Cascade Brillouin Lasing in a Tellurite-Glass Microsphere Resonator with Whispering Gallery Modes

Abstract

Brillouin microlasers based on microresonators with whispering gallery modes (WGMs) are in high demand for different applications including sensing and biosensing. We fabricated a microsphere resonator with WGMs from a synthesized high-quality tellurite glass with record high Q-factors for tellurite microresonators (Q ≥ 2.5 × 10⁷), a high Brillouin gain coefficient (compared to standard materials, e.g., silica glasses), and a Brillouin frequency shift of 9 ± 0.5 GHz. The high density of excited resonance modes and high loaded Q-factors allowed us to achieve experimentally cascade Stokes-Brillouin lasing up to the 4th order inclusive. The experimental results are supported by the results of the theoretical analysis. We also theoretically obtained the dependences of the output Brillouin powers on the pump power and found the pump-power thresholds for the first five Brillouin orders at different values of pump frequency detuning and Q-factors, and showed a significant effect of these parameters on the processes under consideration.

Keywords: Brillouin lasing; Q-factor; microresonator with whispering gallery modes; tellurite-glass microsphere.

Figure 1

(a) Transmittance spectra of produced tellurite-glass samples with photo of 0.23 cm sample in the inset. (b) Absorption spectrum within OH band of 6 cm sample.

Figure 2

Schematic representation of the successive stages of fabrication of microresonators from single-index tellurite fiber.

Figure 3

(a) Examples of calculated electric fields of eigenmodes with different indices for 75 µm tellurite microsphere resonator. (b) Calculated effective mode volume for eigenmodes with different indices for this resonator.

Figure 4

Schematic diagram of cascade Brillouin lasing in microsphere. Even-order Brillouin waves propagate in forward direction and odd-order Brillouin waves propagate in backward direction relative to pump wave. Aj is intracavity field amplitude, Pj is output power, subscript j indicates the jth order of the Brillouin cascade, j = 0 corresponds to pump wave. Only Brillouin orders considered in this study are indicated.

Figure 5

Simplified schematic diagram of the experimental setup. Inset: microphoto of the used tellurite microsphere and silica fiber taper.

Figure 6

(a) Experimental resonance dips of eigenmodes of the produced 75 µm tellurite microsphere resonator recorded for the output pump power of 0.3 µW with the oscilloscope at the pump-laser-sweeping rate of 10 GHz/s. (b) Statistics of Q-factors for these resonances. (c) Resonance dip on magnified scale and its Lorentz approximation demonstrating loaded Q-factor.

Figure 7

Experimental spectra measured for waves propagating co-directionally with pump. Spectra demonstrating cascade Stokes–Brillouin lasing: (a,b) of the 2nd order; (c,d) up to the 4th order.

Figure 8

Eigenfrequencies of ideal 75 µm tellurite microsphere near λ = 1.55 μm for TE (a) and TM (b) modes with different radial indices q; vertical lines show resonance positions. Resulting splitting of the fundamental TE mode for microresonator with the shape-deformation parameter η defined based on Equation (3); η = 0.001 (c), η = 0.005 (d).

Figure 9

(a,b) 2nd-order dispersion of TE (a) and TM modes (b) of ideal microsphere as a function of frequency; only modes with odd q are shown. (c,d) 2nd-order dispersion of TE modes with one radial variation for microresonator with η = 0.001 ((c), every 20th mode is shown), η = 0.005 ((d), every 10th mode is shown); red line marks the dispersion of the corresponding modes of ideal microsphere.

Figure 10

Theoretically calculated output powers of generated Stokes–Brillouin waves of the 1st order (a), 2nd order (b); 3rd order (c); 4th order (d); and 5th order (e) as functions of pump power for zero detuning (Δω₀ = 0) and loaded Q-factors Q = 2.5 × 10⁷.

Figure 11

Theoretically calculated threshold pump powers as functions of Q-factors for cascade Brillouin waves of the 1st–5th orders for zero detuning (Δω₀ = 0). Thresholds for waves of the 6th and higher orders are not shown.

Figure 12

Theoretically calculated diagram demonstrating the number of Brillouin laser cascades for different pump powers and detuning for loaded Q-factors: Q = 2.5 × 10⁷ (a) and Q = 1 × 10⁷ (b).