A multi-channel omnidirectional tunable filter in one-dimensional tilted ternary plasma photonic crystal

Transcription

1 JOURNAL OF INTENSE PULSED LASERS AND APPLICATIONS IN ADVANCED PHYSICS Vol. 4, No. 3, 4, p A multi-channel omnidirectional tunable filter in one-dimensional tilted ternary plasma photonic crystal M. UPADHYAY a *, A. MEHTA b, S. K. AWASTHI a, S. K. SRIVASTAVA c, S. N. SHUKLA c, S. P. OJHA d a Department of Physics and Material Science and Engineering, Jaypee Institute of Information Technology, Deemed University, Noida, 34, India b Department of Electronics and Communication Engineering, Jaypee Institute of Information Technology, Deemed University, Noida, 34, India c Department of Physics, Amity Institute of Applied Sciences, Amity University, Noida 34, India d Department of Applied Physics, Institute of Technology, Banaras Hindu University, Varanasi, 5, India. We show theoretically that a one-dimensional (D) ternary plasma photonic crystal (TPPC) containing dispersive plasma has an omnidirectional photonic band gap (OBG) which can be tuned further by using a D tilted ternary plasma photonic crystal (TTPPC) structure. A TTPPC structure is similar to the conventional TPPC structure with the only difference that in this case alternate layers are inclined at certain angle to the direction of propagation of electromagnetic waves. We adopt the transfer matrix method (TMM) to analyze the reflectance spectra of the proposed structure. Our analysis of the reflectance spectra, shows that for the values of tilt angle up to 67. OBG shift towards lower frequency side with a marginal decrease in the width of individual OBGs though the number of OBGs remain same i.e. two. At larger values of tilt angle, multi-channel OBGs appear, this feature is more pronounced when is greater than 7. Thus multi-channel tunable OBGs can be obtained for desired frequency ranges in the microwave region, without changing the structural parameters of TTPPC. These findings may provide theoretical instructions for design of new kind of a narrow band multi-channel omnidirectional filters and many other optoelectronic devices, which offer potential applications in the field of photonics and optical communication. (Received June 8, 4; Accepted August, 4) Keywords: Omnidirectional bandgap, Photonic crystal, Transfer matix method. Introduction Electromagnetic wave propagation in spatially multilayer periodic structures called photonic crystals (PCs) was first studied by Lord Rayleigh in 887 and was extensively investigated years later by two pioneers, Yablonovitch and John in 987 []. The subject has attracted growing interest in recent years. It has been proved that a photonic bandgap (PBG) could be formed as a result of the interference of Bragg scattering in a period dielectric structure. PBGs thus formed are strongly dependent on the geometry of the lattice and the dielectric constants of the components. Therefore, much attention has been paid to the periodic multilayered structure of different materials such as dielectrics, semiconductors, liquid crystals, metals and plasma []. If a situation can be arrived at wherein a PBG reflects EM waves incident at any angle with any state of polarization, then an OBG can be obtained with negligible loss in a specific frequency range [3]. Such a PBG material has been the subject of interest in recent years and has in practice being designed using D all-dielectric binary PCs (i.e., two material layers constituting a period of the lattice) [4-8]. Awasthi et al. [4] suggested a novel way to enhance the OBG wavelength range in D PBG material by using a ternary periodic structure (i.e., three dielectric layers constituting a period of the lattice). Recently, a lot of work has been done [9-3] on the plasma photonic crystal (PPC) structure, whose optical properties such as dielectric constant etc. can vary continuously in space with the change of frequency of the incident electromagnetic waves (EMWs). The variation of dielectric constant with frequency makes the PPC very different in behavior from the PC composed of conventional materials []. Plasma is a dispersive medium and electromagnetic waves with frequency below the plasma frequency cannot propagate through bulk plasma. However, the plasma can combine with a dielectric material to form a PPC through which EMWs can be guided even below the plasma frequency [3]. The technological applications of PPC are now expanding widely as, for example, in plasma lens [4], plasma antenna [5], plasma stealth aircraft [6-9] etc. and OBGs can be utilized as omnidirectional or large incident angle filters in microwave devices. Moreover, by replacing dielectric materials with plasma, two important features are added to conventional PCs viz time-varying controllability and strong dispersion around the electron plasma density. These two features make the frequency of EM wave propagating in a PPC range from microwaves to THz waves, according to the scale and the electron density of plasma []. The photonic band structure of a TPPC has been theoretically investigated by X-K Kong et al. []. They have shown that the TPPC has a superior feature in the enhancement of the OBG range and the modulation of

2 46 M. Upadhyay, A. Mehta, S. K. Awasthi, S. K. Srivastava, S. N. Shukla, S. P. Ojha OBG as compared to the usual binary PPC. H-F Zhang et al. [] have reported further enhancement of the OBG range as compared to that of the TPPC by proposing a heterostructured dielectric plasma photonic crystal with a matching layer. In the present paper, the propagation of EMWs through D tilted ternary plasma photonic crystal (TTPPC) is theoretically examined by using transfer matrix method (TMM) [-4]. A TTPPC structure is similar to the conventional TPPC structure with the only difference that in this case alternate layers are inclined at certain angle with the normal to the direction of propagation of EMWs. The thicknesses of these layers have been tailored so as to achieve maximum OBG range at tilt angle. As compared to results of X-K Kong et al. [] and H-F Zhang et al. [], the OBG range of the proposed structure is significantly enlarged with reduced structure size. Next, the structure is tilted, and the OBG ranges for different tilt angles are determined. It has been observed that at 3 tilt angle, the OBG range of the proposed structure contains the entire OBG range reported in reference [], while at 4 tilt angle, the entire OBG range reported in reference [] is contained in the OBG range of proposed structure. At larger tilt angles, multi-channel OBGs appear. Thus the OBG s can be tuned for different frequency ranges simply by varying the angle of tilt, without having to change the structural parameters of the device. Omnidirectional reflectors or filters have been widely reported, but to the best our knowledge, a multi-channeled tunable omnidirectional filter has not been reported as yet. Therefore, this study may be considered to be physically more realistic in order to obtain different tunable OBG regions inside the single PC without changing lattice parameters. The OBG reported by us which originates from Bragg gap, is fundamentally different from zero- n gap and SNG gap as reported by Wang et. al. [6] and Jiang et. al. [7].. Theoretical analysis Consider the D TPPC with the periodic structure of (ABC) N where A, B and C represent quartz glass, plasma and air respectively, N is the number of periods. The structure is placed between two semi infinite media of refractive index i.e. air or vacuum. Let a plane wave be incident from vacuum into the D TPPC at an angle θ with the z direction, as shown in figure. For the transverse electric (TE) / the transverse magnetic (TM) wave, the electric field E / the magnetic field H is along the y direction. The dielectric layers are in the x-z plane. x y z A B C A B C θ d d d 3 Fig. : Schematic representation of D TPPC. The characteristic matrix M(Λ) for a single period is expressed as [-3] M i m 3 m cos i - sin i Λ = = Π δ δ η i, m i= m -iηisinδi cosδ i () where m cos cos cos sin sin cos cos sin sin sin cos sin, m i i i i sin cos cos cos sin cos cos cos sin sin sin sin, i m i sin cos cos i cos sin cos i cos cos sin sin sin sin, m cos cos cos sin sin cos cos sin sin sin cos sin

3 A multi-channel omnidirectional tunable filter in one-dimensional tilted ternary plasma photonic crystal 47 here the phase thickness is written as () i ( / c) i i di (sin / i i), where i =, and 3 respectively, θ is the ray angle inside the layer n i, ω is frequency in the incidence medium and c is the speed of light in vacuum. For the TE wave, / (sin / ) and for the TM wave, i i i i i / (sin / ). i i i i i Now we tilt the TPPC structure as suggested by Srivastava et. al. [4] to get TTPPC structure as shown in figure. Here α is the tilt angle which the plane of periodic multilayer structure makes with the x-axis and d, d and d 3 are the thicknesses of the layers quartz glass (A), plasma (B) and air (C) respectively of TPPC. The ' ' ' modified thicknesses d, d and d of layers A, B and, C of TTPPC as shown in figure are given as [4] ' d d d sin(9 ) cos, ' d d 3 and d d ' 3 3. (3) cos cos x d ' d ' d 3 ' A n α d B C A B C d d 3 z Fig. : Schematic representation of D TTPPC. Thus the phase thickness Eq. () is modified as The plasma layer B is assumed to be dispersive and dissipative, with frequency dependent effective dielectric ' ( / c) ' d (sin / ), (4) constant ε given by [,, 5]. i i i i i i The total transfer matrix for the N period of system is given by M M( ) N (5) The reflection coefficient of the multilayered structure for TE and TM waves are given by [8- ] M η +M η η - M - M η (6) r ω=, M η +M η η +M +M η n+ n+ where M, M, M, M are the elements of the total characteristic matrix of the N period multilayer structures. Reflectance spectra of multilayer structure can be obtained by using the expression, R = r = r r *, (7) pe ( ), ( i ) where ω is the incident wave frequency, ω pe = nee /meε is the electron plasma frequency, being a function of the plasma density n e and the collision frequency ν. 3. Result and discussions In this section, we first consider steps to get maximum OBG range in D TPPC without tilting. The period of the proposed TPPC consists of three layers which are quartz glass (A), plasma (B) and air (C) respectively. The total number of periods (N) is equal to 5. In order to obtain OBG in the microwave frequency region with analogous structure parameters selected in reference [], we choose the structure parameters as follows: ε A = 4, μ A =, d A = 4. mm, ε C =, μ C = and d C =. mm. The A and C layers refer to quartz glass and air respectively. For the plasma layer (B), ω p = л rad/s, n e = 9 / m 3 and ʋ = л 6 rad/s. (8)

4 JOURNAL OF INTENSE PULSED LASERS AND APPLICATIONS IN ADVANCED PHYSICS Vol. 4, No. 3, 4, p (GHz) Tilted = o = o = 45 o = 89 o Fig. 3(a): Reflectance spectra of D TPPC composed of alternate layers of Quartz glass (A), Plasma (B) and Air (C) at various angles of incidence with d = 4. mm, d =. mm, d 3 =. mm, N = 5 and tilt angle =. The black solid (dashed) curves are for TE (TM) wave. The gray areas represent the OBGs. 9 5 = o TE Omnidirectional Band Gap TM o Fig. 3(b): Photonic band gap structure of TPPC in terms of angular frequency and incident angle at tilt angle =. The white areas represent the OBGs. The PBG for various frequency ranges and angles of incidence for TE and TM waves both obtained by using eqs. () to (8) is shown in figure. 3(a). Fig. 3(b) plots the dependence of the PBG of TPPC on the angle of incidence and angular frequency for both polarization states. As shown in figure 3(a) and 3(b) TM PBG is narrower than TE one, except for normal incidence, when both polarizations are degenerate. It is the TM PBG that determines the band width of OBG range. In figure3(b) the red areas correspond to the PBGs or high reflectance regions and white areas correspond to OBG ranges. The two OBG ranges are obtained, the narrower one extends from 5 to 6.3 GHz and wider one extends from 5.9 GHz to 8.8 GHz, yielding OBG band widths of.3 GHz and 3.6 GHz respectively. It is seen that though the wider OBG band shows an enhancement as compared to those reported earlier in references [] and [] but it does not cover the entire range of the frequencies of aforesaid references.

5 A multi-channel omnidirectional tunable filter in one-dimensional tilted ternary plasma photonic crystal 49.5 Tilted = 3 o = o.5 = 45 o = 89 o Fig. 4(a): Reflectance spectra of D TPPC composed of alternate layers of Quartz glass (A), Plasma (B) and Air (C) at various angles of incidence with d = 4. mm, d =. mm, d 3 =. mm, N = 5 and tilt angle = 3. The black solid (dashed) curves are for TE (TM) wave. The gray areas represent OBGs =3 o TE Omnidirectional Band Gap TM o Fig. 4(b): Photonic bandgap structure of TPPC in terms of angular frequency and incident angle at tilt angle = 3. The white areas represent the OBGs. In order to achieve the entire range of OBG as reported in references [] and [], we tilt the proposed TPPC structure at different tilt angles as suggested by Srivastava et. al. [4] and the corresponding reflectance spectra are plotted as shown in figures 4 to 7. It is observed that with increase in from to 67., the number of OBGs obtained are still two and both shift towards the lower frequency side, but for values of more than 67., the number of OBGs observed in the region of investigation start to increase (Table-). This feature is more pronounced when is greater than 7.

6 5 M. Upadhyay, A. Mehta, S. K. Awasthi, S. K. Srivastava, S. N. Shukla, S. P. Ojha.5 Tilted = 4 o = o = 45 o = 89 o Fig. 5(a): Reflectance spectra of D TPPC composed of alternate layers of Quartz glass (A), Plasma (B) and Air (C) at various angles of incidence with d = 4. mm, d =. mm, d 3 =. mm, N = 5 and tilt angle = 4. The black solid (dashed) curves are for TE (TM) wave. The gray areas represent OBGs = 4 o TE Omnidirectional Band Gap TM o Fig. 5(b): Photonic bandgap structure of TPPC in terms of angular frequency and incident angle at tilt angle = 4. The white areas represent the OBGs. It is worth mentioning that for values of the tilt angle equal to 3 and 4 the OBGs, obtained in our calculations (figure 4(b) & 5(b)) covers the entire range of OBG region of references [] and [] respectively even though our proposed TTPPC structure is much smaller in size as compared to the structures of references and. Further it is important to note that the Brewster window is not observed for TPPC and TTPPC both. Because in both the cases, the maximum refracted angle is smaller than the internal Brewster angle so that the TM wave does not couple to the Brewster window. Therefore, the incident wave from the outside cannot couple to the Brewster window, leading to the total reflection for all incident and tilt angles.

7 JOURNAL OF INTENSE PULSED LASERS AND APPLICATIONS IN ADVANCED PHYSICS Vol. 4, No. 3, 4, p Tilted = 7 o = 45 o = 89 o Fig. 6(a): Reflectance spectra of D TPPC composed of alternate layers of Quartz glass (A), Plasma (B) and Air (C) at various angles of incidence with d = 4. mm, d =. mm, d 3 =. mm, N = 5 and tilt angle = 7. The black solid (dashed) curves are for TE (TM) wave. The gray areas represent OBGs. = o = 7 o TE Omnidirectional Band Gap TM o Fig. 6(b): Photonic bandgap structure of TPPC in terms of angular frequency and incident angle at tilt angle = 7. The white areas represent the OBGs.

8 5 M. Upadhyay, A. Mehta, S. K. Awasthi, S. K. Srivastava, S. N. Shukla, S. P. Ojha = 89 o.5 Tilted = 75 o = 45 o Fig. 7(a): Reflectance spectra of D TPPC composed of alternate layers of Quartz glass (A), Plasma (B) and Air (C) at various angles of incidence with d = 4. mm, d =. mm, d 3 =. mm, N = 5 and tilt angle = 75. The black solid (dashed) curves are for TE (TM) wave. The gray areas represent OBGs. = o = 75 o TE Omnidirectional Band Gap TM o Fig. 7(b): Photonic bandgap structure of TPPC in terms of angular frequency and incident angle at tilt angle = 75. The white areas represent the multiple OBGs. The proposed structure can thus act as a multi-channel tunable omnidirectional filter and OBGs can be tuned for desired frequency ranges by varying the angle of tilt. All the results are summarized in Table. This tunable feature of OBGs can be explained on the basis of simple interference theory. As we increase tilt angle, effective path length of the light ray inside the material layer is increased in accordance with Eq. (3), which increases optical path of the light ray inside the respective layer. As increases, OBG region not only shift towards lower frequency side but also multi-channel OBGs start to appear as shown in figures. 4 to 7. Thus the proposed study may provide a means of controlling multichannel tunable OBGs, which is useful for the designing of optical devices.

9 A multi-channel omnidirectional tunable filter in one-dimensional tilted ternary plasma photonic crystal 53 Table. Number of OBGs corresponding to various tilt angles along with range and width of OBGs S. No. Tilt angle α No. of OBGs Range of OBG (GHz) Width of OBG (GHz) (a) (b) (a) (b) (a) (b) (a) (b) (a) (b) (c) (a) (b) (c) (a) (b) (c) (d) Conclusion In the D TTPPC based multi-channel tunable omnidirectional filter proposed in the present study, the OBGs can be tuned up to desired frequency ranges simply by tilting the structure at different tilt angles, without affecting the structural parameters. The structure is also smaller in size, and yields a larger OBG as compared to those obtained from the ternary plasma photonic crystal and the heterostructured dielectric plasma photonic crystal with matching layer reported earlier. Such TTPPC structure has not only the optical properties of PBG material, but also the optical properties of plasma. Moreover TTPPCs can significantly contribute to the development of plasma stealth aircraft, plasma antenna and plasma lens etc. This tunable feature of the proposed structure can also be used as narrow band tunable omnidirectional filter, wavelength division multiplexer and in many other optical systems. Acknowledgements Authors are thankful to Department of Physics and Material Science and Engineering, Jaypee University, Sector-8, Noida, India for providing facilities required for this work. Thanks are also extended to Prof. Usha Malaviya for her helpful discussion during the preparation of this manuscript. References [] H. M. Lee, J.- C. Wu, Journal of App. Phys. 7, 9E49-- 9E49-3 (). [] C.- Z. Li, S.- B. Liu, X.- K. Kong, B. Bian, X.- Y. Zhang, App. Opt. 5, 37 ().

10 54 M. Upadhyay, A. Mehta, S. K. Awasthi, S. K. Srivastava, S. N. Shukla, S. P. Ojha [3] X. Y. Dai, Y. J. Xiang, S. C. Wen, PIER, 7 (). [4] S. K. Awasthi, U. Malaviya, S. P. Ojha, J. Opt. Soc. Am. B 3, 566 (6). [5] G. Guida, A. de Lustrac, A. Priou, PIER 4, (3). [6] Li-Gang Wang, Hong Chen, Shi-Yao Zhu, Phys. Rev. B 7, 45- (4). [7] Haito Jiang, Hong Chen, Hongqiang Li, Yewen Zhang, Shiyao Zhu, Appl. Phys. Letters. 83, 5386 (3). [8] M. Upadhyay, S. K. Awasthi, S. K. Srivastava, S. P. Ojha, PIER M 5, (). [9] X. K. Kong, S. B. Liu, H. F. Zhang, H. L. Guan, Optics Commun. 84, 95 (). [] B. Guo, Plasma Sci. Technol., 8 (9). [] L. Shiveshwari, Optik, 53 (). [] B. Guo, M. Gao, Int. J. Appl. Phys. and Math., (). [3] L. Shiveshwari, Plasma Sci. and Techn. 3, 39 (). [4] A. A. Goncharov, A. N. Dobrovolsky, A. V. Zatuagan, I. M. Protsenko, IEEE Trans. Plasma Sci., 573 (993). [5] T. J. Dwyer, J. Greig, D. Murphy, J. Perin, R. Pechaceket, M. Raleigh, IEEE Trans. Antenna and Propag. 3, 4 (984). [6] R. J. Vidmar, IEEE Trans. Plasma Sci. 8, 733 (99). [7] D. L. Tang, A. P. Sun, X. M. Qiu, P. K. Chu, IEEE Trans. Plasma Sci. 3, 45 (3). [8] B. Guo, X. G. Wang, Phys. Plasmas, (5). [9] B. Guo, X. G. Wang, Y. Zhang, Plasma Sci. Technol. 8, 558 (6). [] X. K. Kong, S. B. Liu, H. F. Zhang, C. Z. Li, B. Bian, J. Opt. 3, 35 (). [] H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou L, C. Z. Li, W. S. Qing, Phys Plasmas, 9, 3- (). [] M. Born and E. Wolf, Principles of Optics Cambridge U. Press, pp. 7 (98). [3] H. A. Macleod, Thin-Film Optical Filters, Adam Hilger, Bristol, United Kingdom, pp (986). [4] S. K. Srivastava, Maitreyi Upadhyay, S.K. Awasthi, S. P. Ojha, Optics and Photonics Journal, 3 (). [5] V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas Oxford: Pergamon, (97). * Corresponding author: maitri.du@gmail.com.