Concentration of light in photonic nanocavities is key to enhancing the interaction of light and matter, which is important for numerous optical devices such as optical switches, sensors and low-threshold lasers [1, 2]. The light-matter interaction is enhanced by elongating the time of interaction, quantified by a high cavity quality factor , and by strong spatial localization of the light, quantified by a small mode volume . Recent findings have shown that nanometer-scale features may be employed to realize extreme sub-wavelength confinement due to the discontinuities of either the electric field or the displacement field [4-6]. The optimal shape of the nanocavities has been found to be a bowtie geometry, which can confine the energy density at the apex of two tips to mode volumes of < 10-3(/n)3. Importantly, small mode volumes enable extremely strong light-matter interaction for moderate cavity quality factors, thus allowing for large optical bandwidth, as required for applications requiring short optical pulses or high-speed data signals. Here we investigate three nonlinear effects in a silicon bowtie nanocavity to explore the implications of the extremely small mode volumes on the optical responses: The Kerr effect, carrier dynamics, and thermal effects.The Kerr and thermal effect cause a red-shift of the cavity spectra, while the free carrier dispersion gives rise to a blue-shift. We model the response with coupled-mode theory (CMT), where the effect of each optical nonlinearity on the frequency and loss is treated individually and then combined to yield a set of rate equations. We introduce two nonlinear mode volumes as described in Ref. 7. One mode volume describes the enhancement of the Kerr effect and the associated two-photon absorption, while the other describes the enhancement of the free-carrier absorption. We use the CMT model to investigate the dielectric bowtie nanocavity shown in Fig. 1a, which has been designed using topology optimization . It features a narrow dielectric bowtie in the center and is designed in a 240 nm suspended silicon membrane (n = 3.48), attached only in the corners. We calculate the quasi-normal mode and associated eigenfrequency of the structure using 3D finite element modelling. Then we vary the gap shown in Fig. 1b to investigate nanocavities with varyingspatial confinement. We use the calculated mode volumes and quality factors for the nanocavities with different gaps to explore the impact of the strong spatial confinement. The cavities are excited with a pulsedsignal. The pulse is chosen to have an energy of, U = 200 fJ, and width, FWHM = 10 ps, with the center frequency matching the cavity resonance frequency.Figure 2 shows the change to the spectrum of the outgoing pulse due to the nonlinear interactions. The centerfrequency is unaffected by the enhancement of the nonlinear effects. This is a consequence of the initial fast detuning of the resonance, when the pulse enters the cavity and is thus dependent on the temporal width of the pulse and the response time of the cavity. We observe a spectral broadening at higher frequencies, which isdue to the free-carrier dispersion, which is the dominating nonlinear effect. As the gap decreases further, new fringes are introduced in the spectrum. Analysis of the frequency shifts originating from the different nonlinear effects reveal that thermal and carrier effects are of similar magnitude for the two smallest gaps, while the Kerr effect is negligible. The thermal effect scales faster with the cavity mode energy than the carrier effect and thus the thermal effect is more pronounced for stronger confinement. The fringes appear because the thermal effect and the carrier effect cause opposite shifts to the cavity resonance frequency. These findings may be employed to indirectly measure the spatial confinement of light in the bowtie, while new designs employing an input waveguide can be used to realize specific nonlinear applications.
|Number of pages
|Published - 2022
|47th Micro and Nano Engineering Conference 2021 - Lingotto, Turin, Italy
Duration: 20 Sept 2021 → 23 Sept 2021
Conference number: 47
|47th Micro and Nano Engineering Conference 2021
|20/09/2021 → 23/09/2021