Numerical analysis of photonic crystal fibre with high birefringence and high nonlinearity

Patrick Atsu Agbemabiese; Emmanuel Kofi Akowuah

doi:10.1515/joc-2020-0084

Article Open Access

Numerical analysis of photonic crystal fibre with high birefringence and high nonlinearity

Patrick Atsu Agbemabiese and Emmanuel Kofi Akowuah

Published/Copyright: October 21, 2020

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From the journal Journal of Optical Communications Volume 44 Issue s1

Abstract

A four-ring microstructure photonic crystal fibre with a descending air hole ring cladding is presented. Numerical analysis of the structure is done using full vectorial finite element method with perfectly matched layer (PML) boundary condition. It is demonstrated that it is possible to achieve at 1.55 µm confinement loss of 2.767 × 10⁻⁵ dB/m, birefringence of 0.00346 and a nonlinear co-efficient of 41.77 km⁻¹ W⁻¹. Also, chromatic dispersion realised suggests a tuneable zero dispersion at 0.9–1.1 µm wavelength range.

Keywords: effective index; fabrication; finite element method; perfectly matched layer; photonic crystal fibre; polarisation

1 Introduction

Optical communication has promising advantages such as: immunity to electromagnetic interference, electrical isolation, remote sensing, multiplexing ability, corrosion free and it is able to work in extreme environmental conditions [1]. Conventional fibres were the first fibres to be introduced to the market with its limited bandwidth issues. Advancement in fibre optics has seen the guidance of light on the principle of modified total internal reflection using a single glass with the refractive index between the core and the cladding achieved by the use of air holes in the cladding. PCFs can be grouped into two; effective index guidance and band gap guidance. Effective index guidance is implemented with a solid core and air hole cladding. Band gap has a hollow core and air hole cladding. Also, band gap has a small refractive index contrast between the hollow core and the air hole cladding as compared to effective index guidance with solid core. Photonic crystal fibre (PCF) has seen advancement due to the structure, the application areas and the material used [2]. PCF have some properties that distinguished them from their conventional fibre counterparts like endlessly single mode [3], chromatic dispersion management [4], large mode areas, small mode areas [5] and high birefringence [6].

Birefringence in PCF can be achieved by altering the symmetry of the fibre core; using air hole sizes near the core [7]. A PCF structure with entirely elliptical air holes were designed by [8], [9] to obtain a birefringence of 10⁻³ and 10⁻². The core symmetry of a circular air hole PCF structure [10] is altered with elliptical holes that is arranged vertically to obtain birefringence of 0.022, nonlinear co-efficient of 50 km⁻¹ W⁻¹ and a confinement loss of 10⁻³ dB m⁻¹. These works in refs. [11], [12], [13] realised a birefringence in the order of 10⁻², however the fabrication of the structures would be difficult. A four hexagonal air hole with the core rearranged with seven rectangular air holes has been proposed by reference [14] with a birefringence of 0.075, however this also possess a fabrication issue due to the rectangular hole arrangement at the core. Birefringence of 0.105 at 6.2 THz has been achieved with the air holes around the core infiltrated with materials of different refractive indices [15]. The core can also be filled with liquids for sensing purposes as demonstrated by reference [16] to achieve a birefringence of 10⁻². A PCF with a core of porous elliptical rotated holes has been demonstrated in ref. [17] to achieve ultra-high birefringence of 2.2 × 10⁻³ and nonlinearity of 23.46 W⁻¹ km⁻¹ 1.2 µm wavelength. High nonlinearity of 99.73 W⁻¹ km⁻¹ and confinement loss of 3.41 × 10¹ dB m⁻¹ has been obtained [18] at 1550 nm with tiny holes introduce around the core. Also [19] proposed a birefringence of 0.057 with a core of circular and rectangular holes at 1.01 THz. Khairum Monir et al. [20] showed that birefringence can be improve with a unique structure and a rotated rectangular air hole slot in the core to achieve a birefringence of 0.24 with a confinement loss of 6.5 × 10⁻¹³ dB m⁻¹ at a terahertz regime.

Many types of glass materials have been introduced in the core to increase nonlinearity and birefringence such as TOPAS at 1 THz to achieve birefringence of 1.34 × 10⁻² in ref. [21] but nonlinearity has not been shown. Si₇N₃ has been introduced into an elliptical porous core to obtain nonlinearity of 48,858 W⁻¹ km⁻¹ at 1 µm [22]. Carbon disulphide has been slotted into a hexagonal porous core [23] to obtain nonlinearity of 13,667 W⁻¹ km⁻¹ and a negative dispersion of −254.67 ps nm⁻¹ km⁻¹ at 1000 nm wavelength. Nanocrystal filled core [24], [25] of different shapes obtained a nonlinearity and confinement loss of 321,004 W⁻¹ km⁻¹ and 1 × 10⁻⁸ dB m⁻¹ and 128,873.1183 W⁻¹ km⁻¹ and 1.47 × 10⁻⁵ dB m⁻¹, respectively. Nanoscale gallium phosphide [26] has been introduced into the a hexagonal core to achieve nonlinearity of 62,448.64 W⁻¹ km⁻¹ at 1.04 µm. Quasi lattice structures have been filled with the following materials; chalcogenide [27] in an elliptical porous core to achieved nonlinearity of 4.72 × 10⁴ W⁻¹ km⁻¹ at 1.0 µm wavelength, Ge₂₀Sb₁₅Se₆₅ [28] in rectangular core to achieved a birefringence of 1.46 × 10⁻¹ and nonlinearity of 6.161 × 10³ W⁻¹ km⁻¹ at infrared range, silicon nano crystal [29] in elliptical embedded core to achieve nonlinearity of 4.2 × 10⁵ W⁻¹ km⁻¹ at wavelength of 1 µm and a birefringence of 3.2 × 10⁻¹ at a wavelength of 3 µm and Tellurite [30] in elliptical core to obtain a nonlinearity of 1.5 × 10⁴ W⁻¹ km⁻¹ at 0.6 µm. D shaped lattice structure filled with graphene [31], [32] increased the nonlinearity and birefringence further to 6.01 × 10¹³ W⁻¹ km⁻¹ and 7.1 × 10²⁴ W⁻¹ km⁻¹, respectively.

A square structure of PCF [33] with seven air rings in the cladding and a circular PCF [34] has been demonstrated to exhibit birefringence of 10⁻² with a negative chromatic dispersion and confinement loss of less than 10⁻³ at 1.55 µm. However, the dispersion is not tuneable and the air holes in the core are complex. Rahul [35] proposed a birefringence of 10⁻³, a tuneable dispersion at 0.8 to 0.95 µm and a confinement loss of 39.22 dB m⁻¹ however, it has elliptical holes which would make fabrication a challenge. A double zero tuneable dispersion was proposed by ref. [36] however, there was no record of birefringence and confinement loss.

This paper proposes a PCF structure that utilises a descending hole arrangement to simultaneously obtain confinement loss of 2.4168 × 10⁻² dB m⁻¹, a high birefringence of 0.005384, high nonlinearity of 41.77 W⁻¹ km⁻¹ at a pitch of 1.7 µm and a tuneable zero dispersion at 0.9–1.1 µm. Achieving all these properties simultaneously demonstrates a PCF which would be suitable for optical communication, optical device and sensing applications.

2 Design principle

The proposed PCF as shown in Figure 1, focused on four structures which differ by the pitch (Λ) used thus 2.3, 1.9, 1.8 and 1.7 µm. Perfectly matched layer (PML) has been designed with thickness of W = 2 µm, wx = 20.6 µm, and wy = 24 µm. The structure has been designed with four circular air rings arranged in a descending order of air hole sizes. A descending hole has been used to provide the refractive index contrast needed to achieve high nonlinearity and low confinement loss. The air hole sizes were arranged with d = 1.02 µm, d1 = 0.75d, d2 = 1d, d3 = 1.25d and d4 = 1.5d, thus from the outer ring to the inner ring. The air filling fraction (d/Λ) used for all the design is 0.6. The hole-to-hole spacing between hole ‘a’ and ‘b’ is Λ1 = 1.5 µm which has been used for all the four structures to change the structural symmetry and improve the birefringence while maintaining a high nonlinearity. The background material is Silica. The analysis has been done at a wavelength range of 0.8–2 µm. Comsol Multiphysics which is based on finite element method has been used to run the simulation (Figure 2).

Figure 1:

Structure of PCF.

Figure 2:

Field profile of the proposed PCF at 1.55 µm, d/Λ = 0.6.

The PCF structure is based on Pure Silica and the refractive index of the silica is determined using the Sellmeier equation [37], [38] given by:

(1) n 2 = 1 + B 1 λ 2 λ 2 − C 1 + B 2 λ 2 λ 2 − C 2 + B 3 λ 2 λ 2 − C 3

where n is the refractive index of the silica, λ is the wavelength in µm, B _1,2,3 and C _1,2,3 are Sellmeier constant for silica material. The Sellmeier constants are given in Table 1.

Table 1:

Values of sellmeier co-efficients for background silica material.

Parameters	Constants
A1	0.69675
A2	0.408218
A3	0.890815
B1	0.047701
B2	0.0133777
B3	98.02107
C1	4.67914826e−3
C2	1.35120631e−2
C3	97.9340025

3 Theory

Maxwell equation used for anisotropic PML can be determine in [39]:

(2) ∇ × ( [ s − 1 ] ∇ × E ) − k 2 n 2 [ s ] E = 0

where k ₀ = 2π/λ is the wave number in vacuum, λ is the wavelength, E is the electric field vector, n is the refractive index of the domain, [s] is the PML matrix, [s]⁻¹ is an inverse matrix of [s] [40]. Finite element method solves Maxwell’s equation to obtain the best approximate value of effective refractive index.

Propagation constant β of a leaky mode is a complex value which is determined by β = k ₀. The k ₀ is the wave number in vacuum. The imaginary part of the propagation constant is what determines the loss. The formula that computes the confinement loss (L _C) is given by [39], [41].

(3) confinement loss ( L c ) = 40 π In ( 10 ) λ Im ( n eff ) ( dB m )

The parameter λ is the operating wavelength. I_m (n _eff) is the imaginary value of the effective refractive index and c is the speed of light in free space.

The chromatic dispersion (D), or group velocity dispersion, usefully expressed in ps nm⁻¹ km⁻¹, is a measure of the temporal broadening ∆t, in picoseconds, undergone by a light pulse of spectral bandwidth ∆l, in nanometres, during its propagation over a length L, in kilometres [2].

This parameter is determined from the propagation constant β. The chromatic dispersion is calculated using the real part of the effective index given by [41];

(4) D = − λ C ∂ 2 Re ( n eff ) ∂ λ 2

where c is the velocity of light and R (n _eff) is the real part of the effective index

Chromatic dispersion is a composition of the waveguide dispersion, (D _w) and the material dispersion, (D _m). D _m is a component that depends on the refractive index of the material. This parameter is a factor that relates to the core size and the difference in the refractive index between the core and the cladding,

The effective mode area (A _eff) is a factor that relates to the confinement loss, the numerical aperture splicing loss and the micro-bending. If the effective mode area is small, then the power density required for nonlinear effects would be high.

The effective mode area is given by:

(5) A eff = ( ∬ | E 2 | d x d y ) 2 ∬ | E | 4 d x d y

where E is the amplitude of the transverse electric field.

Nonlinear co-efficient (γ) determined in the core of the fibre is given by [5]:

(6) γ = 2 π λ n 2 A eff

where n ₂ is the refractive index co-efficient which, in this work relates to 2.76 × 10⁻²⁰ m² W⁻¹ [42].

High values of birefringence (B) of the PCF is obtained by breaking the symmetry of the fibre either through the changing of the air hole sizes or by changing the shape of the air holes causing the two orthogonal linearly polarised modes to degenerate and propagate with different phase velocities [6]. Effective refractive indices of the y and the x polarisation modes are given by n _y and n _x. This is calculated by;

(7) B = | n x − n y |

where the beat length (L _B) is related to birefringence and is determined using:

(8) L B = λ | n x − n y | = λ B

Where λ is the operating wavelength.

4 Results and analysis

This section discusses the results obtained from the proposed PCF structure. The objective of this work is to design a PCF structure which provides a high birefringence, low confinement loss, a low effective mode area corresponding to highly nonlinearity with a tuneable chromatic dispersion. Indeed, in analysing the PCF properties, graphs of birefringence, real effective, confinement loss, beat length, nonlinear co-efficients and the chromatic dispersion were drawn against wavelength in the range of 0.7–2 µm.

4.1 The real effective refractive index

The graph shown in Figure 3 indicates that the real effective refractive index decreases with increase in the wavelength. The results also indicate a R(n _eff) decreasing with the Λ. The R (n _eff) range recorded for all the structures at 1.55 µm is between 1.37 and 1.41 which agrees with [10].

Figure 3:

Real effective index of the fundamental mode as a function of wavelength for 1.7, 1.8, 1.9 and 2.3 µm.

4.2 Verification of birefringence and beat length

The birefringence is a property that is very important in sensing applications [43] where light is essential to provide a maintained linear polarisation and it is useful in switching applications. The graph indicates a birefringence of the order of 10⁻³ dB m⁻¹ which corresponds to [13], [35], [44], [45], [46]. Figure 4, shows a relationship between the birefringence and the wavelength and as such, as wavelength increases birefringence increase. A birefringence of 0.00346 has been achieved at Λ = 2.3 µm. Birefringence of 0.005 has been achieved at Λ = 1.9, 1.8 and 1.7 µm. This value is smaller than [12], [14], [43], [47], [48] however, these structures have defects created in the core. The beat length for the PCF decreases as the wavelength increases. The beat length as shown in Figure 5, shows high values at Λ = 2.3 µm and decreased in value as the Λ decreases. The beat length of 0.4483 is realised at 1.55 µm for a refractive index of 1.41005 at Λ = 2.3 µm. At Λ = 1.7 µm the beat length is 0.2879 at a refractive index of 1.37053.

Figure 4:

Birefringence against wavelength for 1.7, 1.8, 1.9 and 2.3 µm.

Figure 5:

Beat length as against wavelength for 1.7, 1.8, 1.9 and 2.3 µm.

4.3 Verification of effective mode area and nonlinear co-efficient

The graph drawn in Figure 6 shows a linear relationship between the wavelength and the effective mode area. The A _eff increases gradually with the wavelength. The structure with the highest Λ gave the highest values of effective mode area at 1.55 µm thus 7.456 µm², agreeing with [13], [47], corresponding to a nonlinear co-efficient of 15.64 W⁻¹ km⁻¹ in Figure 7. However, at a Λ of 1.7 µm the value of 41.769 W⁻¹ km⁻¹of nonlinear co-efficient has been realised which is close to [43] making the structure with Λ of 1.7 µm being highly nonlinear and higher than [13].

Figure 6:

Effective mode area against wavelength for 1.7 , 1.8, 1.9 and 2.3 µm.

Figure 7:

Nonlinear co-efficient as against wavelength.

4.4 Verification of confinement loss

The incident light that propagates through a PCF leaks out of the core. The amount of leakage is a parameter of interest since it decides the confinement loss. The performance of the proposed structure in terms of confinement loss is shown in Figure 8. The result shows an increase in the confinement loss as the wavelength increases with the value of 1.55 µm being 2.767 × 10⁻⁵ dB m⁻¹ at Λ = 2.3 µm which is better than [10], [33], [34], [35]. Regarding the relationship between Λ and the confinement loss, the results shows that as Λ increases the confinement loss decreases with Λ = 2.3 µm given the lowest value.

Figure 8:

Confinement loss as against wavelength for 1.7, 1.8, 1.9 and 2.3 µm.

4.5 Verification of chromatic dispersion

Chromatic dispersion is a property of the PCF which depends on material dispersion and waveguide dispersion of the PCF. Figure 9, indicates increment of chromatic dispersion in accordance with wavelength, from 0.7 µm to the pick around 1.55 µm then decreases as wavelength increase up to 2 µm. An important characteristic of this graph is that, it shows a tuneable zero chromatic dispersion between 0.9 and 1.1 µm for all the values of the Λ agreeing with refs. [35] and [36]. Negative dispersion is also obtained between 0.8–1.0 µm. Table 2 shows the values of the birefringence, confinement loss, nonlinearity and the lattice structure at the respective wavelength values. Table 3 compares the performance of the PCF with other related works. The results in the table indicates that the PCF performs better than other works in the table in terms of nonlinearity and is in the same orders in terms of birefringence, with the related papers in the table.

Figure 9:

Confinement loss as against wavelength for 1.7, 1.8, 1.9 and 2.3 µm.

Table 2:

Results of the proposed PCF at the telecommunication wavelength of 1.55 µm.

PCF structure, Λ (µm)	R (n _eff)	B	L _C (dB m⁻¹)	A _eff (µm²)	γ (km⁻¹ W⁻¹)
2.3y	1.41005	0.00346	2.767 × 10⁻⁵	7.3911	15.64
2.3x	1.40659		1.237 × 10⁻⁴	7.4561	15.50
1.9y	1.3874	0.00521	2.053 × 10⁻³	3.9715	29.10
1.9x	1.39265		4.664 × 10⁻⁴	4.0818	28.32
1.8y	1.37996	0.00553	4.178 × 10⁻³	3.3417	34.59
1.8x	1.38549		1.312 × 10⁻³	3.4351	33.66
1.7y	1.37053	0.00538	2.4168 × 10⁻²	2.7678	41.77
1.7x	1.37592		8.637 × 10⁻³	2.8377	40.74

Table 3:

Comparison between properties of the proposed PCF and other PCFs.

References	PCF structure/rings	B	L _C (dB m⁻¹)	γ (km⁻¹ W⁻¹)	λ (µm)
[49]	Rhombic/6	8.0 × 10⁻³	–	–	–
[50]	Circular/9	9.3 × 10⁻³	–	–	1.87
[17]	Square/	2.2 × 10⁻³	–	23.46	1.20
[18]	Square/6	–	3.4 × 10¹	99.73
Proposed	Hexagon/4	3.5 × 10⁻³	2.8 × 10⁻⁵	15.64	1.55
		5.4 × 10⁻³	2.4 × 10⁻²	41.77	1.55

5 Conclusion

The PCF structure proposed has shown remarkable properties of high nonlinearity of 41.769 W⁻¹ km⁻¹ at a pitch of 1.7 µm and the confinement loss of 2.767 × 10⁻⁵ was realised at a pitch of 2.3 µm. The structure also gave a tuneable zero chromatic dispersion at a wavelength range of 0.9–1.10 µm for all the structures. This PCF structure presented can be used for optical communication application, sensing, supercontinuum, optical code division multiple access and optical devices. The value of dispersion at 850 nm is −120 ps km⁻¹ nm⁻¹ at a pitch of 2.3 µm which would be suitable for applications in short data transmission and local area networks. Since circular hole PCF structures are easy to fabricate the PCF structure presented can be easily fabricated using stack and draw method [51].

Corresponding author: Patrick Atsu Agbemabiese, Department of Computer Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana, E-mail: paagbemabiese@gmail.com

Acknowledgments

The authors would like to thank Prof. K.O. Boateng for his support and guidance as well as Dr. Selorm Klogo and Dr. Henry Nunoo Mensah for their support.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

1. Johny, J, Prabhu, R, Fung, WK. Computational study of nanostructured composite materials for photonic crystal fibre sensors. In: IOP conference series: materials science and engineering; 2017:012012 p.10.1088/1757-899X/195/1/012012Search in Google Scholar

2. Thévenaz, L. Advanced fiber optics. Switzerland: EPFL Press; 2011.10.1201/b16404Search in Google Scholar

3. Akowuah, EK, Ademgil, H, Haxha, S, AbdelMalek, F. An endlessly single-mode photonic crystal fiber with low chromatic dispersion, and bend and rotational insensitivity. J Lightwave Technol 2009;27:3940–7. https://doi.org/10.1109/jlt.2009.2021284.Search in Google Scholar

4. Renversez, G, Kuhlmey, B, McPhedran, R. Dispersion management with microstructured optical fibers: ultraflattened chromatic dispersion with low losses. Optic Lett 2003;28:989–91. https://doi.org/10.1364/ol.28.000989.Search in Google Scholar PubMed

5. Agrawal, GP. Nonlinear fiber optics. In: Nonlinear science at the dawn of the 21st century. Berlin Heidelberg: Springer; 2000:195–211 pp.10.1007/3-540-46629-0_9Search in Google Scholar

6. Ortigosa-Blanch, A, Knight, J, Wadsworth, W, Arriaga, J, Mangan, B, Birks, T, et al. Highly birefringent photonic crystal fibers. Opt Lett 2000;25:1325–7. https://doi.org/10.1364/ol.25.001325.Search in Google Scholar PubMed

7. Ju, J, Jin, W, Demokan, M. Properties of a highly birefringent photonic crystal fiber. IEEE Photonics Technol Lett 2003;15:1375–7. https://doi.org/10.1109/lpt.2003.818051.Search in Google Scholar

8. Wang, J, Jiang, C, Hu, W, Gao, M. High birefringence photonic bandgap fiber with elliptical air holes. Opt Fiber Technol 2006;12:265–7. https://doi.org/10.1016/j.yofte.2005.11.002.Search in Google Scholar

9. Saha, R, Hossain, MM, Rahaman, ME, Mondal, HS. Design and analysis of high birefringence and nonlinearity with small confinement loss photonic crystal fiber. Front Optoelectron 2019;12:165–73. https://doi.org/10.1007/s12200-018-0837-6.Search in Google Scholar

10. Yang, T, Wang, E, Jiang, H, Hu, Z, Xie, K. High birefringence photonic crystal fiber with high nonlinearity and low confinement loss. Opt Express 2015;23:8329–37. https://doi.org/10.1364/oe.23.008329.Search in Google Scholar PubMed

11. Kim, SE, Kim, BH, Lee, CG, Lee, S, Oh, K, Kee, C-S. Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion. Opt Express 2012;20:1385–91.https://doi.org/10.1364/oe.20.001385.Search in Google Scholar PubMed

12. Liu, Q, Liu, Q, Sun, Y, Liu, W, Liu, C, Li, Q, et al. A high-birefringent photonic quasi-crystal fiber with two elliptical air holes. Optik 2019;184:10–5. https://doi.org/10.1016/j.ijleo.2019.03.017.Search in Google Scholar

13. Arif, MFH, Biddut, MJH. 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 2017;12:8–14. https://doi.org/10.1016/j.sbsr.2016.11.003.Search in Google Scholar

14. Habib, MA, Reza, MS, Abdulrazak, LF, Anower, MS. Extremely high birefringent and low loss microstructure optical waveguide: design and analysis. Opt Commun 2019;446:93–9. https://doi.org/10.1016/j.optcom.2019.04.060.Search in Google Scholar

15. Yang, T, Ding, C, Ziolkowski, RW, Guo, YJ. High birefringent ENZ photonic crystal fibers. In: International conference on numerical simulation of optoelectronic devices (NUSOD); 2018:85–6 pp.10.1109/NUSOD.2018.8570268Search in Google Scholar

16. Wang, J, Jiang, C, Hu, W, Gao, M. Modified design of photonic crystal fibers with flattened dispersion. Opt Laser Technol 2006;38:169–72. https://doi.org/10.1016/j.optlastec.2004.11.016.Search in Google Scholar

17. Ahmed, K, Paul, BK, Islam, MS, Chowdhury, S, Sen, S, Islam, MI, et al. Ultra high birefringence and lower beat length for square shape PCF: analysis effect on rotation angle and eccentricity. Alexandria Eng J 2018;57:3683–91. https://doi.org/10.1016/j.aej.2018.01.018.Search in Google Scholar

18. Islam, MI, Ahmed, K, Paul, BK, Chowdhury, S, Sen, S, Islam, MS, et al. Ultra-high negative dispersion and nonlinearity based single mode photonic crystal fiber: design and analysis. J Opt 2019;48:18–25. https://doi.org/10.1007/s12596-018-0499-1.Search in Google Scholar

19. Reza, KS, Paul, BK, Ahmed, K. Highly birefringent, low loss single-mode porous fiber for THz wave guidance. Results Phys 2018;11:549–53. https://doi.org/10.1016/j.rinp.2018.09.053.Search in Google Scholar

20. Monir, MK, Hasan, M, Paul, BK, Ahmed, K, El-Khozondar, HJ, Amiri, I. High birefringent, low loss and flattened dispersion asymmetric slotted core-based photonic crystal fiber in THz regime. Int J Mod Phys B 2019;33:1950218. https://doi.org/10.1142/s0217979219502187.Search in Google Scholar

21. Paul, BK, Ahmed, K. Highly birefringent TOPAS based single mode photonic crystal fiber with ultra-low material loss for Terahertz applications. Opt Fiber Technol 2019;53:102031. https://doi.org/10.1016/j.yofte.2019.102031.Search in Google Scholar

22. Paul, BK, Ahmed, K. Si7N3 material filled novel heptagonal photonic crystal fiber for laser applications. Ceram Int 2019;45:1215–8. https://doi.org/10.1016/j.ceramint.2018.09.307.Search in Google Scholar

23. Paul, BK, Ahmed, K, Aktar, MN. Carbon disulphide (CS2) enriched photonic crystal fiber for nonlinear application: a FEM scheme. Opt Quant Electron 2020;52. https://doi.org/10.1007/s11082-020-02363-z.Search in Google Scholar

24. Hossain, MN, Ahmed, F, Khan, MS, Ahmed, K, Sharma, M, Dhasarathan, V. Highly nonlinear Silicon Nanocrystal doped photonic crystal fibers with low confinement loss. Phys B Condens Matter 2020;577:411802. https://doi.org/10.1016/j.physb.2019.411802.Search in Google Scholar

25. Paul, BK, Ahmed, F, Moctader, MG, Ahmed, K, Vigneswaran, D. Silicon nano crystal filled photonic crystal fiber for high nonlinearity. Opt Mater 2018;84:545–9. https://doi.org/10.1016/j.optmat.2018.07.054.Search in Google Scholar

26. Paul, BK, Moctader, MG, Ahmed, K, Khalek, MA. Nanoscale GaP strips based photonic crystal fiber with high nonlinearity and high numerical aperture for laser applications. Results Phys 2018;10:374–8. https://doi.org/10.1016/j.rinp.2018.06.033.Search in Google Scholar

27. Paul, BK, Khalek, MA, Chakma, S, Ahmed, K. Chalcogenide embedded quasi photonic crystal fiber for nonlinear optical applications. Ceram Int 2018;44:18955–9. https://doi.org/10.1016/j.ceramint.2018.07.134.Search in Google Scholar

28. Amiri, I, Khalek, MA, Chakma, S, Paul, BK, Ahmed, K, Dhasarathan, V, et al. Design of Ge20Sb15Se65 embedded rectangular slotted quasi photonic crystal fiber for higher nonlinearity applications. Optik 2019;184:63–9. https://doi.org/10.1016/j.ijleo.2019.01.006.Search in Google Scholar

29. Paul, BK, Chakma, S, Khalek, MA, Ahmed, K. Silicon nano crystal filled ellipse core based quasi photonic crystal fiber with birefringence and very high nonlinearity. Chin J Phys 2018;56:2782–8. https://doi.org/10.1016/j.cjph.2018.09.030.Search in Google Scholar

30. Maheswaran, S, Paul, BK, Khalek, MA, Chakma, S, Ahmed, K, Rajan, MM. Design of tellurite glass based quasi photonic crystal fiber with high nonlinearity. Optik 2019;181:185–90. https://doi.org/10.1016/j.ijleo.2018.12.033.Search in Google Scholar

31. Mehedi, ST, Shamim, AAM, Paul, BK, Ahmed, K. Graphene injected D-shape photonic crystal fiber for nonlinear optical applications. Silicon 2019;12:2293–300. https://doi.org/10.1007/s12633-019-00323-1.Search in Google Scholar

32. Ahmed, K, Paul, BK, Jabin, MA, Biswas, B. FEM analysis of birefringence, dispersion and nonlinearity of graphene coated photonic crystal fiber. Ceram Int 2019;45:15343–7. https://doi.org/10.1016/j.ceramint.2019.05.027.Search in Google Scholar

33. Lee, YS, Lee, CG, Jung, Y, Oh, MK, Kim, S. Highly birefringent and dispersion compensating photonic crystal fiber based on double line defect core. J Opt Soc Korea 2016;20:567–74. https://doi.org/10.3807/josk.2016.20.5.567.Search in Google Scholar

34. Hasan, MR, Islam, MA, Rifat, AA, Hasan, MI. A single-mode highly birefringent dispersion-compensating photonic crystal fiber using hybrid cladding. J Mod Optic 2017;64:218–25. https://doi.org/10.1080/09500340.2016.1224941.Search in Google Scholar

35. Gangwar, RK, Singh, VK. Study of highly birefringence dispersion shifted photonic crystal fiber with asymmetrical cladding. Optik 2016;127:11854–9. https://doi.org/10.1016/j.ijleo.2016.09.101.Search in Google Scholar

36. Huang, D, Huang, Z, Zhan, D. Novel large negative dispersion and tunable zero dispersion wavelength of photonic crystal fiber. Waves Random Complex Media 2018;28:624–9. https://doi.org/10.1080/17455030.2017.1378458.Search in Google Scholar

37. Bjarklev, A, Broeng, J, Bjarklev, AS. Photonic crystal fibres. USA: Springer Science & Business Media; 2012. https://doi.org/10.1007/978-1-4615-0475-7.Search in Google Scholar

38. Malitson, I. Interspecimen comparison of the refractive index of fused silica. J Opt Soc Am 1965;55:1205–9. https://doi.org/10.1364/josa.55.001205.Search in Google Scholar

39. Saitoh, K, Koshiba, M, Hasegawa, T, Sasaoka, E. Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion. Opt Express 2003;11:843–52. https://doi.org/10.1364/oe.11.000843.Search in Google Scholar PubMed

40. Akowuah, E, Ademgil, H, Haxha, S. Design and analysis of photonic crystal fibres (PCFs) for broadband applications. In: 2012 IEEE 4th International conference on adaptive science & technology (ICAST); 2012:114–20 pp.10.1109/ICASTech.2012.6381077Search in Google Scholar

41. Zolla, F. Foundations of photonic crystal fibres. London: Imperial College Press; 2005.10.1142/p367Search in Google Scholar

42. Kato, T, Suetsugu, Y, Nishimura, M. Estimation of nonlinear refractive index in various silica-based glasses for optical fibers. Opt Lett 1995;20:2279–81. https://doi.org/10.1364/ol.20.002279.Search in Google Scholar PubMed

43. Tabassum, N, Rashid, MM, Yesmin, A, Islam, ME. Highly nonlinear and highly birefringent hybrid photonic crystal fiber. In: 2019 International conference on robotics, electrical and signal processing techniques (ICREST); 2019:292–6 pp.10.1109/ICREST.2019.8644459Search in Google Scholar

44. Ademgil, H, Haxha, S. PCF based sensor with high sensitivity, high birefringence and low confinement losses for liquid analyte sensing applications. Sensors 2015;15:31833–42. https://doi.org/10.3390/s151229891.Search in Google Scholar PubMed PubMed Central

45. Ademgil, H, Haxha, S. Highly birefringent nonlinear PCF for optical sensing of analytes in aqueous solutions. Optik 2016;127:6653–60. https://doi.org/10.1016/j.ijleo.2016.04.137.Search in Google Scholar

46. Arif, MFH, Biddut, MJH. Enhancement of relative sensitivity of photonic crystal fiber with high birefringence and low confinement loss. Optik 2017;131:697–704. https://doi.org/10.1016/j.ijleo.2016.11.203.Search in Google Scholar

47. Kumar, P, Fiaboe, KF, Roy, JS. Highly birefringent do-octagonal photonic crystal fibers with ultra flattened zero dispersion for supercontinuum generation. J Microwaves Optoelectron Electromagn Appl 2019;18:80–95. https://doi.org/10.1590/2179-10742019v18i11454.Search in Google Scholar

48. Prabu, K, Malavika, R. Highly birefringent photonic crystal fiber with hybrid cladding. Opt Fiber Technol 2019;47:21–6. https://doi.org/10.1016/j.yofte.2018.11.015.Search in Google Scholar

49. Gao, Y, Sima, C, Cheng, J, Cai, B, Yuan, K, Lian, Z, et al. Highly-birefringent and ultra-wideband low-loss photonic crystal fiber with rhombic and elliptical holes. Opt Commun 2019;450:172–5. https://doi.org/10.1016/j.optcom.2019.06.004.Search in Google Scholar

50. Lee, YS, Lee, CG, Bahloul, F, Kim, S, Oh, K. Simultaneously achieving a large negative dispersion and a high birefringence over Er and Tm dual gain bands in a square lattice photonic crystal fiber. J Lightwave Technol 2019;37:1254–63. https://doi.org/10.1109/jlt.2019.2891756.Search in Google Scholar

51. Monro, TM, Richardson, D, Broderick, N, Bennett, P. Holey optical fibers: an efficient modal model. J Lightwave Technol 1999;17:1093–102. https://doi.org/10.1109/50.769313.Search in Google Scholar

Received: 2020-04-14

Accepted: 2020-09-17

Published Online: 2020-10-21

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/joc-2020-0084

Keywords for this article

effective index; fabrication; finite element method; perfectly matched layer; photonic crystal fibre; polarisation

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