Design and optimization of tapered optical fiber probes for SERS utilizing FDTD method

doi:10.21203/rs.3.rs-1524686/v1

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Design and optimization of tapered optical fiber probes for SERS utilizing FDTD method

https://doi.org/10.21203/rs.3.rs-1524686/v1

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In this work, we report a strategy of Ag nanoparticles (Ag NPs) coated tapered optical fiber probes by finite difference time domain (FDTD) simulations. Investigation shows that the fiber tip decorated Ag NPs have excellent electric field enhancement and confinement of light capabilities compared with fiber tips. Moreover, we demonstrate the effect of key parameters such as tip radius, conical angle, Ag NPs size and gaps between them on the field enhanced utilizing typical excitation wavelength of 532, 633 and 785 nm. To further improve the electrical field effect, a noble metal substrate is introduced below the tip apex which exhibits a higher field enhancement generated by tip-substrate coupling. The presence of the Au substrate does not lead to a significant change in the plasma characteristic peak of the probes at 490 nm. This study provides a useful reference for the fabrication of tapered optical fiber with plasmonic nanostructures and the design of robust tapered fiber-optic Raman sensors.

Tapered optical fiber

Ag NPs

FDTD simulation

Surface enhanced Raman scattering

Sensitive optical fiber as a powerful sensing technology can be used in various applications, such as food safety, environmental, chemical, and biological sensing [1–3]. With the development of optical fiber technology, several studies combining the surface enhanced Raman scattering (SERS) with optical fiber to develop promising LSPR and SERS fiber probe have been reported [4, 5]. Compared with tradition SERS substrates, the fiber probes can not only realize large SERS enhancement but also provide an ideal platform for remote measurements and making in situ sensing possible [6–8]. As a result, the development of excellent SERS-based sensors has received widely attention in both industry and academia.

The key principle of the SERS fiber probes is the preparation of nano-structures at the end of the excitation fiber and modified SERS-active sensing layer such as noble metal nanoparticles and metal films. In addition, it is known fact that the detection sensitivity of the probes is related to the local electric field enhancement generated by the plasma micro/nanostructure, in which the fiber probe can be delivered both the excitation light to the sample and the backscattered SERS signal to the Raman spectrometer. To date, there are various types of optical fiber structures serving developed as SERS fiber probe [9–13]. Although many fibers probe have been prepared and the excellent Raman signals obtained, the practical applications of SERS are still limited especially the knowledge of electromagnetic field enhancement mechanism [14, 15]. The current theoretical analysis method for SERS fiber probes, numerical analysis is a powerful tool for analyzing of electromagnetic field enhancement and for system design of the probes. To obtain high Raman enhancement, several performance improvement methods are usually combined with numerical simulations to optimize the geometry of the fiber probes and shearing the SERS-active layer. Tang et al. [16] successfully have fabricated spherical SERS fiber probes and coated the spherically fiber tips with Ag NPs. The high SERS enhancement factor can be obtained by optimizing the diameter of the fiber spheres. A grid nanostructured SERS fiber sensor using the numerical simulation analysis has presented and shown a double characteristic peak, which offers the possibility to realize plasmon resonance excitation mode [17]. In addition, the field enhancement properties and parameter optimization of tapered fiber SERS probes coated with Au NPs on their tip have also investigated using the FDTD method [18]. The FDTD method are also applicable to the design of gas fiber probes to analysis of the electric field distribution and polarization properties, and the interpretation of the physical mechanisms [19, 20]. The three-dimensional computation numerical can be used to pinpoint the location of hot spots on the probe surface and to analyze the ultrashort pulse propagation of the tapered optical fiber probe [21]. Both the above theoretical and experimental studies show that the higher SERS sensitivity of the probe are strongly influenced by fiber geometry, and the NPs. At present, various methods are used to fabricate SERS fiber probes with randomly undefined shapes and sizes [22, 23]. This is mainly due to the effect of fiber size, poor operability, and controllability of the fabrication procedures. Therefore, it is necessary to combine numerical modeling simulation to design probes, which can get further insights into the general importance of identified relationships, and reduce production cost and improve production efficiency of the probes. Among them, tapered fiber probes have a larger specific surface area than other shape probe and show many advantages of the high light transmission efficiency and large interaction area for the excitation light and SERS signal [24].

In this study, a FDTD simulations is used to design and to numerical simulate the tapered fiber probes. The results show that the field enhancement properties of the fiber tip modified Ag NPs are significantly improved. Moreover, the relevant parameters including tip radius, cone angles, Ag NPs size and gaps between them were optimized. Finally, the electric field strength can be further improved by introducing a noble metal substrate below the fiber tip. This study provides a realistic theoretical reference for the application study of tapered fiber probes in Raman spectroscopy.

Firstly, we designed a tapered fiber probe with Ag NPs modified on the surface of fiber tip. A default design parameter with a reasonable range of the tapered angle (θ = 41.2°), tip radius (50 nm), Ag NPs radius (50 nm), the gap between Ag NPs (5 nm), and gap between the Ag NPs and fiber tip surface of 1 nm was provided [25]. Subsequently, the full-field electromagnetic simulations were performed using FDTD method via a commercial software package (Lumerical Solutions, Inc.) to investigate the local electric field enhancement and SERS enhancement factor (EF). The base solver directly solves Maxwell’s equations in both time and space on a spatial grid where is without any simplifying approximations, making analysis far accurate. Moreover, the FDTD provides three-dimensional (3D) and two-dimensional (2D) models, as well as intuitive CAD modeling windows which is suitable for simulating of any complex model and showing results. To improve simulation efficiency, trade-off memory requirements and simulation time for an ordinary computer, a 2D simulations model of tapered fiber coated with Ag NPs were designed on x-y plane, as shown in Fig. 1. This appropriate simplified 2D scattering problem will not reduce results accuracy [26]. Gaussian Beam was used as excitation light with a same total width as the excitation boundary, and the excitation field amplitude (E₀) was set 1 V/m. The vector K was defined to propagate in the y direction with a polarization mode either in the x- or z-directions (p- and s polarization, respectively). Perfectly matched layers (PML) were used in the x-y directions as the boundaries conditions to truncate computational regions. According to Drude model, the dielectric constant (ε_m) of Au in the visible and near-IR can be written as [27].

$${\epsilon }_{m}\left(\omega \right)={\epsilon }_{{\infty }}-\frac{{\omega }_{p}^{2}}{{\omega }^{2}+{i\omega \omega }_{c}}$$

Where${\epsilon }_{{\infty }}$is the angular frequency of incident light, ω_p is the plasma frequency of Ag which is the frequency of the oscillations of electron density in the metal, ω_c stands for collision frequency, which corresponds to the damping of electron density oscillations due to collisions among the electrons, and the data are given by Johnson and Christy [28]. As for calculation capability, the mesh spacing is fixed at dx = 0.001 µm and dy = 0.001 µm to ensure accuracy sufficient and stability for this study.

3.1. Uncoated tapered optical fiber

Before studying other parameters, the optical propagation characteristic in an uncoated tapered optical fiber was analyzed by two different polarization directions. The incident light is perpendicular to excitation boundary, the shape of the fiber tip was determined by tip radius 50 nm, excitation boundary of the radius width 0.8 µm and cone angle of 41.2°. Figure 2 shows the spatial field distribution of the fiber tip calculated by 2D-FDTD simulations. For two different polarizations: Fig. 2(a) is p-polarised and Fig. 2(b) is s-polarised light excited by 785 nm, respectively. The color map represents the maximum electric field value. From this Figure, it can also be observed that the intensity radiation shows an enhancement close to the fiber tip, the electric field intensity (|E|/|E₀|_max) of a p- and s-polarised is 1.52 and 1.89, respectively. In addition, the tapered region is smaller along the axial direction of the fiber tip and the fiber’s cross section decreases due to the tapering of the fiber, resulting the diffractive effect is significantly enhanced and the light escapes to the surrounding area via the evanescent field. The energy of the evanescent field is inherently related to the refractive index, indicating that higher the refractive index of the surrounding medium the fiber, the less confined will be the light in the fiber [25]. Therefore, the uncoated tapered optical fiber is poor confinement of light field in a small cross-section area.

3.2. Tapered optical fiber with Ag nanoparticles

A tapered optical fiber of the local electric field enhancement is investigated when Ag NPs are coated at the fiber tip. As above, the shape of the fiber tip was determined using default value, the radius of the Ag NPs is taken as 50 nm and the gap between them is 5 nm, and the NPs are 1 nm away from the fiber tip surface. For p-polarisation, Fig. 3 shows a simulated electric field distribution of a tapered optical fiber with different wavelengths of 532, 633, and 785 nm. These results demonstrate that the electric field can be significant enhanced in p-polarised light due to the light leaking out from fiber and excitation of localized surface plasmons (LSPs) between the Ag NPs. Furthermore, the “hot spot” which is dependent on the interaction between the nano-structures and excitation light occurs between the Ag NPs, and the positions moved at different wavelength. The |E|/|E₀|_max is arrived at 15.8 in case of tapered optical fiber at 532 nm. For s-polarised light, Fig. 4 shows that the evanescent field uncoupling the LSPs between neighboring Ag NPs, obviously, they do provide a reflective layer, like a mirror, that reflects light back into the tip, creating a standing wave [25]. The maximum electric field intensity is 4.46. The s-polarized electric field characteristics do not exhibit obvious variers in all wavelengths. Thus, we will focus on p-polarized light in the subsequent analyses.

Further, the optical characteristic of the proposed probes was performed which transmission spectrums is measured by frequency-domain field and power, and the monitor present on 20 nm underneath the fiber tip. Figure 5 (a), a peaks concave at 490 nm is observed. This phenomenon indicates that excitation wavelength at 490 nm is due to absorption between the Ag NPs, resulting the transmission spectrum is concaved. For SERS fiber probes, it is important to select the appropriate lasers to excite plasmon which is advantageous in Raman applications and enhanced signals. So, we analyze maximum electric field along a line connecting the Ag NPs at different wavelength, as shown in Fig. 5(b). The result suggests that the electric field intensity in 490 nm is significantly higher than over the whole wavelength from 450 to 800 nm. This is expected since the fiber tip coated Ag NPs, the dip of the transmission spectrum is the signature of the excitation of the fundamental gap plasmon resonance [25, 29]. On the other hand, the p-polarized light with the electric field perpendicular to the tapered surface of the Ag NPs is coupled to the surface Plasmons Polaritons (SPPs) supported TM mode in the probes [30].

3.3 Parameter optimization of tapered optical fiber

Notably, SERS study indicates that optimization geometric parameters of the fiber probes are important, since the optimal fiber probes can obtain most efficient SERS signal and electric field enhancement. Therefore, we simulated four different parameters setting, including tip radius, conical angle, Ag NPs size and the gap between them to record the effect of electric field using most common laser excitation wavelengths of 532, 633 and 785 nm. A single-valued variable method is used for optimization, other parameters set as default tapered angle (θ = 41.2°), tip radius (50 nm), Ag NPs radius (50 nm), the gap between Ag NPs (5 nm), and the gap between an Ag NPs and fiber tip surface is 1 nm. As shown in Fig. 6(a), the effect of tip radius ranges from 50 to 500 nm, the |E|/|E₀|_max between Ag NPs along a line connecting the Ag NPs is calculated. Note that the electric field under wavelength of 532 nm is larger than that of 633 and 785nm, especially, when the tip radius is less than 300 nm. As the tip radius is reduced, more evanescent field outside the walls of the taper increases to couple with the NPs and the energy density in the optical fiber increases, resulting the electric field between Ag NPs is also higher. In general, the effect of electric field is stronger in 532 nm and the emission energy is higher compared to the long wavelength. Figure 6(b), the effect of cone angle with varied from 10 to 70° are calculated. The electric field enhancement fluctuated in excitation wavelengths of 532 nm and 633 nm are change more obvious than 785 nm, and the optimum field enhancement is obtained at a cone angle between 25° and 35°, whereas the change of the electric field at excitation wavelength of 785 nm is not significantly in all conical angle. The effect of gap between the Ag NPs on the electric field enhancement curve is investigated, as shown in Fig. 6(c). Figure indeed shows that the electric field intensity is rapidly reduction as the spacing between the Ag NPs increased. In other words, the strongest hotspots exists when the dimers of Ag NPs gap distance are less 5 nm region, and the enhanced Raman scattering more apparently [31]. Finally, the effect of the Ag NPs radius was evaluated in size range from 30 nm to 100 nm, as shown in Fig. 6(d). As expected, the acquired electric fields at the three wavelengths show that the optimal electric fields at each wavelength corresponds to different NPs size. For 532, 633 and 785 nm excitation, the optimal size of the radius is 55, 70 and 95 nm, respectively. It can be explained that the wavelengths of LSPs are slightly different for certain dimensions of the Ag NPs excitation. Moreover, we observe a redshift of the plasmon resonance wavelength when the NPs radius is increased.

3.4 The tapered optical fiber probe with substrate

In the above analysis, we discuss the field enhancement characteristics of the proposed probes only included fiber tip coated Ag NPs. To further improve the electrical field enhancement, we designed a noble metal (Au) substrate located L = 23 nm below the probes-tip and 2 nm from the Ag NPs, as shown in Fig. 7(a). The higher enhanced electric fields can be found between the tip-substrate coupling and gap region between the Ag NPs in Fig. 7(b). The coupling field enhancement mainly depends on the excitation wavelength, substrate and relative distance between the fiber tip and substrate. Here, we main pay attention to the excitation wavelength is 785 nm. As shown in Fig. 7(c), the field intensity of the tip-substrate coupling is significantly larger than the fiber tip without substrate with a wavelength range between 450 to 800 nm. At the same time, the two curves have the same change in electric field strength at the maximum peak of 490 nm, and we note that the presence of the Au substrate does not lead to a significant change in the wavelength at 490 nm. This again proves that the peak of 490nm is represent plasmon resonance peak generated between Ag NPs on the fiber tip surface, because the wavelength of plasmon resonance peak of the fiber probes is not related to the substrate. Figure 7(d) shows the variation of the electric field in the x-y plane with the gap between the fiber tip-substrate, which the gap distance was defined as L varied from 23 to 400 nm. It is show that the strong electric field is reduced as the increase of distance L, when the L is less than 26 nm the maximum electric field arrived at 22.3 attributed by tip-substrate coupling. Whereas, when the distance L was greater than 26 nm, the electric field between adjacent Ag NPs is higher than tip-substrate coupling mainly dominated by both plasmonic gap-modes and image-force effect [32]. On the other hand, As the distance increased the field strength between silver nanoparticles is enhanced, which can effectively avoid the detection distance problem in the application of probe detection. Further, Fig. 8 is investigated the effective model area in both model that is the tip without substrate coupling Fig. 8(a) and the tip-substrate coupling Fig. 8(b). The latter has a higher enhancement of the electric field and the effective mode area severely reduced due to strong mode coupling.

Finally, we compared the fields enhancement that two substrate-Au and Ag were used to evaluate the tip-substrate coupling efficiency. The structural parameters of the probe are consistent with above. Table 1 shows that field enhancement performance is best for the Ag substrate, followed by Au, which is calculated by numerical simulation. In addition, the EF were calculated that the probes with Ag substrates have stronger EF in wavelengths of 532nm. On the contrary, Au substrates have a more stable EF in different wavelength. In the actual SERS system, the Ag substrate obviously has a larger SERS signal enhancement than Au and Cu substrate. The result of our simulation is consistent with other model simulation obtained in previous reports [33–35], indicating that the model is feasible. In general, above obtained results indicate that the simulation model and calculation results provide best model for tapered SERS fiber probes applications in the Raman fields.

Table 1

The electric field and enhancement factors of the presented probes in different noble metal substrate and excitation wavelength.
Substrate	λ (nm)	E_max (v/m)	EF
Au	532	23.1	2.9×10⁵
	633	23.7	3.2×10⁵
	785	22.3	2.5×10⁵
Ag	532 633 785	33.2 20.0 22.4	1.2×10⁶ 1.6×10⁵ 2.5×10⁵

In this study, we have reported a design to tapered optical fiber probes using Ag NPs deposited the fiber tip. The electrical field enhancement and spectrum properties are obtained using 2D-FDTD method. The analysis shows that the electric field enhancement is related to the transmission spectrum. The probe has a stronger electric field intensity compared to the reported modified Au NPs. The influence of the tip radius, conical angle, Ag NPs size and gaps between them on the electric field enhanced has been quantified under typical excitation wavelength of 532, 633 and 785 nm. Moreover, the electric field of the proposed probe is further enhanced from 13.9 to 22.3 times when Au substrate was introduced under the tapered fiber tip. This study can provide theoretical support for tapered fiber probes and assist in preparation of Ag NPs modified fiber tip, and have a reference value for the preparation of tapered fiber optic probes for biosensing applications.

Funding: This work was partially supported by the National Natural Science Foundation of China (Grant NO. 61771240 and 61475071) and the Six Talent Peaks Project in Jiangsu Province of China (XYDXX-058).

Conflicts of Interest: The authors declare no conflicts of interest.

Availability of data and material: Data may be obtained from the authors upon reasonable request.

Authors’ Contributions: Xiaolei Yu and Zhimin Zhao performed the conceptualization, methodology, editing, and overall supervision. Ciyong Gu performed the model, writing and simulation. Delong Meng contributed to the data analysis.

Ethics approval: Approved.

Consent to participate: Approved.

Consent for publication: Approved.

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Reviewers agreed at journal
31 May, 2022
Reviewers invited by journal
25 Apr, 2022
Editor assigned by journal
07 Apr, 2022
First submitted to journal
05 Apr, 2022

You are reading this latest preprint version

Design and optimization of tapered optical fiber probes for SERS utilizing FDTD method

Status:

Version 1

Abstract

Figures

1. Introduction

2. Propose Structure Description And Fdtd Simulation

3. Results And Discussion

3.1. Uncoated tapered optical fiber

3.2. Tapered optical fiber with Ag nanoparticles

3.3 Parameter optimization of tapered optical fiber

3.4 The tapered optical fiber probe with substrate

4. Conclusion

Declarations

References

Status:

Version 1