Parametric Oscillation Studies

Toroid microcavities on a chip are surface-tension-induced resonators which exhibit long photon storage times in excess of 100 ns (equivalently ultra-high-Q of more than 100 million), while possessing small modal volume (typically less than 500 cubic-wavelengths).  Their optical modes can be efficiently coupled to tapered optical fibers, which can both serve to pump a WGM, as well as to extract waves generated by nonlinear processes. This combination of properties makes it possible to exceed the threshold for the Kerr and Raman nonlinearity at threshold pump  powers typically around 100 micro-Watts.  As  Raman scattering is intrinsically phase matched, and possesses a large gain-bandwidth  of more than 10 THZ, it is readily observable at threshold levels as low as 74-micro-Watts. Figure 1 shows Raman oscillation in a toroid microcavity,  and the pump-to-Raman conversion, exhibiting a slope efficiency of 45%. It should be noted that compared to Raman oscillation in microspheres, the toroid microcavities were found to emit single mode, owing to the significantly  reduced number of azimuthal modes.

In contrast to Stimulated Raman, optical parametric oscillation requires phase matching of the involved fields.  Here we show how  by controlling the cavity geometry of ultra-high-Q toroid microcavities, a transition from stimulated Raman to the parametric oscillation regime is achieved. In order for parametric oscillations to efficiently occur, both energy and momentum must be conserved in this process.  In whispering-gallery-type resonators, such as micro-toroids, momentum is intrinsically conserved when signal and idler  angular mode numbers are symmetrically located with respect to the pump mode. Energy conservation, on the other hand, is not expected to be satisfied a priori, since the resonant frequencies are discrete and, in general, irregularly  spaced. As a result, the parametric gain is a function of the frequency detuning,  which effectively gives the degree to which the interaction violates strict  energy conservation. Figure 1 shows the regime of detuning and cavity loading  (K) in which parametric oscillation has a lower threshold than the competing  Raman process. Threshold values are color coded as indicated. In order to achieve parametric oscillation, the detuning frequency must fall within the parametric gain bandwidth. A reduction of the toroidal cross-sectional area will produce a two-fold benefit in this respect. First, it increases the parametric gain bandwidth through its dependence on the effective  parametric nonlinearity , while second, it reduces Dw. The latter occurs because of increased modal overlap with the surrounding dielectric medium (air) and hence flattening of the modal dispersion. Thus,  the desired transition can be induced with toroidal geometries of high principal-to-minor toroid diameter (high aspect ratio D/d, where the principal diameter, D, denotes the outer cavity diameter and the  minor diameter, d, refers to the smaller, toroid cross-sectional diameter).

We have experimentally verified this theoretical prediction, by fabricating micro-toroids having different aspect ratios. Coupling is achieved using tapered optical fibers.  For micro-toroids having an aspect ratio (D/d)  in excess of ca. 15 a transition (and a subsequent quenching of Raman) to parametric oscillation was observed. Figure 3 shows a parametric oscillation  emission spectra for a micro-toroid with d=3.9 micron, D=67 micron and Q0=0.5x108.  The parametric interaction in the micro-cavity causes emission of co-propagating  signal and idler modes that are coupled into the forward direction of the  tapered fiber. The generated signal and idler modes had identical oscillation threshold, within the experimental resolution set primarily by taper coupling variations (ca.±5%). 

More information can be found in the following papers:

B. Min, L. Yang, and K. J. Vahala,
"Controlled transition between parametric and Raman oscillations in ultrahigh-Q silica toroidal microcavities"
Applied Physics Letters, vol. 87, issue 18, October 2005.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala
Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity”
Physical Review Letters, Volume 93, No. 8, 083904 August 20, 2004

D. K. Armani, T. J. Kippenberg, S. M. Spillane and K. J. Vahala
"Ultra-high-Q toroid microcavity on a chip"
Nature, vol. 421, pp. 925-929, 27 February 2003.



Figure 1. Raman emission spectrum of a toroid microcavity showing single mode oscillation. The pump is located at  1550 nm and the Raman emission is 12.5 THz shifted into the 1650 nm band. Inset: Bidirectional Raman emission as a function of pump power for a 58-mm-diameter toroid microcavity (Q0=0.6´108) at the critical point. The threshold is ca. 250 micro-Watts and the bidirectional conversion efficiency  is ca. 45%


Figure 2. Raman and Parametric oscillation in a micro-cavity with D=50 micron, d=4 micron and Q0=108.  The vertical axis denotes coupling strength K of the waveguide-resonator system. The dark blue region denotes areas where Raman oscillation occurs. The color-coded  region corresponds to the parametric oscillation regime (where the parametric threshold is indicated by color in micro-Watts).


Figure 3. Parametric-oscillation spectrum  measured for a 67-micron–diameter toroidal micro-cavity.  The pump is located at 1565 nm and power levels are far above threshold. The  signal and idler are modes are spaced by twice the free spectral range (7.6 nm). Inset: Measured Idler power plotted versus Signal power. The signal-to-idler power ratio is 0.97±0.03.  For higher pump powers deviation is observed due to appearance of secondary  oscillation peaks (I’,S’) (compare main figure).