Model of thermo-optic nonlinear dynamics of photonic crystal cavities

Abstract

The wavelength scale confinement of light offered by photonic crystal (PhC) cavities is one of the fundamental features on which many important on-chip photonic components are based, opening silicon photonics to a wide range of applications from telecommunications to sensing. This trapping of light in a small space also greatly enhances optical nonlinearities and many potential applications build on these enhanced light-matter interactions. In order to use PhCs effectively for this purpose it is necessary to fully understand the nonlinear dynamics underlying PhC resonators. In this work, we derive a first principles thermal model outlining the nonlinear dynamics of optically pumped silicon two-dimensional (2D) PhC cavities by calculating the temperature distribution in the system in both time and space. We demonstrate that our model matches experimental results well and use it to describe the behavior of different types of PhC cavity designs. Thus, we demonstrate the model's capability to predict thermal nonlinearities of arbitrary 2D PhC microcavities in any material, only by substituting the appropriate physical constants. This renders the model critical for the development of nonlinear optical devices prior to fabrication and characterization.

Thermo-optically induced transparency on a photonic chip

“…( 1 ), by introducing up to three interacting heat capacities, thus providing an approximation of the thermal response of the system but still allowing for an analytic solution (see SOM for details). The use of three different heat capacities approximates correctly the description provided by our numerical simulation 21 and it can be intuitively justified by considering that heat is generated in the very small modal volume of the microcavity through optical absorption, then it rapidly diffuses through the PhC lattice around the cavity, and it is eventually dissipated to the surroundings.…”

“…( 1 ) is a too crude approximation. To fully understand the thermal response of the system, we have developed a numerical description of the heat diffusion problem within the PhC microcavity, which yields the distribution of Δ T as a function of both spatial coordinates and time 21 . The spatially varying temperature is then linked to the optical length of the cavity, and we see that the silicon photonics platform is capable of accessing the induced transparency regime using coupled pumping powers of the order of few microwatts.…”

“…Recently, an impressive demonstration of a related phenomenon was realized 25 , achieving millisecond delay and a similar delay-bandwidth product to our work, using a large thermally isolated table-top setup, in which heat transfer is fixed. On the other hand, the engineering of thermal energy flow from PhC cavities is a well-studied problem, where the heat flow rate can be increased through the inclusion of additional materials, for example graphene 26 , or reduced by structuring the surrounding material 21 . In ref.…”

“…In ref. 21 we present a numerical model for the accurate description of the thermo-optic response of a cavity such as the one studied here under a constant pump scenario and show that structuring of the surrounding medium can engineer the heat flow out of the cavity. Applied to the TOIT effect, we here show an example (see SOM ) where support bridges are used to thermally isolate the PhC membrane from the remainder of the sample, reducing the thermal decay rate—and hence the transparency linewidth—by more than one order of magnitude.…”

“…A full description of this model, its numerical solution, as well as an experimental validation of the results in the different pumping regimes has been recently published in ref. 21 , to which we refer for details.…”