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Register a new userMulti-scale dynamical symmetries and selection rules in nonlinear optics
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Symmetries and their associated selection rules are extremely useful in all fields of science. In particular, for system that include electromagnetic (EM) fields interacting with matter, it has been shown that both of symmetries of matter and EM fields time-dependent polarization play a crucial role in determining the properties of linear and nonlinear responses. The relationship between the systems symmetry and the properties of its excitations facilitate precise control over light emission and enable ultrafast symmetry-breaking spectroscopy of variety of properties. Here. we formulate the first general theory that describes the macroscopic dynamical symmetries (including quasicrystal-like symmetries) of an EM vector field, revealing many new symmetries and selection rules in light-matter interactions. We demonstrate an example of multi-scale selection rules experimentally in the framework of high harmonic generation (HHG). This work waves the way for novel spectroscopic techniques in multi-scale system as well as for imprinting complex structures in EUV-X-ray beams, attosecond pulses, or the interacting medium itself.
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Symmetry is one of the most generic and useful concepts in physics and chemistry, often leading to conservation laws and selection rules. For example, symmetry considerations have been used to predict selection rules for transitions in atoms, molecules, and solids. Floquet systems also demonstrate a variety of symmetries which are spatiotemporal (i.e. dynamical symmetries (DSs)). However, the derivation of selection rules from DSs has so far been limited to several ad hoc cases. A general theory for deducing the impact of DSs in physical systems has not been formulated yet. Here we explore symmetries exhibited in Floquet systems using group theory, and discover novel DSs and selection rules. We derive the constraints on a general systems temporal evolution, and selection rules that are imposed by the DSs. As an example, we apply the theory to harmonic generation, and derive tables linking (2+1)D and (3+1)D DSs of the driving laser and medium to allowed harmonic emission and its polarization. We identify several new symmetries and selection rules, including an elliptical DS that leads to production of elliptically polarized harmonics where all the harmonics have the same ellipticity, and selection rules that have no explanation based on currently known conservation laws. We expect the theory to be useful for manipulating the harmonic spectrum, and for ultrafast spectroscopy. Furthermore, the presented Floquet group theory should be useful in various other systems, e.g., Floquet topological insulators and photonic lattices, possibly yielding formal and general classification of symmetry and topological properties.
Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for example, parasitic nonlinear effects, damage problems and geometrical considerations. Here, we show that many nonlinear optics phenomena in gaseous media are scale-invariant if spatial coordinates, gas density and laser pulse energy are scaled appropriately. We develop a general scaling model for (3+1)-dimensional wave equations, demonstrating the invariant scaling of nonlinear pulse propagation in gases. Our model is numerically applied to high-order harmonic generation and filamentation as well as experimentally verified using the example of pulse post-compression via filamentation. Our results provide a simple recipe for up-or downscaling of nonlinear processes in gases with numerous applications in many areas of science.
Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.
The ability to generate complex optical photon states involving entanglement between multiple optical modes is not only critical to advancing our understanding of quantum mechanics but will play a key role in generating many applications in quantum technologies. These include quantum communications, computation, imaging, microscopy and many other novel technologies that are constantly being proposed. However, approaches to generating parallel multiple, customisable bi- and multi-entangled quantum bits (qubits) on a chip are still in the early stages of development. Here, we review recent developments in the realisation of integrated sources of photonic quantum states, focusing on approaches based on nonlinear optics that are compatible with contemporary optical fibre telecommunications and quantum memory infrastructures as well as with chip-scale semiconductor technology. These new and exciting platforms hold the promise of compact, low-cost, scalable and practical implementations of sources for the generation and manipulation of complex quantum optical states on a chip, which will play a major role in bringing quantum technologies out of the laboratory and into the real world.
High-index dielectrics can confine light into nano-scale leading to enhanced nonlinear response. However, increased momentum in these media can deteriorate the overlap between different harmonics which hinders efficient nonlinear interaction in wavelength-scale resonators in the absence of momentum matching. Here, we propose an alternative approach for light confinement in anisotropic particles. The extra degree of freedom in anisotropic media allows us to control the evanescent waves near the center and the radial momentum away from the center, independently. This can lead to a strong light confinement as well as an excellent field overlap between different harmonics which is ideal for nonlinear wavelength conversion. Controlling the evanescent fields can also help to surpass the constrains on the radiation bandwidth of isotropic dielectric antennas. This can improve the light coupling into these particles, which is crucial for nano-scale nonlinear optics. We estimate the second-harmonic generation efficiency as well as optical parametric oscillation threshold in these particles to show the strong nonlinear response in these particles even away from the center of resonances. Our approach is promising to be realized experimentally and can be used for many applications, such as large-scale parallel sensing and computing.
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