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Research on SAD-PRD losses in semiconductor waveguide for application in photonic integrated circuits
Optik 154 (2018) 748–754
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Research on SAD-PRD losses in semiconductor waveguide for application in photonic integrated circuits Abinash Panda a , Partha Sarkar b , G. Palai a,∗ a b
Gandhi Institute for Technological Advancement (GITA), Bhubaneswar, India Biju Patnaik University of Technology, Odisha, India
a r t i c l e
i n f o
Article history: Received 9 August 2017 Accepted 23 October 2017 Keyword: SOI Semiconductor waveguide SAD-PRD losses Grating structure
a b s t r a c t Scattering, absorption, diffraction, polarization, reflection and dispersion (SAD-PRD) losses in semiconductor waveguide at wavelength 1550 nm is dissected in present research. Two types of semiconductor waveguides such as silicon-Air and GaAs-Air deal with the current work to increase the efficiency of photonic integrated circuit. The appraisal of aforementioned losses is divulged using disparate notion, for example; reflection loss is scrutinized by employing transfer matrix method (TMM) whereas Maxwell’s equation is deployed to disclose absorption loss. Further dispersion, diffraction, polarization and scattering losses are examined with the help of mathematical formulation. Eventually, the outcomes of the above investigation affirmed that the overall transmitted efficiency of Si-Air and GaAs-Air waveguide is more than 90% and 89% respectively pertaining to angle of deviation (−12◦ to 12◦ ) from Bragg’s angle. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Silicon photonics has been acquired ample momentum over the preceding years owing to its superior properties. Silicon is considered to be a good candidate for designing optical waveguide because of its larger refractive index and its compatibility with the telecommunication windows of 1310 nm and 1550 nm [1,2]. Further Silicon based devices are evolving as the great platform for large scale integration of optical functions [3]. The semiconductor SOI waveguide structures find extensive application in designing several passive devices such as wavelength filters, multimode couplers and WDM filters [4–6]. In optical communication systems, SOI waveguide structure can be efficiently used as optical interconnector [7,8].Precise quantification of different sorts of losses in SOI waveguides play a vital for the design of efficient silicon photonic devices [9–11] and have gained extensive interest recently. The conventional waveguide agonizes from different losses such as reflectance, diffraction, polarization, scattering, dispersion that exists in the system. In optoelectronics device design, the above mentioned losses play a significant role and cannot be ignored. As far as different losses are considered, in reference [12] the author has given an experimental demonstration of silicon on insulator waveguide structure where the output transmitted efficiency is found to be 70% only. In reference [13], author proposed an efficient polymer grating SOI structure which is operated at 1550 nm.But this is hard to fabricate because of presence of defects at different position in the polymer grating structure. In reference [14,15] author analysed reflectance, diffraction, absorption and polarization losses to maximise the transmitted efficiency. In addition to above losses, scattering and dispersion losses manipulate with serious
∗ Corresponding author. E-mail addresses: [email protected], g [email protected] (G. Palai). https://doi.org/10.1016/j.ijleo.2017.10.130 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
A. Panda et al. / Optik 154 (2018) 748–754
749
Fig. 1. SOI grating structure, S- Si/GaAs, A- Air.
problem during light transmission through photonics waveguide structures. This proposed work indicates semiconductor grating SOI structure in consideration of reflectance, diffraction, absorption and polarization losses along with scattering and dispersion to achieve high transmitted efficiency. This paper is prepared as follows: proposed grating SOI grating structure is reflected inspection where mathematical formulations is manipulated in Section 2.Simulation outcomes and interpretations are divulged in Section 4 and lastly conclusions are cited in Section 5. 2. Structural analysis Here we suggest an efficient semiconductor grating SOI structure shown in Fig. 1. The above proposed structure is not new pertaining to recent work, because similar types of structures [16–22] have already used for sensing and communication applications using one dimensional grating structure. However the present work has bountiful newness as compared to previous work. Related works is made with the consideration of absorption and reflection only, where few other papers deals with similar types of works with the cogitation of absorption, reflection, diffraction only. Apart from this, little research also proposed similar types of structures with defect at grating structures. However, the present structure has some newness such as, (i) size of the structure is realized with nanometer scale which can be a suitable candidate for photonic integrated circuit. (ii) the manipulating wavelength is 1550 nm, which is an operating signal in communication window(iii) there is no inclusion of defects, which leads to easy fabrication. Again analyzing Fig. 1, grating structure is developed on the oxide layer which is placed on the silicon substrate. Here we propose two different grating structures that consist of periodic arrangement of Si-Air and GaAs-Air respectively. Both the grating structures contain 25 numbers of layers. The odd layers are of semiconductor (Si/GaAs) and the even layers are of Air. The reason for choosing above semiconductor material is that absorption loss is nearly zero and can be neglected at the wavelength of 1550 nm. However, other sorts of losses like reflection, diffraction, polarization, scattering and dispersion will be accomplished with the above said structure at the aforementioned wavelength. By choosing apposite thickness of odd and even layers of the grating structure, and by properly selecting the number of grating layers, we can minimize different losses, which are encountered problem during transportation of signal. It is also observed from the simulation results (which is discussed in Section 4) that reflectance loss is nearly zero for proper structural parameters. Finally, we obtained results for other losses such as diffraction,polarization, scattering and dispersion with respect to detuning Bragg’s angle −12◦ to 12◦ and found that these losses are to a greater extent below 10% for two grating structures. By combining all the aforementioned losses, we explore that the grating SOI structure bestow high transmission efficiency at wavelength 1550 nm. 3. Mathematical treatment Due to adverse effect of different losses (reflection, absorption, diffraction, polarization, scattering, dispersion) on the efficiency of SOI grating structure, we in this paper have chosen appropriate structure parameters to eradicate these losses. Here the input signal to the grating structure is assumed to be a plane wave having constant frequency and lunched normal to the grating structure. Confining our analysis to single mode of propagation, we found reflectance of both Si-Air and GaAs-Air grating structure by using transfer matrix method [23] at wavelength 1550 nm. To the extent absorption loss is concerned, it is found to be zero for the above semiconductor grating structures. Taking absorbance and reflectance into account, we develop a mathematical equation for computing efficiency [24] which is given by, 1 = (1 − R) e−Pˇ(t1+t2)
(1)
Where, R: reflectance from the grating structure, P is the number of grating period, t1 , t2: thickness of the odd and even layer respectively,  (4k/) is absorption constant. For the above proposed grating structures, the value of k (i.e. extinction coefficient describing how strongly a material absorbs light for a given wavelength) is found to be zero at wavelength 1550 nm [25]. Hence absorption loss is zero. The mathematical equation for diffraction loss is given by, 2 = sin2 (
nl ) cos
Where, l is a grating length = P(t1 + t2 ), n be an effective refractive index and is detuning Bragg’s angle.
(2)
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A. Panda et al. / Optik 154 (2018) 748–754
Table 1 Input parameters of proposed SOI grating structures. SOI grating structures
Refractive index
Si-Air GaAs-Air
Thickness in nm.
Odd layer(n1 )
Even layer(n2 )
Odd layer(t1 )
Even layer(t2 )
3.55 3.92
1.00 1.00
0.001 0.004
0.018 0.013
Number of grating layers
Wavelength () in nm.
25
1550
We also reported polarization efficiency and thereby polarization loss that varies as the polarization state of the travelling light wave changes. This loss consequences because of peak-to-peak difference in transmission of optical signal pertaining to all the possible state of polarization. We tried to minimize this loss in order to get maximum transmitted efficiency. The mathematical expression for polarization loss [26] is given as, 3 =
N N+
2n n2 −1
cos2 ()
(3)
Where, is the angle of deviation from Bragg’s angle, N be the total number of grating layers, n is the effective refractive index. Likewise, we have reported scattering loss, which mainly arises due to imperfection present in the material and surface irregularities. These imperfections may arise because of voids in the material or contaminant atoms [27,28]. Scattering loss employs severe limitations in attaining maximum transmitted efficiency, hence should be minimized. Scattering loss is given by,
4 = C (1 − R) tan(/d) = C (1 − R) /{d
1 + 2nl/ 2}
(4)
Where, R is reflectance, C is a constant (nearly equal to 1), l be the grating length, is the angle of deviation from Bragg’s angle. Lastly we found dispersion loss present in the grating SOI structure. Dispersion loss results due to different wavelength of light signal that enters the grating structure at one time and exit the structure at different times. Also variation of refractive index with respect to wavelength leads to dispersion loss [29]. Dispersion loss depends on the structure parameters and mathematically can be given by,
5 =
1.633 ∗ sin3 ∗ N ∗ n ∗ c2 ∗ l
(5)
Where, N: total number of layers in semiconductor grating structure, n: effective refractive index, l: grating length is light velocity and is angle of deviation from Bragg’s angle. Bearing to above mentioned losses, overall transmitted efficiency can be determined by, = 1. 2. 3. 4. 5
(6)
4. Simulation results and interpretations Further memorizing proposed structure, we have considered two types of grating structures each consists of 25 number of layers, where the odd layers comprises(Si/GaAs) and even layers is made up of air. Different structural parameters(number of grating layers, thickness of each grating layers, refractive index) are carefully selected to achieve utmost transmitted efficiency and proposed parameters are listed in Table 1. Cogitating mentioned values of Table 1, we carry out simulation for reflectance by using transfer matrix method(TMM) for both the grating structures. Interestingly we got some positive outcomes pertaining to same i.e. reflectance of 0.0003758 for Si-Air grating structure and 0.001621 for GaAs-Air grating structure at wavelength 1550 nm, which are shown in Fig. 2(a) and (b) respectively. In the above figures, reflectance in Arbi.unit is plotted along vertical axis whereas wavelength in um is taken along horizontal axis. Though statement delivers jovial results with respect to transmitted efficiency, but diffraction loss is encountered serious problem. Thereafter, we performed simulation for diffraction efficiency by using Eq. (2) for both the considered grating structures with respect to the detuning from Bragg’s angle at wavelength of 1550 nm. From Fig. 3(a) and (b), it is observed that diffraction efficiency is 0.992(diffraction loss is 0.008) for Si-Air grating structure and 0.9925(diffraction loss is 0.0075) for GaAs-Air grating structure respectively. Like diffraction, a definite polarization loss exists with the same. We carried out simulation for polarization efficiency with respect to detuning from Bragg’s angle for both the grating structures at 1550 nm by referring Eq. (3). Fig. 4(a) and (b) shows that, polarization efficiency is 0.9016(polarization loss of 0.0984) for Si-Air grating structure and 0.8972 (polarization loss of 0.1028) for GaAs-Air grating structure, for the incident angle lies in between −12◦ to 12◦ . From Fig. 4(a) and (b), it is inferred that polarization efficiency is maximum at 0◦ and gradually decreases with increase in detuning Bragg’s angle. After that, we made simulation for scattering loss for both the proposed and grating structures at 1550 nm using Eq. (4). Fig. 5(a) and (b) represent scattering loss for Si-Air and GaAs-Air grating structures respectively. Here y- axis represents scattering loss in dB/nm and x-axis represents detuning from Bragg’s angle in radian. It is acquired that scattering loss is 0.002 dB/nm for both the grating structures. Finally, we simulated both the proposed grating structures for
A. Panda et al. / Optik 154 (2018) 748–754
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Fig. 2. (a) Reflectance variation with respect to wavelength for Si-Air grating SOI structure. (b) Reflectance variation with respect to wavelength for GaAs-Air grating SOI structure.
Fig. 3. (a) Diffraction efficiency variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b)Diffraction efficiency variation with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
calculation of dispersion loss at 1550 nm. Fig 6(a) and (b) shows the curve for dispersion loss as a variation of detuning from Bragg’s angle. From the above figures, it is perceived that dispersion loss is zero within the Bragg’s angle −12◦ to 12◦ .At the end, we settled down to a conclusion that all kind of losses (reflection, absorption, diffraction, polarization, scattering, and dispersion) are suppressed to minimum value by properly selecting the structure parameters. Considering the above losses,
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A. Panda et al. / Optik 154 (2018) 748–754
Fig. 4. (a) Polarization efficiency variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b) Polarization efficiency variation with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
Fig. 5. (a) Scattering loss variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b) Polarization loss variation with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
A. Panda et al. / Optik 154 (2018) 748–754
753
Fig. 6. (a) Dispersion loss variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b) Dispersion loss variations with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
transmitted efficiency is found to be 90.1% for Si-Air grating structure and 89.0% for GaAs-Air grating structure, which is a remarkable achievement. 5. Conclusions The core objective in this paper is to develop an effective Si-Air and GaAs-Air grating structures for application in photonic integrated circuit. Eqs. (1)–(5) are used to investigate different forms of losses like reflection, diffraction, polarization, scattering, dispersion respectively. It is noteworthy from the above equations that, different losses have strong dependence on the structure parameters. By properly choosing structure parameters, we computed reflectance by using transfer matrix method (TMM) at 1550 nm wavelength, whereas other losses (reflection, diffraction, polarization, scattering, dispersion) are analysed with respect to detuning from Bragg’s angle −12◦ to 12◦ . Finally, considering all the aforementioned losses, overall transmitted efficiency is obtained. Excitingly, overall transmitted efficiency is attained to be 90.1% and 89.0% for Si-Air and GaAs-Air grating structures respectively at wavelength 1550 nm. Hence the above structures came up as a good candidate as optical interconnector in photonics integrated circuits. References [1] M. Loncar, T. Doll, J. Vuckovic, “Design and fabrication of silicon photonic CrystalOptical waveguides”, J. Lightwave Technol. 18 (October 2000) (2017) 1402–1411. [2] K.K. Lee, D.R. Lim, L.C. Kimerling, Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction, Opt. Lett. 26 (2001) 1888–1890. [3] C.K. Tang, A.K. Kewell, G.T. Reed, A.G. Rickman, F. Namavar, Development of a library of low-loss silicon-on-insulator optoelectronic devices, IEE Proc. Opto-Electron. 143 (1996) 312–315. [4] M. Lipson, Guiding, modulating, and emitting light on silicon—challenges and opportunities, J. Lightwave Technol. 23 (2005) 4222–4238. [5] Haibo Liang, Richard Soref, Jianwei Mu, Arka Majumdar, Xun Li, Wei-Ping Huang, Simulations of silicon-on-insulator channel-waveguide electrooptical 2 × 2 switches and 1 × 1 modulators using a Ge2Sb2Te5 self-holding layer, J. Lightwave Technol. 33 (9) (2015) (MAY 1). [6] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Taka-hashi, T. Shoji, E. Tamechika, E. Itabashi, H. Morita, Microphotonics de-vices based on silicon microfabrication technology, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 232–240. [7] Z. Cheng, X. Chen, C.Y. Wong, K. Xu, C.K.Y. Fung, Y.M. Chen, H.K. Tsang, Mid-infrared grating couplers for silicon-on-sapphire waveguides, IEEE Photonics J. 4 (February) (2012) 104–113.
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[8] G. Palai, S.K. Tripathy, N. Muduli, S.K. Patnaik, Optimization of efficiency in a 1D gratingstructure at 1310 nm wavelength for application in optical interconnect Asian, Asian J. Phys. 21 (2017) 145–152 (May 2012). [9] G. Palai, S.K. Tripathy, Efficient silicon grating for SOI applications, Optik-Int. J. Light Electron Opt. 124 (2017) 2645–2649 (September 2013). [10] A. Panda, P. Sarkar, G. Palai, Studies on temperature variation in semiconductor waveguide through ARDP loss for nanophotonic applications, Optik-Int. J. Light Electron Opt. 127 (2017) 5439–5442 (July 2016). [11] C.S. Mishra, G. Palai, Optical nonlinearity in germanium and silicon semiconductor vis-a-vis temperature and wavelengths for sensing application, Optik-Int. J. Light Electron Opt. 137 (2017) 37–44 (May 2017). [12] T. Ang, G. Reed, A. Vonsovici, A. Evans, P. Routley, M. Josey, Effects of grating heights on highly efficient unibond SOI waveguide grating couplers, IEEE Photonics Technol. Lett. 12 (2000) 59–61. [13] P. LyanD. Vermeulen, G. Roelkens, D. Van Thourhout, R. Baets, S. Brision, P. Gautier, J.-M. Fedeli, High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit, Appl. Phys. Lett. 92 (2008) 131101–131103. [14] G. Palai, T.K. Dhir, B. Nath, S.L. Patra, Modelling overall transmitted efficiency at 1550 nm for polymer grating Silicon-on-insulator structure with defect, Front. Optoelectron 6 (2017) 153–159 (May 2013). [15] G. Palai, S.K. Sahoo, Optimization of Power in SOI structure at 1550 nm for nanophotonic application, Trends Opto-Electro Opt. Commun. 3 (2017) (May 2013). [16] G. Palai, Realization of temperature in semiconductor using optical principle, Optik- Int. J. Light Electron Opt. 125 (2014) 6053–6057. [17] G. Palai, S.K. Tripathy, T. Sahu, A novel technique to measure the sucrose concentration in hydrogel sucrose solution using two dimensional photonic crystal structures, Optik- Int. J. Light Electron Opt. 125 (2014) 349–352. [18] G. Palai, S.K. Tripathy, Measurement of glycerol concentration in B?H?G solution using 3D photonic crystal structure, Optik- Int. J. Light Electron Opt. 125 (2014) 2875–2879. [19] G. Palai, Optimization of optical waveguide for optical DEMUX at optical windows, Optik- Int. J. Light Electron Opt. 127 (2016) 2590–2593 (Palai). [20] C.S. Mishra, G. Palai, Manipulating light with porous silicon for investigation of porosity using finite difference time domain method, Optik- Int. J. Light Electron Opt. 127 (2016) 1195–1197. [21] G. Palai, T.K. Dhir, Theoretical model to measure the concentration of hemoglobin in human blood using 3D photonic crystal structure, Optik- Int. J. Light Electron Opt. 126 (2015) 478–482. [22] G. Palai, Analysis and simulation of silicon grating structure for spectral beam combining application, Optik – Int. J. Light Electron Opt. 126 (2015) 4974–4976. [23] Ryanb Balili, ‘Transfer matrix method in nanophotonics, Int. J. Mod. Phys.: Conf. Seri. 17 (2012) 159–168. [24] M. Vijaya, G. Rangarajan, Materials Science, Tata McGraw-Hill Education, NewDelhi, 2003. [25] A. Andriesh, V. Zhornik, A. Mironos, A.S. Smirnova, Changes in the diffraction efficiency of grating structures formed in thin films of glassychalcogenide semiconductors by neutron irradiation, Sov. J. Quantum Electron. 15 (1985) 1284–1286. [26] Md. Moquim, Engineering Physics, B.K., Publication, India, 2003. [27] F.P. PAYNE, J.P.R. LACEY, A theoretical analysis of scattering loss from planar optical waveguides, Opt. Quantum. Electron. 26 (1994) 977–986. [28] Toshihiko Baba, Ayumu Motegi, Takeshi Iwai, Naoyuki Fukaya, Yoshitaka Watanabe, Atsushi Sakai, Light propagation characteristics of straight single-Line-Defect waveguides in photonic crystal slabs fabricated into a silicon-on-Insulator substrate, IEEE J. Quantum Electron. 38 (NO. 2) (2002). [29] W. Wang, Losses and Dispersion in Waveguides, Southern Taiwan University of Technology, 2017 depts.washington.edu/mictech/optics/tainan 2004/waveguide week3.pdf.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Research on SAD-PRD losses in semiconductor waveguide for application in photonic integrated circuits Abinash Panda a , Partha Sarkar b , G. Palai a,∗ a b
Gandhi Institute for Technological Advancement (GITA), Bhubaneswar, India Biju Patnaik University of Technology, Odisha, India
a r t i c l e
i n f o
Article history: Received 9 August 2017 Accepted 23 October 2017 Keyword: SOI Semiconductor waveguide SAD-PRD losses Grating structure
a b s t r a c t Scattering, absorption, diffraction, polarization, reflection and dispersion (SAD-PRD) losses in semiconductor waveguide at wavelength 1550 nm is dissected in present research. Two types of semiconductor waveguides such as silicon-Air and GaAs-Air deal with the current work to increase the efficiency of photonic integrated circuit. The appraisal of aforementioned losses is divulged using disparate notion, for example; reflection loss is scrutinized by employing transfer matrix method (TMM) whereas Maxwell’s equation is deployed to disclose absorption loss. Further dispersion, diffraction, polarization and scattering losses are examined with the help of mathematical formulation. Eventually, the outcomes of the above investigation affirmed that the overall transmitted efficiency of Si-Air and GaAs-Air waveguide is more than 90% and 89% respectively pertaining to angle of deviation (−12◦ to 12◦ ) from Bragg’s angle. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Silicon photonics has been acquired ample momentum over the preceding years owing to its superior properties. Silicon is considered to be a good candidate for designing optical waveguide because of its larger refractive index and its compatibility with the telecommunication windows of 1310 nm and 1550 nm [1,2]. Further Silicon based devices are evolving as the great platform for large scale integration of optical functions [3]. The semiconductor SOI waveguide structures find extensive application in designing several passive devices such as wavelength filters, multimode couplers and WDM filters [4–6]. In optical communication systems, SOI waveguide structure can be efficiently used as optical interconnector [7,8].Precise quantification of different sorts of losses in SOI waveguides play a vital for the design of efficient silicon photonic devices [9–11] and have gained extensive interest recently. The conventional waveguide agonizes from different losses such as reflectance, diffraction, polarization, scattering, dispersion that exists in the system. In optoelectronics device design, the above mentioned losses play a significant role and cannot be ignored. As far as different losses are considered, in reference [12] the author has given an experimental demonstration of silicon on insulator waveguide structure where the output transmitted efficiency is found to be 70% only. In reference [13], author proposed an efficient polymer grating SOI structure which is operated at 1550 nm.But this is hard to fabricate because of presence of defects at different position in the polymer grating structure. In reference [14,15] author analysed reflectance, diffraction, absorption and polarization losses to maximise the transmitted efficiency. In addition to above losses, scattering and dispersion losses manipulate with serious
∗ Corresponding author. E-mail addresses: [email protected], g [email protected] (G. Palai). https://doi.org/10.1016/j.ijleo.2017.10.130 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
A. Panda et al. / Optik 154 (2018) 748–754
749
Fig. 1. SOI grating structure, S- Si/GaAs, A- Air.
problem during light transmission through photonics waveguide structures. This proposed work indicates semiconductor grating SOI structure in consideration of reflectance, diffraction, absorption and polarization losses along with scattering and dispersion to achieve high transmitted efficiency. This paper is prepared as follows: proposed grating SOI grating structure is reflected inspection where mathematical formulations is manipulated in Section 2.Simulation outcomes and interpretations are divulged in Section 4 and lastly conclusions are cited in Section 5. 2. Structural analysis Here we suggest an efficient semiconductor grating SOI structure shown in Fig. 1. The above proposed structure is not new pertaining to recent work, because similar types of structures [16–22] have already used for sensing and communication applications using one dimensional grating structure. However the present work has bountiful newness as compared to previous work. Related works is made with the consideration of absorption and reflection only, where few other papers deals with similar types of works with the cogitation of absorption, reflection, diffraction only. Apart from this, little research also proposed similar types of structures with defect at grating structures. However, the present structure has some newness such as, (i) size of the structure is realized with nanometer scale which can be a suitable candidate for photonic integrated circuit. (ii) the manipulating wavelength is 1550 nm, which is an operating signal in communication window(iii) there is no inclusion of defects, which leads to easy fabrication. Again analyzing Fig. 1, grating structure is developed on the oxide layer which is placed on the silicon substrate. Here we propose two different grating structures that consist of periodic arrangement of Si-Air and GaAs-Air respectively. Both the grating structures contain 25 numbers of layers. The odd layers are of semiconductor (Si/GaAs) and the even layers are of Air. The reason for choosing above semiconductor material is that absorption loss is nearly zero and can be neglected at the wavelength of 1550 nm. However, other sorts of losses like reflection, diffraction, polarization, scattering and dispersion will be accomplished with the above said structure at the aforementioned wavelength. By choosing apposite thickness of odd and even layers of the grating structure, and by properly selecting the number of grating layers, we can minimize different losses, which are encountered problem during transportation of signal. It is also observed from the simulation results (which is discussed in Section 4) that reflectance loss is nearly zero for proper structural parameters. Finally, we obtained results for other losses such as diffraction,polarization, scattering and dispersion with respect to detuning Bragg’s angle −12◦ to 12◦ and found that these losses are to a greater extent below 10% for two grating structures. By combining all the aforementioned losses, we explore that the grating SOI structure bestow high transmission efficiency at wavelength 1550 nm. 3. Mathematical treatment Due to adverse effect of different losses (reflection, absorption, diffraction, polarization, scattering, dispersion) on the efficiency of SOI grating structure, we in this paper have chosen appropriate structure parameters to eradicate these losses. Here the input signal to the grating structure is assumed to be a plane wave having constant frequency and lunched normal to the grating structure. Confining our analysis to single mode of propagation, we found reflectance of both Si-Air and GaAs-Air grating structure by using transfer matrix method [23] at wavelength 1550 nm. To the extent absorption loss is concerned, it is found to be zero for the above semiconductor grating structures. Taking absorbance and reflectance into account, we develop a mathematical equation for computing efficiency [24] which is given by, 1 = (1 − R) e−Pˇ(t1+t2)
(1)
Where, R: reflectance from the grating structure, P is the number of grating period, t1 , t2: thickness of the odd and even layer respectively,  (4k/) is absorption constant. For the above proposed grating structures, the value of k (i.e. extinction coefficient describing how strongly a material absorbs light for a given wavelength) is found to be zero at wavelength 1550 nm [25]. Hence absorption loss is zero. The mathematical equation for diffraction loss is given by, 2 = sin2 (
nl ) cos
Where, l is a grating length = P(t1 + t2 ), n be an effective refractive index and is detuning Bragg’s angle.
(2)
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A. Panda et al. / Optik 154 (2018) 748–754
Table 1 Input parameters of proposed SOI grating structures. SOI grating structures
Refractive index
Si-Air GaAs-Air
Thickness in nm.
Odd layer(n1 )
Even layer(n2 )
Odd layer(t1 )
Even layer(t2 )
3.55 3.92
1.00 1.00
0.001 0.004
0.018 0.013
Number of grating layers
Wavelength () in nm.
25
1550
We also reported polarization efficiency and thereby polarization loss that varies as the polarization state of the travelling light wave changes. This loss consequences because of peak-to-peak difference in transmission of optical signal pertaining to all the possible state of polarization. We tried to minimize this loss in order to get maximum transmitted efficiency. The mathematical expression for polarization loss [26] is given as, 3 =
N N+
2n n2 −1
cos2 ()
(3)
Where, is the angle of deviation from Bragg’s angle, N be the total number of grating layers, n is the effective refractive index. Likewise, we have reported scattering loss, which mainly arises due to imperfection present in the material and surface irregularities. These imperfections may arise because of voids in the material or contaminant atoms [27,28]. Scattering loss employs severe limitations in attaining maximum transmitted efficiency, hence should be minimized. Scattering loss is given by,
4 = C (1 − R) tan(/d) = C (1 − R) /{d
1 + 2nl/ 2}
(4)
Where, R is reflectance, C is a constant (nearly equal to 1), l be the grating length, is the angle of deviation from Bragg’s angle. Lastly we found dispersion loss present in the grating SOI structure. Dispersion loss results due to different wavelength of light signal that enters the grating structure at one time and exit the structure at different times. Also variation of refractive index with respect to wavelength leads to dispersion loss [29]. Dispersion loss depends on the structure parameters and mathematically can be given by,
5 =
1.633 ∗ sin3 ∗ N ∗ n ∗ c2 ∗ l
(5)
Where, N: total number of layers in semiconductor grating structure, n: effective refractive index, l: grating length is light velocity and is angle of deviation from Bragg’s angle. Bearing to above mentioned losses, overall transmitted efficiency can be determined by, = 1. 2. 3. 4. 5
(6)
4. Simulation results and interpretations Further memorizing proposed structure, we have considered two types of grating structures each consists of 25 number of layers, where the odd layers comprises(Si/GaAs) and even layers is made up of air. Different structural parameters(number of grating layers, thickness of each grating layers, refractive index) are carefully selected to achieve utmost transmitted efficiency and proposed parameters are listed in Table 1. Cogitating mentioned values of Table 1, we carry out simulation for reflectance by using transfer matrix method(TMM) for both the grating structures. Interestingly we got some positive outcomes pertaining to same i.e. reflectance of 0.0003758 for Si-Air grating structure and 0.001621 for GaAs-Air grating structure at wavelength 1550 nm, which are shown in Fig. 2(a) and (b) respectively. In the above figures, reflectance in Arbi.unit is plotted along vertical axis whereas wavelength in um is taken along horizontal axis. Though statement delivers jovial results with respect to transmitted efficiency, but diffraction loss is encountered serious problem. Thereafter, we performed simulation for diffraction efficiency by using Eq. (2) for both the considered grating structures with respect to the detuning from Bragg’s angle at wavelength of 1550 nm. From Fig. 3(a) and (b), it is observed that diffraction efficiency is 0.992(diffraction loss is 0.008) for Si-Air grating structure and 0.9925(diffraction loss is 0.0075) for GaAs-Air grating structure respectively. Like diffraction, a definite polarization loss exists with the same. We carried out simulation for polarization efficiency with respect to detuning from Bragg’s angle for both the grating structures at 1550 nm by referring Eq. (3). Fig. 4(a) and (b) shows that, polarization efficiency is 0.9016(polarization loss of 0.0984) for Si-Air grating structure and 0.8972 (polarization loss of 0.1028) for GaAs-Air grating structure, for the incident angle lies in between −12◦ to 12◦ . From Fig. 4(a) and (b), it is inferred that polarization efficiency is maximum at 0◦ and gradually decreases with increase in detuning Bragg’s angle. After that, we made simulation for scattering loss for both the proposed and grating structures at 1550 nm using Eq. (4). Fig. 5(a) and (b) represent scattering loss for Si-Air and GaAs-Air grating structures respectively. Here y- axis represents scattering loss in dB/nm and x-axis represents detuning from Bragg’s angle in radian. It is acquired that scattering loss is 0.002 dB/nm for both the grating structures. Finally, we simulated both the proposed grating structures for
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Fig. 2. (a) Reflectance variation with respect to wavelength for Si-Air grating SOI structure. (b) Reflectance variation with respect to wavelength for GaAs-Air grating SOI structure.
Fig. 3. (a) Diffraction efficiency variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b)Diffraction efficiency variation with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
calculation of dispersion loss at 1550 nm. Fig 6(a) and (b) shows the curve for dispersion loss as a variation of detuning from Bragg’s angle. From the above figures, it is perceived that dispersion loss is zero within the Bragg’s angle −12◦ to 12◦ .At the end, we settled down to a conclusion that all kind of losses (reflection, absorption, diffraction, polarization, scattering, and dispersion) are suppressed to minimum value by properly selecting the structure parameters. Considering the above losses,
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Fig. 4. (a) Polarization efficiency variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b) Polarization efficiency variation with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
Fig. 5. (a) Scattering loss variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b) Polarization loss variation with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
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Fig. 6. (a) Dispersion loss variation with respect to detuning from Bragg’s angle for Si-Air grating SOI structure. (b) Dispersion loss variations with respect to detuning from Bragg’s angle for GaAs-Air grating SOI structure.
transmitted efficiency is found to be 90.1% for Si-Air grating structure and 89.0% for GaAs-Air grating structure, which is a remarkable achievement. 5. Conclusions The core objective in this paper is to develop an effective Si-Air and GaAs-Air grating structures for application in photonic integrated circuit. Eqs. (1)–(5) are used to investigate different forms of losses like reflection, diffraction, polarization, scattering, dispersion respectively. It is noteworthy from the above equations that, different losses have strong dependence on the structure parameters. By properly choosing structure parameters, we computed reflectance by using transfer matrix method (TMM) at 1550 nm wavelength, whereas other losses (reflection, diffraction, polarization, scattering, dispersion) are analysed with respect to detuning from Bragg’s angle −12◦ to 12◦ . Finally, considering all the aforementioned losses, overall transmitted efficiency is obtained. Excitingly, overall transmitted efficiency is attained to be 90.1% and 89.0% for Si-Air and GaAs-Air grating structures respectively at wavelength 1550 nm. Hence the above structures came up as a good candidate as optical interconnector in photonics integrated circuits. References [1] M. Loncar, T. Doll, J. Vuckovic, “Design and fabrication of silicon photonic CrystalOptical waveguides”, J. Lightwave Technol. 18 (October 2000) (2017) 1402–1411. [2] K.K. Lee, D.R. Lim, L.C. Kimerling, Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction, Opt. Lett. 26 (2001) 1888–1890. [3] C.K. Tang, A.K. Kewell, G.T. Reed, A.G. Rickman, F. Namavar, Development of a library of low-loss silicon-on-insulator optoelectronic devices, IEE Proc. Opto-Electron. 143 (1996) 312–315. [4] M. Lipson, Guiding, modulating, and emitting light on silicon—challenges and opportunities, J. Lightwave Technol. 23 (2005) 4222–4238. [5] Haibo Liang, Richard Soref, Jianwei Mu, Arka Majumdar, Xun Li, Wei-Ping Huang, Simulations of silicon-on-insulator channel-waveguide electrooptical 2 × 2 switches and 1 × 1 modulators using a Ge2Sb2Te5 self-holding layer, J. Lightwave Technol. 33 (9) (2015) (MAY 1). [6] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Taka-hashi, T. Shoji, E. Tamechika, E. Itabashi, H. Morita, Microphotonics de-vices based on silicon microfabrication technology, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 232–240. [7] Z. Cheng, X. Chen, C.Y. Wong, K. Xu, C.K.Y. Fung, Y.M. Chen, H.K. Tsang, Mid-infrared grating couplers for silicon-on-sapphire waveguides, IEEE Photonics J. 4 (February) (2012) 104–113.
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