Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

Abstract

We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V eff ). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illustrate the design concept with a silicon-air one-dimensional photon crystal cavity that reaches an ultrasmall mode volume of V eff ∼ 7.01 × 10 −5 λ 3 at λ ∼ 1550 nm. We show that the extreme light concentration in our design can enable ultrastrong Kerr nonlinearities, even at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics. DOI: 10.1103/PhysRevLett.118.223605 Optical nanocavities with small mode volume (V eff ) and high quality factor (Q) can greatly increase light-matter interaction [1] and have a wide range of applications including nanocavity lasers [2-4], cavity quantum electrodynamics [5,6], single-molecule spectroscopy [7], and nonlinear optics [8][9][10]. Planar photonic crystal cavities can enable high Q factors, exceeding 10 6 [11], together with mode volumes that are typically on the order of a qubic wavelength. However, it was shown that by introducing an air slot into a photonic crystal (PhC) cavity, it is possible to achieve the electromagnetic (EM) mode with small V eff on the order of 0.01λ 3 [12], where λ is the freespace wavelength. This field concentration results from the boundary condition on the normal component of the electric displacement ( ⃗ D). Here, we propose a method to further reduce V eff by making use of the second EM boundary condition, the conservation of the parallel component of the electric field. Furthermore, these field concentration methods can be concatenated to reduce V eff even further, limited only by practical considerations such as fabrication resolution. The extreme field concentration of our cavity design opens new possibilities in nonlinear optics. In particular, we show that Kerr nonlinearities, which are normally weak, would be substantially enhanced so that even a single photon may shift the cavity resonance by a full linewidth, under realistic assumptions of materials and fabrication tolerances.The mode volume of a dielectric cavity [described by the spatially varying permittivity ϵð ⃗rÞ] is given by the ratio of the total electric energy to the maximum electric energy density [13],In typical PhC cavity designs, the minimum cavity mode volume is given by a half-wavelength bounding box, or3 [14], agreeing with the diffraction limit. However, as is clear from Eq. (1), the mode volume is determined by the electric energy density at the position where it is maximized. Thus, it is not strictly restricted by the diffraction limit. A strong local inhomogeneity in ϵð ⃗rÞ can greatly increase this electric energy density and correspondingly shrink the mode volume. Figure 1(a) plots the fundamental mode of a silicon-air one-dimensional PhC cavity produced by three-dimensional FDTD simulati...

Controlling rare-earth ions in a nanophotonic resonator using the ac Stark shift

“…To achieve a single-photon ACSS of this order would require an increase in g by a factor between 3 and 10 (the ACSS is proportional to g 2 ). One effective strategy to pursue this goal would be to change the cavity design to incorporate dielectric discontinuities [46][47][48], thereby reducing the mode volume. Previous work in the design of such cavities indicates that a 100× reduction in the mode volume is certainly feasible.…”

Controlled-Phase Gate Using Dynamically Coupled Cavities and Optical Nonlinearities

“…We do this using the parameters listed in the caption of Fig. 4 for a silicon cavity with an ultra-small mode volume [21][22][23]. Fig.…”

“…Table I lists the values of C (k) for the two most promising χ (2) materials and the most common χ (3) material, silicon. The table also lists the required intrinsic quality factor to achieve a conditional fidelity of 99% for an ultra-small mode volume, V (k) m = 10 −3 [21][22][23], and a standard size for one-dimensional photonic crystal cavities, V (k) m = 0.5. The numbers seem prohibitively…”

Fractal-like Mechanical Resonators with a Soft-Clamped Fundamental Mode

“…Coast lines are a famous example-their length is loosely defined at geographic scale [1]. In the domain of optics, it was found that self-similar cavities can support modes with arbitrarily small mode volume [2] at a given wavelength. Meanwhile, hierarchical metamaterials can have improved stiffness per unit mass [3,4] compared to natural materials.…”