Monolithic Silicon-Based Nanobeam Cavities for Integrated Nonlinear and Quantum Photonics

J.P. Vasco, D. Gerace, K. Seibold, and V. Savona

Phys. Rev. Applied 13, 034070 – Published 30 March 2020

Abstract

Photonic resonators that allow an electromagnetic field to be confined in an ultrasmall volume with a long decay time are crucial to a number of applications requiring enhanced nonlinear effects. For applications to integrated photonic devices on chip, compactness and optimized in-plane transmission become relevant figures of merit as well. Here we optimize an encapsulated $Si / {Si O}_{2}$ photonic-crystal nanobeam cavity at telecom wavelengths by means of a global optimization procedure, where only the first few holes surrounding the cavity are varied to decrease its radiative losses. This strategy allows us to theoretically achieve intrinsic quality factors close to 10 million, sub-diffraction-limited mode volumes, and in-plane transmission above 65%, in a structure with a very small footprint of about $8 μ m^{2}$ . We address and quantitatively assess the dependence of the main figures of merit on the nanobeam length and on fabrication disorder. Finally, we study a system of two optimized and laterally coupled nanobeam cavities with the goal of demonstrating an unconventional photon blockade at room temperature in a monolithic passive device. We estimate the single-photon nonlinearity of this device and discuss the relevant figures of merit, which lead to sub-Poissonian photon statistics of the transmitted signal. Our results hold promise for prospective experiments in low-power nonlinear and quantum photonics.

Received 9 December 2019
Revised 4 March 2020
Accepted 5 March 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.034070

Physics Subject Headings (PhySH)

Integrated optics Nanophotonics Nonlinear optics Photon statistics Photonic crystals Semiconductor quantum optics

Coupled oscillators

Cavity resonators

Nonlinear DynamicsGeneral PhysicsAtomic, Molecular & Optical

Authors & Affiliations

J.P. Vasco ^1,*, D. Gerace ², K. Seibold¹, and V. Savona ¹

¹Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne EPFL, CH-1015 Lausanne, Switzerland
²Dipartimento di Fisica, Università di Pavia, via Bassi 6, I-27100 Pavia, Italy

^*juan.vasco@epfl.ch

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Vol. 13, Iss. 3 — March 2020

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Images

Figure 1
(a) Schematic representation of a nanobeam cavity with a total of $N$ holes on each side, and a lattice offset $Δ x_{c}$ . The red holes are allowed to vary (in size and position), and $Δ x_{c}$ is also allowed to vary while preserving the mirror symmetry with respect to the center of the cavity. (b) Parameters of the nanobeam unit cell. (c) Structure of the TE-like bands of (b) in the projected Brillouin zone, where the dashed horizontal line represents the nonoptimized cavity mode with $f = 193 THz$ and $Q_{c} = 3.1 \times 10^{4}$ . The band-gap and light-cone regions are highlighted in yellow and gray, respectively. (d) Electric-field-intensity profile $| E |^{2}$ of the cavity mode at $z = 0$ . (e) As (d), for $y = 0$ .
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Figure 2
Total quality factor $Q$ (left axis, continuous black line) and in-plane transmission $T$ (right axis, dashed blue line) as a function of the total number of holes on each side of the cavity, optimized with five varying holes. The case of $N = 15$ is highlighted as a good compromise, with large $Q$ and $T$ while keeping a short nanobeam.
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Figure 3
Cavity quality factor $⟨ Q_{c} ⟩$ averaged over 100 disorder realizations as a function of the disorder parameter for the optimized cavity with five varying holes. The red curve corresponds to disorder in both the positions and sizes of the holes, while the blue curve corresponds to disorder in the hole sizes only.
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Figure 4
(a) Tunnel-coupling rate between two encapsulated nanobeam resonators (defined as in the text), and (b) loss rates of symmetric and antisymmetric normal modes as a function of the cavity-to-cavity distance as defined in the inset of panel (a); the loss rate of the isolated nanobeam cavity is also shown as a reference. All the loss-rate values include a disorder contribution (corresponding to $σ / a = 0.002$ in Fig. 3). (c) Schematic representation of an experimental configuration with a coupled-nanobeam device that allows one to measure photon statistics at the output of the driven cavity channel, and (d) the corresponding calculated second-order correlation function at zero time-delay obtained from cavity 1, as a function of both the distance between the coupled resonators and the pump-cavity detuning (taking the resonance of the isolated nanobeam as a reference). The color-scale plot represents $g_{1}^{(2)} (0)$ on a logarithmic scale, and the highlighted regions correspond to experimental conditions leading to antibunched output statistics.
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Figure 5
(a) Projected Fourier transform of the component $E_{y}$ along the $x$ direction at $z = y = 0$ for the optimized cavity with five varying holes (continuous red line), superimposed on the corresponding curve for the nonoptimized cavity (dashed black line). The light lines for the optimized cavity are shown as dashed blue lines. (b) As (a), for the optimized cavity with eight varying holes.
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