The theory of surface-second-harmonic generation in a dielectric microsphere using whispering-gallery modes ͑WGMs͒ is developed. The second-order nonlinearity is restricted to the surface of the sphere. The coupling coefficients for a coupled-mode theory are derived and conditions for double resonance and phase matching are discussed for TE and TM polarizations. We demonstrate that phase matching of WGMs amounts to conservation of the angular momentum of the electromagnetic mode while at the same time we obtain an analytical expression for the coherence length.

Passive parity-time symmetry breaking transitions, where long-lived eigenmodes emerge in a locally dissipative system, have been extensively studied in recent years. Conventional wisdom says that they occur at exceptional points. Here we report the observation of multiple transitions showing the emergence of slowly decaying eigenmodes in a dissipative, Floquet electronic system with synthetic components. Remarkably, in our system, the modes emerge without exceptional points. Our setup uses an electrical oscillator inductively coupled to a dissipative oscillator, where the time-periodic inductive coupling and resistive-heating losses are independently controlled. With a Floquet dissipation, slowly-decaying eigenmodes emerge at vanishingly small dissipation strength in the weak coupling limit. With a moderate Floquet coupling, multiple instances of their emergence and disappearance are observed. With an asymmetric dimer model, we show that these transitions, driven by avoided-levelcrossing in purely dissipative systems, are generically present in static and Floquet domains.

Noise is generally thought as detrimental for energy transport in coupled oscillator networks. However, it has been shown that for certain coherently evolving systems, the presence of noise can enhance, somehow unexpectedly, their transport efficiency; a phenomenon called environment-assisted quantum transport (ENAQT) or dephasing-assisted transport. Here, we report on the experimental observation of such effect in a network of coupled electrical oscillators. We demonstrate that by introducing stochastic fluctuations in one of the couplings of the network, a relative enhancement in the energy transport efficiency of 22.5 ± 3.6% can be observed.

Unmarked sensitive detection of molecules is needed in environmental pollution monitoring, disease diagnosis, security screening systems and in many other situations in which a substance must be identified. When molecules are attached or adsorbed onto an interface, detecting their presence is possible using second harmonic light generation, because at interfaces the inversion symmetry is broken. However, such light generation usually requires either dense matter or a large number of molecules combined with high-power laser sources. Here we show that using high-Q spherical microresonators and low average power, between 50 and 100 small non-fluorescent molecules deposited on the outer surface of the microresonator can generate a detectable change in the second harmonic light. This generation requires phase matching in the whispering gallery modes, which we achieved using a new procedure to periodically pattern, with nanometric precision, a molecular surface monolayer.

Over the last fifteen years, a series of theoretical and experimental investigations have demonstrated the usefulness of circular geometries to tailor second-order nonlinear optical effects. However, until recently, such effects have remained rather weak, calling for their enhancement. In parallel, developments in the field of high quality factor spherical or ring resonators have shown that many different types of light-matter interactions can be dramatically amplified when light is coupled in the whispering gallery modes of such resonators. In high-quality spherical micro-resonators, close to one million interactions can occur between a nonlinear molecule and a circulating light pulse. Recent research on nonlinear optics in spherical geometry is reviewed, from micrometer-size spheres to whispering gallery mode resonators.