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A nonlinear photonic crystal fiber for liquid sensing application with high birefringence and low confinement loss
Sensing and Bio-Sensing Research 22 (2019) 100252
Contents lists available at ScienceDirect
Sensing and Bio-Sensing Research journal homepage: www.elsevier.com/locate/sbsr
A nonlinear photonic crystal fiber for liquid sensing application with high birefringence and low confinement loss
T
Md. Faizul Huq Arifa,d, , Mohammad Mobarak Hossainc,d, Nazrul Islamb, Shah Mostafa Khaleda,d ⁎
a
Institute of Information Technology (IIT), University of Dhaka, Dhaka 1000, Bangladesh Department of Information and Communication Technology (ICT), Mawlana Bhashani Science and Technology University, Santosh, Tangail 1902, Bangladesh c Department of Computer Science and Engineering (CSE), Dhaka University of Engineering and Technology (DUET), Gazipur, Dhaka, Bangladesh d Researcher, SenSyss, Bangladesh b
ARTICLE INFO
ABSTRACT
Keywords: Photonic Crystal Fiber Nonlinearity Birefringence Sensitivity Confinement loss Effective Area
This paper presents a nonlinear Photonic Crystal Fiber (PCF) based sensor to detect liquid analytes. An extensive analysis has been presented at wide range of wavelength (0.6 μm−1.6 μm) in order to investigate the impact of some design parameters. The numerical investigation has been done using the full vector Finite Element Method (FEM). The proposed model provides an outstanding nonlinear coefficient value with high birefringence, high sensitivity, and low confinement loss. The designed model can be used in sensing and bio-sensing research and their applications.
1. Introduction Photonic Crystal Fiber (PCF) is a promising technology having lots of advantages over the conventional optical fiber. PCF is a new class of optical fiber which is based on the properties of photonic crystals. It can change the way light is generated, delivered and used. PCF technology has gained attention to the researchers because of its design flexibility and the potentiality to develop different kinds of applications in both telecom and non-telecom sectors [1]. Therefore, PCF is considered as the next generation optical fiber. Classical optical fibers have some fundamental limitations related to their structures. Photonic Crystal Fiber (PCF), with their structural features removes those limitations. Photonic crystals are periodic dielectric structures. PCF is designed with periodic arrangement of microstructure holes which affect the motion of Photons. Light is guided inside the PCF by either modified total internal reflection or photonic band gap guidance. The background material is often developed with pure silica and the low index region is generally provided by air holes running along the length of the fiber. In information processing, nonlinear optics has emerged as one of the most attractive field of study [1]. The main advantage of using nonlinear medium is that their nonlinear response is ultrafast. Moreover, highly nonlinear optical fiber leads to novel nonlinear effects. In optical fiber, a narrow core and high doping levels can reduce effective area and enhance nonlinearity. Hence, PCF can obtain high
⁎
nonlinearity. Because of its high sensitivity, low confinement loss, high birefringence, nonlinearity and flexibility in design, PCF can be used in varieties of applications in the field of fiber-optics [1]. PCF is finding applications in fiber optic communication, nonlinear devices, fiber lasers, high power transmission, highly sensitive chemical sensors, and many other areas. The advancement of nanotechnology allows us to obtain exceptional propagation properties by choosing appropriate design parameters. Due to the design flexibility of PCF, desired propagation properties can be obtained by changing lattice structure and some parameters like pitch (hole to hole distance), diameter of air holes and the number of air hole rings in the cladding region. Various research studies have been demonstrated to enhance propagation characteristics of PCF [2–4]. The variation of geometries of the PCF structure has a great influence on the optical properties of PCFs [5]. In addition various shapes of air holes have also influence on changing the guiding properties of the fiber [5]. Ademgil. [6] proposed a highly birefringent and nonlinear PCF structure with supplementary liquid filled air holes in the core region. The article [7] introduced a PCF structure with different orientation of elliptical air holes in the core and cladding. Kim et al. [4] have theoretically demonstrated a PCF structure with elliptical air holes to get high birefringence with dispersion control simultaneously. According to the article [5], elliptical air holes in the core reduce the relative sensitivity. However, elliptical holes in both core and cladding are
Corresponding author. E-mail address: [email protected] (Md. F.H. Arif).
https://doi.org/10.1016/j.sbsr.2018.100252 Received 8 November 2018; Received in revised form 3 December 2018; Accepted 4 December 2018 2214-1804/ © 2018 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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responsible to increase birefringence. In this research, an evanescent hexagonal PCF structure with an elliptical shaped hole in the core is investigated for liquid sensing applications. Moreover, the effect of the orientation of the elliptical hole is analyzed. In order to obtain high sensitivity, high birefringence, high nonlinearity and low confinement loss simultaneously, the proposed design has been demonstrated. Furthermore, the effect of the variation of operating wavelength and the ellipticity of the core hole are analyzed for the proposed structure. 2. Design of the proposed PCF Fig. 1. The cross-sectional view of the proposed designs: (a) PCF1: Horizontally aligned core and (b) PCF2: Vertically aligned core.
In this work, an index guided PCF structure has been designed with a hexagonal arrangement of circular air holes in the cladding. In the core there is an infiltrated elliptic shaped hole. The background material is pure silica (SiO2). The refractive index of the fused silica and analyte infiltrated in the core hole are governed by the Sellmeier's equation [8,9]. 3
n ( )2 = 1 + i=1
Bi
2
2
Ci
Here, B1, B2, B3 and C1, C2, C3 are Sellmeier's coefficients for specific material. The refractive index is n and λ is the operating wavelength. Sellmeier constants values for silica and water have been presented in Table 1. The core hole is infiltrated with the targeted material. Generally, Water or Ethanol are treated as primary liquids. In this study, the numerical study has been done for Water. The cladding assembles four rings of air holes, which are arranged in hexagonal configuration. The diameter (d) of each holes is kept same. In this structure the hole to hole distance (also known as pitch) in the cladding is set to Ʌ=1.7 μm, and the air filling ratio, d/Ʌ=0.9. Fig. 1 shows the cross-sectional view of the designed PCF structures. It can be seen from the Fig. 1(a) that elliptical hole in the core is horizontally aligned and the structure in the Fig. 1(b) shows that it has a vertically aligned elliptical hole in the core. The lengths of the semi-major axis and the semi-minor axis of the elliptical core hole are A and B respectively, where the area of the hole is 0.9 μm2. The ellipticity ε is calculated with the following equation:
=
A
B A
=1
Fig. 2. Infiltrated elliptical hole in the core.
2.1. Principles of operation Full vectorial Finite Element Method (FEM) with the Perfectly Match Layer (PML) boundary condition is applied for numerical investigation. Fig. 3 illustrates a one quarter of the computational window together with a Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundary conditions. In addition, an anisotropic Perfectly Matched Layer (PML) is placed outside the outermost ring of holes in order to evaluate the confinement loss and to reduce the computational window [11]. Using mesh analysis the cross section of the PCFs is sub divided into some triangular subspaces. In this simulation, the fiber is sub-divided into 11,580 triangular elements with 104761 degrees of freedom. Using Finite Element Method (FEM) the Maxwell's equations are solved by accounting the neighboring subspaces. The following equations can be derived from the Maxwell's equations [12].
B A
where, A ≥ B. In the designed PCF, the ellipticity is set to, ε=0.55. The structure of the core hole is presented in the Fig. 2. The index refraction of the cladding holes are set to 1. It is worth noting that the lower refractive index and higher air filling ratio around the core provides strong confinement ability. Some electro-magnetic waves scattered in outer boundary regions of PCF. In this regard, circular anisotropic perfectly matched layered structure is applied to avoid this.
× ([S ]
B1 C1(μm2) B2 C2(μm2) B3 C3(μm2)
Sellmeier constants values Silica
Water
0.696166300 4.67914826 × 10−3 0.407942600 1.35120631 × 10−2 0.897479400 97.9340025
0.75831 0.01007 0.08495 8.91377 – –
× E )
K 02 n2 [S ] E = 0
where, E is the electric field vector and λ is the operating wavelength. The free-space wavenumber K0 = 2π/λ, and [S] and [S]−1 are PML matrix and inverse PML Matrix respectively. The propagation constant β can be represented by the following equation [12].
Table 1 Sellmeier Constants for silica and water at a temperature of 20 °C [10] Parameters
1
= neff k 0 Polarization and propagation of light effect on the refractive index. Therefore, refractive indexes of the two fundamental modes will not be the same. The difference between the two fundamental modes is known as birefringence. After calculating the complex effective index (neff), the modal birefringence can be determined by the following equation [10]. 2
Sensing and Bio-Sensing Research 22 (2019) 100252
Md. F.H. Arif et al.
Fig. 3. Computational window with applied boundary condition and FEM mesh for (a) PCF1 and (b) PCF2. x |neff
B
neffy |
Aeff =
where neffx and neffy are the effective refractive index for x and y polarized fundamental modes respectively. A small portion of leakage of light or confinement loss (dB/m) may occur due to the finite number of air holes in the cladding part. This is an additional form of loss which generally occurs in single material fibers, particularly in PCFs. This confinement loss Lc (dB/m) can be obtained by the imaginary part of the effective refractive index, neff by the following equation [10].
Lc =
Aeff =
=
r
m lc ]
nr f neff
where, neff is the modal effective index and nr represents the refractive index of the material to be sensed. The power fraction is denoted by f which can be defined as [14],
f=
Re (Ex Hy
Ey Hx )
total
Re (Ex Hy
Ey Hx )
|H|4 dxdy
2
n2 Aeff
This research is based on liquid sensing application with PCF. In this study we selected Water (n = 1.3201 at λ = 1.3 μm) as a targeted material for analyzing the structure. The modal analysis is performed in the x-y plane of the cross-section as the wave propagates in the z direction. Fig. 4 shows the fundamental mode field distribution of the proposed PCF with colour indicator scale at the wavelength of λ = 1.3 μm for the x-mode and y-mode polarization respectively. According to this 2D plots from the Fig. 4 it can be justified that the field has confined well in the core. Initially, the impact of the operating wavelength on the effective refractive index (x polarized) is shown in the Fig. 5. It can be seen from the figure that the effective refractive index of the fundamental mode is decreasing with increasing the wavelength for the analyte to be detected. It seems that the effective refractive indexes are similar for both PCF structures. Fig. 6 shows the birefringence values for the corresponding wavelength. It is found that at the wavelength λ = 1.3 μm the magnitude of the index difference or birefringence of PCF1 is 5.09 × 10−3. At the same wavelength the birefringence of PCF2 is 4.23 × 10−3. In addition, it is clearly seen that the value of birefringence decreases with the increase of the wavelength of light. The attenuation caused by the geometry of waveguide is called confinement loss. Fig. 7 describes the variation of confinement loss with the operating wavelength of light. It demonstrates that the confinement
m lc
sample
|H|2 dxdy ) 2
3. Results and discussion
The relative sensitivity r is calculated by the following equation [14].
r=
(
where, n2 is the nonlinear refractive index. The higher order of nonlinearity is responsible for super-continuum generation (SCG). For the calculation of the nonlinearity of the nonlinearity index of SiO2 is taken as n2=3.2 × 10−20 m2/W.
where I(f) and I0(f) are input and output intensities of light, r is the relative sensitivity, and αm is the absorption of light. The channel length is lc and f is the operating frequency. The absorbance of the targeted material can be obtained by [12,13],
I = I0
|E|4 dxdy
where Et and Ht are transverse electric field vector and magnetic field vector respectively. In high bit rate data transmission system large effective mode area is required. However, in nonlinear applications lower effective mode area is required. Nonlinearity is closely related to effective area of the fiber. The nonlinear coefficient can be calculated by the following equation [15]:
The relative sensitivity of PCF based sensor can be obtained from the intensity of light interaction with the analyte to be sensed. The amount of light interaction with the material to be sensed can be measured through the absorption coefficient at a particular frequency. The amount of light attenuation with the intensity of light absorbance of the evanescent field can be measured by [12,13],
A = log
|E|2 dxdy )2
Or
40 × 106 i Im {neff }, i = x, y ln(10)
I (f ) = I0 (f ) exp[ r
(
× 100
Here Ex, Ey and HxHy are electric field and magnetic field of the guided mode respectively. The effective mode area is related to the effective area of the fiber core area, which is computed using transverse electric field and magnetic field vector of the whole cross sectional area of the PCF. It is generally considered as the light carrying region. The effective area of the fiber core Aeff is defined by the following equation [15]. 3
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Fig. 4. Field distributions for (a) x-polarization mode and (b) y-polarization mode at λ = 1.3 μm. Red colour represents the highest intensity and blue represents the lowest. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The wavelength depending effective mode index of the fundamental mode (X-Polarization).
Fig. 6. Variation of the birefringence of the proposed designs as a function of operating wavelength.
loss increases with the increase of the wavelength for the both PCF structures. The sensitivity curves are increasing with the increase of wavelength. Fig. 8 illustrates the sensitivity response of the proposed PCF for water. It is clearly visualized that the sensitivity responses of 41.36% and 40.19% are gained in the PCF1 and PCF2 respectively at the wavelength λ = 1.3 μm. Highly nonlinear PCFs are the most desirable for many practical
applications. The nonlinear properties of PCF depend on the core diameter which determines the effect of the mode area [16]. Fig. 9 illustrates the nonlinear coefficient of the proposed designs of PCF. It can be seen that the PCF2 shows higher nonlinearity than the PCF1. There is a great impact of the ellipticity of the core hole to the performance of the fiber. It is worth noting that the cladding air holes are perfectly circular when ε = 0. 4
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Fig. 7. Variation of confinement loss (dB/m) as a function of operating wavelength.
Fig. 9. Nonlinear coefficient of the proposed PCF structure as a function of operating wavelength.
Fig. 8. Variation of sensitivity coefficient as a function of operating wavelength.
Fig. 10. Variation of birefringence as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm.
Fig. 10 shows the effect of ellipticity є on the birefringence, where the wavelength is fixed to =1.3 μm. It can be seen that the birefringence is increasing with the increase of ellipticity. Fig. 11 depicts that confinement loss is gradually increasing with the increase of ellipticity. It also shows that there is no significant difference between PCF1 and PCF2 in terms of confinement loss. Fig. 12 illustrates that the sensitivity coefficient is gradually decreasing with the increase of ellipticity. The obtained maximum values of relative sensitivity are 43.80% and 43.20% for PCF1 and PCF2 respectively, when the ellipticity is 0.25. Fig. 13 shows that the nonlinear coefficient is increasing with the increase of ellipticity. PCF2 exhibits outstanding values of nonlinear coefficient. The obtained maximum values of nonlinear coefficients are 72 and 76 for PCF1 and PCF2 respectively, when the ellipticity is 0.65. The overall performance analysis illustrates that except nonlinearity, the PCF with horizontally aligned elliptical hole (PCF1) shows better performance than the PCF2. Therefore, the geometries of PCF1 are optimized in this research work. In this research, our outcomes are expected to provide an extensive literature review to describe the fabrication process of the proposed
PCF structures. Several techniques are available for selectively filling the air holes with analytes. In terms of analyte filling in the core hole, the complexity is increased in the core area. However, the article [17] presented a unique method which allows for selectively filling the PCF holes with analytes. Moreover, several methods have been developed for the fabrication of microstructured fiber, like stack and draw [18],drilling [19], extrusion [20], sol-gel casting [21] etc. Stack and draw method can be used to closest-packed geometries. Drilling technique is generally limited to small number of holes. Extrusion technique provides freedom in design, but it is limited to soft glasses for which the material loss values are excessively high. Bise et al. [21] introduced a sol-gel method to fabricate PCFs with complex structure. In addition, sol-gel method provides flexibility in design which is essential for the proposed PCFs. Recently, Luo et al. [22] and Gerosa et al. [23] have experimentally shown that it is possible to fabricate the PCF structures with liquid filled core/cladding. In this regard, our proposed PCFs can be fabricated with current available nanotechnology. After forming the performance graphs of the proposed PCFs, it is needed to check the accuracy of the design. According to the article [24], in a standard fiber draw ± 1% variations in fiber global 5
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Fig. 11. variation of confinement loss as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm.
Fig. 13. Variation of nonlinear coefficient as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm. Table 2 Variation of overall performance of the PCF1 for the changes in global parameters at the wavelength λ = 1.3 μm. Variations of global parameters (%)
Birefringence
Confinement loss (dB/m)
Sensitivity (%)
Nonlinearity (W−1Km−1)
−3 −2 -1 Optimum +1 +2 +3
0.004992 0.005054 0.005074 0.00509 0.00511 0.00513 0.005165
2.84489E-10 2.77079E−10 2.45366E-10 2.16552E-10 9.45906E-11 2.42314E-11 2.31813E-11
41.90692314 41.73294961 41.55333198 41.3670971 40.97974722 40.98046652 40.77808544
77.73201 76.73698 75.74113 74.75272 73.64572 72.81018 71.84957
Table 3 Comparison of the performances in terms of birefringence, confinement loss, sensitivity and nonlinearity among the proposed PCF1 and prior PCFs for Water at the wavelength λ = 1.3 μm.
Fig. 12. Analysis of sensitivity performance as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm.
parameter may occur during the fabrication process. The article [21] shows that in the sol-gel technique there may occur variation in hole size is less than 3% over 2 km spans for the fabrication of microstructure optical fiber. In order to account for this structural variation, the global parameter is varied up to ± 3% from their optimum values. From the Table 2 it can be observed that the overall performance in terms of birefringence, confinement loss, sensitivity and nonlinearity are affected by the variation in global parameters. Table 3 shows the comparative performance between our proposed PCF1 and the PCF structures proposed in the articles [6,7], in terms of Water as a targeted material. The proposed PCF is such that it provides a high birefringence, high relative sensitivity, high nonlinearity and low confinement loss for the entire spectral range compared to the prior PCFs. Therefore, this model is highly applicable for sensing and biomedical imaging applications.
PCFs
Birefringence
Confinement loss (dB/m)
Sensitivity (%)
Nonlinearity (W−1Km−1)
Ref. [6] Ref. [7] Proposed PCF1
0.00085 0.002700 0.00509
6 × 10−1 1.10 × 10−1 2.16552E-10
6 21 41.3670971
– – 74.75272
addition, it is found that there is a significant effect on the overall performance of the PCF for the variation of ellipticity of the core hole. A bunch of tiny elliptical air holes in the core may increase birefringence more, but it will add fabrication complexity. Considering the reduction of fabrication complexity and maintaining the critical trade-off between sensitivity and nonlinearity we have optimized horizontally aligned core hole. According to the numerical discussion, both PCFs show excellent performance in terms of nonlinearity and the values are 74.75272 and 84.51089264 for PCF1 and PCF2 respectively (λ = 1.3 μm). It may open a new window of research in the field of nonlinear optics and their applications.
4. Conclusion To summarize, we have successfully demonstrated the effects of the elliptical shaped infiltrated hole in the core. Moreover, a brief comparative study is done on the alignment of the elliptical hole. In
Conflict of interest All authors contributed equally. There is no conflict of interest. 6
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Acknowledgement
Photonics, 2009, May73570Q. [12] M.F.H. Arif, K. Ahmed, S. Asaduzzaman, M.A.K. Azad, Design and optimization of photonic crystal fiber for liquid sensing applications, Photonic Sensors 6 (3) (2016) 279–288. [13] M.S. Islam, J. Sultana, A. Dinovitser, K. Ahmed, M.R. Islam, M. Faisal, B.W.H. Ng, D. Abbott, A novel Zeonex based photonic sensor for alcohol detection in beverages, Telecommunications and Photonics (ICTP), 2017 IEEE International Conference, IEEE, 2017, Dec., pp. 114–118. [14] C.M. Cordeiro, M.A. Franco, G. Chesini, E.C. Barretto, R. Lwin, C.B. Cruz, M.C. Large, Microstructured-core optical fibre for evanescent sensing applications, Opt. Express 14 (26) (2006) 13056–13066. [15] R.A. Aoni, R. Ahmed, M.M. Alam, S.A. Razzak, Optimum design of a nearly zero ultra-flattened dispersion with lower confinement loss photonic crystal fibers for communication systems, Int. J. Sci. Eng. Res. 4 (2013) 1–4. [16] B.K. Paul, S. Chakma, M.A. Khalek, K. Ahmed, Silicon nano crystal filled ellipse core based quasi photonic crystal fiber with birefringence and very high nonlinearity, Chin. J. Phys. 56 (6) (2018) 2782–2788. [17] Y. Huang, Y. Xu, A. Yariv, Fabrication of functional microstructured optical fibers through a selective-filling technique, Appl. Phys. Lett. 85 (22) (2004) 5182–5184. [18] J. Broeng, D. Mogilevstev, S.E. Barkou, A. Bjarklev, Photonic crystal fibers: a new class of optical waveguides, Opt. Fiber Technol. 5 (3) (1999) 305–330. [19] M.N. Petrovich, A. Van Brakel, F. Poletti, K. Mukasa, E. Austin, V. Finazzi, P. Petropoulos, E. O'Driscoll, M. Watson, T. Delmonte, T.M. Monro, Microstructured fibers for sensing applications, Photonic Crystals and Photonic Crystal Fibers for Sensing Applications, Vol. 6005 International Society for Optics and Photonics, 2005, November60050E. [20] H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R.C. Moore, K. Frampton, F. Koizumi, D.J. Richardson, T.M. Monro, Bismuth glass holey fibers with high nonlinearity, Opt. Express 12 (21) (2004) 5082–5087. [21] R.T. Bise, D. Trevor, Solgel-derived microstructured fibers: Fabrication and characterization, Optical Fiber Communication Conference (p. OWL6), Optical Society of America, 2005, Mar. [22] M. Luo, Y.G. Liu, Z. Wang, T. Han, Z. Wu, J. Guo, W. Huang, Twin-resonancecoupling and high sensitivity sensing characteristics of a selectively fluid-filled microstructured optical fiber, Opt. Express 21 (25) (2013) 30911–30917. [23] R.M. Gerosa, D.H. Spadoti, C.J. de Matos, L.D.S. Menezes, M.A. Franco, Efficient and short-range light coupling to index-matched liquid-filled hole in a solid-core photonic crystal fiber, Opt. Express 19 (24) (2011) 24687–24698. [24] F. Poletti, V. Finazzi, T.M. Monro, N.G. Broderick, V. Tse, D.J. Richardson, Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers, Opt. Express 13 (10) (2005) 3728–3736.
This research is supported by the fellowship from ICT division, Ministry of posts, Telecommunications and Information Technology, Bangladesh. Fellowship No- 56.00.000.028.33.073.16-50. References [1] M.F.H. Arif, M.J.H. Biddut, A new structure of photonic crystal fiber with high sensitivity, high nonlinearity, high birefringence and low confinement loss for liquid analyte sensing applications, Sens. Bio-Sens. Res. 12 (2017) 8–14. [2] K. Saitoh, M. Koshiba, T. Hasegawa, E. Sasaoka, Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion, Opt. Express 11 (8) (2003) 843–852. [3] M.J. Steel, R.M. Osgood, Elliptical-hole photonic crystal fibers, Opt. Lett. 26 (4) (2001) 229–231. [4] S.E. Kim, B.H. Kim, C.G. Lee, S. Lee, K. Oh, C.S. Kee, Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion, Opt. Express 20 (2) (2012) 1385–1391. [5] S. Rana, N. Kandadai, H. Subbaraman, A highly sensitive, polarization maintaining photonic crystal fiber sensor operating in the THz regime, Photonics, Vol. 5 (4) Multidisciplinary Digital Publishing Institute, 2018, Oct, p. 40. [6] H. Ademgil, S. Haxha, Highly birefringent nonlinear PCF for optical sensing of analytes in aqueous solutions, Optik Int. J. Light Electron Optics 127 (16) (2016) 6653–6660. [7] H. Ademgil, S. Haxha, PCF based sensor with high sensitivity, high birefringence and low confinement losses for liquid analyte sensing applications, Sensors 15 (12) (2015) 31833–31842. [8] K. Saitoh, M. Koshiba, Single-polarization single-mode photonic crystal fibers, IEEE Photon. Technol. Lett. 15 (10) (2003) 1384–1386. [9] Absar, R., Fatema, S., Reja, M.I. and Akhtar, J., Elliptically infiltrated core nonlinear photonic crystal fiber with two zero dispersion wavelengths and ultra high birefringence for supercontinuum generation. [10] M.F.H. Arif, M.J.H. Biddut, Enhancement of relative sensitivity of photonic crystal fiber with high birefringence and low confinement loss, Optik Int. J. Light Electron Optics 131 (2017) 697–704. [11] J. Kanka, Dispersion optimization of nonlinear glass photonic crystal fibers and impact of fabrication tolerances on their telecom nonlinear applications performance, Photonic Crystal Fibers III, Vol. 7357 International Society for Optics and
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Contents lists available at ScienceDirect
Sensing and Bio-Sensing Research journal homepage: www.elsevier.com/locate/sbsr
A nonlinear photonic crystal fiber for liquid sensing application with high birefringence and low confinement loss
T
Md. Faizul Huq Arifa,d, , Mohammad Mobarak Hossainc,d, Nazrul Islamb, Shah Mostafa Khaleda,d ⁎
a
Institute of Information Technology (IIT), University of Dhaka, Dhaka 1000, Bangladesh Department of Information and Communication Technology (ICT), Mawlana Bhashani Science and Technology University, Santosh, Tangail 1902, Bangladesh c Department of Computer Science and Engineering (CSE), Dhaka University of Engineering and Technology (DUET), Gazipur, Dhaka, Bangladesh d Researcher, SenSyss, Bangladesh b
ARTICLE INFO
ABSTRACT
Keywords: Photonic Crystal Fiber Nonlinearity Birefringence Sensitivity Confinement loss Effective Area
This paper presents a nonlinear Photonic Crystal Fiber (PCF) based sensor to detect liquid analytes. An extensive analysis has been presented at wide range of wavelength (0.6 μm−1.6 μm) in order to investigate the impact of some design parameters. The numerical investigation has been done using the full vector Finite Element Method (FEM). The proposed model provides an outstanding nonlinear coefficient value with high birefringence, high sensitivity, and low confinement loss. The designed model can be used in sensing and bio-sensing research and their applications.
1. Introduction Photonic Crystal Fiber (PCF) is a promising technology having lots of advantages over the conventional optical fiber. PCF is a new class of optical fiber which is based on the properties of photonic crystals. It can change the way light is generated, delivered and used. PCF technology has gained attention to the researchers because of its design flexibility and the potentiality to develop different kinds of applications in both telecom and non-telecom sectors [1]. Therefore, PCF is considered as the next generation optical fiber. Classical optical fibers have some fundamental limitations related to their structures. Photonic Crystal Fiber (PCF), with their structural features removes those limitations. Photonic crystals are periodic dielectric structures. PCF is designed with periodic arrangement of microstructure holes which affect the motion of Photons. Light is guided inside the PCF by either modified total internal reflection or photonic band gap guidance. The background material is often developed with pure silica and the low index region is generally provided by air holes running along the length of the fiber. In information processing, nonlinear optics has emerged as one of the most attractive field of study [1]. The main advantage of using nonlinear medium is that their nonlinear response is ultrafast. Moreover, highly nonlinear optical fiber leads to novel nonlinear effects. In optical fiber, a narrow core and high doping levels can reduce effective area and enhance nonlinearity. Hence, PCF can obtain high
⁎
nonlinearity. Because of its high sensitivity, low confinement loss, high birefringence, nonlinearity and flexibility in design, PCF can be used in varieties of applications in the field of fiber-optics [1]. PCF is finding applications in fiber optic communication, nonlinear devices, fiber lasers, high power transmission, highly sensitive chemical sensors, and many other areas. The advancement of nanotechnology allows us to obtain exceptional propagation properties by choosing appropriate design parameters. Due to the design flexibility of PCF, desired propagation properties can be obtained by changing lattice structure and some parameters like pitch (hole to hole distance), diameter of air holes and the number of air hole rings in the cladding region. Various research studies have been demonstrated to enhance propagation characteristics of PCF [2–4]. The variation of geometries of the PCF structure has a great influence on the optical properties of PCFs [5]. In addition various shapes of air holes have also influence on changing the guiding properties of the fiber [5]. Ademgil. [6] proposed a highly birefringent and nonlinear PCF structure with supplementary liquid filled air holes in the core region. The article [7] introduced a PCF structure with different orientation of elliptical air holes in the core and cladding. Kim et al. [4] have theoretically demonstrated a PCF structure with elliptical air holes to get high birefringence with dispersion control simultaneously. According to the article [5], elliptical air holes in the core reduce the relative sensitivity. However, elliptical holes in both core and cladding are
Corresponding author. E-mail address: [email protected] (Md. F.H. Arif).
https://doi.org/10.1016/j.sbsr.2018.100252 Received 8 November 2018; Received in revised form 3 December 2018; Accepted 4 December 2018 2214-1804/ © 2018 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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responsible to increase birefringence. In this research, an evanescent hexagonal PCF structure with an elliptical shaped hole in the core is investigated for liquid sensing applications. Moreover, the effect of the orientation of the elliptical hole is analyzed. In order to obtain high sensitivity, high birefringence, high nonlinearity and low confinement loss simultaneously, the proposed design has been demonstrated. Furthermore, the effect of the variation of operating wavelength and the ellipticity of the core hole are analyzed for the proposed structure. 2. Design of the proposed PCF Fig. 1. The cross-sectional view of the proposed designs: (a) PCF1: Horizontally aligned core and (b) PCF2: Vertically aligned core.
In this work, an index guided PCF structure has been designed with a hexagonal arrangement of circular air holes in the cladding. In the core there is an infiltrated elliptic shaped hole. The background material is pure silica (SiO2). The refractive index of the fused silica and analyte infiltrated in the core hole are governed by the Sellmeier's equation [8,9]. 3
n ( )2 = 1 + i=1
Bi
2
2
Ci
Here, B1, B2, B3 and C1, C2, C3 are Sellmeier's coefficients for specific material. The refractive index is n and λ is the operating wavelength. Sellmeier constants values for silica and water have been presented in Table 1. The core hole is infiltrated with the targeted material. Generally, Water or Ethanol are treated as primary liquids. In this study, the numerical study has been done for Water. The cladding assembles four rings of air holes, which are arranged in hexagonal configuration. The diameter (d) of each holes is kept same. In this structure the hole to hole distance (also known as pitch) in the cladding is set to Ʌ=1.7 μm, and the air filling ratio, d/Ʌ=0.9. Fig. 1 shows the cross-sectional view of the designed PCF structures. It can be seen from the Fig. 1(a) that elliptical hole in the core is horizontally aligned and the structure in the Fig. 1(b) shows that it has a vertically aligned elliptical hole in the core. The lengths of the semi-major axis and the semi-minor axis of the elliptical core hole are A and B respectively, where the area of the hole is 0.9 μm2. The ellipticity ε is calculated with the following equation:
=
A
B A
=1
Fig. 2. Infiltrated elliptical hole in the core.
2.1. Principles of operation Full vectorial Finite Element Method (FEM) with the Perfectly Match Layer (PML) boundary condition is applied for numerical investigation. Fig. 3 illustrates a one quarter of the computational window together with a Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundary conditions. In addition, an anisotropic Perfectly Matched Layer (PML) is placed outside the outermost ring of holes in order to evaluate the confinement loss and to reduce the computational window [11]. Using mesh analysis the cross section of the PCFs is sub divided into some triangular subspaces. In this simulation, the fiber is sub-divided into 11,580 triangular elements with 104761 degrees of freedom. Using Finite Element Method (FEM) the Maxwell's equations are solved by accounting the neighboring subspaces. The following equations can be derived from the Maxwell's equations [12].
B A
where, A ≥ B. In the designed PCF, the ellipticity is set to, ε=0.55. The structure of the core hole is presented in the Fig. 2. The index refraction of the cladding holes are set to 1. It is worth noting that the lower refractive index and higher air filling ratio around the core provides strong confinement ability. Some electro-magnetic waves scattered in outer boundary regions of PCF. In this regard, circular anisotropic perfectly matched layered structure is applied to avoid this.
× ([S ]
B1 C1(μm2) B2 C2(μm2) B3 C3(μm2)
Sellmeier constants values Silica
Water
0.696166300 4.67914826 × 10−3 0.407942600 1.35120631 × 10−2 0.897479400 97.9340025
0.75831 0.01007 0.08495 8.91377 – –
× E )
K 02 n2 [S ] E = 0
where, E is the electric field vector and λ is the operating wavelength. The free-space wavenumber K0 = 2π/λ, and [S] and [S]−1 are PML matrix and inverse PML Matrix respectively. The propagation constant β can be represented by the following equation [12].
Table 1 Sellmeier Constants for silica and water at a temperature of 20 °C [10] Parameters
1
= neff k 0 Polarization and propagation of light effect on the refractive index. Therefore, refractive indexes of the two fundamental modes will not be the same. The difference between the two fundamental modes is known as birefringence. After calculating the complex effective index (neff), the modal birefringence can be determined by the following equation [10]. 2
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Fig. 3. Computational window with applied boundary condition and FEM mesh for (a) PCF1 and (b) PCF2. x |neff
B
neffy |
Aeff =
where neffx and neffy are the effective refractive index for x and y polarized fundamental modes respectively. A small portion of leakage of light or confinement loss (dB/m) may occur due to the finite number of air holes in the cladding part. This is an additional form of loss which generally occurs in single material fibers, particularly in PCFs. This confinement loss Lc (dB/m) can be obtained by the imaginary part of the effective refractive index, neff by the following equation [10].
Lc =
Aeff =
=
r
m lc ]
nr f neff
where, neff is the modal effective index and nr represents the refractive index of the material to be sensed. The power fraction is denoted by f which can be defined as [14],
f=
Re (Ex Hy
Ey Hx )
total
Re (Ex Hy
Ey Hx )
|H|4 dxdy
2
n2 Aeff
This research is based on liquid sensing application with PCF. In this study we selected Water (n = 1.3201 at λ = 1.3 μm) as a targeted material for analyzing the structure. The modal analysis is performed in the x-y plane of the cross-section as the wave propagates in the z direction. Fig. 4 shows the fundamental mode field distribution of the proposed PCF with colour indicator scale at the wavelength of λ = 1.3 μm for the x-mode and y-mode polarization respectively. According to this 2D plots from the Fig. 4 it can be justified that the field has confined well in the core. Initially, the impact of the operating wavelength on the effective refractive index (x polarized) is shown in the Fig. 5. It can be seen from the figure that the effective refractive index of the fundamental mode is decreasing with increasing the wavelength for the analyte to be detected. It seems that the effective refractive indexes are similar for both PCF structures. Fig. 6 shows the birefringence values for the corresponding wavelength. It is found that at the wavelength λ = 1.3 μm the magnitude of the index difference or birefringence of PCF1 is 5.09 × 10−3. At the same wavelength the birefringence of PCF2 is 4.23 × 10−3. In addition, it is clearly seen that the value of birefringence decreases with the increase of the wavelength of light. The attenuation caused by the geometry of waveguide is called confinement loss. Fig. 7 describes the variation of confinement loss with the operating wavelength of light. It demonstrates that the confinement
m lc
sample
|H|2 dxdy ) 2
3. Results and discussion
The relative sensitivity r is calculated by the following equation [14].
r=
(
where, n2 is the nonlinear refractive index. The higher order of nonlinearity is responsible for super-continuum generation (SCG). For the calculation of the nonlinearity of the nonlinearity index of SiO2 is taken as n2=3.2 × 10−20 m2/W.
where I(f) and I0(f) are input and output intensities of light, r is the relative sensitivity, and αm is the absorption of light. The channel length is lc and f is the operating frequency. The absorbance of the targeted material can be obtained by [12,13],
I = I0
|E|4 dxdy
where Et and Ht are transverse electric field vector and magnetic field vector respectively. In high bit rate data transmission system large effective mode area is required. However, in nonlinear applications lower effective mode area is required. Nonlinearity is closely related to effective area of the fiber. The nonlinear coefficient can be calculated by the following equation [15]:
The relative sensitivity of PCF based sensor can be obtained from the intensity of light interaction with the analyte to be sensed. The amount of light interaction with the material to be sensed can be measured through the absorption coefficient at a particular frequency. The amount of light attenuation with the intensity of light absorbance of the evanescent field can be measured by [12,13],
A = log
|E|2 dxdy )2
Or
40 × 106 i Im {neff }, i = x, y ln(10)
I (f ) = I0 (f ) exp[ r
(
× 100
Here Ex, Ey and HxHy are electric field and magnetic field of the guided mode respectively. The effective mode area is related to the effective area of the fiber core area, which is computed using transverse electric field and magnetic field vector of the whole cross sectional area of the PCF. It is generally considered as the light carrying region. The effective area of the fiber core Aeff is defined by the following equation [15]. 3
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Fig. 4. Field distributions for (a) x-polarization mode and (b) y-polarization mode at λ = 1.3 μm. Red colour represents the highest intensity and blue represents the lowest. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The wavelength depending effective mode index of the fundamental mode (X-Polarization).
Fig. 6. Variation of the birefringence of the proposed designs as a function of operating wavelength.
loss increases with the increase of the wavelength for the both PCF structures. The sensitivity curves are increasing with the increase of wavelength. Fig. 8 illustrates the sensitivity response of the proposed PCF for water. It is clearly visualized that the sensitivity responses of 41.36% and 40.19% are gained in the PCF1 and PCF2 respectively at the wavelength λ = 1.3 μm. Highly nonlinear PCFs are the most desirable for many practical
applications. The nonlinear properties of PCF depend on the core diameter which determines the effect of the mode area [16]. Fig. 9 illustrates the nonlinear coefficient of the proposed designs of PCF. It can be seen that the PCF2 shows higher nonlinearity than the PCF1. There is a great impact of the ellipticity of the core hole to the performance of the fiber. It is worth noting that the cladding air holes are perfectly circular when ε = 0. 4
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Fig. 7. Variation of confinement loss (dB/m) as a function of operating wavelength.
Fig. 9. Nonlinear coefficient of the proposed PCF structure as a function of operating wavelength.
Fig. 8. Variation of sensitivity coefficient as a function of operating wavelength.
Fig. 10. Variation of birefringence as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm.
Fig. 10 shows the effect of ellipticity є on the birefringence, where the wavelength is fixed to =1.3 μm. It can be seen that the birefringence is increasing with the increase of ellipticity. Fig. 11 depicts that confinement loss is gradually increasing with the increase of ellipticity. It also shows that there is no significant difference between PCF1 and PCF2 in terms of confinement loss. Fig. 12 illustrates that the sensitivity coefficient is gradually decreasing with the increase of ellipticity. The obtained maximum values of relative sensitivity are 43.80% and 43.20% for PCF1 and PCF2 respectively, when the ellipticity is 0.25. Fig. 13 shows that the nonlinear coefficient is increasing with the increase of ellipticity. PCF2 exhibits outstanding values of nonlinear coefficient. The obtained maximum values of nonlinear coefficients are 72 and 76 for PCF1 and PCF2 respectively, when the ellipticity is 0.65. The overall performance analysis illustrates that except nonlinearity, the PCF with horizontally aligned elliptical hole (PCF1) shows better performance than the PCF2. Therefore, the geometries of PCF1 are optimized in this research work. In this research, our outcomes are expected to provide an extensive literature review to describe the fabrication process of the proposed
PCF structures. Several techniques are available for selectively filling the air holes with analytes. In terms of analyte filling in the core hole, the complexity is increased in the core area. However, the article [17] presented a unique method which allows for selectively filling the PCF holes with analytes. Moreover, several methods have been developed for the fabrication of microstructured fiber, like stack and draw [18],drilling [19], extrusion [20], sol-gel casting [21] etc. Stack and draw method can be used to closest-packed geometries. Drilling technique is generally limited to small number of holes. Extrusion technique provides freedom in design, but it is limited to soft glasses for which the material loss values are excessively high. Bise et al. [21] introduced a sol-gel method to fabricate PCFs with complex structure. In addition, sol-gel method provides flexibility in design which is essential for the proposed PCFs. Recently, Luo et al. [22] and Gerosa et al. [23] have experimentally shown that it is possible to fabricate the PCF structures with liquid filled core/cladding. In this regard, our proposed PCFs can be fabricated with current available nanotechnology. After forming the performance graphs of the proposed PCFs, it is needed to check the accuracy of the design. According to the article [24], in a standard fiber draw ± 1% variations in fiber global 5
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Fig. 11. variation of confinement loss as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm.
Fig. 13. Variation of nonlinear coefficient as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm. Table 2 Variation of overall performance of the PCF1 for the changes in global parameters at the wavelength λ = 1.3 μm. Variations of global parameters (%)
Birefringence
Confinement loss (dB/m)
Sensitivity (%)
Nonlinearity (W−1Km−1)
−3 −2 -1 Optimum +1 +2 +3
0.004992 0.005054 0.005074 0.00509 0.00511 0.00513 0.005165
2.84489E-10 2.77079E−10 2.45366E-10 2.16552E-10 9.45906E-11 2.42314E-11 2.31813E-11
41.90692314 41.73294961 41.55333198 41.3670971 40.97974722 40.98046652 40.77808544
77.73201 76.73698 75.74113 74.75272 73.64572 72.81018 71.84957
Table 3 Comparison of the performances in terms of birefringence, confinement loss, sensitivity and nonlinearity among the proposed PCF1 and prior PCFs for Water at the wavelength λ = 1.3 μm.
Fig. 12. Analysis of sensitivity performance as a function of ellipticity є, when the wavelength is fixed to λ = 1.3 μm.
parameter may occur during the fabrication process. The article [21] shows that in the sol-gel technique there may occur variation in hole size is less than 3% over 2 km spans for the fabrication of microstructure optical fiber. In order to account for this structural variation, the global parameter is varied up to ± 3% from their optimum values. From the Table 2 it can be observed that the overall performance in terms of birefringence, confinement loss, sensitivity and nonlinearity are affected by the variation in global parameters. Table 3 shows the comparative performance between our proposed PCF1 and the PCF structures proposed in the articles [6,7], in terms of Water as a targeted material. The proposed PCF is such that it provides a high birefringence, high relative sensitivity, high nonlinearity and low confinement loss for the entire spectral range compared to the prior PCFs. Therefore, this model is highly applicable for sensing and biomedical imaging applications.
PCFs
Birefringence
Confinement loss (dB/m)
Sensitivity (%)
Nonlinearity (W−1Km−1)
Ref. [6] Ref. [7] Proposed PCF1
0.00085 0.002700 0.00509
6 × 10−1 1.10 × 10−1 2.16552E-10
6 21 41.3670971
– – 74.75272
addition, it is found that there is a significant effect on the overall performance of the PCF for the variation of ellipticity of the core hole. A bunch of tiny elliptical air holes in the core may increase birefringence more, but it will add fabrication complexity. Considering the reduction of fabrication complexity and maintaining the critical trade-off between sensitivity and nonlinearity we have optimized horizontally aligned core hole. According to the numerical discussion, both PCFs show excellent performance in terms of nonlinearity and the values are 74.75272 and 84.51089264 for PCF1 and PCF2 respectively (λ = 1.3 μm). It may open a new window of research in the field of nonlinear optics and their applications.
4. Conclusion To summarize, we have successfully demonstrated the effects of the elliptical shaped infiltrated hole in the core. Moreover, a brief comparative study is done on the alignment of the elliptical hole. In
Conflict of interest All authors contributed equally. There is no conflict of interest. 6
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Acknowledgement
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