Probing a chiral drug using long period fiber gratings

Maoyan Wang; Hailong Li; Tong Xu; Guiping Li; Mengxia Yu; Baojun Jiang; Jun Xu; Jian Wu

doi:10.1364/OE.27.031407

1. Introduction

Long-period fiber gratings (LPFGs) have been extensively investigated for physical, chemical, and biological sensing applications in the refractive index, temperature, strain, and torsion detection [1–26]. Chiavaioli et al. reviewed the biosensing with optical fiber gratings [9]. Tian et al. developed a lab-on-fiber optofluidic platform with a long-period grating for in situ monitoring of the drug release [10]. Yin et al. presented an optical fiber long-period grating biosensor integrated microfluidic chip for ultrasensitive glucose detection [15]. Luo et al. reported a highly sensitive and selective glucose sensor based on tilted fiber grating inscribed in the thin-cladding optical fiber [17]. These sensors are designed by simply considering the surrounding refractive-index and cannot determine the response of the LPFGs is generated by the change of the chirality or that of the refractive index. Therefore the surrounding chirality needs to be further taken into account during the synthesis process. Up to now, the simultaneous sensing of the refractive index and chirality of a chiral drug via a LPFG has not been reported.

A chiral drug contains two enantiomers with opposite handedness [27,28]. The enantiomers generally have identical composition and functional groups, yet show different toxicities to cells. The pharmacological effects of chiral drugs are strongly influenced by the optical activity. The chirality detection of drugs is important to determine the content of enantiomers in fields of the drug development, agrochemistry, and food environment [27–39]. Compared with the chromatography and optical rotation methods [37], the fiber sensing method is nondestructive, high sensitivity, reliable, and real-time monitoring for the chirality detection [38,39]. Wang et al. proposed a surface plasmon resonance (SPR) based optical fiber sensor [38] and an angle dependent Kretschmann configuration SPR sensor to probe bianisotropic biomolecules [39], respectively. However, the chirality sensitivity of the SPR-based sensors is low and it is impossible to detect the small chirality. The LPFGs may overcome these shortcomings.

The theory of electromagnetic wave propagation in inhomogeneous media [40–55] has been used to study electromagnetic characteristics of optical fibers. Erdogan et al. presented a straightforward theory for cladding-mode resonances in short- and long-period achiral fiber grating filters [40]. Xu et al. studied the conversion of orbital angular momentum of light in chiral fiber gratings [54]. Cao et al. theoretically investigated chiral negatively refractive fibers that guide transverse electromagnetic modes [55]. Xian et al. demonstrated a paired helical long-period fiber grating sensor for simultaneous measurement of temperature and torsion [56]. The decomposition and coupling of cladding modes in the LPFGs are more complicated owing the introduction of the surrounding chirality. To sense a chiral drug with a long-period fiber grating, the electromagnetic field theory for the step-index fiber geometry requires further study.

The remainder of this paper is organized as follows. In section 2 the theory used to probe a magnetoelectric coupling chiral drug based on an LPFG is described. The Debye potentials for a chiral drug are given by employing the wave decomposition and transformation techniques. The electromagnetic field distributions and solving process for propagation constants of cladding modes in the LPFG are presented. In section 3, the transmission spectra of an uncoated LPFG are analyzed. Section 4 discusses the mode effective index and transmission characteristics of a coated LPFG. Finally, some conclusions are included in section 5.

2. Theory

2.1 Constitutive relations for a chiral drug

The constitutive relations for a homogeneous chiral drug [16,33] can be expressed as [27–32]

D = ε E + j γ H, B = μ H - j γ E .

where ε, μ, and γ are the permittivity, permeability, and magnetoelectric coupling chirality, respectively. The real part of chirality is related to the optical activity, which is described by the rotation of polarization plane of a linearly polarized light. The imaginary part of the chirality is related to the circular dichroism, which causes different absorption losses or gain for right- and left-hand circularly polarized waves.

2.2 Wave decomposition and transformation

Based on the Bohren’s wave decomposition technique [57], the electromagnetic fields can be expanded as

E = (E_{R} + E_{L}), H = - j \sqrt{ε / μ} (E_{R} - E_{L}) .

In Eq. (2), E_R and E_L are the right- and left-hand circularly polarized electric fields supported in the chiral drug. The chirality (mirror symmetry breaking of molecules) of the chiral drug will give rise to the bifurcation of cladding modes. The chirality introduced may cause the impedance-matching, which changes cladding mode resonances in LPFGs.

The transformation from circularly to linearly polarized electric field components are

E_{∥} = \sqrt{2} (E_{R} + E_{L}) / 2, E_{⊥} = j \sqrt{2} (E_{R} - E_{L}) / 2.

2.3 Debye potentials for a chiral drug

Therefore, we can get scalar Debye potentials for a chiral drug

\begin{array}{l} Ψ_{4} = [A_{4} K_{v} (w_{4 R} r) + B_{4} K_{v} (w_{4 L} r)] f_{v} (j v φ), \\ Φ_{4} = [A_{4} K_{v} (w_{4 R} r) - B_{4} K_{v} (w_{4 L} r)] f_{v} (j v φ) . \end{array}

In Eq. (4), the interdependent A₄ and B₄ are field expansion coefficients. The azimuthal order v is an integer. K_ν is the modified Bessel function of the second kind of order ν. The two types of equivalent bulk wave numbers w₄_R and w₄_L are

w_{4 R} = \sqrt{k_{0}^{2} [n_{e f f}^{2} - {(n_{4} + γ)}^{2}]}, w_{4 L} = \sqrt{k_{0}^{2} [n_{e f f}^{2} - {(n_{4} - γ)}^{2}]} .

where n₄ is the refractive index of the chiral drug and n_eff is the mode effective index of the cladding mode.

2.4 Field distributions

The time harmonic electromagnetic fields in the stratified fiber can be written by the following expressions [41]

\begin{array}{l} E = [\partial Ψ / r \partial φ - (β / ω ε_{i}) \partial Φ / \partial r] r - [\partial Ψ / \partial r + (β / ω ε_{i}) \partial Φ / r \partial φ] φ \\ - [(k_{0}^{2} n_{i}^{2} - β^{2}) / j ω ε_{i}] Φ z, \\ H = [\partial Φ / r \partial φ + (β / ω μ_{i}) \partial Ψ / \partial r] r - [\partial Φ / \partial r - (β / ω μ_{i}) \partial Ψ / r \partial φ] φ \\ + [(k_{0}^{2} n_{i}^{2} - β^{2}) / j ω μ_{i}] Ψ z . \end{array}

where r, φ, and z denote the unit radial, tangential, and axial vectors, respectively. ω is the circular frequency of the light. β and k₀ are propagataion constants of the light in the LPFG and free space, respectively. ε_i and μ_i are the region-dependent permittivity and permeability, respectively.

Figure 1 shows the diagram of the transverse refractive index of a thin-film coated LPFG in the chiral drug. r₁ and r₂ are radii of the core and cladding, respectively. r₃-r₂ is the overlay thickness. n₁, n₂, n₃, and n₄ are refractive indices of the core, cladding, thin-film, and chiral drug, respectively.

Fig. 1 Transverse index profile of the LPFG.

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The z components of electromagnetic fields for the cladding modes in the LPFG take the following form

e_{z} = {\begin{cases} - u_{1}^{2} A_{1} J_{v} (u_{1} r) e^{j v φ} / (j ω ε_{1}), r \leq r_{1}, \\ - u_{2}^{2} [A_{2} J_{v} (u_{2} r) + B_{2} Y_{v} (u_{2} r)] e^{j v φ} / (j ω ε_{2}), r_{1} \leq r \leq r_{2}, \\ - u_{3}^{2} [A_{3} J_{v} (u_{3} r) + B_{3} Y_{v} (u_{3} r)] e^{j v φ} / (j ω ε_{3}), r_{2} \leq r \leq r_{3}, \\ [w_{4 R}^{2} A_{4} K_{v} (w_{4 R} r) / (j ω ε_{4}) - w_{4 L}^{2} B_{4} K_{v} (w_{4 L} r) / (j ω ε_{4})] e^{j v φ}, r > r_{3}, \end{cases}

h_{z} = {\begin{cases} u_{1}^{2} C_{1} J_{v} (u_{1} r) e^{j v φ} / (j ω μ_{1}), r \leq r_{1}, \\ u_{2}^{2} [C_{2} J_{v} (u_{2} r) + D_{2} Y_{v} (u_{2} r)] e^{j v φ} / (j ω μ_{2}), r_{1} \leq r \leq r_{2}, \\ u_{3}^{2} [C_{3} J_{v} (u_{3} r) + D_{3} Y_{v} (u_{3} r)] e^{j v φ} / (j ω μ_{3}), r_{2} \leq r \leq r_{3}, \\ [- w_{4 R}^{2} A_{4} K_{v} (w_{4 R} r) / (j ω μ_{4}) - w_{4 L}^{2} B_{4} K_{v} (w_{4 L} r) / (j ω μ_{4})] e^{j v φ}, r > r_{3}, \end{cases}

where

u_{i}^{2} = k_{0}^{2} (n_{i}^{2} - n_{e f f}^{2})

. Field coefficients A₁, C₁, A₂, B₂, C₂, D₂, A₃, B₃, C₃, and D₃ are chosen to weight the fields. J_v and Y_v are the Bessel functions.

By applying boundary conditions of tangential fields e_z, h_z, e_φ, and h_φ at r = r₁, r = r₂, and r = r₃, we can determine the dispersion relation for cladding modes

M_{12 \times 12} [A_{1}, C_{1}, A_{2}, B_{2}, C_{2}, D_{2}, A_{3}, B_{3}, C_{3}, D_{3}, A_{4}, B_{4}] = 0,

and relations between electromagnetic fields in adjacent media

\begin{array}{l} M_{2} {[A_{2} B_{2} C_{2} D_{2}]}^{T} = M_{1} {[A_{1} C_{1} 0 0]}^{T}, M_{6} {[A_{4} B_{4} 0 0]}^{T} = M_{5} {[A_{3} B_{3} C_{3} D_{3}]}^{T}, \\ M_{4} {[A_{3} B_{3} C_{3} D_{3}]}^{T} = M_{3} {[A_{2} B_{2} C_{2} D_{2}]}^{T} . \end{array}

where coefficient matrices

M_{1} = [\begin{array}{l} σ_{2} J_{v} (U_{1}) / (n_{1}^{2} r_{1}) u_{1} {J^{'}}_{v} (U_{1}) 0 0 \\ u_{1} {J^{'}}_{v} (U_{1}) - σ_{1} J_{v} (U_{1}) / (μ_{r 1} r_{1}) 0 0 \\ u_{1}^{2} J_{v} (U_{1}) / n_{1}^{2} 0 0 0 \\ 0 - u_{1}^{2} J_{v} (U_{1}) / μ_{r 1} 0 0 \end{array}],

M_{2} = [\begin{array}{l} σ_{2} J_{v} (U_{2}) / (n_{2}^{2} r_{1}) σ_{2} Y_{v} (U_{2}) / (n_{2}^{2} r_{1}) u_{2} {J^{'}}_{v} (U_{2}) u_{2} {Y^{'}}_{v} (U_{2}) \\ u_{2} {J^{'}}_{v} (U_{2}) u_{2} {Y^{'}}_{v} (U_{2}) - σ_{1} J_{v} (U_{2}) / (μ_{r 2} r_{1}) - σ_{1} Y_{v} (U_{2}) / (μ_{r 2} r_{1}) \\ u_{2}^{2} J_{v} (U_{2}) / n_{2}^{2} u_{2}^{2} Y_{v} (U_{2}) / n_{2}^{2} 0 0 \\ 0 0 - u_{2}^{2} J_{v} (U_{2}) / μ_{r 2} - u_{2}^{2} Y_{v} (U_{2}) / μ_{r 2} \end{array}],

M_{3} = [\begin{array}{l} σ_{2} J_{v} (U_{3}) / (n_{2}^{2} r_{2}) σ_{2} Y_{v} (U_{3}) / (n_{2}^{2} r_{2}) u_{2} {J^{'}}_{v} (U_{3}) u_{2} {Y^{'}}_{v} (U_{3}) \\ u_{2} {J^{'}}_{v} (U_{3}) u_{2} {Y^{'}}_{v} (U_{3}) - σ_{1} J_{v} (U_{3}) / (μ_{r 2} r_{2}) - σ_{1} Y_{v} (U_{3}) / (μ_{r 2} r_{2}) \\ u_{2}^{2} J_{v} (U_{3}) / n_{2}^{2} u_{2}^{2} Y_{v} (U_{3}) / n_{2}^{2} 0 0 \\ 0 0 - u_{2}^{2} J_{v} (U_{3}) / μ_{r 2} - u_{2}^{2} Y_{v} (U_{3}) / μ_{r 2} \end{array}],

M_{4} = [\begin{array}{l} σ_{2} J_{v} (U_{4}) / (n_{3}^{2} r_{2}) σ_{2} Y_{v} (U_{4}) / (n_{3}^{2} r_{2}) u_{3} {J^{'}}_{v} (U_{4}) u_{3} {Y^{'}}_{v} (U_{4}) \\ u_{3} {J^{'}}_{v} (U_{4}) u_{3} {Y^{'}}_{v} (U_{4}) - σ_{1} J_{v} (U_{4}) / (μ_{r 3} r_{2}) - σ_{1} Y_{v} (U_{4}) / (μ_{r 3} r_{2}) \\ u_{3}^{2} J_{v} (U_{4}) / n_{3}^{2} u_{3}^{2} Y_{v} (U_{4}) / n_{3}^{2} 0 0 \\ 0 0 - u_{3}^{2} J_{v} (U_{4}) / μ_{r 3} - u_{3}^{2} Y_{v} (U_{4}) / μ_{r 3} \end{array}],

M_{5} = [\begin{array}{l} σ_{2} J_{v} (U_{5}) / (n_{3}^{2} r_{3}) σ_{2} Y_{v} (U_{5}) / (n_{3}^{2} r_{3}) u_{3} {J^{'}}_{v} (U_{5}) u_{3} {Y^{'}}_{v} (U_{5}) \\ 0 0 u_{3}^{2} J_{v} (U_{5}) / μ_{r 3} u_{3}^{2} Y_{v} (U_{5}) / μ_{r 3} \\ - u_{3} {J^{'}}_{v} (U_{5}) - u_{3} {Y^{'}}_{v} (U_{5}) σ_{1} J_{v} (U_{5}) / (μ_{r 3} r_{3}) σ_{1} Y_{v} (U_{5}) / (μ_{r 3} r_{3}) \\ u_{3}^{2} J_{v} (U_{5}) / n_{3}^{2} u_{3}^{2} Y_{v} (U_{5}) / n_{3}^{2} 0 0 \end{array}],

M_{6} = [\begin{array}{l} w_{4 R} {K^{'}}_{v} (U_{6 R}) + σ_{2} K_{v} (U_{6 R}) / (n_{4}^{2} r_{3}) w_{4 L} {K^{'}}_{v} (U_{6 L}) - σ_{2} K_{v} (U_{6 L}) / (n_{4}^{2} r_{3}) 0 0 \\ - w_{4 R}^{2} K_{v} (U_{6 R}) / μ_{r 4} - w_{4 L}^{2} K_{v} (U_{6 L}) / μ_{r 4} 0 0 \\ σ_{1} K_{v} (U_{6 R}) / (μ_{r 4} r_{3}) - w_{4 R} {K^{'}}_{v} (U_{6 R}) σ_{1} K_{v} (U_{6 L}) / (μ_{r 4} r_{3}) + w_{4 L} {K^{'}}_{v} (U_{6 L}) 0 0 \\ - w_{4 R}^{2} K_{v} (U_{6 R}) / n_{4}^{2} w_{4 L}^{2} K_{v} (U_{6 L}) / n_{4}^{2} 0 0 \end{array}],

\begin{array}{l} u_{1}^{2} = k_{0}^{2} (n_{1}^{2} - n_{e f f}^{2}), u_{2}^{2} = k_{0}^{2} (n_{2}^{2} - n_{e f f}^{2}), u_{3}^{2} = k_{0}^{2} (n_{3}^{2} - n_{e f f}^{2}), \\ U_{1} = u_{1} r_{1}, U_{2} = u_{2} r_{1}, U_{3} = u_{2} r_{2}, U_{4} = u_{3} r_{2}, U_{5} = u_{3} r_{3}, U_{6 R} = w_{4 R} r_{3}, \\ U_{6 L} = w_{4 L} r_{3}, β = n_{e f f} k_{0}, σ_{1} = β j v / (ω μ_{0}), σ_{2} = β j v / (ω ε_{0}) . \end{array}

We reorganize Eq. (10) as

M_{6} {[A_{4} B_{4} 0 0]}^{T} = M_{5} {[M_{4}]}^{+} M_{3} {[M_{2}]}^{+} M_{1} {[A_{1} C_{1} 0 0]}^{T} .

By solving Eqs. (18) and (10), one can successively find the field coefficients expressed in C₁. C₁ can be calculated by determining the following propagation constants and specifying that each cladding mode carry a power of 1W [40].

2.5 Propagation constants

A iterative scheme is proposed to get complex roots β_m of the matrix determinant f(β) = |M_{12 × 12}| = 0. β_m = β_m_,_r + jβ_m_,_i represents the complex propagation constants of the mth mode. β_m_,_r and β_m_,_i denote real and imaginary parts of β_m, respectively.

1) The chirality γ is set as a certain value and the initial value of β_m_,_i (that is, $β_{m, i}^{0}$ ) is taken as zero.
2) The first order approximation $β_{m, r}^{1}$ of $β_{m, r}$ is obtained by plotting the Re(f( $β_{r}, β_{i} = β_{m, i}^{0}$ )) as a function of $β_{r}$ along the real axis which is peaked at $β_{m, r}^{1}$ .
3) The first order approximation $β_{m, i}^{1}$ of $β_{m, i}$ is got by plotting the abs(f( $β_{r} = β_{m, r}^{1}, β_{i}$ )) as a function of $β_{i}$ along the imaginary axis which is peaked at $β_{m, i}^{1}$ .
4) The second order approximation $β_{m, r}^{2}$ of $β_{m, r}$ is found by plotting the abs(f( $β_{r}, β_{i} = β_{m, i}^{1}$ )) as a function of $β_{r}$ which is peaked at $β_{m, r}^{2}$ .

Procedures 3) and 4) are repeated several times until the values of β_m_,_r and β_m_,_i converge. Then the complex mode effective indices of the cladding modes β_m/k₀ can be got.

The modes, coupling coefficients, and coupled-mode theory for the sensing of the chiral drug by using the long-period fiber gratings somewhat follow those in [40].

3. Transmission spectra of an uncoated LPFG

A SMF28 single mode fiber [25] is considered. If there is no special instructions, medium parameters considered for the LPFGs simulated by using the Matlab software are r₁ = 4.15 μm, r₂ = 62.5 μm, n₁ = 1.4681, and n₂ = 1.4628.

The resonant peaks of dual-resonance LPFGs shift in opposite directions with the variation of surrounding refractive index, very high sensitivity can be achieved [1–5]. The manufacturing parameters of the LPFGs are obtained by finding the right combination of parameters (especially the amplitude of the modulation, length, and period of the LPFGs) to attain the dual-band feature in the transmission spectrum. The LPFGs are designed to operate near the turn-around point of the phase-matching curve, which are extremely sensitive to the surrounding changes [1–5]. The resonance between the core mode and the EH_1,20 cladding mode near its turn-around point in this paper produces dual attenuation bands in the working wavelength range.

Figure 2 plots the transmission spectra of an uncoated long-period fiber grating for sensing the chiral drug with n₄ = 1.33, 1.355, and γ = 0, 0.0001, respectively. The amplitude of the modulation, length, and period of the LPFG are 1.86 × 10⁻⁴, 4.7 cm, and 185.6 μm, respectively.

Fig. 2 Transmission spectra of an uncoated LPFG versus the working wavelength for various medium parameters.

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The sensitivity in this paper is expressed as the variation of the difference between two resonance wavelengths against the variation of the refractive index (or the chirality) [1,19]. As shown in Fig. 2, the refractive index sensitivity for the drug with γ = 0 is 1620 nm/RIU and for the chiral drug with γ = 0.0001 is 1418 nm/RIU. The refractive index sensitivity of the uncoated LPFG is small, whereas the dynamic range of the refractive index sensing is relatively large. The chirality sensitivity for the chiral drug with n₄ = 1.33 is 0 nm/chirality and for the chiral drug with n₄ = 1.355 is 50633 nm/chirality, respectively.

In Fig. 2, the left minimum transmission decreases as the chirality of the chiral drug increases and refractive index decreases. The right minimum transmission is more sensitive to the smaller variation of the chirality than the bigger variation of the refractive index. By comparing with numerical results in [25], one can find that the effects of the chirality of the drug on resonance wavelengths and minimum transmissions of the LPFG are similar to those of real and imaginary parts of the refractive index of the overlay. Maybe the obvious change of minimum transmissions is caused by the impedance-matching owing to the chirality of the chiral drug.

4. Numerical analysis of a coated LPFG

A thin-film coated long-period fiber grating is proposed in this section to probe the chiral drug by by optimizing the thickness of the film and parameters of the long-period fiber gratings [1–8]. The thin film is a high refractive index polymeric overlay [7]. The thickness and refractive index of the thin film are 280 nm and n₃ = 1.578 [7], respectively. The amplitude of the modulation for the grating is 1.73 × 10⁻⁴. The length and grating period of the LPFG are 1.9 cm and 189.4 μm, respectively.

4.1 Mode effective index

Figure 3 compares real and imaginary parts of the mode effective index of the EH_1,20 (the tenth EH_1,j) cladding mode as a function of the working wavelength and chirality of the chiral drug. In Figs. 3(a) and 3(b), the imaginary part of the chirality Im(γ) is zero. In Figs. 3(c) and 3(d), the real part of the chirality Re(γ) is zero.

Fig. 3 Mode effective index of the coated LPFG versus the working wavelength and chirality of the chiral drug. (a) Re(n_eff) versus λ and Re(γ), (b) Im(n_eff) versus λ and Re(γ), (c) Re(n_eff) versus λ and Im(γ), (d) Im(n_eff) versus λ and Im(γ).

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The searching upper limit of the mode effective index of the cladding mode in the LPFG is n₃ instead of n₂. Therefore, there is no distinct mode transition versus the working wavelength in Figs. 3(a) and 3(b). Both Re(n_eff) and Im(n_eff) increase with the increase of Re(γ). Re(n_eff) decreases and Im(n_eff) increases with the increase of the working wavelength.

As Im(γ) is larger than 2 × 10⁻⁴, both Re(n_eff) and Im(n_eff) exhibit considerable vibrations in Figs. 3(c) and 3(d). One can find that Im(n_eff) generated by Re(γ) and Im(γ) differ by several orders of magnitude. The imaginary part of the mode effective index represents the power loss, which may cause the decrease of the transmission. The shift of Im(n_eff) generally induces the variation of resonance strengths, whereas Re(n_eff) affects resonance wavelengths of the coated LPFG.

4.2 Transmission spectra

Figure 4 illustrates the effects of the refractive index, real and imaginary parts of the chirality on the transmission spectra of the LPFG immersed in the chiral drug.

Fig. 4 Transmission spectra of the coated LPFG structure versus the working wavelength for various medium parameters. (a) γ_i = 0, (b) n = 1.35.

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In Fig. 4(a), the LPFG possesses two resonance wavelengths for various medium parameters. The left resonance wavelengths are 1411 nm and 1401 nm, and right resonance wavelengths are 1614 nm and 1624 nm for the achiral drug with n = 1.348 and n = 1.35, respectively. The refractive index sensitivity 10000 nm/RIU is achieved as the chirality γ is zero. The two resonance wavelengths of the coated LPFG are insensitive and minimum transmissions are very sensitive to Re(γ)-induced changes in the transmission spectra. As the refractive index of the chiral drug is 1.35 and chirality γ is less than or equal to 0.001, the resonance wavelengths are 1401 nm and 1624 nm, respectively. The left and right minimum transmissions are −16.4 and −13.0 for γ = 0, −18.1 and −13.9 for γ = 0.0005, −23.5 and −13.8 for γ = 0.001, −20.7 and −11.9 for γ = 0.002, respectively. The left resonance wavelength becomes 1396 nm as the chirality of the chiral drug is 0.002. The change of minimum transmissions caused by the comparatively small chirality may be due to the impedance-matching.

As the imaginary part of the chirality increases ranging from 0 to 0.0002 in Fig. 4(b), the two resonance wavelengths keep invariant, the left minimum transmission decreases, and right minimum transmission increases. As Im(γ) is larger than 0.0002, both the right resonance wavelength and two minimum transmissions are sensitive to the variation of the imaginary part of the chirality.

4.3 Resonance wavelengths and minimum transmissions

Figure 5 displays resonance wavelengths and minimum transmissions of the LPFG in the chiral drug with various medium parameters. As the refractive index of the chiral drug increases, the right resonance wavelength and right minimum transmission increase; and the left resonance wavelength decreases. As the chirality becomes γ = 0.001 and 0.002, the left minimum transmission fluctuates with the increase of the refractive index.

Fig. 5 Resonance wavelengths and minimum transmissions of the coated LPFG structure for different chirality and refractive indices. (a) Resonance wavelengths, (b) Minimum transmissions.

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The influences of the real part of the chirality on the two resonance wavelengths are small. In Fig. 5(b), the left resonant peak for the chiral drug with γ = 0 is −19.05 dB for n₄ = 1.345 and −16.42 dB for n₄ = 1.35. The left resonant peak for the chiral drug with n₄ = 1.35 and γ = 0.001 is −23.55 dB. The changes of the minimum transmission are 526 dB/RIU for γ = 0 and 7130 dB/chirality for n₄ = 1.35, respectively. The shifts of the two minimum transmissions caused by the chirality of the chiral drug in Fig. 5(b) are more obvious than those caused by the refractive index.

5. Conclusion

An uncoated and a high refractive index coated long-period fiber grating are proposed to investigate the sensing of the chiral drug by integrating the magnetoelectric coupling constitutive relations into the electromagnetic field theory for the four step-index fiber geometry. The responses of the LPFGs to the surrounding refractive index, real and imaginary parts of the chirality are studied. We observe that the mode effective index of the LPFG is complex and the imaginary part of the mode effective index generated by the chirality can explain the variations of the two minimum transmissions. The two resonance wavelengths of the coated LPFG are very sensitive to the refractive index of the chiral drug, whereas the two minimum transmissions are more sensitive to the real and imaginary parts of the chirality due to the impedance-matching. The resonance wavelengths for the chiral drug with n₄ = 1.35 keep invariant as the chirality change from 0 to 0.001. The amplitude sensitivity of the chirality is larger than that of the refractive index for the chiral drug with n₄ = 1.35. If the two minimum transmissions of the LPFGs change and resonance wavelengths keep invariant, the change is induced by the comparatively small chirality of the chiral drug. If the amplitude sensitivity is larger, the response of the LPFGs is mainly generated by the chirality. By incorporating the developed electromagnetic field theory and coupled-mode theory into the genetic algorithm, we can further obtain the refractive index and chirality of the chiral drug based on measured transmission coefficients by fabricating and using the proposed coated LPFG. Moreover, the surrounding refractive index and chirality sensitivities of the LPFG can be enhanced by etching the fiber cladding. The reported findings are believed to provide guidelines for LPFG based chemical and biological sensors’ potential applications in the noninvasive enantiomeric content detection of chiral drugs.

Funding

Sichuan Science and Technology Program under Grant 2019YJ0188; National Key Laboratory of Electromagnetic Environment.

Disclosures

The authors declare no conflicts of interest.

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Probing a chiral drug using long period fiber gratings

Abstract

1. Introduction

2. Theory

2.1 Constitutive relations for a chiral drug

2.2 Wave decomposition and transformation

2.3 Debye potentials for a chiral drug

2.4 Field distributions

2.5 Propagation constants

3. Transmission spectra of an uncoated LPFG

4. Numerical analysis of a coated LPFG

4.1 Mode effective index

4.2 Transmission spectra

4.3 Resonance wavelengths and minimum transmissions

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (5)

Equations (18)

Optics Express