A scatterer-assisted whispering-gallery-mode microprobe

2.1 The coupling process and the spectrum

The experimental setup is illustrated in Figure 1A. A microsphere resonator with a diameter of 35 μm and a fiber nanotip with a diameter of around 0.2 μm at the very top of the cone shape [44] are used in the experiments. The probe laser in 1550 nm band is first coupled into a fiber and then focused onto the surface of the microsphere by a GRIN lens with a working distance of 200 μm. Different from the traditional focusing method, here we develop a special two-step focusing technique. Specifically, the focused laser with a beam size of around 6 μm is further focused by the microsphere itself onto the nanotip located at the back surface of the microsphere. Most of the light scattered by the nanotip is coupled into the resonant mode with the help of the Purcell effect when the incident light is scanned across a WGM. Meanwhile, the cavity-mode field can also be coupled out of the cavity by the same nanotip in the reversed optical path and then collected by the same GRIN lens and fiber. Finally, the collected reflection signal is routed by a circulator and detected by a photodetector, which is connected with an oscilloscope to monitor the reflection spectrum of the resonant system. In the experiments, three 3-axis nano-stages are used to control the relative positions of the microsphere, the nanotip, and the incident laser beam to optimize the coupling condition.

Figure 1:

(A) Illustration of the experimental setup.

TL, tunable laser; PD, photo-detector; CL, circulator; GRIN LENS, graded-index lens; MS, microsphere; NS, nano-scatterer. Inset: optical image of a microsphere approached by a fiber nanotip in the experiment. (B) Reflection spectra with (black) and without (red) a nanotip. (C) Optical spectra of a microsphere resonator with the scatterer-assisted coupling (red) and the fiber taper coupling (black).

A typical reflection spectrum is shown as the black curve in Figure 1B. As a comparison, the red curve in Figure 1B shows the reflection spectrum of the same mode with the nanotip removed from the surface of the microsphere, in which the resonant peaks disappear subsequently. Therefore, we conclude that the resonant peaks are caused by the Rayleigh scattering of the nanotip. Note that the doublet peak indicates a clear mode splitting, which is caused by the mode coupling of the clockwise (CW) and counter-clockwise (CCW) modes induced by the scattering of the nanotip [11]. It further proves the role of the nanotip in the Rayleigh scattering. In other words, the nanotip in the coupling system not only couples light into and out of WGMs of the microsphere but also enables mode coupling between the CW and CCW modes. Moreover, this coupling mechanism is free from the phase-matching condition and applies to all the modes in the microsphere. As shown in Figure 1C, there are five spikes in the reflection spectrum (red curve), showing the same frequencies with resonant dips in the transmission spectrum (black curve), which is obtained by a traditional fiber taper coupling method. It is worth noting that some modes are not excited by the nanotip, which can be attributed to the mismatching between the mode distributions and the location of the nanotip.

An overall coupling efficiency of 2.8% is derived from the measured peak power of the reflection signal divided by the input probe power. It should be noted that the overall coupling efficiency includes both the input and the output coupling processes, which are two reversible processes and thus should have similar coupling efficiency. Therefore, the approximate coupling efficiency of the proposed coupling method is the square root of the overall coupling efficiency, that is, 16.8%. The high scattering-based coupling efficiency is attributed to both Purcell effect and the proposed two-step focusing technique.

2.2 The coupling efficiencies as a function of the positions of the lens

The free-space coupling efficiency is typically determined by the matching between the resonant emission pattern and the incident probe laser beam [33], which is affected by the alignment between the microsphere and the GRIN lens in our design. In our experiments, a GRIN lens with a working distance of around 200 μm is utilized to focus the probe laser beam down to around 6 μm. The divergence angle of the focused beam is about 3.27°. To measure the divergence angle of the nanotip-induced scattering pattern, we excite the resonant mode by a tapered fiber and measure the three-dimensional scattering pattern collected by the GRIN lens, which is mounted on a 3-axis nano-stage. By fitting the focused profile of the emission pattern from the resonator as shown in Figure 2, we find a divergence angle of 4.18°, which is similar to the divergence angle of the incoming beam to the resonator. By adjusting the position of the GRIN lens that provides incident light to the microsphere resonator, we could optimize the overlap between the free-space light beam and scatterer-induced scattering pattern to improve the coupling efficiency. Note that the GRIN lens also collects the scattering pattern.

Figure 2:

Nanotip-induced emission pattern measured at different positions from the resonator.

Inset: sketch illustrating the light emission from the microsphere resonator to free space.

To study the dependence of the coupling efficiencies on the relative position of the lens to the resonator, we mount the GRIN lens, the microsphere, and the nanotip on three 3-axis nano-stages, respectively. By moving the GRIN lens solely, we investigate how the coupling efficiencies of a WGM with Q factor around 5.6×10⁶ vary with the positions of the lens, which affect both the incident light and the collected light from the resonator (Figure 3). The coordinate system is defined in Figure 1A. The maximum reflection intensities, which indicate the coupling efficiencies, as a function of the relative x and y between the probe laser beam and the microsphere are shown in Figure 3A and B, respectively. Reflection peaks are observed when adjusting both x and y positions of the GRIN lens. The widths of the peaks are 3.2 and 7.1 μm for the relative x and y, respectively. In other words, the coupling system has a position tolerance of about 2–4 times of the wavelength in the lateral plane. Note that the y-related width is more than two times of that in the x direction, because here the scatterer is a nanotip with a larger dimension in the y direction than in the x direction. Different from x and y positions, there is a periodic oscillation of the reflection signal with varied z position, as shown in Figure 3C. The period of the oscillation is about 0.77 μm, which is the half of the probe light wavelength. This oscillation stems from the interference between the reflected light from the end-face of the GRIN lens and the resonant emission from the microsphere. The average reflection signal decreases less than 20% in a range of 10 μm, showing a very large position tolerance in the z direction. It is worth noting that the x-related curve is asymmetric in Figure 3A, which is attributed to the non-resonant reflection by the microsphere. Specifically, at position A, where the input light aims at the center of the microsphere, the non-resonant reflection of the probe light by the microsphere can be collected by the coupling lens, and then forms a high reflection background, as shown in the frequency-scanning curve in Figure 3D. On the other hand, at position C, where the probe beam is far away from the microsphere, neither resonant nor non-resonant light can be reflected.

Figure 3:

The amplitude of the reflection as a function of the spatial position of the GRIN lens (incident beam).

Peaks in the reflection spectra vary with the relative position Δx_l (A), Δy_l (B), and Δz_l (C) of the GRIN lens (incident beam) when keeping the nanotip-sphere coupling system invariant. (D) Reflection spectra at three positions of Δx_l. The letters A, B and C in (A) and (D) represent three cases of relative position Δx_l between the incident beam (arrows in the schematic diagram beside the letters) and the microsphere.

2.3 The coupling efficiencies as a function of the positions of the nanotip and the microsphere

In this section, we investigate the coupling efficiencies varying with the relative positions of the nanotip on the equator of the microsphere. The experiment is performed by moving both the nanotip and the microsphere in the x axis with the incident laser beam focused. More specifically, the microsphere moves with a step of 2 μm. For every position of the microsphere, we move the nanotip along the equator of the microsphere in the x-z plane continuously and record both the top-view imaging by a CCD camera and the reflection spectrum with a frame rate of ~3 Hz (see Visualization 1, a composite video at Δ_χs=–11 μm).

The position of the nanotip on the microsphere is characterized by a polar coordinate, θ, in the x-z plane, as defined in the left inset of Figure 4A. Specifically, when the nanotip is near or on the equator of the microsphere, a light spot caused by the resonant scattering of a illumination light can be imaged in the top view, which can help to mark the position of the nanotip, θ. Meanwhile, the reflection signal, which is proportional to the coupling efficiency of every nanotip position, is acquired by the photodetector. Figure 4A shows the reflection as a function of the nanotip position with the microsphere fixed at Δx_s=–11 μm, where a main peak accompanied with several side lobes is presented. The width of the main peak is about 3° corresponding to 0.9 μm along the equator of the microsphere. A 2D simulation of a Gaussian beam focused by a microsphere explains the fringes. The simulated field distribution around the rim of the microsphere is shown in the right inset of Figure 4A, where several fringes can be clearly seen on the surface of the microsphere. Note that the size of the nanotip (~0.2 μm) is much smaller than the period of the fringes (~1 μm). Thus the fringes can be resolved by the nanotip moving along the ring of the spherical resonator. In addition, the fluctuation of the coupling efficiency maps the distribution of the intensity of the focused field, which further verifies that the resonant coupling is caused by the nanotip.

Figure 4:

The amplitude of the reflection as a function of the spatial position of the microsphere and the nanotip.

(A) Peak value of the reflection varies with the position of the nanotip on the sphere with the microsphere fixed at Δx_s=–11 μm. Left inset: top view of the sphere-tip coupling system. The white arrow points out the scattering spot of the nanotip. Right inset: simulated distribution of a Gaussian beam focused by the microsphere. (B) Maximum peak value in the reflection spectrum (black solid curve) and the corresponding position of the nanotip (blue dashed curve) vary with the position of the sphere, Δx_s, when the incident beam is fixed. The vertical red dot-dashed lines indicate the boundaries of the microsphere at Δx_s=0 μm.

In the experiment, for every position of the microsphere, the maximum reflection and the corresponding azimuth angle θ_max are recorded, as shown in the black and blue curves in Figure 4B, respectively. The two vertical red dot-dashed lines in Figure 4B mark the two boundaries of the microsphere. A relatively high coupling efficiency can be achieved in a large range of ~15 μm, in which most of the incident Gaussian beam illuminates on the microsphere. It is worth noting that the reflection curve deviates from the mirror symmetry relative to the center of the microsphere (Δx_s~0). This deviation may be attributed to the misalignment between the incident Gaussian beam and the z axis. The azimuth angle θ_max shows an approximately linear relationship with Δx_s (blue curve in Figure 4B). The results show the critical role of the two-step focusing technique that requires alignment of the GRIN lens and the microsphere resonator as well as the position of the scatterer to effectively couple light in and out of a high-Q WGM resonator through a single-mode optical fiber.