Perturbative analytic theory of an ultrahigh-Q toroidal microcavity

A perturbation theoretic approach is proposed as an efficient characterization tool for a tapered fiber coupled ultrahigh-quality factor (Q) toroidal microcavity with a small inverse aspect ratio. The Helmholtz equation with an assumption of quasi-TE/TM modes in local toroidal coordinates is solved via a power series expansion in terms of the inverse aspect ratio and the expanded eigenmode solutions are further manipulated iteratively to generate various characteristic metrics of the ultrahigh-Q toroidal microcavity coupled to a tapered fiber waveguide. Resonance wavelengths, free spectral ranges, cavity mode volumes, phase-matching conditions, and radiative Q factors are derived along with a mode characterization given by a characteristic equation. Calculated results are in excellent agreement with full vectorial finite-element simulations. The results are useful as a shortcut to avoid full numerical simulation, and also render intuitive insight into the modal properties of toroidal microcavities

Controlled transition between parametric and Raman oscillations in ultrahigh-Q silica toroidal microcavities

A controllable and reversible transition between parametric and Raman oscillations in an ultrahigh-Q silica toroidal microcavity is experimentally demonstrated and theoretically analyzed. By direct change of cavity loading and indirect adjustment of frequency detuning, parametric and/or Raman oscillation can be accessed selectively without modification of cavity geometry in a toroidal microcavity with a large enough aspect ratio. Based on an effective cavity gain theory, this transition is analyzed in terms of cavity loading and frequency detuning leading to a better understanding of the combined effects of parametric and Raman processes in silica microcavities

Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators

The ability to tune resonant frequency in optical microcavities is an essential feature for many applications. Integration of electrical-based tuning as part of the fabrication process has been a key advantage of planar microresonant devices. Until recently, the combination of these features has not been available in devices that operate in the ultrahigh-Q regime where device quality factors (Q) can exceed 100 million. In this letter, we demonstrate an electrically tunable resonator on a chip with ultrahigh-quality factors. Futhermore, the devices have demonstrated tuning rates in excess of 85 GHz/V2 and are capable of tuning more than 300 GHz

Compact, fiber-compatible, cascaded Raman laser

Cascaded Raman Stokes lasing in an ultrahigh-Q silica microsphere resonator coupled to a tapered fiber is demonstrated and analyzed. With less than 900 μW of pump power near 980 nm, five cascaded Stokes lasing lines are generated. In addition, a threshold power of 56.4 μW for the first-order Stokes lasing is achieved. The Stokes lasing lines exhibit distinct characteristics depending on their order, as predicted by theoretical analysis

Solgel route to erbium-doped microlasers and Raman microlasers on-a-chip

Ultra-high-Q microresonators are fabricated on silicon chips by the solgel technique. Using wafer-based processing and selective reflow, we create toroid-shaped Er-doped microlasers directly from Er-doped solgel layers and Raman microlasers from undoped silica solgel layers

Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process

We report high-Q sol–gel microresonators on silicon chips, fabricated directly from a sol–gel layer deposited onto a silicon substrate. Quality factors as high as 2.5×10^7 at 1561 nm were obtained in toroidal microcavities formed of silica sol–gel, which allowed Raman lasing at absorbed pump powers below 1 mW. Additionally, Er3+-doped microlasers were fabricated from Er3+-doped sol–gel layers with control of the laser dynamics possible by varying the erbium concentration of the starting sol–gel material. Continuous lasing with a threshold of 660 nW for erbium-doped microlaser was also obtained

Theoretical and experimental study of stimulated and cascaded Raman scattering in ultra-high-Q optical microcavities

Stimulated Raman scattering (SRS) in ultra-high-Q surface-tension-induced spherical and chip-based toroid microcavities is considered both theoretically and experimentally. These microcavities are fabricated from silica, exhibit small mode volume (typically 1000 $\mu m^{3}$) and possess whispering-gallery type modes with long photon storage times (in the range of 100 ns), significantly reducing the threshold for stimulated nonlinear optical phenomena. Oscillation threshold levels of less than 100 $\mu$% -Watts of launched fiber pump power, in microcavities with quality factors of 100 million are observed. Using a steady state analysis of the coupled-mode equations for the pump and Raman whispering-gallery modes, the threshold, efficiencies and cascading properties of SRS in UHQ devices are derived. The results are experimentally confirmed in the telecommunication band (1550nm) using tapered optical fibers as highly efficient waveguide coupling elements for both pumping and signal extraction. The device performance dependence on coupling, quality factor and modal volume are measured and found to be in good agreement with theory. This includes analysis of the threshold and efficiency for cascaded Raman scattering. The side-by-side study of nonlinear oscillation in both spherical microcavities and toroid microcavities on-a-chip also allows for comparison of their properties. In addition to the benefits of a wafer-scale geometry, including integration with optical, electrical or mechanical functionality, microtoroids on-a-chip exhibit single mode Raman oscillation over a wide range of pump powers.Comment: 12 pages, 15 figure

Erbium-implanted high-Q silica toroidal microcavity laser on a silicon chip

Lasing from an erbium-doped high-Q silica toroidal microcavity coupled to a tapered optical fiber is demonstrated and analyzed. Average erbium ion concentrations were in the range 0.009–0.09 at. %, and a threshold power as low as 4.5 µW and an output lasing power as high as 39.4 µW are obtained from toroidal cavities with major diameters in the range 25–80 µm. Controlling lasing wavelength in a discrete way at each whispering-gallery mode was possible by changing the cavity loading, i.e., the distance between the tapered optical fiber and the microcavity. Analytic formulas predicting threshold power and differential slope efficiency are derived and their dependence on cavity loading, erbium ion concentration, and Q factor is analyzed. It is shown that the experimental results are in good agreement with the derived formulas

Transition between parametric and Raman oscillation in high-Q silica toroidal microcavities

A controlled and reversible transition between parametric and Raman oscillation in a high-Q silica toroidal microcavity is demonstrated. By changing cavity loading and frequency detuning, parametric or Raman oscillation can be accessed without any modification of cavity geometry

Ultralow threshold on-chip microcavity nanocrystal quantum dot lasers

Chemically synthesized nanocrystal, CdSe/ZnS (core/shell), quantum dots are coated on the surface of an ultrahigh-Q toroidal microcavity and the lasing is observed at room and liquid nitrogen temperature by pulsed excitation of quantum dots, either through tapered fiber or free space. Use of a tapered fiber coupling substantially lowered the threshold energy when compared with the case of free space excitation. The reason for the threshold reduction is attributed to the efficient delivery of pump pulses to the active gain region of the toroidal microcavity. Further threshold reduction was possible by quantum dot surface-coverage control. By decreasing the quantum dot numbers on the surface of the cavity, the threshold energy is further decreased down to 9.9 fJ