1. Introduction

Micro bottle resonators (MBRs) are prolate resonators with cylindrical symmetry. MBR supports two types of high quality factor (Q) whispering gallery modes (WGMs), one is the traditional “equatorial” WGM that light propagates in closed loop around the equator, the other is so called “bottle mode” that light spirals back and forth along the resonator axis between two turning points [1, 2 ]. The bottle mode adds a large number of high axial modes to the WGM family, leads to new phenomena such as reduced free spectral range and provides a new platform for studying cavity QED [3, 4 ]. Hollow MBRs (i.e., micro bubble resonators) are perfect microfluidic lab-on-a-tube devices for bio-chemical sensing [5–11 ].

MBRs can be prepared by forming prolate spheroid on glass capillary or optical fibers. The most widely explored methods to fabricate MBRs is by CO2 laser heating [3, 5, 12 ], hydrogen torch heating [13] or using a fusion splicer [9, 11 ]. Very recently, a simple, nonmechanical and self-assembling method for realizing polymer-based MBRs was reported [14, 15 ]. However, no reports on bottle mode laser in active MBRs can be found, and method to control the bottle modes in lasing MBRs needs to be explored as well.

In this paper, we prepared both passive and active SU-8 WGM bottle resonators on fiber to achieve small size MBRs. We obtained a loaded Q above 10⁵ in passive MBRs. By doping SU-8 with Rhodamine B as an active medium, lasing with threshold as low as 1 nJ/pulse was realized. Higher order axial lasing modes are selectively generated as well.

2. High-Q passive MBRs

MBRs were fabricated by transferring SU-8 (refractive index n = 1.581 around 850 nm) droplets onto microfiber as in [14]. After UV and heat curing steps, solid MBRs were finally formed. Figure 1(a) shows the optical microscope image of a MBR. Following [16], the profile of the MBR can be fitted with a truncated harmonic oscillator profile, i.e., D(z) = D_b[1 + (Δk × z)²]^-1/2, |z| ≤ L_b/2 and D(z) = D_a, |z| ≥ L_b/2 with D_b = 38 μm, D_a = 25 μm, L_b = 76 μm and Δk = 0.03012 μm⁻¹, in which D_b is the diameter of the bottle. WGMs from MBR can be characterized by three numbers: m, p, q [2, 7 ]. m and p are mode numbers denoting “equatorial” WGMs, indicating the number of peaks along the circumference of the bottle in the direction of circulation of the WGMs, and the number of peaks in intensity inside the bottle in the radial direction, respectively. q characterizes the mode number of “bottle” WGMs, indicating the number of field nodes along the axis of the bottle. Field distributions of radial third-order mode (m = 211, p = 3, q = 0) and high order bottle mode (m = 211, p = 3, q = 5) are shown in Fig. 1(b). Resonant modes in the cavity are numerically calculated by FEM method (COMSOL Multiphysics 3.5a) [17]. Obviously the lowest order bottle mode (q = 0) locates at the center region of the bottle, meanwhile higher order bottle modes have intensity maximum away from the center. Spectroscopically, degeneracy of bottle modes is broken due to strong asphericity of the MBR, bottle modes with different q number (fixed m and p) split and their interval can be represented by [2]

 

Fig. 1 (a) Optical microscope image of a WGM bottle resonator. (b) Calculated field distributions of a fundamental (p = 3, q = 0) and a high order bottle mode (p = 3, q = 5). (c) Transmission spectra of a WGM bottle resonator (D_b = 38 μm) excited by a tapered fiber at the center of the MBR. (d) Fine transmission spectrum of a WGM, its FWHW is 530 MHz. (e) Calculated effective index of different radial mode and tapered fiber (diameter ~1.5 μm) mode.

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Tapered optical fiber was used to couple light both into and out of the MBR by touching with the central region of the MBR. Light from a tunable (838 nm-853 nm, linewidth < 200 kHz) single frequency diode laser is launched into the tapered fiber, the transmitted light is detected by a photodiode (PD) and the electric signal is sent to an oscilloscope (Techtronix TDS3012).

Figure 1(c) shows a typical transmission spectrum where the dense dips correspond to WGM resonances. The azimuthal FSR (Δλ_m) of the radial third-order mode (p = 3) is about 3.9 nm. Dense higher order bottle modes (q > 0) are clearly visible sitting aside the radial modes. Fine transmission spectrum of a WGM at resonance wavelength of 841.00 nm is shown in Fig. 1(d) with a loaded Q-factor of 7 × 10⁵, which is higher than those in [14, 15, 18 ]. Figure 1(e) shows the effective refractive index of different radial order modes and the tapered fiber waveguide mode, which confirms that p = 3 mode can be excited by the tapered fiber more efficiently than other order of radial modes.

3. Low-threshold active MBRs

To prepare active MBR, 0.3 wt% of Rhodamine B is directly dissolved into the SU-8 polymer matrix (n = 1.592 around 630 nm), active MBR was then fabricated by using the same self-assembling method as described above. A frequency-doubled output of a mode-locked Nd:YAG laser (532 nm, 10 Hz repetition rate, 30 ps pulse width) was used as a pump light. The pump beam passed through an optical lens and focused tangential on the central of the MBR, shown in Fig. 2(a) . Emission spectra were obtained by measuring emitted light with a fiber bundle which was connected to a monochromator (Acton spectrapro 2750) and a cooled charge coupled device (Andor iXon^EM). The measurement system has a spectral resolution of 0.023 nm.

 

Fig. 2 (a) Schematic diagram of the photoluminescence measurement system. (b) Emission intensity vs pump energy of a active MBR equatorial WGM with D_b = 230 μm, D_a = 125 μm, L_b = 690 μm and Δk = 0.0045 μm⁻¹, lasing threshold is about 49 nJ/mm². Y-axis is the total integrated intensity of the mode and the same as in Fig. 3. Inset: Optical micrographs of emitted light above the threshold from the MBR. (c) Emission spectrum of the MBR at I_pump = 53.2 nJ/mm². (d) Emission spectrum of another active MBR with D_b = 40 μm, D_a = 31 μm, L_b = 98 μm and Δk = 0.0166 μm⁻¹.

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Figure 2(b) shows the relation between emitting light intensity and pump energy for an active MBR with D_b = 230 μm, D_a = 125 μm, L_b = 690 μm and Δk = 0.0045 μm⁻¹. A lasing threshold as low as 49 nJ/mm² can be clearly recognized. This lasing threshold is at least one order of magnitude less than two-dimensional micro-capillary and micro-cylinder resonators [19, 20 ], as the resonant mode supported in MBR is strongly localized along the axial direction [16, 21 ]. Lasing spectrum above threshold is shown in Fig. 2(c), regular periodic resonances can be seen, with a mode spacing of 0.35 nm which matches well with the calculated azimuthal FSR Δλ_m = 0.36 nm. This is because in this pumping scheme, only the equatorial part of the MBR (~40 μm m wide pump belt) is sufficiently pumped, therefore fundamental WGMs (p = 1, q = 0) lase. On the other hand, when the size of the MBR is smaller, higher order bottle modes can be excited as well, as can be seen in Fig. 2(d). Here a MBR with D_b = 40 μm, D_a = 31 μm, L_b = 98 μm and Δk = 0.0166 μm⁻¹ is pumped, the lasing spectrum is complicated and no observable period can be identified.

Dense and complicated transmission spectrum in passive MBRs may be a major drawback if the passive MBR is used as a sensor. Several mechanisms, such as microdroplet [7] and microgroove scars [22] have been used to clean-up the spectrum. However, in this work, laser spectrum is much simpler than passive resonators even for a large size MBR (D_b = 230 μm). The simple lasing spectral feature is highly advantageous when the active MBR is used as a sensor.

Selective excitation of individual high order bottle mode in passive MBR was achieved by carefully selecting coupling point of input light on MBR. Excitation near the neck of the MBR helps generating much clean spectrum [16]. In order to generate high order lasing bottle modes in small MBR, we used tapered fiber to selectively couple pump light into the cavity.

Figure 3(a) illustrates schematically the experimental setup. Pulsed 532 nm light was coupled into a tapered fiber. Light coming out from the other end of the tapered fiber was collected by a fiber bundle and recorded by a spectrometer. The fiber diameter is about 1 μm at the coupling position. Figures 3(c), 3(e), 3(g), 3(i) and 3(k) show the the relation between emitting light intensity and pump energy and lasing emission spectra when the tapered fiber is placed at various points along the axial length z of an active MBR with D_b = 32 μm, D_a = 27 μm, L_b = 102 μm and Δk = 0.0124 μm⁻¹. The absorbed pump energy/pulse was measured as the difference of launched energy/pulse into the tapered fiber and the transmitted energy/pulse after the tapered fiber. When the tapered fiber is located at the center of the bottle (denoted as the origin along the z direction), the threshold is as low as 1.1 nJ/pulse. The lasing spectrum shown in Fig. 3(h) exhibits a wavelength period of 2.58 nm, matched well with the calculated azimuthal FSR Δλ_m = 2.54 nm of the fundamental mode (p = 1, q = 0). When the tapered fiber is moved from center to the neck of the bottle directions, higher order bottle modes (q > 1) were excited and their lasing threshold increases as shown in Fig. 3(b). This is because higher order bottle modes suffer from higher losses [16].

 

Fig. 3 (a) Schematic diagram of the photoluminescence measurement system via a tapered fiber. (b) Measured lasing threshold as a function of the pumping point positions. Figures 3(c)-(l) Emission intensity vs pump energy and lasing emission spectra by pumping the MBR at different positions shown in the inset of (c), (e), (g), (i) and (k), respectively. Insets in (d), (h) and (l) are spectra with pumped intensity of 6 nJ, 4 nJ, and 6 nJ, respectively.

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When the tapered fiber is placed at the center region of the MBR, almost only the q = 0 mode lases with pump energy being 1.6 nJ/pulse (Fig. 3(h)). At higher pump energy (4 nJ/pulse), side band which comes from higher order axial modes appears. However the q = 0 serie is still dominant. When the tapered fiber moves toward the neck of the bottle, more bottle modes lase. Figure 3(f) and 3(j) show that the lasing spectra become complicated when the tapered fiber are ± 16 μm away from the center. However, when the tapered fiber moves further to ± 32 μm, clear periodic lasing resonances appear again, as can be seen in Figs. 3(d) and 3(l). The mode spacing is about 0.51 nm. We assigned the dense periodic resonances as higher order bottle modes (q > 0), the 0.51 nm spacing is very close to Δλ_q = 0.49 nm calculated from Eq. (1). The spectra do not change significantly at lower or higher pump energy. FSR of azimuthal whispering gallery mode is Δλ_m = 2.54 nm, 5 times as much as Δλ_q.

Figure 4(a) illustrates field distributions of axial mode q = 0, 26 and 96, respectively. Axial mode with q = 96 has altogether 97 light spots, and the field peak is at ± 32 μm away from the center region of the bottle. Accordingly axial mode with q around 26 is peaked at ± 16 μm away from the center region of the bottle. When tapered fiber is placed at center region of the bottle, field spot of q = 0 overwhelmingly occupies the central region, thus only q = 0 mode serie is excited. When tapered fiber is placed ± 16 μm away from the center region of the bottle, axial modes with q around 26 are excited. Moreover, modes with q around 34 will also be excited (Fig. 4(b)) because their second field peak enters the tapered fiber region. Therefore, the observed lasing spectrum becomes very complicated. When the tapered fiber is placed further to ± 32 μm away from the center, axial modes with q around 96 are excited. As can be seen, the high order axial mode is very close to the neck of the bottle, gain layer (SU-8 film) becomes thinner, and the Q factor of these high order axial modes drop much faster. Therefore, only a few q number modes (q = 94-98) are excited, and when the azimuthal FSRs is approximately integral multiple of the axial FSRs, different m and q peaks will occasionally overlap, a single periodic series with FSR of Δλ_q appears (Fig. 4(c)).

 

Fig. 4 (a) Field distributions of axial modes with q = 0, 26 and 96. Red dashed lines indicate positions 0, 16 μm and 32 μm away from the center, respectively. (b) Resonant wavelength of (m, q) modes at q = 23-35. Tapered fiber overlaps with the largest mode spot of q = 23-30 and second mode spot of q = 33-35. (c) Resonant wavelength of (m, q) modes at q = 94-98. Tapered fiber overlaps with the largest mode spot.

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4. Conclusion

In summary, passive and active polymer MBRs are fabricated. For passive MBRs, dense and rich transmissions lines with Q factor above 10⁵ are obtained. For active MBRs, lasing action with threshold as low as 1 nJ/pulse is realized. High order bottle modes lasing is achieved. Clear periodic high order bottle mode and equatorial whispering gallery modes can be selectively excited by placing the coupling fiber either far away from bottle center or right at the center.