Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme, this is impossible because both up-and down-converted sidebands are necessarily present. Here, we demonstrate true single-sideband up-or down-conversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a 3 orders of magnitude improvement of the electro-optical conversion efficiency, reaching 0.1% photon number conversion for a 10 GHz microwave tone at 0.42 mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for nonclassical state conversion and communication. Our conversion bandwidth is larger than 1 MHz and is not fundamentally limited.

Recent experiments on similarly shaped polymer micro-cavity lasers show a dramatic difference in the far-field emission patterns. We show for different deformations of the ellipse, quadrupole and hexadecapole that the large differences in the far-field emission patterns is explained by the differing ray dynamics corresponding to each shape. Analyzing the differences in the appropriate phase space for ray motion, it is shown that the differing geometries of the unstable manifolds of periodic orbits are the decisive factors in determining the far-field pattern. Surprisingly, we find that strongly chaotic ray dynamics is compatible with highly directional emission in the far-field.

High speed optical telecommunication is enabled by wavelength division multiplexing, whereby hundreds of individually stabilized lasers encode the information within a single mode optical fiber. Higher bandwidths require higher a total optical power, but the power sent into the fiber is limited by optical non-linearities within the fiber and energy consumption of the light sources starts to become a significant cost factor [1]. Optical frequency combs have been suggested to remedy this problem by generating multiple laser lines within a monolithic device, their current stability and coherence lets them operate only in small parameter ranges [2][3][4]. Here we show that a broadband frequency comb realized through the electro-optic effect within a high quality whispering gallery mode resonator can operate at low microwave and optical powers. Contrary to the usual third order Kerr non-linear optical frequency combs we rely on the second order non-linear effect which is much more efficient. Our result uses a fixed microwave signal which is mixed with an optical pump signal to generate a coherent frequency comb with a precisely determined carrier separation. The resonant en- * harald.schwefel@otago.ac.nz hancement enables us to operate with microwave powers three orders of magnitude smaller than in commercially available devices. Such an implementation will be advantageous for next generation long distance telecommunication which relies on coherent emission and detection schemes to allow for operation with higher optical powers and at reduced cost [5].The data capacity of the internet is expected to grow by a factor of two every year [6], but current optical techniques are not able to meet the rising demand on the bandwidth of the undersea fibre network [7]. Techniques such as space division multiplexing [8], modedivision multiplexing [9] and wavelength division multiplexing (WDM) [5] in combination with time domain multiplexing (TDM) are being investigated to exploit the existing network to its full capacity. Current WDM systems employ an array of individually stabilized lasers, which are not phase locked to each other. For the next generation a major shift in the paradigm from multiple independent optical carriers to coherent optical frequency combs (OFCs) [7] combined with real time numerical calculation of the nonlinear pulse [5] will be necessary. The advantage of OFCs is that they can be generated from a single laser, potentially reducing the overall energy consumption of the system considerably. Furthermore, depending on the method of comb generation, OFCs can feature high phase and frequency stability, and may also arXiv:1808.10608v2 [physics.optics] 10 Jan 2019 2 a) top view WGM microwave antenna side pump laser OSA b) frequency detuning linewidth microwave frequency Ω Ω Ω 2Γ o Δ SFG SFG DFG Ω SFG DFG DFG Ω SFG DFG FIG. 1. Principles of χ (2) WGM-based frequency combs generation a) Schematic of the setup for the creation of electro-optic χ (2) -frequency combs.The interacting fields are resonantly enhanced by...

We study lasing emission from asymmetric resonant cavity GaN microlasers. By comparing far-field intensity patterns with images of the microlaser we find that the lasing modes are concentrated on three-bounce unstable periodic ray orbits; i.e., the modes are scarred. The high-intensity emission directions of these scarred modes are completely different from those predicted by applying Snell's law to the ray orbit. This effect is due to the process of "Fresnel filtering" which occurs when a beam of finite angular spread is incident at the critical angle for total internal reflection.