The whispering gallery modes (WGMs) in an optical microsphere resonator have been used extensively in fundamental research such as cavity-QED studies and applied research such as opto-electronics [1–3]. Recently, the bio/chemical sensing applications of microspheres have drawn increasing attention [3–8]. Tuning the WGM of a sphere to match the atomic/molecular transitions or the laser frequencies is imperative in these applications in order to fully utilize the resonant characteristics of the spheres. In addition, multiplexed detection capability for high throughput, as shown in Fig. 1, is one of the most desirable features in bio/chemical microsphere sensor development. Simultaneously tuning the WGM of the constituent spheres to a specific spectral location in a simple and cost-effective manner is key to viable microsphere based sensor arrays. The WGM spectral position is, however, highly dependent upon the sphere geometric parameters such as size and eccentricity [1]. Controlling the WGM position during the sphere fabrication is extremely difficult, if not impossible. For example, in order to control the WGM position to 1 pm at 980 nm, only 0.1 nm size variation is allowed for a sphere of 100 μm in radius, corresponding to a fractional change of only 10^-6.

 

Fig. 1. A conceptual illustration of multiplexed detection using optical microspheres

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To date, several post-fabrication tuning approaches have been demonstrated. The temperature dependence of the WGMs allows for a mode tuning at -2.5 GHz/K for a silica microsphere [9]. However, this method becomes impractical for large tuning ranges. Mechanical tuning including squeezing or stretching a microsphere was also employed [10–12]. Despite its flexibility and wide tuning ranges, mechanical tuning involves sophisticated apparatuses, making it hard to implement, especially when tuning of multiple spheres is needed. Recently, trimming the WGMs of a germanium-doped silica microsphere was achieved when the sphere was illuminated with a high power UV laser [13]. While it can potentially be used to tune multiple spheres, small tuning ranges may limit its usage.

In this paper, we demonstrate a new method to tune the WGMs of a silica microsphere over a wide spectral range without the aid of any bulky devices. We accomplish this by removing silica atoms from the sphere surface with low concentrations of hydrofluoric acid (HF) solution, which gradually reduces the sphere size and hence the WGM resonant wavelengths. This etching process can be monitored at sub-atomic scale and terminated once the desired WGM spectral position is achieved, permitting precise tuning of the WGMs. Furthermore, utilizing the multiplexing platform illustrated in Fig. 1, the tuning process can concomitantly take place on all constituent microsphere resonators, which is especially useful when spectral alignment of the WGMs of multiple spheres is required.

For demonstration purposes, only one channel in Fig. 1 is used in our experiment. The experimental setup is similar to what is reported previously [7]. Briefly, the microsphere is created by melting the tip of a silica optical fiber with a CO₂ laser and submerged in a fluidic well initially containing de-ionized (DI) water. Pre-diluted HF solution or DI water is then added to the well to achieve the desired concentration. The excitation light from a tunable diode laser (690 nm, New Focus) is coupled into the microsphere either through a fiber prism [7,14] or a fiber taper [15]. The WGM’s spectral position is monitored by a computer at a 0.8 Hz scanning rate. While HF may also slightly etch the prism (or the taper), the spheres remain in physical contact with the prism (or the taper) throughout the experiment.

 

Fig. 2. (a) The resonances of three adjacent azimuthal WGMs shift to lower wavelengths when HF etches spheres of r = 135 μm (solid line) and r = 62.5 μm (dashed line). (b) Size dependent WGM spectral shift rate. HF concentration for both (a) and (b): 0.1% (v/v). Upper inset: Concentration dependent WGM shift rate for an r = 90 μm sphere. Lower inset: the etching process can be promptly changed by diluting HF solution. Arrow indicates when DI water is added to dilute HF.

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Upon the injection of HF solution, the WGM resonant wavelength (λ₀ ~ 690 nm) decreases in response to the decrease in sphere radius r, as shown in Fig. 2 (A). This relation can be expressed as:

for large spheres (r>>λ), regardless of the WGM polarization and the mode number [7, 10]. As the etching process is determined only by the chemical reaction on the sphere surface, the fractional change in Fig. 2, δλ/λ and hence δr/r, should be independent of the laser wavelength. Our previous results have shown that the detectable fractional change is on the order of 10^-7, corresponding to a radial decrease of 10 pm (or 3% silica monolayer) in sphere with a 100 μm radius [7]. This enables us to precisely monitor the WGM shift during the etching process. Figure 2(a) plots the fractional change for three adjacent azimuthal WGMs (m-modes) of two spheres. The orbital planes of these m-modes are oriented at different angles relative to the sphere equator and therefore sample the geometrical change at the different locations on the sphere surface [1]. Unlike in the mechanical tuning where the m-mode spacing changes due to the change in sphere eccentricity [10], the initial m-mode spacing is preserved in our method, even after much longer etching than shown in Fig. 2(a), indicative of an isotropic etching process.

To investigate the size dependence of the WGM tuning rate, we perform the etching of spheres of different sizes under the same conditions by immersing all spheres in the same HF solution. In this experiment, we use a fiber taper with a 1.5 μm radius to couple the light into the spheres, which allows us to monitor the respective WGM shifts nearly simultaneously [15]. During the experiment, the spheres are in contact with the taper. Although the silica fiber taper is also etched by the HF, the WGM spectral position measurement will not be affected. The spectral shift of spheres of two different sizes is plotted in Fig. 2(a). Figure 2(b), calculated from Fig. 2(a), shows that the rate of the WGM fractional shift depends linearly on r^-1, suggesting that the silica layer is removed from the sphere surface at the same rate for all sphere sizes, which is estimated from the slope to be 1 nm/min for 0.1% HF concentration. Due to the nature of the chemical reaction, the WGM tuning rate is sensitive to the HF concentration and temperature at the sphere surface. While temperature can also be explored to control the WGM tuning process, adjusting the HF concentration is advantageous in terms of convenience and response time. The two insets in Fig. 2(b) show that the HF concentration has a drastic impact on the WGM tuning rate, which can be changed quickly (in two seconds) when the HF concentration changes.

Figure 3 illustrates how we tune one WGM for 18 pm to match another one that we select arbitrarily and whose spectral position is pre-recorded and displayed on the computer for etching guidance. The etching process is depicted in Inset (A). The initial HF concentration is 0.1%. Multiple dilutions are used in order for the WGM to controllably approach the target spectral position. The final concentration is lower than 0.01% before the tuning process is terminated with DI water rinsing. Inset (B) shows that we are able to match the WGM position with an accuracy of 0.2 pm (130 MHz), even without any active temperature stabilization, as water in the fluidic cell acts as a thermal reservoir.

Chemical etching can potentially provide nearly unlimited tuning range. In Fig. 4, we show that a tuning of 660 pm (430 GHz) on an r = 100 μm sphere can be achieved after 40-min etching, which is more than one free spectral range (FSR). Such wide and accurate tuning capability ensures the alignment of any two arbitrary WGMs. It also allows us to match the WGM with any laser line or atomic/molecular transition.

 

Fig. 3. WGM initially at position (I) is tuned to a new position (II) to match another WGM whose position (III) is arbitrarily chosen and pre-recorded. Inset (A): WGM tuning is achieved by an initial fast etching followed by multiple dilutions of HF. The etching process is terminated at the final step by rinsing the HF off the fluidic well. Inset (B): The fluctuation in resultant spectral position is less than 0.2 pm.

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Fig. 4. WGM can be tuned over one FSR of an r = 100 μm sphere.

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The results presented thus far indicate that HF etching is an effective method to precisely tune the WGM with virtually unlimited tuning range. However, one concern is that the HF etching would degrade the Q-factor of the microsphere by introducing additional roughness to the sphere surface. To inspect the surface defects due to etching, a sphere is placed in a 1% HF solution (ten times the concentration normally used) and etched for 40 minutes. The sphere radius is estimated to decrease by over 400 nm. A histogram analysis of the atomic force microscope (AFM) images taken on a 2 μm × 2 μm grid (Fig. 4) shows that the sphere roughness, σ, is 0.53 nm and 0.77 nm for the unetched and etched spheres, respectively. While the sphere roughness seems to become slightly higher after etching, both roughness values are still within the range reported previously for high-Q microspheres [16, 17].

 

Fig. 5. AFM images of the surface of the unetched (A) and etched (B) sphere. Histogram analysis on the right side of the images shows the roughness σ is 0.53 nm and 0.77 nm for (A) and (B), respectively.

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To further verify that any Q-factor degradation is minimal, we compare the Q-factor of a 100-μm radius sphere before and after HF etching. In this experiment, we once again use a fiber taper of 1.5 μm in radius. The resonant scattering of the WGM is collected by a large-core fiber in close proximity of the sphere. The Q-factor of the unetched sphere is first measured when the sphere is in contact with the taper and when the sphere is pushed away by a piezo nanopositioner (Fig. 6(a)). The sphere is then immersed in 1% HF solution for 10 minutes (enough to etch more than one FSR), thoroughly rinsed with DI water and ethanol, and finally dried with a heat gun. The Q-factor of the eteched sphere is measured in the same fashion and plotted in Fig. 6(b). The intrinsic Q-factor, Q₀, can be estimated by:

where Q_c is the Q-factor due to the coupling between the taper and the sphere when both are in touch. γ accounts for the effects of the gap between the taper and the sphere [18], and can be estimated from the scattering signal intensity. Q₀ is deduced to be 1×10₈ for both before and after etching, similar to what was reported previously [14]. Both AFM and Q measurement results indicate that the etching processes will not degrade the Q-factor at the level of 10⁸ – 10⁹. Considering the fact that much less tuning or etching is needed in practice, the contribution of the sphere surface roughness to the reduction in Q-factor under study (~10⁶) is negligible.

 

Fig. 6. Normalized WGM scattering spectra when the sphere is in air. (a) before etching. Q = 1×10⁷ and 1.5×10⁷ when the sphere is in contact (upper curve) and when the sphere is out of contact with the taper, respectively; (b) after etching. Q = 1×10⁷ and 2.3×10⁷ when the sphere is in contact (upper curve) and when the sphere is out of contact with the taper, respectively.

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In summary, we have shown precise yet simple tuning of the WGM spectral position without sacrificing performance using chemical etching. The WGMs can be tuned over one FSR with accuracy better than 0.2 pm. In particular, since our experimental configuration is compatible with that in microsphere biosensor arrays in an aqueous environment, the method presented in this letter can readily be implemented for in-situ WGM alignment in sensor development. For microsphere applications in air, the calibration issue between the WGM in water and in air should be addressed in the future.