented in Fig. 8, which is verified by its truth table given in Table. In Fig. 8, the first three rows represent the tiing signals for input signals, and the fourth row represents the tiing signals for the generated output of the odd parity generator, which is truly atched with its truth table. In tiing diagra at the fourth row, tiing signals with low and high agnitudes only represent the presence and absence of optical signals at the desired output. Optical signal () Optical signal (B) Optical signal () Odd parity generator Tie (s) Tie (s) Tie (s) Tie (s) Fig. 8 Tiing diagra of odd parity generator. 3. Siulation results using FDTD The finite difference tie doain (FDTD) ethod has been used for analysis of propagation of optical signals through the design of parity generator circuits, and their verifications are done by using MTLB. The continuous wave (W) source is used to provide the input signals with Gaussian distribution under the transverse agnetic (TM) polarization at the wavelength of 55 n. The Gaussian distribution of signals spectru is very useful because the interference occurs with side lobes of spectru, while the axiu inforation is transitted on the peak lobe which reains unaffected. For the siulation of the proposed device, perfect atched layers are considered as boundary layers for all interfaces of etal and dielectric with e as reflection coefficient. The half width of input source is.39 within the esh size of x=. and z=.5, under the perfect atched layer (PML) as boundary conditions for all interfaces of etal and dielectric. 3. Siulation results of even parity generator The siulation result of propagation of light through the even parity generator with cobination of all possible input signals is presented in Fig. 9. () ase I: =, B=, = In this case, =B== eans all three input ports are fed with optical signals having low input power, and thus by following the phenoenon of SPM, these signals are obtained at the first output ports of MZI, MZI, and MZI3. Hence, there is no signal at the output port of the even parity generator as shown in Fig. 9, which is truly atched with its truth table given in Table. () ase II: =, B=, = Here, =B= eans low-power signals are

8 Lokendra SINGH et al.: Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides 89 incident at the second input ports of MZI and MZI, and by obeying the principle of SPM, they arrive at the first output ports of the sae MZIs. While = eans optical high-power signals of high power are provided at the second input port of MZI3 and due to XPM, they arrive at the second output port, where they propagate through D3 and get split into two equal parts. Then MZI5 gets input optical signals at its first input port fro the first output port of D3, where they obey the laws of SPM due to its low power and are obtained at the second output port of MZI5, which is considered as the output port of EPG. Signals fro the second output port of D3 propagate through MZI6 by obeying the laws of SPM and arrive at its second output port. Thus, in this case, optical signals arrive at the desired output port of EPG due to optical signals of high power at input of MZI3 as shown in Fig. 9. (3) ase III: =, B=, = Here, == eans the low-power optical signala are given at the second input ports of MZI and MZI3. B= eans optical high-power signals are incident at the second input port of MZI. Thus, output optical signals arrive at the desired output port of EPG due to the presence of optical high-power signals at MZI, which is truly atched with the truth table given in Table. (4) ase IV: =, B=, = In this case, = eans low-power signals are given at the second input port of MZI. B== eans signals of high power are incident at second input ports of MZI and MZI3. Hence, in this case output of EPG is zero as shown in Fig. 9. (5) ase V: =, B=, = Here, = eans high-power signals are given at the second input port of MZI. B== eans low-power signals are given at second input ports of MZI and MZI3. In this case, optical signals arrive at the desired output port of EPG, due to the presence of high-powers signal at the second input port of MZI (as shown in Fig. 9). Input signals B Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () Input signal () OUTPUT Fig. 9 Propagation of the optical signals through the even parity generator circuit for all possible cobinations of input signals obtained through the FDTD ethod. (6) ase VI: =, B=, = Here, == eans high-power signals are given at the second input ports of MZI and MZI3. B= eans low-power signals are given at the second input port of MZI. In this case, there is no optical signal at the desired output port of EPG, which is truly atched with the truth table shown in Table. (7) ase VII: =, B=, = In this case, =B= eans high-power signals are given at the second input ports of MZI and MZI. = eans low-power signals are given at the second input port of MZI3. Thus, in this case there is no optical signal at the desired output port of EPG. (8) ase VIII: =, B=, = In this case, =B== eans high-power signals are given at the second input ports of MZI, MZI, and MZI3. Hence, in this case optical signals

9 9 Photonic Sensors are obtained at the desired port of EPG, which is truly atched with its truth table. 3. Siulation results odd parity generator The propagation of light through its odel with all possible cobinations of input signals is presented in Fig.. Input signals B B B B B B B B B Outputs Fig. Propagation of optical signals through the odel of the odd parity generator for all cobinations of inputs obtained through the FDTD ethod. () ase I: =, B=, = In this case, =B== eans low-power signals are given at the second, first, and second input port of MZI, MZI, and MZI3, respectively, and by obeying the phenoenon of SPM the signals are obtained at the first, second, and first output ports of sae MZIs. Then signals fro the second and first output port of MZI and MZI3 are cobined together to feed the MZI4 at its second input port, and by following the laws of XPM they arrive at the second output port of sae MZI, where they propagate through D5 and get equally split. Then signals fro the first output ports of MZI and D5 are cobined together to feed MZI6 at its first input port, and due to its high power they obey the laws of XPM and arrive at the first output port of MZI6, which is considered as the output port for odd parity generator. Thus, in this case an optical signal arrives at the desired output port of OPG, which is truly atched with its truth table given in Table. () ase II: =, B=, = Here, =B= eans low-power signals are given at the second and first input ports of MZI and MZI, where they obey the phenoenon of SPM and arrive at the first and second output ports of sae MZI. Then signals fro the first output port of MZI propagate through MZI6 and due to the low power they arrive at the second output port due to SPM. While signals fro the second output port of MZI are given to the second input port of MZI4, and after travelling through it signals arrive at its first output port due to the low power. Then MZI5 gets optical signals at its second input port fro the first output port of MZI4, and after propagating through MZI5, the signals arrive at first output ports of sae MZI. = eans high power signals are given at the second input port of MZI3 and arrive at the second output port due to XPM, where they propagate through D3 and get equally split. Further, signals fro the first output port of D3 is again split by D4, and then signals fro the second and first output ports of MZI6 and D4 are cobbled together to feed MZI7 at its first input port. fter propagating through MZI7, signals will appear at its second output port due to the low power. Thus in this case, there is no signal at desired output port of OPG. (3) ase III: =, B=, = Here, == eans signals with low powers are

10 Lokendra SINGH et al.: Modeling of ll-optical Even and Odd Parity Generator ircuits Using Metal-Insulator-Metal Plasonic Waveguides 9 incident at the second input ports of MZI and MZI3. B= eans high-power signals are given at the first input port of MZI. Thus, in this case there is no optical signal at the desired output port of OPG. (4) ase IV: =, B=, = Here, = eans the second input port of MZI. B== eans high intensity signals are given at the first and second input ports of MZI and MZI3. Hence, in this case optical signals are obtained at the desired output port of OPG, which is truly atched with its truth table. (5) ase V: =, B=, = In this case, = eans signals with high power are given at the second input port of MZI. B== eans low-power signals are given at the first and second input ports of MZI and MZI3. Thus, in this case there is no optical signal at desired output port of OPG. (6) ase VI: =, B=, = Here, == eans the second input ports of MZI and MZI3 are fed with high-power signals. B= eans low-power signals are incident at the first input port of MZI. Thus, in this case optical signals arrive at the desired output port of OPG, which is truly atched with the truth table given in Table. (7) ase VII: =, B=, = Here, =B= eans high-power signals are given at the second and first input ports of MZI and MZI. = eans low-power signals are fed at the second input port of MZI3. Finally, output signals approach to the port which is assigned as output port for OPG. (8) ase VIII: =, B=, = Here, as =B== eans high-power signals are given at the second, first, and second input ports of MZI, MZI, and MZI3. Thus, in this case there is no optical signal at desired output port of OPG. 4. onclusions In this paper, odels of even and odd parity generator are projected by using MIM plasonic waveguides due to their enorous capability of confining the surface plasons up to a deep subwavelength scale. The concept of nonlinear MZI using MIM plasonic waveguides has been used to cascade the desired structures. The proposed concept of cascading the MZIs is useful for integrating the all-optical devices. The circuits of parity generators are ainly used for error detection and correction in optical counication networks. Open ccess This article is distributed under the ters of the reative oons ttribution 4. International License ( which perits unrestricted use, distribution, and reproduction in any ediu, provided you give appropriate credit to the original author(s) and the source, provide a link to the reative oons license, and indicate if changes were ade. References [] W. Wei, X. Zhang, and X. Ren, syetric hybrid plasonic waveguide with centietric scale propagation length under subwavelength confineent for photonic coponents, Nanoscale Research Letters, 4, 9(): 8. [] W. L. Barnes,. Dereux, and W. E. Thoas, Surface plason subwavelength optics, Nature, 3, 44(695): [3] D. K. Graotnev and S. I. Bozhelvonyi, Plasonics beyond the diffraction liit, Nature Photonics,, 4(): [4] Y. hen and H. Ming, Review of surface plason resonance and localized surface plason resonance sensor, Photonic Sensors,, (): [5] G. Veronis and S. H. Fan, Guided subwavelength plasonic ode supported by a slot in a thin etal fil, Optics Letters, 5, 3(4): [6] L. Liu, H. Zhanghua, and H. Sailing, Novel surface plason waveguide for high integration, Optics Express, 5, 3(7): [7]. Boltasseva, S. V. Valentyn, B. N. Rasus, M. Esteban, G. R. Sergio, and I. B. Sergey, Triangular etal wedges for subwavelength plason polariton guiding at teleco wavelengths, Optics Express, 8, 6(8): [8]. Kuar, J. Gosciniak, V. S. Volkov, S. Papaioannou, D. Kalavrouziotis, K. Vyrsokinos, et al., Dielectric-loaded plasonic waveguide coponents: going practical, Laser & Photonics Reviews, 3, 7(6):

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