Numerical analysis of the highly non-linear and ultra-sensitive modified core of a photonic crystal fiber sensor for detection of liquid analytes

Farhan Mumtaz; Ghulam Yaseen; Muhammad Roman; Lashari Ghulam Abbas; Muhammad Aqueel Ashraf; Muhammad Arshad Fiaz; Yutang Dai; Yutang Dai

doi:10.1364/JOSAB.478468

Journal of the Optical Society of America B
Vol. 40,
Issue 1,
pp. 142-150
(2023)
•https://doi.org/10.1364/JOSAB.478468

Numerical analysis of the highly non-linear and ultra-sensitive modified core of a photonic crystal fiber sensor for detection of liquid analytes

Farhan Mumtaz, Ghulam Yaseen, Muhammad Roman, Lashari Ghulam Abbas, Muhammad Aqueel Ashraf, Muhammad Arshad Fiaz, and Yutang Dai

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Farhan Mumtaz, Ghulam Yaseen, Muhammad Roman, Lashari Ghulam Abbas, Muhammad Aqueel Ashraf, Muhammad Arshad Fiaz, and Yutang Dai, "Numerical analysis of the highly non-linear and ultra-sensitive modified core of a photonic crystal fiber sensor for detection of liquid analytes," J. Opt. Soc. Am. B 40, 142-150 (2023)

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Abstract

A design of the highly non-linear and ultra-sensitive modified core of a photonic crystal fiber (PCF) sensor is reported for the detection of various liquid analytes. The sensor design comprises three rings of a hexagonal lattice around the liquid-infiltrated hollow core. A steric-shaped hollow core design in PCF effectively optimizes the sensor’s sensitivity and performance. The design is analyzed numerically by using the full vector finite element method with perfectly matched layers to find a rigorous solution. The proposed PCF sensor exhibits ultra-high relative sensitivity, a high power fraction, high non-linearity coefficient, low confinement loss, ultra-low chromatic dispersion, compact effective mode area, and single-mode operation in a wider wavelength range, i.e., within visible and infrared wavelength regimes. At an operating wavelength of 1.0 µm, optimum relative sensitivities of 96.37%, 97.40%, and 99.82% with high non-linear coefficients of ${78.0}\;{{\rm W}^{- 1}}\;{{\rm km}^{- 1}}$, ${66.09}\;{{\rm W}^{- 1}}\;{{\rm km}^{- 1}}$, and ${62.57}\;{{\rm W}^{- 1}}\;{{\rm km}^{- 1}}$ and extremely low confinement loss of ${\sim}{{10}^{- 10}}\;{\rm dB}/{\rm m}$ are obtained for water, ethanol, and benzene analytes, respectively. Further, waveguiding characteristics of the PCF sensor endorse its usage for a range of liquid analyte detections. It is a simple design and can be fabricated using existing manufacturing technologies.

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Materials	$A$	$B$	$C$	$a$ ( ${µ m}^{2}$ )	$b$ ( ${µ m}^{2}$ )	$c$ ( ${µ m}^{2}$ )	$d$ ( ${µ m}^{- 2}$ )
Silica	0.6961663	0.4079426	0.8974794	0.0684043	0.1162414	9.896161	–
Water	0.75831	0.01007	–	0.07895	8.91377	–	–
Ethanol	0.83189	0.00930	–	−0.15582	49.45200	–	–
Benzene	2.170184597	–	–	$2.3 \times 10^{- 2}$	$4.99 \times 10^{- 4}$	$1.78 \times 10^{- 4}$	$5.9 \times 10^{- 4}$

Change in	Variation in Cladding Air Holes ( $Λ = 2.\bf 0 µ m$ , $ρ_{co} = 2.824 µ m$ , $λ = 1.\bf 0 µ m$ )				Variation in Core ( $Λ = 2.\bf 0 um$ , $ρ_{ah} = 1.9$ , $λ = 1.\bf 0 µ m$ )
Dimension	$ρ_{a h}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$	$ρ_{c o}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$
−5.0%	1.758	$2.08 \times 10^{- 9}$	97.91	1.909%	2.683	$1.74 \times 10^{- 9}$	95.96	3.864%
−2.5%	1.853	$9.06 \times 10^{- 10}$	99.22	0.596%	2.753	$1.83 \times 10^{- 9}$	99.10	0.716%
0.0%	1.900	$7.88 \times 10^{- 10}$	99.82	0%	2.824	$7.88 \times 10^{- 10}$	99.82	0%
2.5%	1.948	$2.79 \times 10^{- 9}$	100.00	0.185%	2.895	$1.07 \times 10^{- 9}$	98.20	1.622%
5.0%	–	–	–	–	–	–	–	–
	Variation in Cladding Air Holes ( $Λ = 2.\bf 1 µ m$ , $ρ_{co} = 2.824 µ m$ , $λ = 1.\bf 0 µ m$ )				Variation in Core ( $Λ = 2.\bf 1 um$ , $ρ_{ah} = 1.9$ , $λ = 1.\bf 0 µ m$ )
	$ρ_{ah}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$	$ρ_{co}$	$L_{c}$ (dB/m)	$L_{c}$ (dB/m)	$r$ (%)
$- 5.0 %$	1.758	$1.41 \times 10^{- 10}$	98.34	0.230%	2.683	$2.45 \times 10^{- 10}$	96.83	1.302%
$- 2.5 %$	1.853	$1.79 \times 10^{- 11}$	98.19	0.082%	2.753	$2.28 \times 10^{- 10}$	97.53	0.588%
0.0%	1.900	$3.10 \times 10^{- 10}$	98.11	0%	2.824	$3.10 \times 10^{- 10}$	98.11	0%
2.5%	1.948	$2.74 \times 10^{- 10}$	98.01	0.102%	2.895	$2.69 \times 10^{- 10}$	98.57	0.473%
5.0%	2.045	$1.56 \times 10^{- 9}$	97.77	0.242%	2.965	$2.40 \times 10^{- 10}$	98.93	0.839%
	Variation in Cladding Air Holes ( $Λ = 2.\bf 2 µ m$ , $ρ_{co} = 2.824 µ m$ , $λ = 1.\bf 0 µ m$ )				Variation in Core ( $Λ = 2.\bf 2 um$ , $ρ_{ah} = 1.9$ , $λ = 1.\bf 0 µ m$ )
	$ρ_{ah}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$	$ρ_{co}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$
$- 5.0 %$	1.758	$3.15 \times 10^{- 10}$	97.32	1.137%	2.683	$7.49 \times 10^{- 11}$	97.45	1.004%
$- 2.5 %$	1.853	$2.03 \times 10^{- 10}$	98.10	0.342%	2.753	$3.92 \times 10^{- 10}$	98.00	0.453%
0.0%	1.900	$1.43 \times 10^{- 10}$	98.44	0%	2.824	$1.43 \times 10^{- 10}$	98.44	0%
2.5%	1.948	$5.00 \times 10^{- 11}$	98.74	0.299%	2.895	$4.58 \times 10^{- 11}$	98.80	0.361%
5.0%	2.045	$1.57 \times 10^{- 10}$	99.20	0.469%	2.965	$1.71 \times 10^{- 10}$	99.07	0.638%

		Relative Sensitivity (%)			Confinement Loss (dB/m)			Non-linear Coefficient ( $W^{- 1} {k m}^{- 1}$ )
PCF Sensor Design		Water	Ethanol	Benzene	Water	Ethanol	Benzene	Water	Ethanol	Benzene
5-ring octagonal lattice [15]		52.07	56.75	58.86	$\sim 10^{- 10}$	$\sim 10^{- 10}$	$\sim 10^{- 10}$	2.24	2.16	2.10
5-ring hexagonal lattice [14]		57.00	57.18	57.27	$\sim 10^{- 11}$	$\sim 10^{- 11}$	$\sim 10^{- 11}$	11.82	11.95	12.02
3-ring hexagonal lattice [4]		62.60	65.34	74.50	$\sim 10^{- 7}$	$\sim 10^{- 8}$	$\sim 10^{- 11}$	69.4	73.8	95.4
5-ring hexagonal lattice [16]		88.93	91.87	97.89	$\sim 10^{- 10}$	$\sim 10^{- 10}$	$\sim 10^{- 10}$	29.0	30.0	33.0
3-ring hexagonal lattice [19]		90.01	92.65	98.44	$\sim 10^{- 12}$	$\sim 10^{- 13}$	$\sim 10^{- 17}$	–	–	–
3-ring hexagonal lattice [20]		94.26	95.82	99.58	$\sim 10^{- 11}$	$\sim 10^{- 12}$	$\sim 10^{- 16}$	84.55	90.26	110.39
This work, 3-ring hexagonal lattice	S-1	96.37	97.39	99.82	$\sim 1 0^{- 10}$	$\sim 1 0^{- 10}$	$\sim 1 0^{- 10}$	62.57	66.02	78.00
	S-2	90.90	93.11	98.27	$\sim 1 0^{- 10}$	$\sim 1 0^{- 10}$	$\sim 1 0^{- 10}$	56.66	61.54	79.16
	S-3	82.59	86.60	96.14	$\sim 1 0^{- 10}$	$\sim 1 0^{- 10}$	$\sim 1 0^{- 10}$	50.80	56.65	80.61

Materials	$A$	$B$	$C$	$a$ ( ${µ m}^{2}$ )	$b$ ( ${µ m}^{2}$ )	$c$ ( ${µ m}^{2}$ )	$d$ ( ${µ m}^{- 2}$ )
Silica	0.6961663	0.4079426	0.8974794	0.0684043	0.1162414	9.896161	–
Water	0.75831	0.01007	–	0.07895	8.91377	–	–
Ethanol	0.83189	0.00930	–	−0.15582	49.45200	–	–
Benzene	2.170184597	–	–	$2.3 \times 10^{- 2}$	$4.99 \times 10^{- 4}$	$1.78 \times 10^{- 4}$	$5.9 \times 10^{- 4}$

Change in	Variation in Cladding Air Holes ( $Λ = 2.\bf 0 µ m$ , $ρ_{co} = 2.824 µ m$ , $λ = 1.\bf 0 µ m$ )				Variation in Core ( $Λ = 2.\bf 0 um$ , $ρ_{ah} = 1.9$ , $λ = 1.\bf 0 µ m$ )
Dimension	$ρ_{a h}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$	$ρ_{c o}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$
−5.0%	1.758	$2.08 \times 10^{- 9}$	97.91	1.909%	2.683	$1.74 \times 10^{- 9}$	95.96	3.864%
−2.5%	1.853	$9.06 \times 10^{- 10}$	99.22	0.596%	2.753	$1.83 \times 10^{- 9}$	99.10	0.716%
0.0%	1.900	$7.88 \times 10^{- 10}$	99.82	0%	2.824	$7.88 \times 10^{- 10}$	99.82	0%
2.5%	1.948	$2.79 \times 10^{- 9}$	100.00	0.185%	2.895	$1.07 \times 10^{- 9}$	98.20	1.622%
5.0%	–	–	–	–	–	–	–	–
	Variation in Cladding Air Holes ( $Λ = 2.\bf 1 µ m$ , $ρ_{co} = 2.824 µ m$ , $λ = 1.\bf 0 µ m$ )				Variation in Core ( $Λ = 2.\bf 1 um$ , $ρ_{ah} = 1.9$ , $λ = 1.\bf 0 µ m$ )
	$ρ_{ah}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$	$ρ_{co}$	$L_{c}$ (dB/m)	$L_{c}$ (dB/m)	$r$ (%)
$- 5.0 %$	1.758	$1.41 \times 10^{- 10}$	98.34	0.230%	2.683	$2.45 \times 10^{- 10}$	96.83	1.302%
$- 2.5 %$	1.853	$1.79 \times 10^{- 11}$	98.19	0.082%	2.753	$2.28 \times 10^{- 10}$	97.53	0.588%
0.0%	1.900	$3.10 \times 10^{- 10}$	98.11	0%	2.824	$3.10 \times 10^{- 10}$	98.11	0%
2.5%	1.948	$2.74 \times 10^{- 10}$	98.01	0.102%	2.895	$2.69 \times 10^{- 10}$	98.57	0.473%
5.0%	2.045	$1.56 \times 10^{- 9}$	97.77	0.242%	2.965	$2.40 \times 10^{- 10}$	98.93	0.839%
	Variation in Cladding Air Holes ( $Λ = 2.\bf 2 µ m$ , $ρ_{co} = 2.824 µ m$ , $λ = 1.\bf 0 µ m$ )				Variation in Core ( $Λ = 2.\bf 2 um$ , $ρ_{ah} = 1.9$ , $λ = 1.\bf 0 µ m$ )
	$ρ_{ah}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$	$ρ_{co}$	$L_{c}$ (dB/m)	$r$ (%)	% change in $r$
$- 5.0 %$	1.758	$3.15 \times 10^{- 10}$	97.32	1.137%	2.683	$7.49 \times 10^{- 11}$	97.45	1.004%
$- 2.5 %$	1.853	$2.03 \times 10^{- 10}$	98.10	0.342%	2.753	$3.92 \times 10^{- 10}$	98.00	0.453%
0.0%	1.900	$1.43 \times 10^{- 10}$	98.44	0%	2.824	$1.43 \times 10^{- 10}$	98.44	0%
2.5%	1.948	$5.00 \times 10^{- 11}$	98.74	0.299%	2.895	$4.58 \times 10^{- 11}$	98.80	0.361%
5.0%	2.045	$1.57 \times 10^{- 10}$	99.20	0.469%	2.965	$1.71 \times 10^{- 10}$	99.07	0.638%

Abstract

Data availability

Cited By

Figures (7)

Tables (3)

Equations (15)

Journal of the Optical Society of America B