- Email: [email protected]
Characteristics analysis of metamaterial based optical fiber
Accepted Manuscript Title: Characteristics Analysis of Metamaterial based Optical Fiber Author: R. Yamunadevi D. Shanmuga Sundar A. Sivanantha Raja PII: DOI: Reference:
S0030-4026(16)30779-3 http://dx.doi.org/doi:10.1016/j.ijleo.2016.07.014 IJLEO 57934
To appear in: Received date: Revised date: Accepted date:
16-2-2016 4-7-2016 4-7-2016
Please cite this article as: Yamunadevi R., Shanmuga Sundar D., Sivanantha Raja A., Characteristics Analysis of Metamaterial based Optical Fiber, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.07.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Characteristics Analysis of Metamaterial based Optical Fiber R.Yamunadevi, D.Shanmuga sundar and A.Sivanantha Raja * 1
Alagappa Chettiar College of Engineering & Technology, Karaikudi, Tamilnadu *[email protected]
Abstract - Optical fiber plays an important role as a transmission channel in fiber optic communication. In this work, the design of optical fiber using integration of metamaterial which allows waveguidance through subwavelength geometry is proposed. Transmission of information through surface plasmon mediated or through classical core guidance is made possible, with metamaterial as either core or cladding. Here, the alternate combination of Ag/Al2O3 layers are used, which acts as an anisotropic metamaterial (AMM), supporting plasmonic propagation, depending upon the wavelength (around UVRegion). Parameters such as confinement loss and dispersion characteristics are analyzed for different proportions of metal and dielectric layers. Propagation of desired modes are confirmed by the obtained simulation results by Finite element method. Keywords - Metamaterial, Optical fiber, Surface plasmon propagation, Subwavelength geometry.
I. INTRODUCTION Fiber optic systems, in recent days, generate a great interest and have various applications in new communication technologies [1]. This fiber optic communication system greatly depends on optical fiber as a communication channel which helps in transmitting Digital and analog audio/video signals [2] and also has the greater advantage of using it as fiber optic sensors [3]-[5]. Over the past decades, Single mode fibers made-up of silicon, has been proven to provide low loss at the transmission wavelength of 1.55µm [6]. In this paper, attempts have been made to transmit the light of smaller wavelength, (i.e.,) of wavelength around 300nm, that supports the transmission in UV – Region. Metamaterials are the specially classified materials, which can be structured to have unique properties that are not found in natural materials [7], such as backward propagation, negative refraction [8,9]. Therefore, the choice of metamaterial for designing the fiber, makes the transmission at lower wavelength easier. Numerous researches and experiments on metamaterials, has paved a way to important applications such as cloaking devices [10], subdiffraction imaging systems [11] and surface plasmon waveguides [12]. Propagation of electromagnetic waves through the circular waveguides with negative refractive index was experimented to form a metamaterial fiber [13,14]. Metamaterial fibers are then designed for the special applications such as to have zerogroup velocity in the wave propagation at optical frequencies
[15] and also to operate in the frequencies over the range of terahertz region [16]. The concept of anisotropy with metamaterials was also introduced in the fibers to extend their applications [17, 18]. Based on the application for which the metamaterial is to be utilized, one can choose the appropriate metal and metal oxide combinations to form the metamaterials accordingly. The combination of the metal and metal oxide results in the anisotropic characteristics as well as negative index nature then the materials can be used as metamaterials. In some of the papers, they have used Ag and TiO2 combination for the multiband perfect absorber applications [19]. Metamaterials are not limited by type of materials to be used, but their entire characteristics can be decided by the choice of the individual materials used [7]. In this paper, the alternating layers of metal and a metal oxide is used as a metamaterial, which has anisotropic characteristics. Ag and Al2O3 are chosen as the preferred metal and metal oxide, due to the negative index nature of Ag [20] and crystalline nature of Al2O3 [21], which could be easier to develop a negative index medium. Ag and Au are commonly found metals with natural negative index of refraction. Here, we have chosen Ag (Silver) as the metal because of its easy affordable nature than Au (Gold) and the choice of Al2O3 is preferred for its amorphous form that could help in strong anisotropy when combined with Ag (Silver) [22], which could be at ease when extended for a practical implementation from the simulation point of view. The use of metamaterial as either a cladding or core in a hollow fiber helps in both ordinary core guidance [23] and surface plasmon propagation of waves [24] based on the wavelength tuning. This in turn also supports, transmitting the information through subwavelength geometry and hence provides miniaturization advancement in the field of optoelectronic components. Both normal core guidance (Fig 1.a) and surface plasmon propagation (Fig 1.b) for the metamaterial cladding fiber can be obtained at different wavelength. Furthermore, the dispersion characteristics and the confinement loss for three different metal-dielectric proportions are analyzed. Fig 1(c) shows the ray diagram, when the proposed metamaterial is used as core, it acts as a normal single mode fiber, at the core radius less than the propagation wavelength. This AAM
cladding fiber can serve as an effective chemical sensor [25], when the core is filled with gas or liquid.
individual permittivity of the metal and dielectric and also the ratio of thickness of metal and dielectric layer to one another [27]. This effective permittivity of the structured AMM varies according to the wavelength which is obvious from the Fig 3(a) and Fig 3(b) which shows the anisotropy of the designed metamaterial. Careful designing of such metamaterial enables the effective tuning of effective permittivity based on specific wavelength, which stands as the major advantage of AMM. ɛ┴
- Cm ɛ‖
- Cd
Fig. 1. Ray diagram of (a) Hollow core guidance (b) Surface plasmon propagation through AMM cladding and (c) Core propagation when AMM is used as core of the fiber.
II. DESIGN MECHANISMS
The proposed Ag and Al2O3 layers, each of thickness Cm = Cd are stacked alternatively to provide anisotropy. These stacked layers shown in Fig.2 can be rolled-up through nanotechnology [26] to provide hollow core AMM cladding fiber. The stacked layers may also be designed to have variations in the ratios of metal/dielectric thickness. This should be carefully designed, so that their parameters can be altered to desired wavelength. An Electromagnetic (EM) wave propagating in a cylindrical waveguide takes the form of Maxwell’s equation as follows, E = E0 (r,φ) exp [i(βz-ωt)]
- [1]
H = H0 (r,φ) exp [i(βz-ωt)]
- [2]
where ω and β are the frequency and the wavenumber of the EM wave propagating inside the fiber, and (r,φ,z) are the cylindrical co-ordinates arises due to the planar to cylindrical conversion of stacked layers, which have the potential to act as an efficient optical fiber. An electromagnetic wave propagating inside a fiber has two important parameters to be considered, which are permittivity (ɛ) and permeability (µ). Limiting the magnetic response of the cladding metamaterial, we assume µ = 1, and the permittivity tensor is given by,
Fig 2. Lattice diagram of the alternatively stacked layers (Ag/Al2O3), where Cm and Cd are the ratio of proportion of metal and dielectric respectively and ┴ and ‖ represents the perpendicular and parallel components of the structure.
10 0 Permittivity
A. Effective permittivities of layered AMM
0
eps_pr eps_pl
Wavelength (nm) Fig 3.(a) Variation of the calculated real part of perpendicular and parallel effective permittivity of AMM with respect to the wavelength
25
2
ɛ┴ sin (φ) + ɛ‖ cos (φ) 0 -[3] 0
-30
-50
ɛ‖
where [ɛeff] is the effective permittivity tensor and ɛ┴ , ɛ‖ are the perpendicular and parallel components of the effective permittivity. These perpendicular and parallel components of the effective permittivity is given by, Ԑ┴eff
= (Cm + Cd) Ԑm Ԑd / (Cm Ԑd + Cd Ԑm) - [4]
Ԑ‖eff
= (Cm Ԑm + Cd Ԑd)/ (Cm + Cd)
- [5]
where Ԑm and Ԑd are the permittivity of the metal and dielectric respectively. Cm and Cd are the ratios of metal and dielectric respectively in the entire composition. From equation [4] and equation [5], it is clear that, the perpendicular and parallel components of the effective permittivity depends on the
20 Permittivity
[ɛ ]= (ɛ┴ - ɛ‖) sin (φ) cos (φ)
2
300 310 320 330 340 350 360 380
-20
-40
ɛ┴ cos2 (φ) + ɛ‖ sin2 (φ) (ɛ┴ - ɛ‖) sin (φ) cos (φ) 0 eff
-10
15 10 5
eps_pr(img) eps_pl(img)
0 300 310 320 330 340 350 360 370 Wavelength (nm) Fig 3.(b) Variation of the calculated imaginary part of perpendicular and parallel effective permittivities of AMM with respect to the wavelength
A hollow core fiber with an inner radius of 2 μm, integrating a metamaterial as the cladding layer with a thickness of 500 nm is designed. The effective permittivity tensor of the cladding layer, which is consecutively related to the individual permittivities of metal and dilectric layer is varied based on the corresponding wavelength of incidence. This change in the effective permittivity provides the classical waveguiding or plasmonic propagation at particular wavelength. Particularly, at the wavelength where ɛ┴ is positive and ɛ‖ is negative, the incident light is guided through the core and surface propagation is achieved at the wavelength where both parallel and perpendicular components of the effective permittivities are positive. Fiber with the proposed metamaterial as core of 200 nm supports subwavelength propagation. The 2D cross-section of the designed AMM cladding fiber is shown in Fig 4(a) and that of AMM core fiber is shown in the Fig 4(b). ɛ=1 ɛ = [ɛ]
The material with loaded effective permittivity acts as a metamaterial. This effective permittivity tensor is anisotropic in nature and hence supports anisotropy. B. Mode analysis of Hollow core AMM fiber and AMM core fiber In cylindrical coordinate systems, Bessel functions of various kinds ruled by Maxwell’s equations [28] are used to describe the electromagnetic components in the core of a cylindrical waveguide as described as follows, E¬z = AJn(K0r) exp (inφ)
[6.1]
Er = i ( β∂rEz + (ωµ0/r) ∂φHz ) / K02
[6.2]
Eφ = i ( β∂φEz/r - (ωµ0/r) ∂rHz ) / K02
[6.3]
H¬z = BJn(K0r) exp (inφ)
[6.4]
Hr = i ( β∂rHz - (ωɛ0/r) ∂φEz ) / K02
[6.5]
Hφ = i ( β∂φHz/r + (ωɛ0/r) ∂rEz ) / K02
[6.6]
where K0 = k0(ɛd – neff2)1/2 and neff = β/k0, k0 is the wavenumber in free space respectively. The above set of equations from [6.1] to [6.6] describes the EM components for a wave inside the core of the fiber, which takes another form that includes the variations in the diagonal components of the dielectric tensor when it is in the form of diagonal matrix. Here it seems to have the dielectric tensor with elements other than diagonal elements and the electromagnetic components propagating in the cladding of a cylindrical waveguide is given as, Fig 4.(a) Cross-section geometry of designed fiber with AMM as cladding.
ɛ=1 ɛ = [ɛ]
E¬z = CJn(K0r) exp (inφ)
[7.1]
Er = -i ( β∂rEz + (ωµn/r) ∂φHz ) / K02
[7.2]
Eφ = -i ( β∂φEz/r - (ωµn/r) ∂rHz ) / K02
[7.3]
H¬z = DJn(K0r) exp (inφ) / K02
[7.4]
Hr = -i ( β∂rHz - (ωɛn/r) ∂φEz ) / K02
[7.5]
Hφ = -i ( β∂φHz/r + (ωɛn/r) ∂rEz ) / K02
[7.6]
where ɛn and µn are the multiples of available number of permittivities and permeabilities in the tensor.
Fig 4.(b) Cross-section geometry of designed fiber with AMM as core.
In this paper, only the change in permittivity is considered and hence the value of µn is considered to be unity. As the effective permittivity tensor of the fiber is changed gradually, the electromagnetic components are also changed ( change in the set of equations from [6.1]-[6.6] into another set of equations as described in [7.1]-[7.6] ) and the negative sign in the equations [7.2], [7.3], [7.5] and [7.6] shows the change in direction of the wave propagation from core to the cladding guidance, which can be explained further with the simulations obtained using Finite element method (FEM).
By deliberate tuning of the effective permittivities of the AMM, the designed optical fiber can provide hollow guidance or core guidance (CG) and surface plasmon (SP) guidance. Here, the normal core guidance is due to the total internal reflection in which the numerical aperture should approach unity. In order to achieve total internal reflection, the angle of incidence of light must be greater than the critical angle of light at the metal interface [29]. If the critical angle is given by θc = Sin-1(Ԑeff1/2) and the Ԑeff is less than air, it supports total internal reflection. This is satisfied only if the effective permittivity approaches zero from positive, which makes the critical angle to approach zero making numerical aperture as unity, which is given by NA = Cos (θc). Naturally, the anisotropic and negative characterization of the permittivity components allows SP guidance in the cladding [18]. This surface propagation is mainly influenced by the parallel component of the effective permittivity which corresponds to AMM.
Fig 5. (b) SP guidance through the hollow core AMM fiber.
The way in which the total internal reflection supports the core guidance, certain resonance condition have to be satisfied to achieve plasmonic propagation. This resonance condition is established when the frequency of incident photons matches the natural frequency of oscillating surface electrons [30], which is supported by the anisotropic charecteristics of the proposed metamaterial. The combination of proposed metal/oxide layer, also provides the possibility of subwavelngth propagation (d < λ) of the incident light, when it acts as core of the fiber.
Fig 6. Sub-wavelength propagation of surface plasmon modes with AMM as core, having the diameter(d) of 200 nm at the incident wavelength of 342 nm (λ). act as a conventional single mode fiber.
Fig 5. (a) Mode propagation in the AMM cladding fiber showing Normal core guidance
A metamaterial core whose diameter less than the wavelength of the incident light can still support propagation of EM waves as shown in the Fig 6. Such transmission is made easier through plasmonic propagation of modes at the resonance frequency between the incident photon and the oscillating electrons at the metal/dielectric interface [31]. This subwavelength geometry could provide further miniaturization of components. Moreover, classical fibers are limited by the greater wavelength compared to their geometry, as a typical single mode fiber has core diameter between 8 and 10.5 µm and cladding diameter of about 125 µm [32]. C. Dispersion characteristics of hollow core AMM fiber for various metal/dielectric proportions The above mode analysis are made, with the equal ratios of proportions of metal/dielectric thickness (Cm = Cd). Following analysis of dispersion characteristics of the proposed AMM
cladding fiber are made for variation in the metal/dielectric thickness (Cm > Cd and Cm < Cd). The dispersion plot is made for the metamaterial cladding fiber, which could act as a conventional hollow core fiber [22] and the dispersion is calculated from the equation [6] as, D = -λ/c * (d2neff /dλ2)
- [6]
where λ is the incident wavelength, c is the velocity of light and neff is the effective mode index of the desired mode. Analyses are made by varying the operating wavelength of the incident light for different composition of metal/dielectric layers. Dispersion in a fiber occurs mainly due to the variation in group velocity of the propagating waves [33]. If a fiber has negative dispersion, it can be used as a dispersion compensation fiber. Fig 7.(a) shows that the curve obtained for Cm = Cd, the dispersion decays exponentially from positive to negative values and the dispersion curve for C m > Cd as shown in the Fig 7.(b) is parabolic. Then Fig 7.(c) shows the exponentially growing dispersion curve for C m
Fig 7. Dispersion characteristics of the AMM cladding fiber for various thickness of metal/ dielectric layers. (a) Cm=Cd (b) Cm>Cd (c) Cm
D. Confinement loss of hollow core AMM fiber During propagation of modes along the fiber, some amount of light does not confine in to the core region. Hence the calculation of confinement loss in an optical fiber plays an important role. Confinement loss is calculated from the imaginary part (Im) of the complex effective index, which occurs due to the imaginary part of parallel effective permittivity, using the equation, Lc = 8.686 k0 Im[neff], where Im is the imaginary part of effective mode index , and 𝑘0 is the free space wave number, which is equal to 2π/λ.
Confinement loss (dB/km)
[3] [4]
0.00006 0.00005 0.00004 0.00003
[5] Cm < C d [6] Cm > Cd [7]
0.00002 0.00001
Cm = C d
0
[8]
300 302 304 306 308 310 312 314 316 318 320 322
[9] [10]
Wavelength (nm) [11] Fig 8. Confinement loss for various proportions of metal/dielectric layer thickness.
The confinement loss for the AMM cladding fiber is shown in the Fig 8. Variation of confinement loss is plotted against the wavelength for different ratios of metal and dielectric in the entire composition of metamaterial. It is obvious from the plot that, the confinement loss decreases as the increase in wavelength irrespective of the thickness proportions of the metal and dielectric layers. It is very interesting to note that the confinement loss is very low in the case, where the values of Cm and Cd are equal and particularly at the wavelength of 323 nm. UV-rays of wavelengths shorter than 325 nm are commercially generated using diode-pumped solid-state lasers, which can be perfectly transmitted through the designed fiber. III. SUMMARY
[12]
[13] [14]
[15]
[16]
[17]
[18]
In summary, a special class of material called anisotropic metamaterial, possessing plasmonic characteristics is used to design an optical fiber. The effective permittivity tensor of this metamaterial is varied to achieve core guidance and surface plasmon propagation by proper tuning of wavelength. The design of fiber in which the same AMM is used as core supporting the subwavelength plasmonic propagation at the wavelength of 342 nm, is also made possible here. The results obtained shows that the designed fiber with metamaterial cladding, supporting the classical core guidance, with equal proportions of metal/dielectric layers provides low dispersion characteristics and has very low confinement loss at the wavelength of 323 nm. This design, mainly focus on the wavelength around 300 nm and has applications in transmitting the ultraviolet rays generated by Ultraviolet Lasers and Ultraviolet LEDs with an advantage of miniature in size.
[19]
REFERENCES
[27]
[1] [2]
Vivek Alwayn, “Fiber-Optic Technologies”, Content 2, Cisco Press, 2004. Reinhold Noé, “Essentials of Modern Optical Fiber Communication”, 2010.
[20] [21] [22]
[23] [24]
[25] [26]
[28] [29]
B. Culshaw and J. Dakin, Eds, “Optical Fiber Sensors: Systems and Applications”, Vol. II, Artech House, 1989. Bahareh Gholamzadeh, and Hooman Nabovati, “Fiber Optic Sensors”, International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering, Vol 2, No 6, 2008. Massood Tabib-Azar, “Integrated Optics, Microstructures, and Sensors”, Page(s): 307-340, 2013. R.F. Kearns and E.E. Basch, “Computer Analysis of Single-Mode Fiber Optic Systems”, GTE Laboratories Incorporated, Page(s): 579-583, 1988. M. Lapine, et al.,”Contemporary notes on metamaterials”, IET Microw. Antennas Propag., 2007. V.G. Veselago, “The electrodynamics of substances with simultaneously negative Values of ɛ and µ”, P.N. Lebedev Physics Institute, Academy of Sciences, U.S.S.R., 517-526, 1964. R. A. Shelby, et al., “Experimental Verification of a Negative Index of Refraction”, Science, vol. 292, 2001. Wenshan Cai, et al., “Optical cloaking with metamaterials”, Nature Photonics, vol 1, 2007. Yi Xiong, et al., “Two-Dimensional Imaging by Far-Field Superlens at Visible Wavelength”, Nano Letters, vol 7, 2007. Hsuan-Hao Liu, et al.,” Leaky Surface Plasmon Polariton Modes at an Interface Between Metal and Uniaxially Anisotropic Materials”, Vol 5, No 6, 2013. A. V Novitsky, “Negative-refractive-index fibres: TEM modes”, Journal of Optics A: Pure and Applied Optics, Vol 8, No 10, 2006. Min Yan, Niels Asger Mortensen, Min Qiu, “Engineering modes in optical fibers with metamaterial”, Frontiers of Optoelectronics in China, Vol 2:153, 2009. Zhang Qi, Tian Jiang and Yijun Feng, “Slow-light propagation in a cylindrical dielectric waveguide with metamaterial cladding”, Journal of Physics D: Applied Physics, Vol 44, Page(s): 475103-475108, 2011. Alessandro Tuniz, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances”, Nature communications, Vol 4, No 2706, 2013. S. Anantha Ramakrishna, et al., “Anisotropic Metamaterial optical fibers: Bessel modes with imaginary orders and nanoporous alumina microtubes”, International Conference on Fibre Optics and Photonics, ISBN: 978-1-55752-882-7, 2014. Dheeraj Pratap, et al., “Anisotropic Metamaterial Optical Fibers”, Optical Society of America, 2014. Sreekanth, K. V. et al. A multiband perfect absorber based on hyperbolic metamaterials. Sci. Rep. 6, 26272; doi: 10.1038/srep26272 (2016). P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals”, Phys. Rev. B, 1972. Edward D Palik, “Handbook of optical constants of solids”, Academic Press: San Diego, CA, Pages: 653-689, 1998. E. William Cowell, et al., “Amorphous multi-component metal/metal oxide nanolaminate metamaterials and devices based thereon”, Publication no: US20140302310-A1, 2014. Min Yan, et al, “Hollow-core infrared fiber incorporating metal-wire metamaterial”, Optical Society of America, 2010. Fabrizio Renna, et al., “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers”, Optical Society of America, 2010. Zoran Jakšić, “Optical Chemical Sensors for Industrial Applications”, International Symposium on Industrial Electronics, 2014. Yongfeng Mei, et al., “Versatile Approach for Integrative and Functionalized Tubes by Strain Engineering of Nanomembranes on Polymers”, Adv. Mater. 20, 4085–4090, 2008. Harrington R F, “Time-harmonic Electromagnetic Fields” Page(s): 5759, New York: Wiley, 2001. Huanyang Chen and C. T. Chan, “Electromagnetic wave manipulation using layered systems”, Phys. Rev. B 78, 054204, 2008. Action Nechibvute, et al., “Modelling Of Optical Waveguide Using COMSOL Multiphysics”, IJERT, Vol 2, Issue 5, 2013.
[30] Junichi Takahara, et al., “Mutual mode control of short- and long-range surface plasmons”, Optical Society of America, 2013. [31] Rashid Zia, et al, “Geometries and materials for subwavelength surface plasmon modes”, Optical Society of America, 2004.
[32] William L. Barnes, “Surface plasmon subwavelength optics”, Nature, vol 424, 2003. [33] Govind P. Agrawal, “Fiber-Optic Communications Systems”, John Wiley & Sons, Inc., Pages 37-45, 2002.
S0030-4026(16)30779-3 http://dx.doi.org/doi:10.1016/j.ijleo.2016.07.014 IJLEO 57934
To appear in: Received date: Revised date: Accepted date:
16-2-2016 4-7-2016 4-7-2016
Please cite this article as: Yamunadevi R., Shanmuga Sundar D., Sivanantha Raja A., Characteristics Analysis of Metamaterial based Optical Fiber, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.07.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Characteristics Analysis of Metamaterial based Optical Fiber R.Yamunadevi, D.Shanmuga sundar and A.Sivanantha Raja * 1
Alagappa Chettiar College of Engineering & Technology, Karaikudi, Tamilnadu *[email protected]
Abstract - Optical fiber plays an important role as a transmission channel in fiber optic communication. In this work, the design of optical fiber using integration of metamaterial which allows waveguidance through subwavelength geometry is proposed. Transmission of information through surface plasmon mediated or through classical core guidance is made possible, with metamaterial as either core or cladding. Here, the alternate combination of Ag/Al2O3 layers are used, which acts as an anisotropic metamaterial (AMM), supporting plasmonic propagation, depending upon the wavelength (around UVRegion). Parameters such as confinement loss and dispersion characteristics are analyzed for different proportions of metal and dielectric layers. Propagation of desired modes are confirmed by the obtained simulation results by Finite element method. Keywords - Metamaterial, Optical fiber, Surface plasmon propagation, Subwavelength geometry.
I. INTRODUCTION Fiber optic systems, in recent days, generate a great interest and have various applications in new communication technologies [1]. This fiber optic communication system greatly depends on optical fiber as a communication channel which helps in transmitting Digital and analog audio/video signals [2] and also has the greater advantage of using it as fiber optic sensors [3]-[5]. Over the past decades, Single mode fibers made-up of silicon, has been proven to provide low loss at the transmission wavelength of 1.55µm [6]. In this paper, attempts have been made to transmit the light of smaller wavelength, (i.e.,) of wavelength around 300nm, that supports the transmission in UV – Region. Metamaterials are the specially classified materials, which can be structured to have unique properties that are not found in natural materials [7], such as backward propagation, negative refraction [8,9]. Therefore, the choice of metamaterial for designing the fiber, makes the transmission at lower wavelength easier. Numerous researches and experiments on metamaterials, has paved a way to important applications such as cloaking devices [10], subdiffraction imaging systems [11] and surface plasmon waveguides [12]. Propagation of electromagnetic waves through the circular waveguides with negative refractive index was experimented to form a metamaterial fiber [13,14]. Metamaterial fibers are then designed for the special applications such as to have zerogroup velocity in the wave propagation at optical frequencies
[15] and also to operate in the frequencies over the range of terahertz region [16]. The concept of anisotropy with metamaterials was also introduced in the fibers to extend their applications [17, 18]. Based on the application for which the metamaterial is to be utilized, one can choose the appropriate metal and metal oxide combinations to form the metamaterials accordingly. The combination of the metal and metal oxide results in the anisotropic characteristics as well as negative index nature then the materials can be used as metamaterials. In some of the papers, they have used Ag and TiO2 combination for the multiband perfect absorber applications [19]. Metamaterials are not limited by type of materials to be used, but their entire characteristics can be decided by the choice of the individual materials used [7]. In this paper, the alternating layers of metal and a metal oxide is used as a metamaterial, which has anisotropic characteristics. Ag and Al2O3 are chosen as the preferred metal and metal oxide, due to the negative index nature of Ag [20] and crystalline nature of Al2O3 [21], which could be easier to develop a negative index medium. Ag and Au are commonly found metals with natural negative index of refraction. Here, we have chosen Ag (Silver) as the metal because of its easy affordable nature than Au (Gold) and the choice of Al2O3 is preferred for its amorphous form that could help in strong anisotropy when combined with Ag (Silver) [22], which could be at ease when extended for a practical implementation from the simulation point of view. The use of metamaterial as either a cladding or core in a hollow fiber helps in both ordinary core guidance [23] and surface plasmon propagation of waves [24] based on the wavelength tuning. This in turn also supports, transmitting the information through subwavelength geometry and hence provides miniaturization advancement in the field of optoelectronic components. Both normal core guidance (Fig 1.a) and surface plasmon propagation (Fig 1.b) for the metamaterial cladding fiber can be obtained at different wavelength. Furthermore, the dispersion characteristics and the confinement loss for three different metal-dielectric proportions are analyzed. Fig 1(c) shows the ray diagram, when the proposed metamaterial is used as core, it acts as a normal single mode fiber, at the core radius less than the propagation wavelength. This AAM
cladding fiber can serve as an effective chemical sensor [25], when the core is filled with gas or liquid.
individual permittivity of the metal and dielectric and also the ratio of thickness of metal and dielectric layer to one another [27]. This effective permittivity of the structured AMM varies according to the wavelength which is obvious from the Fig 3(a) and Fig 3(b) which shows the anisotropy of the designed metamaterial. Careful designing of such metamaterial enables the effective tuning of effective permittivity based on specific wavelength, which stands as the major advantage of AMM. ɛ┴
- Cm ɛ‖
- Cd
Fig. 1. Ray diagram of (a) Hollow core guidance (b) Surface plasmon propagation through AMM cladding and (c) Core propagation when AMM is used as core of the fiber.
II. DESIGN MECHANISMS
The proposed Ag and Al2O3 layers, each of thickness Cm = Cd are stacked alternatively to provide anisotropy. These stacked layers shown in Fig.2 can be rolled-up through nanotechnology [26] to provide hollow core AMM cladding fiber. The stacked layers may also be designed to have variations in the ratios of metal/dielectric thickness. This should be carefully designed, so that their parameters can be altered to desired wavelength. An Electromagnetic (EM) wave propagating in a cylindrical waveguide takes the form of Maxwell’s equation as follows, E = E0 (r,φ) exp [i(βz-ωt)]
- [1]
H = H0 (r,φ) exp [i(βz-ωt)]
- [2]
where ω and β are the frequency and the wavenumber of the EM wave propagating inside the fiber, and (r,φ,z) are the cylindrical co-ordinates arises due to the planar to cylindrical conversion of stacked layers, which have the potential to act as an efficient optical fiber. An electromagnetic wave propagating inside a fiber has two important parameters to be considered, which are permittivity (ɛ) and permeability (µ). Limiting the magnetic response of the cladding metamaterial, we assume µ = 1, and the permittivity tensor is given by,
Fig 2. Lattice diagram of the alternatively stacked layers (Ag/Al2O3), where Cm and Cd are the ratio of proportion of metal and dielectric respectively and ┴ and ‖ represents the perpendicular and parallel components of the structure.
10 0 Permittivity
A. Effective permittivities of layered AMM
0
eps_pr eps_pl
Wavelength (nm) Fig 3.(a) Variation of the calculated real part of perpendicular and parallel effective permittivity of AMM with respect to the wavelength
25
2
ɛ┴ sin (φ) + ɛ‖ cos (φ) 0 -[3] 0
-30
-50
ɛ‖
where [ɛeff] is the effective permittivity tensor and ɛ┴ , ɛ‖ are the perpendicular and parallel components of the effective permittivity. These perpendicular and parallel components of the effective permittivity is given by, Ԑ┴eff
= (Cm + Cd) Ԑm Ԑd / (Cm Ԑd + Cd Ԑm) - [4]
Ԑ‖eff
= (Cm Ԑm + Cd Ԑd)/ (Cm + Cd)
- [5]
where Ԑm and Ԑd are the permittivity of the metal and dielectric respectively. Cm and Cd are the ratios of metal and dielectric respectively in the entire composition. From equation [4] and equation [5], it is clear that, the perpendicular and parallel components of the effective permittivity depends on the
20 Permittivity
[ɛ ]= (ɛ┴ - ɛ‖) sin (φ) cos (φ)
2
300 310 320 330 340 350 360 380
-20
-40
ɛ┴ cos2 (φ) + ɛ‖ sin2 (φ) (ɛ┴ - ɛ‖) sin (φ) cos (φ) 0 eff
-10
15 10 5
eps_pr(img) eps_pl(img)
0 300 310 320 330 340 350 360 370 Wavelength (nm) Fig 3.(b) Variation of the calculated imaginary part of perpendicular and parallel effective permittivities of AMM with respect to the wavelength
A hollow core fiber with an inner radius of 2 μm, integrating a metamaterial as the cladding layer with a thickness of 500 nm is designed. The effective permittivity tensor of the cladding layer, which is consecutively related to the individual permittivities of metal and dilectric layer is varied based on the corresponding wavelength of incidence. This change in the effective permittivity provides the classical waveguiding or plasmonic propagation at particular wavelength. Particularly, at the wavelength where ɛ┴ is positive and ɛ‖ is negative, the incident light is guided through the core and surface propagation is achieved at the wavelength where both parallel and perpendicular components of the effective permittivities are positive. Fiber with the proposed metamaterial as core of 200 nm supports subwavelength propagation. The 2D cross-section of the designed AMM cladding fiber is shown in Fig 4(a) and that of AMM core fiber is shown in the Fig 4(b). ɛ=1 ɛ = [ɛ]
The material with loaded effective permittivity acts as a metamaterial. This effective permittivity tensor is anisotropic in nature and hence supports anisotropy. B. Mode analysis of Hollow core AMM fiber and AMM core fiber In cylindrical coordinate systems, Bessel functions of various kinds ruled by Maxwell’s equations [28] are used to describe the electromagnetic components in the core of a cylindrical waveguide as described as follows, E¬z = AJn(K0r) exp (inφ)
[6.1]
Er = i ( β∂rEz + (ωµ0/r) ∂φHz ) / K02
[6.2]
Eφ = i ( β∂φEz/r - (ωµ0/r) ∂rHz ) / K02
[6.3]
H¬z = BJn(K0r) exp (inφ)
[6.4]
Hr = i ( β∂rHz - (ωɛ0/r) ∂φEz ) / K02
[6.5]
Hφ = i ( β∂φHz/r + (ωɛ0/r) ∂rEz ) / K02
[6.6]
where K0 = k0(ɛd – neff2)1/2 and neff = β/k0, k0 is the wavenumber in free space respectively. The above set of equations from [6.1] to [6.6] describes the EM components for a wave inside the core of the fiber, which takes another form that includes the variations in the diagonal components of the dielectric tensor when it is in the form of diagonal matrix. Here it seems to have the dielectric tensor with elements other than diagonal elements and the electromagnetic components propagating in the cladding of a cylindrical waveguide is given as, Fig 4.(a) Cross-section geometry of designed fiber with AMM as cladding.
ɛ=1 ɛ = [ɛ]
E¬z = CJn(K0r) exp (inφ)
[7.1]
Er = -i ( β∂rEz + (ωµn/r) ∂φHz ) / K02
[7.2]
Eφ = -i ( β∂φEz/r - (ωµn/r) ∂rHz ) / K02
[7.3]
H¬z = DJn(K0r) exp (inφ) / K02
[7.4]
Hr = -i ( β∂rHz - (ωɛn/r) ∂φEz ) / K02
[7.5]
Hφ = -i ( β∂φHz/r + (ωɛn/r) ∂rEz ) / K02
[7.6]
where ɛn and µn are the multiples of available number of permittivities and permeabilities in the tensor.
Fig 4.(b) Cross-section geometry of designed fiber with AMM as core.
In this paper, only the change in permittivity is considered and hence the value of µn is considered to be unity. As the effective permittivity tensor of the fiber is changed gradually, the electromagnetic components are also changed ( change in the set of equations from [6.1]-[6.6] into another set of equations as described in [7.1]-[7.6] ) and the negative sign in the equations [7.2], [7.3], [7.5] and [7.6] shows the change in direction of the wave propagation from core to the cladding guidance, which can be explained further with the simulations obtained using Finite element method (FEM).
By deliberate tuning of the effective permittivities of the AMM, the designed optical fiber can provide hollow guidance or core guidance (CG) and surface plasmon (SP) guidance. Here, the normal core guidance is due to the total internal reflection in which the numerical aperture should approach unity. In order to achieve total internal reflection, the angle of incidence of light must be greater than the critical angle of light at the metal interface [29]. If the critical angle is given by θc = Sin-1(Ԑeff1/2) and the Ԑeff is less than air, it supports total internal reflection. This is satisfied only if the effective permittivity approaches zero from positive, which makes the critical angle to approach zero making numerical aperture as unity, which is given by NA = Cos (θc). Naturally, the anisotropic and negative characterization of the permittivity components allows SP guidance in the cladding [18]. This surface propagation is mainly influenced by the parallel component of the effective permittivity which corresponds to AMM.
Fig 5. (b) SP guidance through the hollow core AMM fiber.
The way in which the total internal reflection supports the core guidance, certain resonance condition have to be satisfied to achieve plasmonic propagation. This resonance condition is established when the frequency of incident photons matches the natural frequency of oscillating surface electrons [30], which is supported by the anisotropic charecteristics of the proposed metamaterial. The combination of proposed metal/oxide layer, also provides the possibility of subwavelngth propagation (d < λ) of the incident light, when it acts as core of the fiber.
Fig 6. Sub-wavelength propagation of surface plasmon modes with AMM as core, having the diameter(d) of 200 nm at the incident wavelength of 342 nm (λ). act as a conventional single mode fiber.
Fig 5. (a) Mode propagation in the AMM cladding fiber showing Normal core guidance
A metamaterial core whose diameter less than the wavelength of the incident light can still support propagation of EM waves as shown in the Fig 6. Such transmission is made easier through plasmonic propagation of modes at the resonance frequency between the incident photon and the oscillating electrons at the metal/dielectric interface [31]. This subwavelength geometry could provide further miniaturization of components. Moreover, classical fibers are limited by the greater wavelength compared to their geometry, as a typical single mode fiber has core diameter between 8 and 10.5 µm and cladding diameter of about 125 µm [32]. C. Dispersion characteristics of hollow core AMM fiber for various metal/dielectric proportions The above mode analysis are made, with the equal ratios of proportions of metal/dielectric thickness (Cm = Cd). Following analysis of dispersion characteristics of the proposed AMM
cladding fiber are made for variation in the metal/dielectric thickness (Cm > Cd and Cm < Cd). The dispersion plot is made for the metamaterial cladding fiber, which could act as a conventional hollow core fiber [22] and the dispersion is calculated from the equation [6] as, D = -λ/c * (d2neff /dλ2)
- [6]
where λ is the incident wavelength, c is the velocity of light and neff is the effective mode index of the desired mode. Analyses are made by varying the operating wavelength of the incident light for different composition of metal/dielectric layers. Dispersion in a fiber occurs mainly due to the variation in group velocity of the propagating waves [33]. If a fiber has negative dispersion, it can be used as a dispersion compensation fiber. Fig 7.(a) shows that the curve obtained for Cm = Cd, the dispersion decays exponentially from positive to negative values and the dispersion curve for C m > Cd as shown in the Fig 7.(b) is parabolic. Then Fig 7.(c) shows the exponentially growing dispersion curve for C m
Fig 7. Dispersion characteristics of the AMM cladding fiber for various thickness of metal/ dielectric layers. (a) Cm=Cd (b) Cm>Cd (c) Cm
D. Confinement loss of hollow core AMM fiber During propagation of modes along the fiber, some amount of light does not confine in to the core region. Hence the calculation of confinement loss in an optical fiber plays an important role. Confinement loss is calculated from the imaginary part (Im) of the complex effective index, which occurs due to the imaginary part of parallel effective permittivity, using the equation, Lc = 8.686 k0 Im[neff], where Im is the imaginary part of effective mode index , and 𝑘0 is the free space wave number, which is equal to 2π/λ.
Confinement loss (dB/km)
[3] [4]
0.00006 0.00005 0.00004 0.00003
[5] Cm < C d [6] Cm > Cd [7]
0.00002 0.00001
Cm = C d
0
[8]
300 302 304 306 308 310 312 314 316 318 320 322
[9] [10]
Wavelength (nm) [11] Fig 8. Confinement loss for various proportions of metal/dielectric layer thickness.
The confinement loss for the AMM cladding fiber is shown in the Fig 8. Variation of confinement loss is plotted against the wavelength for different ratios of metal and dielectric in the entire composition of metamaterial. It is obvious from the plot that, the confinement loss decreases as the increase in wavelength irrespective of the thickness proportions of the metal and dielectric layers. It is very interesting to note that the confinement loss is very low in the case, where the values of Cm and Cd are equal and particularly at the wavelength of 323 nm. UV-rays of wavelengths shorter than 325 nm are commercially generated using diode-pumped solid-state lasers, which can be perfectly transmitted through the designed fiber. III. SUMMARY
[12]
[13] [14]
[15]
[16]
[17]
[18]
In summary, a special class of material called anisotropic metamaterial, possessing plasmonic characteristics is used to design an optical fiber. The effective permittivity tensor of this metamaterial is varied to achieve core guidance and surface plasmon propagation by proper tuning of wavelength. The design of fiber in which the same AMM is used as core supporting the subwavelength plasmonic propagation at the wavelength of 342 nm, is also made possible here. The results obtained shows that the designed fiber with metamaterial cladding, supporting the classical core guidance, with equal proportions of metal/dielectric layers provides low dispersion characteristics and has very low confinement loss at the wavelength of 323 nm. This design, mainly focus on the wavelength around 300 nm and has applications in transmitting the ultraviolet rays generated by Ultraviolet Lasers and Ultraviolet LEDs with an advantage of miniature in size.
[19]
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