We have experimentally studied the plasmon resonance phenomenon of a silver micro–sphere with a diameter of 2.3μm in cone–shaped air cavity of a hollow fiber taper. To take insight into the plasmon resonance phenomenon, we move the micro–sphere along the fiber and observe the significant shift of the resonance peak. We also explore the light response in both infrared and visible wavelength band by finite difference time domain method. The significant variations of the magnetic and power field distribution are observed. The interesting results imply that the configuration has great potential in optical sensors and color filters.
© 2013 Optical Society of America
Surface plasmon resonance (SPR) is the charge density oscillation stimulated by electromagnetic wave and decays evanescently at the metal–dielectric interface. SPR has been an important method in analyzing the biological and chemical reactions due to its convenient and efficient characteristics. Researchers have been dedicated to studying the impact of regular and random metal particle arrangements on the light signal [1–3]. It is well known that the small changes, derived from arrangement, configuration and size of the metal particles, can affect the phase or amplitude of the light signal [4, 5]. The metal particles in random arrangement can produce interesting effects on the light signal, but the manipulation is actually difficult . The experimental repeatability cannot be guaranteed. Meanwhile, the regular arrangement of metal particles relies on the ion beam etching  or lithography technology, resulting in a very complex preparation process for the samples [8, 9]. How to control the nano–scale metal particles effectively is becoming a hot study topic in recent years . The light tweezers or waveguide is an effective method to control the distribution of the metal particles [11, 12]. Recent studies also indicate that the treated fiber has many potential applications. Through the optical coupling between the fiber taper and micro–sphere, a lot of interesting experimental results have been reported . The transmitted light is very sensitive to the surrounding environment, which is used to monitor changes of temperature (as a part of Fabry–Perot interferometer) and refractive index  (as a part of Mach–Zehnder interferometer). In this paper, we study the optical properties of a hollow tapered fiber. The hollow fiber [15, 16] and photonic crystal fiber (PCF)  can be used as a pulse compressor. However, PCF has a core and a muti–layer photonic cladding, in which the optical field is very complex. In addition, its fabrication process and structure are very complicated. In contrast, the hollow fiber is only a hollow tube, where the analysis of light property will be much simple and meaningful when it is used as an optical sensor.
2. Sample preparation
The fiber taper was obtained from a hollow fiber with an air core of 160μm in diameter through special process. First, the coating of the hollow fiber was melt away by a Bunsen burner (by controlling the flame temperature of the Bunsen burner and the stretching speed, one can get the micron hollow fiber cones with different diameters to obtain different transmission spectra); Then, the transparent hollow fiber, similar to the glass capillary except the smaller diameter, was further stretched to 5.8μm in diameter. The diameter of the air core was about 5.2μm. Finally, the micron hollow fiber was pulled into a fiber taper with a cone–shaped air chamber, as shown in Fig. 1. The end of the fiber taper turned into solid due to high temperature and the stretching force.
It is difficult to precisely manipulate an object with several micrometers under the microscope. In this paper, we put a silver sphere with a diameter of 2.3μm in the cone–shaped air cavity of the fiber taper with a fine fiber of 2.5μm in diameter. Figures 1(a)–1(d) shows the diagram of the operating process. First, a single–mode fiber (125 micro–meters in diameter) was stretched into a fine fiber with a diameter of 2.5μm, slightly larger than the diameter of the silver micro–sphere. Next, the fine fiber (used as a push rod) was used to push a silver micro–sphere with a diameter of 2.3μm into the conical cavity of the fiber taper. In this way, one can push the silver micro–sphere into the cone–shaped air cavity under the microscope. Eventually, the fine fiber was withdrawn from the fiber taper, leaving the silver sphere, as shown in Fig. 1(d). Until then, the silver micro–sphere was placed in the fiber taper successfully.
3. Experimental setup and related theory
The schematic of the experimental setup is illustrated in Fig. 2. A light source centered at 1550nm was used in the experiment, and its spectrum ranged from 1530nm to 1560nm, as shown in the inset spectrum. The fibers used for transmitting input light and output light were clamped by the fiber clips, which were fixed on the three–dimensional adjustments with a resolution of 0.1 μm. In this way, we could precisely move the fibers to align the two fibers with the hollow fiber taper, as shown in the insert. The entire operation must be precisely controlled under the microscope. The fibers and a fiber taper with an air cone were placed on a piece of MgF2 crystal to reduce the loss. A microscope was used to observe the specific position of the fiber probes and the fiber taper. We guided the incident light into the fiber taper and measured the spectra of the output light from the probe fiber by regulating the three–dimensional adjustments.
The spectra of the light source and the hollow fiber taper are observed in the spectrometer, as the inset images reveal in Fig. 2. It can be seen from the spectrum that two transmission peaks turn up near 1532nm and 1552nm. The selective absorptions depend on the light interference and micro or nano–size effect of the air conical cavity. The result demonstrates that such a fiber optic taper can be used as an optical filter.
To explore the light response of silver micro–sphere in the quartz fiber, one could introduce the polarizability of micro–sphere with volume V in vacuum from a direct expansion of the first TM mode of Mie theory, which is expressed as 
Here, x = πα/λ0 is called size parameter, dependent on the radius α of the sphere and the free space wavelength λ0; ε ( = ε1 + iε2), εm are the dielectric constant of metal and the surrounding material, respectively; V is the volume of the nano–sphere. The phenomenon resulting from this configuration is much more complex because of the air conical cavity. However, the physical mechanism can be explored from Eq. (1). The quality factor (Q) of the plasmon resonance can be derived from Eq. (1) as 
Here, ω, ωp are the light frequency and the plasmon frequency, respectively. The expression A(L) is a fitting factor in . When Kuwata et. al studied the dependence of the resonant energy on the morphology of Au prolate spheroids and Ag, they introduced A(L) to fit the simulation results, which depends on the depolarization factor L (to reflect the morphology) of the material.
4. Results and discussions
In this section, we experimentally studied the optical response of the hollow fiber taper, as well as the plasmon resonance of the fiber taper filled with a silver micro–sphere.
4.1 Experiment results and analysis
By using the hollow fiber taper with different geometrical parameters, the specific wavelength can be selected. Figure 3 shows the spectra of two micron hollow fiber cones with different diameters (diameters are 9.6μm and 5.8μm, respectively). The transmission wavelength depends on the geometric parameters of the structure.
To take insight into the hollow fiber taper, we did some further research. A silver micro–sphere was pushed into the fiber taper and the corresponding spectra were measured as well. The change is obvious in the transmission spectrum when the silver micro–sphere was moving in the fiber taper, as shown in Fig. 4. The location of the silver sphere was fixed and the fine fiber was taken away before we guided the incident light into the configuration and measured the transmission spectrum.
The involvement of silver micro–sphere leads to the shift of the transmission peak. The non–smooth appearance may be attributed to the surface smoothness and morphology of the micro–sphere, as well as the quality of the fiber taper. Meanwhile, the transmission peak A located near 1525nm is reduced significantly (first 6.7%, then 27.6%). Therefore, it is reasonable to assume that the plasmon resonance between light and the silver micro–sphere affects the transmission spectra. Both peak A and B blue–shifted for about 10nm, because the air cavity with the conical morphology confined the light field around the silver micro–sphere and affected the resonance wavelength. Consequently, one can conclude that the spectrum depends on the location of the silver micro–sphere. It is expected that this fiber taper can be used as optical filter in micron or even nano–scale.
4.2 Simulation results of transmission spectra
Figure 5 shows that both peaks A and B have turned up in the transmission spectra, which is in a good agreement with the experimental results shown in Fig. 4. However, the peaks A in curve b and c are not very obvious. The disagreement may be attributed to the different cone angles of the fiber taper or different light sources, which will change the excited angle of the incident light. Furthermore, the light source of the muti–wavelength LED will result in the uneven intensity of the muti–wavelength from 1530nm to 1560nm. However, the results of the experiment and simulation meet very well and support the conclusion that one can modulate the light response by using this novel configuration.
4.3 Simulation results of sensing properties
To explore the sensing properties of this device, we analysis the reflected spectrum as a function of the external refractive index (RI) by the finite difference time domain (FDTD) method. The silver micro–sphere must be fixed in the hollow fiber cone, so we filled the air cavity of the fiber taper with SiO2 with the RI of 1.68 and defined the RI of the fiber as 1.5 in the simulation. When we changed the RI around the fiber taper, the corresponding reflected spectrum was calculated. Finally, we got the relationship between the RI around this device and the peak intensity and location of the reflected light.
By using TM polarized light as the incident source, the curve of the center peak intensity of reflected light as a function of the external RI is calculated and shown in Fig. 6. When the RI is less than 1.5, the peak change of the reflected light is irregular. Therefore, this device with current parameters cannot be used to monitor the change of RI index from 1 to 1.5; when the RI is greater than 1.5, the center peak splits to two peaks, as the lines (with triangle and round dots) shown in Fig. 6(a). When the RI increased from 1.6 to 2.0, the peak position does not change dramatically, which are marked as the discrete star dots (red) and box dots (gray). These two peaks monotonously increase, as shown in Fig. 6(b), which is one part of the curve in the Fig. 6(a) and marked by a dashed box.
4.4 Simulation results of field distributions
To illustrate the optical field distribution in the configuration by different incident light, and analyze the optical field changes as a function of the location of the silver sphere, we simulate the light intensity distribution and the magnetic intensity distribution by FDTD method, is shown in Fig. 7.
Figure 7(1) shows the diagrammatic sketches of the hollow fiber tapers in Fig. 4. The diameters of the silver micro–sphere, air core and fiber in Figs. 7(a)–7(d) are 2.3μm, 5.2μm and 5.8μm, respectively. We used the Drude Dispersive Model of the silver during the simulation process. The dielectric constant, plasma frequency and collision frequency of the silver micro–sphere are 1.999, 1.34639 × 1016 and 9.61712 × 1013, respectively. The Gauss modulated TM polarization continuous wave (with a half width of 0.5μm and input power of 0.5W/m) was adopted as the light source. We calculated the magnetic intensity distributions in the different configurations, as shown in Fig. 7(2). The evanescent field (caused by the plasmon resonance effect) around the silver sphere could affect the light distribution. That is why the magnetic intensity distribution near the silver micro–sphere was changed significantly. The light at the output port transformed due to the variation of locations of the silver sphere in the hollow fiber taper. In this paper, we used a silver micro–sphere to modulate the light field based on its characteristics of plasmon resonance. The similar results are shown in the Poynting Vector distribution of Fig. 7(3). In order to explore the light response of this configuration in TE polarization light, we made a further simulation, as shown in Fig. 8.
We changed only the light source in Fig. 8, and other parameters were same to the precise simulation in Fig. 7. The Gauss modulated TE polarization continuous wave (with a central wavelength of 1.55μm, half width of 0.5μm and input power of 0.5W/m) was adopted as the light source. The light response is much more obvious than that of the TM polarization light.
A sensor or pulse manipulation with a high Q value means a high sensor sensitivity or spectral resolution. For this configuration, we suggest that it has potential applications in optical filters and optical sensors. If it is explored as an optical filter, one should try to improve the transmittance of a specific wavelength and suppress other wavelengths by enhancing the Q value; if it is explored as an optical sensor, a high Q value will determine its high sensing accuracy.
To explore this configuration into a practical device, the high Q value can be obtained by optimizing the morphological parameters of the fiber cone and the proper size of the micro–sphere (silver or gold). For the fiber cone, the taper angle must be chosen carefully to optimize the fiber cone to improve the Q value. We have calculated the Q values of the fiber cones with different taper angles (28.7°, 32.8°, 38.5°, 44.8°, and 53.6°), which is shown in Fig. 9. In the simulation, we define the air core and the extra diameter of the fiber cone as 5μm and 6μm, respectively. The different taper angles can be got by changing the taper length of the fiber cone.
The simulation results show that the smaller angle will result in a higher Q value. However, the sin of the taper angle is inversely proportional to the taper length of the fiber cone, which is limited by the uniformity of the heating and pulling force in the fabrication process. One should balance the small angle and the fabrication limitation in practice.
In conclusion, the authors try to reconstruct a hollow fiber taper by placing a silver micro–sphere with a diameter of 2.3μm into its cone–shaped air–cavity. When the silver sphere is moved along the fiber, the obvious variation in the transmission spectra is observed. This variation is caused by the plasmon resonance effect of the silver sphere. The resonance peak B blue shift (from 1548nm, 1541nm, to1538nm), as well as the descending resonance peak A in the spectra (from 1534nm, 1529nm, to 1525nm). The simulation spectra meet very well with the experimental results. To further study the light response of this configuration, we calculate the magnetic distribution and poynting vector distribution by FDTD method. The results show that the plasmon resonance can be used to modulate the light distribution. Furthermore, the variation is much more obvious in the TE polarization light than that in the TM polarization light. The Q value can be improved by reducing the taper angle of the fiber cone. This interesting result suggests that such a device has potential applications in optical filters and optical sensors based on its ingenious structure.
The authors thank the constructive suggestions from other colleagues in the slow–light research group of Institute of Opto–Electronics in HIT. The authors thank the support from National Key Laboratory of Tunable Laser Technology, National Natural Science Foundation of China (NSFC) (No. 61078006 and No. 61275066), and National Key Technology Research and Development Program of the Ministry of Science and Technology of China (No.2012BAF14B11).
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