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The spectral mode density in optical micro-bubble resonators is reduced by introducing a loss element of UV curable adhesive to selectively suppress the whispering gallery modal resonances. Asymmetric Fano resonant profile appears after spectral simplification, and the sharp slope amplifies the detecting intensity change by 4.3 times when sensing the liquid core refractive index change.
© 2016 Optical Society of America
Corrections
18 April 2016: A correction was made to the title.
1. Introduction
In the past few years, whispering gallery modes (WGMs) optical microresonators with high Q factors and small mode volumes have attracted considerable attention, and provided potentials ranging from fundamental physics to significant applications, such as cavity quantum electrodynamics [1,2 ], nonlinear optics [3], optical communications [1,4,5 ] and biosensing [6–8 ]. WGMs typically appear as a dense mode spectrum [5,9,10 ]. In microsphere resonators, such a dense spectrum comes from different azimuthal and radial modes [11], while in non-spherical microresonators, like bottle microresonators and micro-bubble resonators (MBRs), the rich spectral features are mainly a combination of equatorial modes and bottle modes [5,12 ]. Although a rich variety of modes in the spectrum is useful in CQED studies [12], it can be a serious problem in many applications. For instance, in systems that require large side mode rejection, a large spectral mode density would limit the filter applications [9]. In applications of optofluidic, refractometric and bio sensing, a dense spectrum would make it difficult to identify and trace the modes [13]. Many efforts have been paid to simplify WGM spectrum. One strategy is to selectively excite modes of the microresonators, which can be realized by shaping the spatial profile of optical pump [14], changing the diameter of the coupling tapered fiber [15], and adjusting the coupling position of tapered fiber [5,10,16 ]. Another method is to artificially attenuate some of the modes by employing small droplets of index matching liquid [17], high-index prisms [9], and focused ion beam (FIB) milling [13]. However, these techniques are either unstable, unrepeatable or costly, requiring complicated technologies.
In this work, we develop a method to significantly reduce the spectral density of a MBR resonator by attaching droplets of UV curable adhesive near the central region of the resonator to strongly deteriorate Q-factors of high order bottle modes. In the meantime, lower order bottle modes experience minimum losses. The method is simple, convenient and fast. Thus, compact, robust and controllable WGM resonators with easily identifiable and traceable spectral features can be fabricated.
In addition to spectrum simplification, coupling of a Q deteriorated mode with a high Q WGM mode generates asymmetric Fano resonance [18–21 ]. The sharp Fano resonance lineshape is used to enhance the detected intensity change in sensing applications. An enhancement about 4 times is obtained. Note that the large slope of the Fano resonance results from the coupling and interference between the two WGMs, the mechanism of enhancement provides a general route to improve the performance not only in biochemical and refractometric sensing, but also in thermal and pressure monitoring [22–25 ].
2. Spectral simplification
The WGM resonators we demonstrate here are hollow MBRs, fabricated by heating a pressurized silica capillary with a standard fusion splicer. These hollow MBRs can be connected to microfluidic systems [8] so that different solutions can be injected into the hollow core. A tiny change of refractive index (RI) in the solution can cause a shift of resonant frequency, which is used for sensing.
In order to introduce the loss element on the MBR, a droplet of UV curable adhesive with a RI of 1.54 is transferred to the MBR from a cutting tapered fiber and exposed to UV light for 30 seconds. In this way, robust and compact MBR with loss element is prepared.
To excite the modes of the MBR, light near 1550 nm from a tunable laser source (Anritsu Tunics Plus CL) is coupled into and out of the resonator via a tapered fiber with a waist diameter of about 2 µm. The transmission light is detected by a photon detector connected to an oscilloscope (Techtronix TDS3012). A function generator is used to sweep the wavelength so as to observe the WGM resonances.
Figures 1(a)-(b) show the spectra of the same MBR with a diameter of 324 µm and a wall thickness of 12 µm, before and after the introduction of loss element, respectively. Apparently, before the loss element is introduced, the spectrum of the MBR is very dense, making it difficult to identify and trace the modes. After the introduction of loss element, the spectrum is significantly simplified, only modes that distributed in the equatorial region of the MBR survive.
Fig. 1 Transmission spectrum (a) before and (b) after the introduction of loss element. Dots in (b) are theoretical calculation results. (c) Image of MBR with a loss element in the lower part of the MBR. (d) Cross-sectional view of normalized electric field intensity distributions of different modes. (e) A typical theoretical and experimental Fano resonance lineshape formed by a high Q mode and a background-like extremely low Q mode.
To identify the surviving modes, intrinsic modes (without considering the loss element) of the resonator are calculated by using a finite-element solver (COMSOL) [26]. Bubble shape radius R(z) along its rotation symmetry axis z follows R(z) = Rb[1 + (∆k·z)2]-1/2, where Rb = 162 µm, ∆k = 0.0017µm−1 are obtained from bubble image. The refractive indexes of the core, the wall and the outside are 1.000, 1.444, 1.000, respectively. Resonant modes in a MBR are classified by azimuthal (m), radial (p) and axial or bottle (q) numbers. Figure 1(d) shows modal distributions of (p,q) = (1,0), (1,5) and (3,2) respectively. After spectral simplification, comparison between calculated and experimental results is possible, because only a few q modes need to be considered. The results are summarized in Fig. 1(b), which shows that most of the resonant modes after simplification are recognized and labeled. Modes with the lowest radial mode number, i.e. p = 1, exhibit the largest transmission depth, which means these modes are efficiently excited and are not strongly affected after introducing the loss element. These modes as well as the modes with p = 3 are in excellent agreement with the theoretical calculation. On the other hand, the calculated p = 2 modes do not agree with the experimental result well, which might be a result that the MBR profile for calculation does not reflect exactly the real profile.
In highly oblate resonators, WGM of an axial mode with mode number q distributes largely at two modal turning points that are Zc = [4(q + 1/2)/ΔEm]1/2 away from the equator (see for example Fig. 1(d)). ΔEm depends on MBR parameters and mode number m and p. Therefore, if the turning point of a mode is covered by the loss element, modal distribution will be strongly affected and the mode suffers Q deterioration. From the expression of modal turning points, it is clear that modes with higher q have larger Zc. Thus, when the position of loss element is expanded from the neck of bottle toward the equatorial region, the modes with higher bottle number will be affected first and the survived modes become less and less. Obviously modes with q = 0 survive at last. Figures 2(a)-(d) show the change of resonance spectra when a polydimethylsiloxane (PDMS) coated cutting tapered fiber touches a MBR with a bottle radius of 118 µm and a wall thickness of 4 µm at various positions. When the coated fiber attached at about 80 µm, 40 µm and 10 µm away from the center, the number of high Q modes within a spectral range of 2 nm (FSRm~2 nm) are about 36, 11 and 0, respectively. Apparently, touching near the bottle center is able to suppress more high order bottle modes, making the spectrum much simplified. However, once the loss element touches right at the center, the modes with low axial mode like q = 0 also suffer the Q deterioration, so no high Q mode exists anymore. In addition, the touching size should be about several dozens of micrometers, so as to suppress more unwanted modes.
Fig. 2 (a) Spectrum of the MBR excited at the center without a loss element attached. (b)-(d) Spectra of the MBR with coated fiber attached at about 80 µm, 40 µm and 10 µm away from the center on one side of MBR, respectively.
3. Fano resonances
The introduction of loss element alters the modal distribution and lead to mode coupling and Q deterioration. When a perturbed mode (with deteriorated Q) couples with a high Q mode, constructive and destructive modal field superposition on two sides of the high Q resonant line generates asymmetric Fano lineshape, which can be understood by regarding the coupling of two modes as a system of two coupled harmonic oscillators [21], described by:
where γ 1 and γ 2 are the frictional parameters of the two oscillators, respectively, ω 1 and ω 2 are the eigen frequencies, a 1 and a 2 are the amplitude of the external force, ω is the frequency of the force and κ is the coupling constant. Here we assume that γ 1>>γ 2, with γ 1 and γ 2 corresponding to the low Q mode and the high Q mode of the MBR, respectively. The harmonic solutions are The transmission is defined through transmission = |a 3|2-|c 1|2-|c 2|2, where |a 3|2 represents the input energy, and |a 3|>|a 1|, |a 2|.Figures 3(a)-(e) are calculated transmission spectra by using κ = 6 × 10−6, γ 1 = 1.2 × 10−5, γ 2 = 4 × 10−7, λ 1 = 1549.9945 nm, Δλ = λ 1-λ 2 = 11.50 pm, 5.75 pm, 1.00 pm, −4.00 pm and −11.70 pm, respectively. They show how the lineshape of the higher Q resonance (with a lower frictional parameter) changes when its resonant frequency detunes with the lower Q resonant frequency. The higher Q mode is obviously asymmetric, because it is out of phase with the lower Q mode at frequencies on the two sides of its resonance. The shape of the Fano resonance mainly depends on the eigen frequencies as well as the Q factors of the coupled modes. Such a change of spectra is experimentally demonstrated by changing the pressure in the MBR [25] to change the resonance frequencies. Figures 3(f)-(j) show experimental changes of Fano lineshape with adopted pressure of about 1.3 bar, 1.7 bar, 2.5 bar, 2.9 bar and 3.3 bar, respectively. When pressure increases, the resonant frequency of the two modes moves at different speed. Thus the high Q modes detunes with the lower Q mode, the interfered spectrum changes from Fano resonance to EIT-like resonance, and back to Fano resonance again. Figure 1(e) shows a typical Fano lineshape in the simplified spectrum when a high Q mode couples with a very low Q mode. The coupling constant κ = 1.65 × 10−4, frictional parameters γ 1 = 9.2 × 10−4 and γ 2 = 3 × 10−7 are used in the calculation. The experimental spectrum can be simulated very well.
Fig. 3 (a)-(e) Theoretical calculation of the spectrum of the coupled system with different wavelength detuning. (f)-(j) Experimental spectrum by changing the inner pressure of the MBR.
4. Refractometric sensing
MBRs with simplified resonant spectra are suitable to improve sensing performance, since it is quite easy to identify and trace the modes. The experiment to detect the changes of RI of ethanol solution is carried out with ethanol solutions of different volumetric concentrations (0%-1% in 5 steps, corresponding to RI change 1.32986-1.33008) pumped through the MBR with a bottle radius of about 140 μm and a wall thickness of about 2 μm. To avoid water absorption, a tunable laser near 780 nm (New Focus TLB 6700-LN) is employed. Figure 4(a) shows the progression of the spectral shift of the Fano resonance as RI increases. The wavelength shift of the resonance is shown in Fig. 4(b) as a function of the RI. The RI sensitivity is 48.8 nm/RIU, which matches with the calculated result of 54.1 nm/RIU for p = 3 modes.
Fig. 4 (a) Spectral shift of the Fano resonances when ethanol solutions of different concentrations flow through the MBR. (b) Wavelength shift of the resonance as a function of the RI.
Detection of RI change can also be realized by measuring the light transmission intensity at a fixed wavelength. In this case, the sensitivity by monitoring the intensity can be express as
The first part is the conventional sensitivity and the second part is associated with the lineshape of resonance. The sharp slope (large dI/dλ) of the Fano resonance helps improving sensitivity (dI/dn). Figure 5(a) shows the typical Fano resonance used in RI sensing, in which the yellow region performs a sharp slope of Fano resonance, about 4.3 times larger compared with the slope in the cyan region. This region covers a spectrum of about 0.1 pm, corresponding to a whole RI sensing range of about 2 × 10−6 RIU. The measurable detection limit is determined by the noise level of the detection system, including thermal noise, photo detector noise, laser intensity fluctuation, etc. The wavelength of the laser is fixed for 100 seconds at the yellow region and the cyan region respectively to determine the noise level. Linear fittings are employed to estimate the long term drift, and the slope of the fitted line in the yellow region (−5.2 × 10−4 V/s) is about 4 times larger than that in the cyan region (1.3 × 10−4 V/s). This agrees with our expectation since the long term drift reflects the sensitivity of the system. In both region, the short term noise is dominantly determined by the photo detector noise and the long term drift is mainly due to the thermal instability and the wavelength drift of the laser. To minimize the influence of the drift noise, the system is packaged in a sealed box and the measurement is implemented when the laser operates stably. Deionized water is filled in the resonator before a new solution is pumped through. The spectrum is recorded right before and after the solution arrives and the drift is much less than the short term noise. The exact wavelength shift induced by the change of liquid core refractive index should be the difference between the resonance of the water and that of the incoming solution. By using deionized water as a standard, drift noise is substantially reduced. With the standard deviation in intensity measurements shown in Fig. 5(b), our MBR is capable to detect the RI changes of 10−7 RIU. Although the preparation of different solutions within such a small RI range is beyond our reach in the experiment, the estimation of the detection limit shows the significant potential of RI sensors by using Fano resonance. The sensitivity can be further enhanced by either enhancing the wavelength shift or enlarging the slope of the mode in spectrum. The former can be achieved by using higher order radial modes and decreasing the wall thickness of the resonator [27]. Meanwhile, the later requires a higher Q factor of the MBR and the configuration of the appropriate working points in sensing [22]. In addition, noise-suppression techniques like temperature and frequency stabilization and self-referencing techniques can be used to further improve the detection limit [28].Fig. 5 (a) The typical Fano resonance used in refractometric sensing. The yellow region features a large slope and can be used in the sensitive detection of small changes of RI. The cyan region can be considered as a typical shape of WGM in traditional MBRs (b) Detected signal fluctuation as a function of time when laser wavelength is fixed at the yellow region and the cyan region, respectively. Red lines are linear fittings.
5. Conclusion
In summary, we present a simple, convenient and fast method to reduce the WGM spectral density in MBR by using a loss element to selectively deteriorate high order bottle modes. The simplified spectrum is much easily recognizable and traceable. This technique can also be implemented to clean-up spectra in other types of optical microresonators with modes distributed differently. Fano resonances are observed and are used to enhance the sensitivity of RI detection by about 4.3 times. The device is capable to detect the RI changes of 10−7 RIU at a fixed wavelength.
Acknowledgments
This work is supported in part by the National Natural Science Foundation of China (NSFC) (Grants No. 61327008, No. 11474070), and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130071130004).
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