Modulation instability and highly sensitive optical fiber biosensor

S. A. Madani; S. A. Madani; M. Bahrami; A. Rostami; A. Rostami

doi:10.1364/OPTCON.456317

1. Introduction

The optical fiber-based technology is one of the most important approaches to the detection and analysis of different important parameters in biomedical issues. Nowadays, optical fiber-based biosensors are very popular in comparison with other biosensors based on surface plasmon resonance [1,2], ring resonator [3,4], interferometry [5,6], etc. The reasons for this popularity are the undeniable advantages such as high sensitivity, simple configuration, low fabrication cost, low transmission loss [7,8]. Furthermore, the optical fiber biosensors based on Fiber Bragg grating, fiber coupler, and fiber Fabry-Perot cavities are optical sensors in which label-free detection is accessible [9–11]. However, these fiber-based biosensors in order to be label-free, require some excessive processes such as the creation of grating and etching the cladding layer. Moreover, these biosensors usually cannot be used as lab-on-a-chip biosensors and their sensing mechanism are not all-optical. To cope with these problems and design ultra-high sensitive sensors, the nonlinear features of the optical fiber can be applied.

Nonlinear optical phenomena are one of the sensing mechanisms in different types of sensors [12,13]. Some of these phenomena, such as second harmonic generation (SHG), third-harmonic generation (THG), etc., cause the generation of high-frequency components [14]. Since the generated harmonics are far away from the input spectrum, the sensing mechanism based on the shift of these harmonics requires detectors with different spectral regions. The difference between the spectrum of input source and detector makes the sensing process to be difficult. In order to overcome this problem, the generated sidebands should be in the input spectrum range. One of the nonlinear phenomena which create the generation of sidebands around the pump frequency is modulation instability (MI). The creating agent of the MI process is the interaction between input photons and phonons of media which leads to the exponential growth of weak perturbation such as quantum noise in the dispersive medium [14–19]. In this process, sidebands are created when all the involved waves are phase-matched [14,20–22]. The generated sidebands are generated during the MI process, are symmetric around the pump frequency because of energy conservation law. These sidebands which have maximum amplitude are referred to as Stokes and anti-Stokes sidebands. The shift of these sidebands could be an appropriate mechanism for sensing. This mechanism is used in the biosensor, strain sensor, refractive index sensor, magnetic field sensor, and temperature sensor [23–29].

In the MI-based fiber-optic biosensor, the sensing mechanism is based on the shift of generated sidebands (Stokes and anti-Stokes) after capturing the target biomolecules. By using this method two different biosensors are proposed [26,27]. One of these biosensors is based on the photonic crystal fiber which its length is 50cm and the peak pump power is 500 W. The sensitivity of this sensor is 10.4 nm/nm [26]. The other biosensor is based on a chalcogenide tapered fiber. The length of this sensor is 1.2 cm, the pump power is 500mW, and the sensitivity of this biosensor is 17.8 nm/nm [27]. The sensitivity of MI-based biosensors is defined based on surface sensitivity, which refers to the shift of the generated sidebands per nanometer of the target molecule at the sensor surface [30,31]. The thickness and refractive index of the biolayer have important roles in sensor sensitivity. According to the concept of surface sensitivity, light propagation in the proposed sensors is such a way that it has maximum interaction with the sensor surface and the attached target molecule. Therefore, maximum sensitivity is obtained.

One of the most crucial factors in the fiber-based biosensors is obtaining the lab-on-a-chip concept [32–35]. In order to achieve this concept in MI-based biosensors, the length of the sensor should be extremely short. To realize this aim, the high nonlinear refractive index materials are selected in order to manufacture biosensors.

In this paper, given all the recent activities in the MI-based sensors field, the importance of DNA detection [36,37], and as well as the advances in optical fiber design and fabrications [38–43], we move towards proposing new structures of optical fiber in order to achieve highly sensitive, label-free, and lab-on-a-chip biosensors. In the proposed MI-based biosensors, after capturing the target biomolecules, Stokes and anti-Stokes sidebands are shifted more than the other MI-based biosensors and, as a result, the proposed sensors are more sensitive. Furthermore, by using the highly nonlinear material in proposed structures, we obtained short-length sensors at low pump power.

This paper is organized as follows: In section 2 theoretical modeling of sensing mechanism and MI process are presented. In section 2 new structures of MI-based optical fiber biosensors are proposed. Section 3 consists of the simulation results and also discussions about the advantages of the proposed structure. Finally, the paper ends with a conclusion.

2. Mechanism and structure of the sensing

The sensing mechanism of the proposed biosensors is based on the shift of Stokes or anti-Stokes sidebands. These sidebands which are generated during the MI process, are symmetric around the pump frequency because of energy conservation law. These sidebands depend on the effective refractive index and total dispersion which consists of material and waveguide dispersion. Therefore, Stokes or anti-Stokes sidebars can be shifted due to changes in total dispersion. These changes in the dispersion can be done through the presence of additional material in propagating medium. This material could be a biolayer that is attached to the sensor. Also, due to the importance of DNA detection in the biological world [36,37], we have considered DNA as the target biolayer.

2.1 MI process

The MI process is similar to degenerate four-wave mixing (FWM), which is the basic principle for detection mechanism in nonlinear optical fiber biosensors [26,27]. The MI is due to the interaction between anomalous group velocity dispersion and the Kerr nonlinearity effect. The effect can be explained using linear stability analysis performed on analytical solutions to the nonlinear Schrödinger equation with considering second-order dispersion [14,44,45]:

(1)$$\frac{{\partial A}}{{\partial z}} + i\frac{{{\beta _2}}}{2}\frac{{{\partial ^2}A}}{{\partial {t^2}}} - i\gamma {|A |^2}A = 0$$

where $A$ is the slowly varying amplitude of the electric field envelope, $\beta {}_2$ is the second-order dispersion coefficient, $\gamma ({{\omega_0}} )= {{{n_2}{\omega _0}} / {c{A_{eff}}}}$ is the nonlinearity parameter, c is the speed of light in vacuum, ${\omega _0}$ is the central frequency of pump, $A{}_{eff}$ is effective-area and $n{}_2$ is the nonlinear refractive index. By solving this equation using the perturbation theory, can be obtained MI gain relation. However, anomalous dispersion (${\beta _2}\langle 0$) is necessary for realizing the MI process [14,22,29,30,46]. In this case (${\beta _2}\langle 0$), sidebands around the pump signal are generated and grow exponentially. Here the gain spectrum is given as:

(2)$$g(\Omega )= |{{\beta_2}\Omega } |\sqrt {\frac{1}{{2|{{\beta_2}} |{L_{NL}}}} - \frac{{{\Omega ^2}}}{{16}}} ,\quad \;{L_{NL}} = \frac{1}{{\gamma {P_0}}}.$$

${L_{NL}}$ is nonlinear length, ${P_0}$ is the peak power of the pump. This equation indicates that the first-order dispersion ${\beta _1}$ has no effect on the MI gain profile. The frequencies with the maximum gain in the MI output spectrum are known as Stokes and anti-Stokes frequencies which are critical parameters in the sensing process. The Stokes and anti-Stokes frequencies are considered as ${\omega _s}$ and ${\omega _{as}}$ in Eq. (3), respectively.

(3)$${\omega _s} = {\omega _0} - {\Omega _{\max }}\quad ,\quad {\omega _{as}} = {\omega _0} + {\Omega _{\max }}\quad ,\quad {\Omega _{\max }} = \sqrt {\frac{{4\gamma {P_0}}}{{|{{\beta_2}} |}}}$$

where ${\Omega _{\max }}$ is the frequency in which the MI gain is maximum. According to Eq. (2), variations in the effective refractive index cause a change in the MI gain profile. As a result, Stokes and anti-Stokes sidebands are shifted. The variations in the effective refractive index may be occurred through attaching the biolayer. Hence the changing in the profile of MI gain can be used for biosensing.

2.2 Proposed structures for biosensor

We investigated different geometric shapes for the proposed structure. Three cases of the best shapes are shown in Fig. 1. These structures consist of four and five cores which are connected together through holders within a cladding. The space between cores and cladding is filled by an aqueous solution during sensing. The use of an aqueous environment increases the interaction of light and the target layer. ${t_{c - layer}}$ represents capture layer that is immobilized on the outer of cores. This layer is used to catch the target biomolecules (DNA). These target molecules are illustrated in Fig. 1 by ${t_{b - layer}}$.

Fig. 1. The proposed setup and structures for MI-based optical fiber biosensors. The dimensions of the biosensor structures (diameters of central and lateral cores, the width of holders, the space between central and lateral cores, the space between lateral cores and cladding) are listed in Table 1. ${t_{c - layer}}$ (=40 nm) and ${t_{b - layer}}$ (=5 nm) are thicknesses of capture layer and target layer.

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The material of the structures is CS 3-68 which is a conventional glass doped by CdS, Se, and S. This material is selected because of its high nonlinear properties. The nonlinear refractive index (${n_2}$) of CS 3-68 is equal to $2.3 \times {10^{ - 10}}{\raise0.5ex\hbox{$\scriptstyle {c{m^2}}$}/\lower0.25ex\hbox{$\scriptstyle W$}}$[47,48]. This value is about ${10^3}({10^6})$ times higher than the nonlinear refractive index of chalcogenide glasses (silica) [49]. Using this material causes the length of the structure to be reduced and also lowers the required pump power. The shorter length of the sensor makes it suitable to be integrated and consequently applicable in lab-on-a-chip.

3. Simulation and discussion

The dimensions of the biosensor structures which are illustrated in Fig. 1 are given in Table 1.

Table 1. Dimensions of the proposed structures.

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Due to the advances in the design and fabrication of optical fibers [38–43], the dimensions of these parameters are considered in such a way that they can be fabricated.

The modal analysis is performed for the biosensor using the finite difference eigenmode (FDE) solver. The analysis is done in the optical C-band around the wavelength of 1.55$\mu m$. The sources which can generate the optical power around this wavelength are easily available. The pump power which is used in the simulation is 100mW. It is five times less than previous research [27]. Regarding the minimum dimension in the structures is 5nm, the mesh step is selected 2nm in order to accurate solving. The refractive indexes of capture and target layers are considered to be 1.45 [26,27,50]. The simulation results of propagation mode profiles in three different situations are illustrated in Fig. 2. Figure 2(a), Fig. 2(d) and Fig. 2(g) demonstrate the mode profiles without capture and target layers in three proposed structures. Considering the target biomolecule to be a simple double-stranded DNA, the capture layer like poly-L-lysine should have at least 40nm thickness [26,50]. The mode profiles of three proposed structures after adding the capture layer are illustrated in Fig. 2(b), Fig. 2(e) and Fig. 2(h). After capturing the target biomolecule with the thickness of 5nm, the mode profiles of the three proposed structures are shown in Fig. 2(c), Fig. 2(f) and Fig. 2(i) [26]. Comparison between the propagation mode profiles shows significant changes. Especially after capturing the target biomolecule.

Fig. 2. Propagation mode profiles of the proposed structures. (a), (d), (g): without any additional layers. (b), (e), (h): after adding capture layer. (c), (f), (i): after capturing the target biomolecule by capture layer.

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The dispersions curves ($D = {{2\pi c{\beta _2}} / {{\lambda ^2}}}$) and second-order dispersions curves (${\beta _2}$) of the proposed structures are shown in Fig. 3. Figure 3(a), Fig. 3(b) and Fig. 3(c) demonstrate dispersions curves of proposed structures. The second-order dispersions curves of proposed structures are illustrated in Fig. 3(d), Fig. 3(e) and Fig. 3(f), respectively. These results are obtained by frequency analysis in the wavelength range 1-1.7$\mu m$.

Fig. 3. (a),(d): Dispersion and second-order dispersions curves of the structure 1. (b),(e): dispersion and second-order dispersions curves of the structure 2. (c),(f): dispersion and second-order dispersions curves of the structure 3. i: without any additional layers, ii: after adding capture layer, iii: after capturing the target biomolecule by capture layer.

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According to the results of Fig. 2, it is expected that the distribution of mode shape and optical power in additional cores leads to high dispersion. This fact is clearly visible in Fig. 3 and Table 2. As an instance, in structure 3 at the wavelength of 1550 nm, the dispersion value is modified from +40.53 to +18.49 after capturing the target biomolecule and causes the foremost of power to be guided in the central core.

Table 2. The optical specifications of the proposed structures at $\lambda = 1550nm$

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In order to obtain parameters of the MI process as the sensing mechanism in the proposed structures, the values of Table 2 are applied in Eq. (2) and Eq. (3). Consequently, the maximum gain frequency, the Stokes, and anti-Stokes frequencies are calculated and given in Table 3. As the length of the sensor is sufficiently short, the propagation loss is negligible and as a result, this loss does not affect the MI gain.

Table 3. The Values of the MI parameters in the proposed structures.

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The obtained MI gain profiles for the proposed structures are shown in Fig. 4. The capture of the target layer changes the total dispersion and effective refractive index of the structures. As a result, the MI gain profiles change, and the stokes and anti-stokes sidebands shift to the lower and higher frequencies, respectively. This frequency shift of the sidebands is the sensing mechanism principle. The maximum MI gain that occurs in stokes and anti-stokes sidebands, is obtained from Eq. (2), ${g_{\max }} = g({{\Omega _{\max }}} )= \gamma {P_0}$. After capturing the target layer, the effective area of the proposed structures is increased (based on Table 2) and consequently, the maximum MI gain is slightly decreased. The MI gain profiles and their variations for the proposed structures are demonstrated in Fig. 4(a), Fig. 4(b), and Fig. 4(c). Based on the MI gain profiles, the pump signal, stokes, and anti-stokes wavelengths are highlighted in Fig. 4(d) Fig. 4(e), and Fig. 4(f).

Fig. 4. (a), (b), (c): MI gain profiles of the proposed structures. (d), (e), (f): Stokes, anti-Stokes, and pump peak of the proposed structures. i: without any additional layers, ii: after adding capture layer, iii: after capturing the target biomolecule by capture layer.

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The shift of the Stokes sideband is greater than the anti-Stokes sideband in the wavelength domain. As an instance, in structure 3 with regard to pump wavelength (1550 nm), the Stokes and anti-Stokes wavelengths are 1864.15 nm and 1326.51 nm, respectively. After capturing the target layer the Stokes and anti-Stokes wavelengths shift to 2038.57 nm and 1250.38 nm, respectively. For this reason, the Stokes sideband is used to express the sensitivity. As mentioned, the sensitivity of the biosensor is defined as the shift of the Stokes sidebands per thickness of target biomolecules [26,27]. Hence, the sensitivity is defined in Eq. (4) which ${\lambda _{s2}}$, ${\lambda _{s1}}$ and t Stokes wavelength after immobilizing the capture layer, Stokes wavelength after capturing the target layer, and thickness of the target layer, respectively.

(4)$$S = \frac{{{\lambda _{s2}}\, - \,{\lambda _{s1}}\,}}{t}.$$

In order to realize the MI process and lab-on-a-chip concept simultaneously, the length of the sensor should be at least the nonlinear length of the proposed structures. The sensitivity and length of the proposed biosensors are given in Table 4. At best (structure 3), the proposed biosensor is about 2 times more sensitive than the previous MI-based biosensor. Furthermore, in this case, the length of the proposed biosensor is more compatible than the previous works with lab-on-a-chip technology [27].

Table 4. The sensitivity and length of the proposed biosensors.

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4. Conclusion

In this paper, MI-based fiber biosensors are introduced whose detection is label-free and selective. The sensing mechanism is based on shifting the Stokes sideband in the MI process after capturing the target layer (DNA). In order to achieve a highly sensitive biosensor, the three structures are presented. The material of the proposed structures is considered to be CS 3-68 glass which has high nonlinear refractive. As a result, the pump power required (in order to occur MI process) and the length of the proposed biosensors are reduced. The reduction of the biosensor length realizes the Lab-on-a-chip concept. Another advantage of the proposed structures is that high sensitivity can be achieved using conventional low-power laser sources. In the best case, we achieved a sensitivity of 34.88 nm/nm and a sensor length of 0.199 cm when the pump power is 100mW at wavelength 1550 nm.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Structure 1 (µm)		Structure 2 (µm)		Structure 3 (µm)
$a_{1}$ =2.4	$a_{2}$ =2.2	$a_{1}$ =2.42	$a_{2}$ =2.2	$a_{1}$ =2.4	$a_{2}$ =2.2
b = 0.3	$c$ =0.75	b = 0.3	$c$ =0.85	b = 0.3	$c_{1}, d_{2}$ =0.6
$d$ =0.7	−	$d$ =0.66	-	$c_{2}$ =1.2	$c_{3}, d_{4}$ =0.8
-	-	-	-	$c_{4}, d_{3}$ =1	$d_{1}$ =1.2

	Structure 1			Structure 2			Structure 3
	D (ps/km.nm)	$β_{2}$ ( $p s^{2}$ /km)	$A_{e f f}$ ( $μ m^{2}$ )	D (ps/km.nm)	$β_{2}$ ( $p s^{2}$ /km)	$A_{e f f}$ ( $μ m^{2}$ )	D (ps/km.nm)	$β_{2}$ ( $p s^{2}$ /km)	$A_{e f f}$ ( $μ m^{2}$ )
without any additional layers	42.83	−54.63	16.29	47.41	−60.46	21.11	38.03	−48.51	16.56
after adding the capture layer	44.56	−56.83	17.13	49.34	−62.92	21.39	40.53	−51.69	17.19
after capturing the target biomolecule	25.26	−32.22	18.75	20.30	−25.89	23.81	18.49	−23.58	18.63

	Structure 1			Structure 2			Structure 3
	$Ω_{m a x}$ (THz)	$λ_{a s}$ (nm)	$λ_{s}$ (nm)	$Ω_{m a x}$ (THz)	$λ_{a s}$ (nm)	$λ_{s}$ (nm)	$Ω_{m a x}$ (THz)	$λ_{a s}$ (nm)	$λ_{s}$ (nm)
without any additional layers	203.63	1326.69	1863.8	170.87	1358.98	1803.59	215.38	1316.72	1883.83
after adding the capture layer	195.65	1335.14	1847.37	166.40	1363.37	1795.91	204.79	1326.51	1864.15
after capturing the target biomolecule	248.37	1287.05	1948.09	245.87	1289.20	1943.17	291.26	1250.38	2038.57

	Sensitivity (nm/nm)	Length (cm)
Structure 1	20.14	0.201
Structure 2	29.45	0.255
Structure 3	34.88	0.199

Structure 1 (µm)		Structure 2 (µm)		Structure 3 (µm)
$a_{1}$ =2.4	$a_{2}$ =2.2	$a_{1}$ =2.42	$a_{2}$ =2.2	$a_{1}$ =2.4	$a_{2}$ =2.2
b = 0.3	$c$ =0.75	b = 0.3	$c$ =0.85	b = 0.3	$c_{1}, d_{2}$ =0.6
$d$ =0.7	−	$d$ =0.66	-	$c_{2}$ =1.2	$c_{3}, d_{4}$ =0.8
-	-	-	-	$c_{4}, d_{3}$ =1	$d_{1}$ =1.2

Modulation instability and highly sensitive optical fiber biosensor

Abstract

1. Introduction

2. Mechanism and structure of the sensing

2.1 MI process

2.2 Proposed structures for biosensor

3. Simulation and discussion

4. Conclusion

Disclosures

Data availability

References

Data availability

Cited By

Figures (4)

Tables (4)

Equations (4)

Optics Continuum