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Investigation on photonic band gap of a magneto photonic crystal
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Investigation on photonic band gap of a magneto photonic crystal N. Abirami*, K.S. Joseph Wilson Arul Anandar College, 625514, Karumathur, Madurai, India
A R T IC LE I N F O
ABS TRA CT
Keywords: Magnetic photonic crystal Yttrium iron garnet (YIG) Transfer matrix method
Magnetic photonic crystal is a subject of extensive research for their remarkable optical and magneto optical responses. In this work a novel one dimensional magneto photonic crystal having a magnetic nanocomposite medium consists of yttrium iron garnet (YIG)and Silver which act as high refractive index layer and air as the low refractive index layer is theoretically designed. Transmission properties of the designed one dimensional photonic crystal is studied using transfer matrix method. The variation of photonic band gap (PBG) have been analysed by varying applied magnetic field, filling factor and number of layers. Appreciable changes in the photonic band gap occurs with porosity.
1. Introduction Photonic crystals (PCs) is a combination of two dielectric materials with different refractive indices which attracted extensive attention. These two dielectric materials are arranged alternately all the three dimensions. Among these PCs, Magnetic Photonic Crystals (MPC) exhibit unique optical and magneto optical responses and have potential applications in novel optical devices [1,2]. By applying magnetic field to the MPC, the photonic bang gap, diffraction pattern and state of polarization are found to be drastically change [3]. In the recent years many research groups have worked on MPCs and new outcomes are theoretically predicted and experimentally observed [4]. The important property of PCs is the Photonic Band Gap(PBG), in which the propagation of electromagnetic waves is strongly forbidden in certain frequency range [5]. In this work, the variation of photonic band gap of onedimensional MPC having silver metal nanoparticles embedded YIG of width d1 and air of width d2 as alternate layer such that lattice constant d = d1+d2. Drude Lorentz theory is used calculate of dielectric contribution of the metal nanoparticle. The effective dielectric constant is calculated using Maxwell Garnett equation. PBG calculated by Transfer matrix method (TMM). The changes in the PBG have been analysed by varying applied magnetic field, porosity and number of layers. Hence, the variation of PBG of a onedimensional PC is analyzed. 2. Theory The effective dielectric function of the magnetic nanocomposite system (Ag-YIG/Air) is given by Maxwell Garnet approximation [8]
εmix =
ε *(1 + 2*p) − 2*ε *(p − 1) ε *(1 − p) + ε *(2 + p)
The relative magnetic permeability is calculated using the following formulas:
⁎
Corresponding author. E-mail address: [email protected] (N. Abirami).
https://doi.org/10.1016/j.ijleo.2019.164092 Received 12 November 2019; Accepted 17 December 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Please cite this article as: N. Abirami and K.S. Joseph Wilson, Optik - International Journal for Light and Electron Optics, https://doi.org/10.1016/j.ijleo.2019.164092
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
N. Abirami and K.S. Joseph Wilson
μr =
μ2 − k 2 ; μ = 1 + (1 − p) μ wire , k = pk wire μ ρπD2
The porosity p is given by p = 4 . D is the pore diameter. Parameters μ wire and k wire are, respectively, the diagonal and offdiagonal elements of the magnetic permeability tensor of one dimensional nanowire given by the classical ferromagnetic resonance (FMR) theory [6,7]
μ wire = 1 + k wire =
ωm (ωr + jωα ) (ωr + jωα )2 − ω2
ωm ω (ωr + jωα )2 − ω2
γM
where ωm = μ S with γ the gyromagnetic ratio, Ms the saturation magnetization, μ0 is the magnetic permeability in vacuum, α is the 0 damping factor, ω is angular frequency and ωr is the FMR angular frequency given by
ωr = ω0 +
1 ωm (1 − 3p) 2
Where ω0 = γHdc with Hdc the applied static magnetic field. The transmission properties of one dimensional MPCs are calculated by Transfer matrix method (TMM).The wave to be incident from the vacuum at an angle θ0. For the TE wave, the characteristic matrix for a single layer is given by
M M12 ⎤ M= ⎡ 11 M ⎣ 21 M22 ⎦
(1)
i ⎡ cos δi − sin δi ⎤ Mi = ⎢ ⎥ Pi ⎢− ipi sin δi cos δi ⎥ ⎣ ⎦ Where δi =
ω nd c i i
cos θi , c is the speed of light in vacuum, pi =
εi μi
cos θi , θi is the angle inside the layer i with refractive index ni, di is
the thickness of the layer i. The value of θi is related to the angle of incidence 1
n 2 sin2 θi 2 cos θi = ⎡1 − i 2 ⎤ ⎥ ⎢ n0 ⎦ ⎣
(2)
The refractive index of layers is given as ni = εi μi [9], where i represents either H and L layer. The suffix H represents the magnetic nanocomposite (Ag-YIG) and L is the air layer. The total transfer matrix for N periods is given by
T = (MH ML ) N
(3)
The transmission coefficient for tunneling through such structure is given by [10]
t=
4 (T11 + T22)2 + (T12 + T21)2
(4)
Where Tij is the elements of the matrix T. 3. Results and discussion The proposed structure of magneto photonic crystal consists of silver doped YIG nanocomposite layer and air. Number of photonic band gaps are formed in a particular frequency region. From the Fig. 1 It is noticed that 5 PBGs are formed in the region of 1–5 GHz. The theoretically designed photonic crystal can be analysed by TMM. The transmission spectra of the magneto photonic crystal is shown in Fig. 1 4. Porosity The transmission spectra of theoretically designed photonic crystals for a porosity values of 0.2 is shown in Fig. 2, in the frequency range 1–150 GHz. There are seven PBGs. The porosity plays an important role in tuning the PBG. When the porosity increases, number of photonic band gaps reduces and the width of a particular band gap increases. The transmission spectra of the photonic crystal, when the porosity becomes 0.4 is as shown in Fig. 3. It is calculated that the width of the photonic band gap becomes maximum when porosity is 0.5. Further increases of the porosity value, the width of the PBG fluctuates. The width of the PBG for different porosity is value are calculated and is given in Table 1. It leads to a fine tuning of photonic band gap. 2
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
N. Abirami and K.S. Joseph Wilson
Fig. 1. Transmission spectra of photonic crystals with number of periods n = 5, porosity p = 0.1 in an applied magnetic field 10 Oe.
Fig. 2. Transmission spectra of magneto photonic crystal with a porosity p = 0.2.
Fig. 3. Transmission spectra of magneto photonic crystal with a porosity p = 0.4. Table 1 Width of the PBG for different values of porosity. SI.No
Porosity
Width of the PBG (GHz)
1 2 3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.6 0.3 0.1 4.3 5 0.4 0.5
5 6 7
3
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
N. Abirami and K.S. Joseph Wilson
Fig. 4. Analysis of photonic band gap width with Number of layers (N).
Fig. 5. Transmission spectra of PBG for Appiled Field (H) Oe.
5. Number of periods The transmission spectra of photonic crystals is also studied by varying the number of periods. Here the PBG can be tunned by varying the number of periods. It is found that PBG increases and gets a maximum value 40 GHz for a period of 8. After that the width of PBG decreases and then become constant for large number of periods. It is shown in Fig. 4 6. Applied field Transmission spectra of the photonic crystal is also studied by varying the applied magnetic field. Here the applied magnetic field is varied from 0 to 1000 Oes and hence the transmission spectra of magnetic photonic crystal is studied. It is observed that there is no appreciable change in PBG with the magnetic field as shown in Fig. 5. 7. Conclusion The tuning of PBG of the magneto photonic crystal is studied by varying the number of layers, the applied magnetic field and the porosity value. It is found that there is no remarkable change in the width of PBG by applying magnetic field. Changes in the width of the PBG is observed by varying the porosity of nanocomposite layer and the period of photonic crystal, which leads to design novel photonic devices. It is concluded that the PBG drastically varied with the porosity of magnetic nanocomposite layer. References [1] [2] [3] [4] [5] [6] [7] [8]
E. Yablonovitch, Phys. Rev. Lett. 58 (1987) 2059. Jianfeng Chen, Wenyao Liang, Zhi-Yuan Li, Phys. Rev. B 99 (2019) 014103. A.M. Merzlikina, A.P. Vinogradova, M. Inoueb, A.B. Khanikaevb, A.B. Granovsky, J. Magn. Magn. Mater. 300 (2006) 108–111. M. Inoue, Member, A.V. Baryshev, A.B. Khanikaev, IEICE Trans. Fundam. Electron. E91–C (10) (2008) 1630–1632. H.F. Zhang1, S.B. Liu1, X.K. Kong1, B.R. Bian1, X. Zhao, Prog. Electromagn. Res. B 40 (2012) 415–431. K.M. Leun, Y.F. Liu, Phys. Rev. Lett. 65 (1990) 2646–2649. A.Z. Genack, N. Garcia, Phys. Rev. Lett. 66 (1991) 2646–2674. P.N. Dyachenko, Y.V. Miklayev, One dimensional photonic crystal based on nanocomposite of metal nanoparticles and dielectric, Opt. Mem. Neural Netw. 16 (2007) 198. [9] Lu Zhaolin, Dennis W. Prather, Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals, Optics Express Vol. 15 (2007) 8340–8345. [10] N.R. Ramanujam, K.S. Joseph Wilson, Optical Properties of Silver Nanocomposites and Photonic Band Gap – Pressure Dependence Optics Communications, 368 (2016), pp. 174–179.
4
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Investigation on photonic band gap of a magneto photonic crystal N. Abirami*, K.S. Joseph Wilson Arul Anandar College, 625514, Karumathur, Madurai, India
A R T IC LE I N F O
ABS TRA CT
Keywords: Magnetic photonic crystal Yttrium iron garnet (YIG) Transfer matrix method
Magnetic photonic crystal is a subject of extensive research for their remarkable optical and magneto optical responses. In this work a novel one dimensional magneto photonic crystal having a magnetic nanocomposite medium consists of yttrium iron garnet (YIG)and Silver which act as high refractive index layer and air as the low refractive index layer is theoretically designed. Transmission properties of the designed one dimensional photonic crystal is studied using transfer matrix method. The variation of photonic band gap (PBG) have been analysed by varying applied magnetic field, filling factor and number of layers. Appreciable changes in the photonic band gap occurs with porosity.
1. Introduction Photonic crystals (PCs) is a combination of two dielectric materials with different refractive indices which attracted extensive attention. These two dielectric materials are arranged alternately all the three dimensions. Among these PCs, Magnetic Photonic Crystals (MPC) exhibit unique optical and magneto optical responses and have potential applications in novel optical devices [1,2]. By applying magnetic field to the MPC, the photonic bang gap, diffraction pattern and state of polarization are found to be drastically change [3]. In the recent years many research groups have worked on MPCs and new outcomes are theoretically predicted and experimentally observed [4]. The important property of PCs is the Photonic Band Gap(PBG), in which the propagation of electromagnetic waves is strongly forbidden in certain frequency range [5]. In this work, the variation of photonic band gap of onedimensional MPC having silver metal nanoparticles embedded YIG of width d1 and air of width d2 as alternate layer such that lattice constant d = d1+d2. Drude Lorentz theory is used calculate of dielectric contribution of the metal nanoparticle. The effective dielectric constant is calculated using Maxwell Garnett equation. PBG calculated by Transfer matrix method (TMM). The changes in the PBG have been analysed by varying applied magnetic field, porosity and number of layers. Hence, the variation of PBG of a onedimensional PC is analyzed. 2. Theory The effective dielectric function of the magnetic nanocomposite system (Ag-YIG/Air) is given by Maxwell Garnet approximation [8]
εmix =
ε *(1 + 2*p) − 2*ε *(p − 1) ε *(1 − p) + ε *(2 + p)
The relative magnetic permeability is calculated using the following formulas:
⁎
Corresponding author. E-mail address: [email protected] (N. Abirami).
https://doi.org/10.1016/j.ijleo.2019.164092 Received 12 November 2019; Accepted 17 December 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Please cite this article as: N. Abirami and K.S. Joseph Wilson, Optik - International Journal for Light and Electron Optics, https://doi.org/10.1016/j.ijleo.2019.164092
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
N. Abirami and K.S. Joseph Wilson
μr =
μ2 − k 2 ; μ = 1 + (1 − p) μ wire , k = pk wire μ ρπD2
The porosity p is given by p = 4 . D is the pore diameter. Parameters μ wire and k wire are, respectively, the diagonal and offdiagonal elements of the magnetic permeability tensor of one dimensional nanowire given by the classical ferromagnetic resonance (FMR) theory [6,7]
μ wire = 1 + k wire =
ωm (ωr + jωα ) (ωr + jωα )2 − ω2
ωm ω (ωr + jωα )2 − ω2
γM
where ωm = μ S with γ the gyromagnetic ratio, Ms the saturation magnetization, μ0 is the magnetic permeability in vacuum, α is the 0 damping factor, ω is angular frequency and ωr is the FMR angular frequency given by
ωr = ω0 +
1 ωm (1 − 3p) 2
Where ω0 = γHdc with Hdc the applied static magnetic field. The transmission properties of one dimensional MPCs are calculated by Transfer matrix method (TMM).The wave to be incident from the vacuum at an angle θ0. For the TE wave, the characteristic matrix for a single layer is given by
M M12 ⎤ M= ⎡ 11 M ⎣ 21 M22 ⎦
(1)
i ⎡ cos δi − sin δi ⎤ Mi = ⎢ ⎥ Pi ⎢− ipi sin δi cos δi ⎥ ⎣ ⎦ Where δi =
ω nd c i i
cos θi , c is the speed of light in vacuum, pi =
εi μi
cos θi , θi is the angle inside the layer i with refractive index ni, di is
the thickness of the layer i. The value of θi is related to the angle of incidence 1
n 2 sin2 θi 2 cos θi = ⎡1 − i 2 ⎤ ⎥ ⎢ n0 ⎦ ⎣
(2)
The refractive index of layers is given as ni = εi μi [9], where i represents either H and L layer. The suffix H represents the magnetic nanocomposite (Ag-YIG) and L is the air layer. The total transfer matrix for N periods is given by
T = (MH ML ) N
(3)
The transmission coefficient for tunneling through such structure is given by [10]
t=
4 (T11 + T22)2 + (T12 + T21)2
(4)
Where Tij is the elements of the matrix T. 3. Results and discussion The proposed structure of magneto photonic crystal consists of silver doped YIG nanocomposite layer and air. Number of photonic band gaps are formed in a particular frequency region. From the Fig. 1 It is noticed that 5 PBGs are formed in the region of 1–5 GHz. The theoretically designed photonic crystal can be analysed by TMM. The transmission spectra of the magneto photonic crystal is shown in Fig. 1 4. Porosity The transmission spectra of theoretically designed photonic crystals for a porosity values of 0.2 is shown in Fig. 2, in the frequency range 1–150 GHz. There are seven PBGs. The porosity plays an important role in tuning the PBG. When the porosity increases, number of photonic band gaps reduces and the width of a particular band gap increases. The transmission spectra of the photonic crystal, when the porosity becomes 0.4 is as shown in Fig. 3. It is calculated that the width of the photonic band gap becomes maximum when porosity is 0.5. Further increases of the porosity value, the width of the PBG fluctuates. The width of the PBG for different porosity is value are calculated and is given in Table 1. It leads to a fine tuning of photonic band gap. 2
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
N. Abirami and K.S. Joseph Wilson
Fig. 1. Transmission spectra of photonic crystals with number of periods n = 5, porosity p = 0.1 in an applied magnetic field 10 Oe.
Fig. 2. Transmission spectra of magneto photonic crystal with a porosity p = 0.2.
Fig. 3. Transmission spectra of magneto photonic crystal with a porosity p = 0.4. Table 1 Width of the PBG for different values of porosity. SI.No
Porosity
Width of the PBG (GHz)
1 2 3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.6 0.3 0.1 4.3 5 0.4 0.5
5 6 7
3
Optik - International Journal for Light and Electron Optics xxx (xxxx) xxxx
N. Abirami and K.S. Joseph Wilson
Fig. 4. Analysis of photonic band gap width with Number of layers (N).
Fig. 5. Transmission spectra of PBG for Appiled Field (H) Oe.
5. Number of periods The transmission spectra of photonic crystals is also studied by varying the number of periods. Here the PBG can be tunned by varying the number of periods. It is found that PBG increases and gets a maximum value 40 GHz for a period of 8. After that the width of PBG decreases and then become constant for large number of periods. It is shown in Fig. 4 6. Applied field Transmission spectra of the photonic crystal is also studied by varying the applied magnetic field. Here the applied magnetic field is varied from 0 to 1000 Oes and hence the transmission spectra of magnetic photonic crystal is studied. It is observed that there is no appreciable change in PBG with the magnetic field as shown in Fig. 5. 7. Conclusion The tuning of PBG of the magneto photonic crystal is studied by varying the number of layers, the applied magnetic field and the porosity value. It is found that there is no remarkable change in the width of PBG by applying magnetic field. Changes in the width of the PBG is observed by varying the porosity of nanocomposite layer and the period of photonic crystal, which leads to design novel photonic devices. It is concluded that the PBG drastically varied with the porosity of magnetic nanocomposite layer. References [1] [2] [3] [4] [5] [6] [7] [8]
E. Yablonovitch, Phys. Rev. Lett. 58 (1987) 2059. Jianfeng Chen, Wenyao Liang, Zhi-Yuan Li, Phys. Rev. B 99 (2019) 014103. A.M. Merzlikina, A.P. Vinogradova, M. Inoueb, A.B. Khanikaevb, A.B. Granovsky, J. Magn. Magn. Mater. 300 (2006) 108–111. M. Inoue, Member, A.V. Baryshev, A.B. Khanikaev, IEICE Trans. Fundam. Electron. E91–C (10) (2008) 1630–1632. H.F. Zhang1, S.B. Liu1, X.K. Kong1, B.R. Bian1, X. Zhao, Prog. Electromagn. Res. B 40 (2012) 415–431. K.M. Leun, Y.F. Liu, Phys. Rev. Lett. 65 (1990) 2646–2649. A.Z. Genack, N. Garcia, Phys. Rev. Lett. 66 (1991) 2646–2674. P.N. Dyachenko, Y.V. Miklayev, One dimensional photonic crystal based on nanocomposite of metal nanoparticles and dielectric, Opt. Mem. Neural Netw. 16 (2007) 198. [9] Lu Zhaolin, Dennis W. Prather, Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals, Optics Express Vol. 15 (2007) 8340–8345. [10] N.R. Ramanujam, K.S. Joseph Wilson, Optical Properties of Silver Nanocomposites and Photonic Band Gap – Pressure Dependence Optics Communications, 368 (2016), pp. 174–179.
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