Optimization of Multimode Fibers for Surface Plasmon Resonance Based Sensors Under Spectral and Single Wavelength Intensity Interrogation

In an optical fiber based SPR sensor, a segment of metal clad silica fiber is used as the sensing element and resonant coupling occurs to the surface plasmon mode excited at the interface of the metal and ambient which surrounds the sensing element. When polychromatic light is transmitted through the sensing element, the spectrum of light detected at the other end shows minima at a resonance wavelength. In wavelength interrogation, the shift in the resonance wavelength is a measure of change in the refractive index of the ambient. Alternatively, intensity interrogation can be used in which the change in transmitted power at a given wavelength is a measure of change in refractive index of the ambient. The sensitivity and detection accuracy of the sensor depend on the numerical aperture (NA) of the multimode optical fiber used to fabricate the sensor. In the present work, we have carried out a study of the dependence of the sensitivity and detection accuracy on numerical aperture to obtain the optimal value for a multimode optical fiber which is used to fabricate the sensing element under both wavelength and intensity interrogation. For a gold clad sensing element with l/a = 33.33 for the refractive index of the ambient in the range 1.33 to 1.38, the optimized numerical aperture is obtained as NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NA$$\end{document}= 0.2 for spectral interrogation mode. At this optimal value, the sensitivity is estimated to be 4040 nm/RIU and detection accuracy lies between 20 and 48 μm−1. In single wavelength intensity interrogation, at the He–Ne laser wavelength (633 nm), the optimized numerical aperture is obtained as NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NA$$\end{document}= 0.42. Experimental results on a sensing element fabricated with gold coating on the core of a plastic clad silica fiber are also reported.


Introduction
A metal-dielectric interface supports a TM (transverse magnetic) surface wave, also known as surface plasmon mode with the propagation constant, a sensitive function of the refractive index of the dielectric layer. This property along with use of dielectric layers in which the refractive index changes due to chemical or biological interactions has resulted in the development of various gas, chemical and bio-molecule sensors [1][2][3][4][5]. These sensors are based on resonant excitation of the surface plasmon waves and are known as surface plasmon resonance (SPR) sensors. Traditionally, SPR was measured in the prism coupling Kretschmann configuration [6][7][8][9][10][11] in which a high index prism coated with a thin metal layer on its base is immersed in the dielectric to be sensed as shown in Fig. 1a. When monochromatic TM polarized light is incident through the prism on the metal surface and the reflected light measured as a function of angle of incidence, an SPR curve of the type shown in Fig. 1b is obtained; the angle at which the minima occurs is the measure of the refractive index ( n d ) of the sensor layer and corresponds to the resonance angle at which c Reflectance as a function of wavelength at angle of incidence = 78° for different refractive indices of the ambient there is maximum coupling to the metal-dielectric surface plasmon mode. Alternatively, a polychromatic source can be used and reflectance measured for a given angle of incidence to obtain SPR curves of the type shown in Fig. 1c. The resonance wavelength shifts with change in the refractive index of the dielectric layer. However, both these configurations use bulk-optics and hence form a relatively large system.
Over the last decade, considerable interest has grown in the use of SPR-based fiber optic sensors [12][13][14][15][16][17][18]. In a fiber-based sensor, a segment of metal clad silica fiber is used as the sensing element and resonant coupling occurs to the surface plasmon mode excited at the metaldielectric (ambient) interface as shown in Fig. 2a. Such sensors are light in weight, rugged, and allow remote sensing. Unlike the Kretschmann configuration, all angles of incidence which are allowed by the numerical aperture (NA) of the coupling fiber are possible on the metal interface. For example, for a NA of 0.2, the allowed range of angles of incidence is from 82 to 90°. The reflectance as a function of wavelength for this range of angles of incidence for n d = 1.33 and n d = 1.38 is shown in Fig. 2b. Within the angular range, resonant coupling occurs at wavelengths varying from 500 to 1100 nm, depending on the refractive index of the dielectric ambient layer. Hence, in fiber optic sensors, polychromatic light is coupled into the fiber and the spectrum of the transmitted light shows a resonance dip which is the signature of the refractive index of the Fig. 2 a Coupling arrangement for the excitation of the surface plasmon wave in the metal clad sensing element of the optical fiber. b Reflectance as a function of wavelength at different angles of incidence for n d = 1.33 (solid line) and 1.38 (dotted line). c Transmittance curves for the SPR-based fiber showing shift in resonance wavelength with change in ambient refractive index. The plastic clad multimode fiber is assumed to have NA = 0.2 with l/a ratio of the sensing element l/a = 33.33 ambient layer as shown in Fig. 2c. The shift in resonance wavelength is used as the sensing parameter and hence the method is referred to as wavelength interrogation mode. Alternatively, fiber sensor can also be used at a single wavelength in intensity interrogation mode. For example, at = 767 nm (marked on Fig. 2b), the normalized transmitted power shows a continuous change with change in refractive index of the ambient. The sensitivity and the detection accuracy of the sensor are strongly dependent on the NA or allowed range of angles of incidence of the coupling fiber. In this paper, we have studied the effect of the numerical aperture for wavelength and single wavelength intensity interrogation mode of the fiber optic sensor and obtained the optimal values.
The SPR-based multimode optical fibers are widely being used in the gas, chemical, and biosensors. The main performance parameters of any sensor are sensitivity and detection accuracy. The sensitivity and detection accuracy of the sensor vary with the numerical aperture (NA), length of the sensing region (l/a, and the refractive index of the ambient region of the multimode optical fiber. In this paper, we have optimized these parameters of the multimode optical fiber to get the good sensitivity with high accuracy for both wavelength and intensity interrogation.
Firstly, we briefly discuss the surface plasmon wave and its excitation in Kretschmann configuration and then present a detailed analysis in the optical fiber configuration to be used in both wavelength and intensity interrogation modes. Finally, a fiber optic SPR sensor has been fabricated and transmittance curves measured with varied refractive indices of the ambient. A satisfactory comparison of shift in resonance wavelength with theoretical calculations is obtained for appropriate choice of the sensor parameters.

Surface Plasmon Mode and Kretschmann Configuration
As mentioned above, a metal-dielectric interface can support a surface plasmon mode propagating along the surface with the field decaying evanescently into both the metal and dielectric. The effective index of the mode is given by where m and d are the dielectric constants of the metal and the dielectric layer. In a typical metal, the dielectric constant can be written as m = mr − j mi , where mr is a negative real part and mi is an imaginary part. The dielectric constant for gold can be evaluated from the extensively used Drude model [7] as For the Kretschmann configuration, a gold metal layer of thickness t = 50 nm can be deposited on a prism made of fused silica with dielectric constant p = n 2 p given by Sellmeier dispersion relation [19] as with the Sellmeier coefficients given by a 1 = 0.6961663, When monochromatic light is incident at an angle , the reflectance R = |r| 2 as a function of angle of incidence θ can be evaluated by where and subscripts a and b are p , m , or d corresponding to the prism, metal, and ambient respectively.
The SPR curves are obtained by plotting reflectance as a function of angle of incidence for different refractive indices of the sensing layer at a given wavelength. For the He-Ne laser, the wavelength = 633 nm, m (Au) = − 13.0822-j0.9977, p = 2.1121 , and the corresponding SPR curves are shown in Fig. 1b. In this angle interrogation mode, the angle at which the reflectance is a minimum corresponds to the situation when the evanescent wave at total internal reflection is phase matched with the propagating surface plasmon wave or More correctly, n e corresponds to the effective index of a leaky mode at the metal-dielectric interface, although the difference for adequately thick metal layers is very small [20].
The Kretschmann configuration can also be used in wavelength interrogation mode, i.e., using a polychromatic source, keeping angle of incidence constant. The plot of reflectance versus wavelength now forms the SPR curves, as shown in Fig. 1c at = 78° for different refractive indices of the dielectric layer. The fiber optic SPR sensor uses a similar wavelength interrogation as discussed in the next section.

The Optical Fiber SPR Sensor and Numerical Aperture
In a fiber optic SPR sensor, the cladding of a plastic clad multimode fiber is removed in mid-length and the silica core with index n 1 is coated with a thin layer of gold ( t=50 nm) to form the sensing element. Figure 2a shows the schematic diagram of coupling arrangement for the excitation of the surface plasmon waves in a metal clad sensing element of the optical fiber. Collimated light from a source is focused at the center of one end of the plastic clad fiber and the transmitted light is detected at the other end of the fiber. The change in the refractive index n d of the ambient which surrounds the sensing element is determined by observing the change in the spectrum in wavelength interrogation method or intensity in the single wavelength interrogation method. Assuming that all the guided rays are launched into the fiber using a collimated beam of intensity I 0 and a microscope objective, the power, dP( ) launched between angle and + d at the input is given by dP = I 0 2 d 2 (tan ∕cos 2 )d and can be related by Snell's law to the power distribution in rays [21,22] incident at an angle between and + d on the silica-metal surface as The number of reflections,N ref ( ) , in the sensing region is a function of angle , as well as the ratio of length of the sensing region, l and diameter of the fiber 2a given by In order to determine the transmitted power, the reflectance for TM polarization for a single reflection is raised to the power of the number of reflections at the metal-dielectric interface at the specific propagating angle. The TE (transverse electric) polarization does not excite the surface wave; hence, the reflection coefficient is equal to unity. Therefore, for an un-polarized collimated light source, the generalized expression for the normalized transmitted power, P out (l) , in an SPR-based fiber optic sensor is given by where c is the critical angle at the silica-plastic clad interface. In writing this expression, it is assumed that light incident on the metal-dielectric interface has equal fraction of TE and TM polarizations. The critical angle c is determined by the numerical aperture of the plastic clad fiber given by where n cl is refractive index of the plastic cladding and c can be shown to be given by c = cos −1 NA∕n 1 .

Wavelength Interrogation
The SPR curves are obtained by plotting the normalized transmitted power as a function of wavelength and are shown in Fig. 2c corresponding to a sensing element with l/a = 33.33 in a plastic clad fiber of NA = 0.2 ( c = 82°). The curves show a minima at the resonance wavelength which shifts with the change in the refractive index of the ambient. The larger is the shift of the resonance wavelength Δ r for a given change in refractive index Δn d , the higher is the sensitivity of the sensor defined as S n = Δ r ∕Δn d in nm/RIU.
Another figure of merit is detection accuracy ( DA ) which is related to the sharpness of the resonance dip. The narrower the resonance dip, the higher is the detection accuracy. Detection accuracy can be well defined as the inverse of the spectral width at a transmittance 5% higher than minima [1] (as marked in Fig. 2c).
For example, the fiber of NA = 0.2 shows a sensitivity of 4040 nm/RIU and detection accuracy varies from 20 to 48 μm −1 for l/a = 33.33 in the range of ambient refractive index 1.33 to 1.38.
To study the effect of NA and l/a ratio on the sensitivity and detection accuracy, we carried out calculations of the SPR curves corresponding to different values of numerical aperture and refractive indices of the ambient. The shift in resonance wavelength with respect to resonance wavelength at n d = 1.33, Δ r , is plotted for n d = 1.38 in Fig. 3 along with the detection accuracy for n d = 1.33 and n d = 1.38 as a function of numerical aperture for three values of l/a ratio. The curves show that although for high numerical apertures the shift in resonance wavelength is large resulting in high sensitivity, the corresponding detection accuracy decreases. Similarly for low numerical apertures, the shift in resonance wavelength is lower, while the detection accuracy is high. Hence, an optimal value needs to be chosen. For an optical fiber of NA = 0.2, the detection accuracy and shift in resonance wavelength are both satisfactory and hence for an NA = 0.2 can be considered to be optimal for wavelength interrogation. The corresponding SPR curves are as shown in Fig. 2c; shifts in resonance wavelength and detection accuracy with the change in refractive index of the sensing layer are plotted in Fig. 4. The sensitivity is obtained as 4040 nm/ RIU and detection accuracy lies between 20 and 48 μm −1 in the range of refractive index of ambient from 1.33 to 1.38.

Intensity Interrogation
As mentioned above, the multimode plastic clad fiber sensor can also be used at a single wavelength in intensity interrogation mode. For the optical fiber of NA = 0.2, the SPR curves plotted in Fig. 2b show that at a chosen wavelength of = 767 nm, the normalized transmitted power continuously increases with change in refractive index from 1.33 to 1.38. Hence, the sensor of numerical aperture 0.2 can be used in the intensity interrogation at wavelength = 767 nm.
The plot of transmitted power versus NA as a function of refractive index of the ambient also shows that NA = 0.2 is the appropriate value as shown in Fig. 5a.
We also looked at the possible use of the single wavelength intensity interrogation mode at the He-Ne laser wavelength of 633 nm. The transmitted power as a function of numerical aperture of the sensor for = 633 nm, plotted in Fig. 5b, shows that for numerical aperture of 0.42, there is continuous and significant change of transmitted power on increasing the refractive index of the sensing medium. The normalized transmitted power keeps on increasing with increase in refractive index of the sensing medium as shown in Fig. 5c. Hence, for He-Ne Laser wavelength (633 nm), the fiber optic sensor of numerical aperture 0.42 is the optimum to be used in the intensity interrogation mode.

Experimental Results
The spectral interrogation was also carried out experimentally by fabricating a sensing element on an available multimode plastic clad fiber with a silica core of radius 300 μm. The plastic cladding was removed from the middle section over a length of 3 cm and the unclad portion was coated with a thin layer of chromium and a gold metal layer by thermal evaporation technique. A chromium layer of 2-3 nm is essential for the adhesion of gold. Light from a polychromatic source (AvaLight-HAL) is focused at the input of the multimode plastic clad fiber using a microscope objective and the transmitted spectra are recorded at the other end of the fiber using a spectrometer (Avaspec ULSi 3648). Figure 6 shows the schematic diagram of the experimental setup. The sensing probe is fixed in a glass flow cell in which sugar solutions (analyte) with varying concentrations (and hence refractive index) can be poured. The refractive indices of the solutions were also measured by Abbe refractometer of accuracy up to third decimal place. The normalized transmission spectra of the fabricated sensor probe measured for different refractive indices of sugar solutions in the range of 1.333 to 1.383 are shown in Fig. 7a. On increasing the refractive index of the sensing medium, the resonance wavelength shifts toward the longer wavelength with sensitivity of 7486 nm/RIU.
To understand the transmittance curves of the fabricated sensor probe fiber theoretically, we considered a silica core of radius 300 μm with l/a = 100. Since the numerical aperture of the fiber and thickness of the gold metal layer of the sensing element were not known accurately, we studied the effect of both simultaneously on transmission spectrum in the range of refractive indices from 1.333 to 1.383. The choice of numerical aperture 0.3 with thickness of gold metal layer of 90 nm gives a shift in resonance wavelength which is comparable with the shift obtained experimentally as can be seen from the SPR curves plotted in Fig. 7b.
The shift in resonance wavelength can be used for refractive index measurement. From Fig. 8, we can conclude that the experimental results obtained match well with the theoretical results simulated by choosing the numerical aperture and thickness of gold metal layer.

Conclusion
In conclusion, we have presented an analysis for the optimization of numerical aperture of a plastic clad multimode fiber to be used for an SPR-based sensor in both spectral interrogation and single wavelength intensity interrogation mode. For a gold clad sensing element with l/a = 33.33 for the refractive index of the ambient in the range 1.33 to 1.38, the optimized numerical aperture is obtained as NA = 0.2 for spectral interrogation mode. At this optimal  value, the sensitivity is estimated to be 4040 nm/RIU and detection accuracy lies between 20 and 48 μm −1 . In single wavelength intensity interrogation, at the He-Ne laser wavelength (633 nm), the optimized numerical aperture is obtained as NA = 0.42. We have also experimentally fabricated a fiber optic SPR sensor and measured the SPR curves. A satisfactory comparison of experimental results to theoretical calculation is obtained by assuming a numerical aperture of 0.3 and gold metal layer thickness 90 nm for the sensing element with l/a = 100 with the sensitivity of 7486 nm/RIU.

Author Contribution
All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Shivani Sital and Anjli Baliyan. The first draft of the manuscript was written by Shivani Sital and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding The authors would like to thank the Council of Scientific and Industrial Research (CSIR), Ministry of Science and Technology, Government of India for the financial support.

Declarations
Ethics Approval This is an observational study. Hence, no ethical approval is required.

Competing Interests
The authors declare no competing interests.