Optical vortex-antivortex crystallization in free space.

Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced, self-organizing into the respective polar lattices. However, these structures are in general highly unstable due to the strong VAV attraction. Here, we demonstrate that multiple optical VAV clusters nested in the propagating coherent field can crystallize into patterns which preserve their lattice structures over distance up to several Rayleigh lengths. To explain this phenomenon, we present a model for effective interactions between the vortices and antivortices at different lattice sites. The observed VAV crystallization is a consequence of the globally balanced VAV couplings. As the crystallization does not require the presence of nonlinearities and appears in free space, it may find applications to high-capacity optical communications and multiparticle manipulations. Our findings suggest possibilities for constructing VAV complexes through the orbit-orbit couplings, which differs from the extensively studied spin-orbit couplings.

Controllable orbital-angular-momentum Hall effect by engineering intrinsic orbit-orbit interaction.

We report both theoretically and experimentally a process of optical intrinsic orbit-orbit interaction with a vortex-antivortex structure nested in a freely propagating light field. The orbit-orbit interaction is originating from the coupling between different vortices and antivortices. Based on this process, we reveal the resultant controllable orbital-angular-momentum Hall effect by considering a typical structure, which comprises a vortex-antivortex pair and another vortex (or antivortex) as a controllable knob. The intrinsic Hall effect can be spatially manipulated by appropriately engineering the orbit-orbit interaction, namely arranging the initial distribution of these elements. This work can find interesting potential applications. For example, it provides an effective technique for controllable paired photon generation.

Shadows of structured beams in lenslike media.

The self-healing phenomenon of structured light beams has been comprehensively investigated for its important role in various applications including optical tweezing, superresolution imaging, and optical communication. However, for different structured beams, there are different explanations for the self-healing effect, and a unified theory has not yet been formed. Here we report both theoretically and experimentally a study of the self-healing effect of structured beams in lenslike media, this is, inhomogeneous lenslike media with a quadratic gradient index. By observing the appearance of a number of shadows of obstructed structured wave fields it has been demonstrated that their self-healing in inhomogeneous media are the result of superposition of fundamental traveling waves. We have found that self-healing of structured beams occurs in this medium and, interestingly enough, that the shadows created in the process present sinusoidal propagating characteristics as determined by the geometrical ray theory in lenslike media. This work provides what we believe to be a new inhomogenous environment to explain the self-healing effect and is expected to deepen understanding of the physical mechanism.

Spin-orbit Rabi oscillations in optically synthesized magnetic fields.

Rabi oscillation has been proven to be one of the cornerstones of quantum mechanics, triggering substantial investigations in different disciplines and various important applications both in the classical and quantum regimes. So far, two independent classes of wave states in the Rabi oscillations have been revealed as spin waves and orbital waves, while a Rabi wave state simultaneously merging the spin and orbital angular momentum has remained elusive. Here we report on the experimental and theoretical observation and control of spin-orbit-coupled Rabi oscillations in the higher-order regime of light. We constitute a pseudo spin-1/2 formalism and optically synthesize a magnetization vector through light-crystal interaction. We observe simultaneous oscillations of these ingredients in weak and strong coupling regimes, which are effectively controlled by a beam-dependent synthetic magnetic field. We introduce an electrically tunable platform, allowing fine control of transition between different oscillatory modes, resulting in an emission of orbital-angular-momentum beams with tunable topological structures. Our results constitute a general framework to explore spin-orbit couplings in the higher-order regime, offering routes to manipulating the spin and orbital angular momentum in three and four dimensions. The close analogy with the Pauli equation in quantum mechanics, nonlinear optics, etc., implies that the demonstrated concept can be readily generalized to different disciplines.

Higher-order optical rabi oscillations.

Rabi oscillations express a phenomenon of periodic conversion between two wave states in a coupled system. The finding of Rabi oscillation has led to important applications in many different disciplines. Despite great progress, it is still unknown whether the Rabi oscillating state can be excited in the framework of the higher-order vector vortex regime. Here, we demonstrate in theory that the higher-order vector vortex light beams can be Rabi oscillating during evolution in an optical coupling system. This new classical oscillating state of light is characterized by a topologically shaped wavefront and coupled with spatially varying polarization. The vector vortex state exhibits a harmonic oscillatory property in the resonant and nonresonant conditions but differs greatly in Rabi oscillating frequencies. During Rabi oscillation, the complex state maintains its topology and intensity profile, while its intrinsic polarization pattern varies adiabatically in a periodic manner. We present an interpretation of the Rabi oscillation of the higher-order wave states in terms of the coupled-mode theory. Furthermore, we reveal a symmetry-protected transition between two Rabi oscillating modes, driven by a slowly varying phase mismatch. This Rabi transition has not been reported in either quantum mechanics or any other physical setting. This work advances the research of Rabi oscillation into the higher-order regime, and it may lead to novel applications in classical and quantum optics.

Theoretical study of freely propagating high-spatial-frequency optical waves.

When it comes to the high-spatial-frequency electromagnetic waves, we usually think of them as the evanescent waves which are bounded at the near-field surface and decay along with propagation distance. A conventional wisdom tells us that the high-spatial-frequency waves cannot exist in the far field. In this work, we show, however, that these high-spatial-frequency waves having wavenumbers larger than the incident one can propagate freely to the far-field regions. We demonstrate theoretically a technique, based on an abrupt truncation of the incident plane wave, to generate these intriguing waves. The truncation functions describing the slit and the complementary slit are considered as typical examples. Our results show that both the slit structures are able to produce the high-spatial-frequency wave phenomena in the far field, manifested by their interference fringes of the diffracted waves. This work introduces the high-spatial-frequency propagating waves. Therefore, it may trigger potential investigations on such an interesting subject, e.g., one may design delicate experiment to confirm this prediction. Besides, it would stimulate potential applications such as in superresolution and precise measurement.

Diffraction-limit focusing using a 60-nm-thick spiral slit.

We demonstrate a technique for diffraction-limit focusing, on the basis of a spatial truncation of incident light using spirally structured slit motifs. The spiral pattern leads to a global phase domain where the diffractive wave vectors are distributed in phase. We fabricate such a spiral pattern on a 60-nm-thick metallic film, capable of converting an orbital-angular-momentum beam to a non-helical high-resolution diffractive focusing beam, resulting in a high numerical aperture of 0.89 in air, and of up to 1.07 in an oil-immersion scenario. The topological complementarity between the incident beam and the slit motifs generates broadband subwavelength focusing. The idea can be extended to large-scale scenarios with larger constituents. The presented technique is more accessible to low-cost fabrications as compared with metasurface-based focusing elements.

Geometric control of vector vortex light beams via a linear coupling system.

We demonstrate a novel theoretical platform to realize geometric control of vector vortex states in an optical coupling system. These complex states are characterized by spatially varying polarizations and coupled with vortex phase profiles. It can be mapped uniquely as a point on a higher-order Poincaré sphere. The geometric theory clearly reveals how a tailored phase mismatch profile, together with a suitable coupling, supports state conversion between these higher-order complex light fields, in analogous to the processes appearing in two-level quantum system as well as three-wave mixing process in nonlinear optics. Specifically, in the phase matching condition, it is shown that these complex states carried by an envelope field exhibit periodic oscillations in the course of state evolution; whereas in the phase mismatching condition the oscillations become detuned, leading to noncyclic state evolution. Intriguingly, when using an adiabatic technique for the phase mismatch, robust state conversion between two arbitrary vector vortex light fields can be realized. Our demonstrations provide a fully control over the vector vortex states on the sphere, and we suggest that it would benefit various potential applications both in the classical and the quantum optics.

Localization-to-delocalization transition of light in frequency-tuned photonic moiré lattices.

We demonstrate in a numerical manner the intriguing localization-to-delocalization transition of light in frequency-tuned photonic moiré lattices, both in the zero-order and the higher-order regimes of light waves. We present a different technique to realize the composite photonic lattices, by means of two relatively twisted sublattices with different modulated lattice constants. Even though various kinds of photonic patterns including the commensurable and the incommensurable lattices can be well constructed, the observed transition between the localization and the delocalization of light field is moiré angle-independent. This angle-insensitive property was not reported before, and cannot be achieved by those photonic moiré lattices that are all moiré angle-dependent. We reveal that the obtained phase transition of light is robust to the changes of refractive index modulation of the photonic lattices. Moreover, we reveal that the effect of moiré angle-independent transition of light can be extended to the higher-order vortex light field, hence allowing prediction, for the first time to our knowledge, of both the localization and the delocalization of the vortex light field in the photonic lattices.

Geometric phase with full-wedge and half-wedge rotation in nonlinear frequency conversion.

When the quasi-phase matching (QPM) parameters of the χ(2) nonlinear crystal rotate along a closed path, geometric phase will be generated in the signal and idler waves that participate in the nonlinear frequency conversion. In this paper, we study two rotation schemes, full-wedge rotation and half-wedge rotation, of the QPM parameters in the process of fully nonlinear three-wave mixing. These two schemes can effectively suppress the uncertainty in creating the geometric phase in the nonlinear frequency conversion process when the intensity of the pump is depleted. The finding of this paper provides an avenue toward constant control of the geometric phase in nonlinear optics applications and quantum information processing.

Vector vortex state preservation in Fresnel cylindrical diffraction.

The vector vortex light beam, which exhibits a space-variant polarization state and is coupled with orbital angular momentum of light, has been drawing much attention due to its fundamental interest and potential applications in a wide range. Here we reveal both theoretically and experimentally that a diffractive structure having cylindrical symmetry is shown to be transparent for the vector vortex state of light with arbitrary topology. We demonstrate such an intriguing phenomenon in the Fresnel diffraction condition, where the vector Helmholtz wave equation can be utilized in the paraxial regime. Our demonstration has implications in control and manipulation of vector vortex light beams in diffractive optics, and hence, it may find potential applications.

Geometric representation and the adiabatic geometric phase in four-wave mixing processes.

The application of the adiabatic geometric phase (AGP) to nonlinear frequency conversion may help to develop new types of all-optical devices, which leads to all-optical modulation of the phase front of one wave by the intensity of other waves. In this paper, we develop the canonical Hamilton equation and a corresponding geometric representation for two schemes of four-wave mixing (FWM) processes (ω1 + ω2 = ω3 + ω4 and ω1 + ω2 + ω3 = ω4), which can precisely describe and calculate the AGP controlled by the quasi-phase matching technique. The AGPs of the idler (ω1) and signal (ω4) waves for these two schemes of FWM are studied systematically when the two pump waves (ω2 and ω3) are in either the undepleted or in the depleted pump cases, respectively. The analysis reveals that the proposed methods for calculating the AGP are universal in both cases. We expect that the analysis of AGP in FWM processes can be applied to all-optically shaping or encoding of ultrafast light pulse.

Spin-Orbit Optical Hall Effect.

The optical Hall effect manifests itself as angular momentum separation induced by the photonic spin-orbit interaction. Such a celebrated Hall effect, at the mercy of the angular momentum conservation law, has attracted tremendous interest owing to its science and potential applications in precision measurements, material characterizations, and photonic devices, as well as quantum optics. However, to date, the Hall effect only expresses angular momentum separation of the spin term (spin-spin separation) or the orbital term (orbit-orbit separation), whereas the spin-orbit angular momentum separation, named as the spin-orbit Hall effect, remains unexplored. Here we demonstrate for the first time that this spin-orbit effect could appear when the polarization state of the light beam evolves adiabatically from the equator toward the poles of the higher-order Poincaré sphere, rather than the conventional Poincaré sphere. In this scenario, the intrinsic spin and orbital components of the light beam become separated, leading to equal nonzero spin and orbital angular momenta in magnitude but with the opposite sign. We further show that the spin-orbit Hall effect can be controlled via crystal birefringence and hence holds promise for applications; e.g., it is shown that the separated orbital angular momentum could be utilized in particle manipulations.

Aperiodic Vogel spirals for broadband optical wave focusing.

We demonstrate both experimentally and numerically a new type of hole array structure that exhibits optically diffractive focusing phenomenon. The hole arrays are designed based on the aperiodic Vogel spirals. In contrast to periodic and quasi-periodic hole arrays that contain discrete Bragg peaks in reciprocal space, the Vogel spiral hole arrays have particularly continuous Fourier components with circular symmetry, which enables optical wave focusing into a diffraction-limited hotspot for a wide range of incident wavelengths. We further demonstrate that the diffracted fields contain local orbital angular momentum (OAM) leading to rotations of the diffractive circular rings around the center, although the total OAM is zero.

Dynamic control of cylindrical vector beams via anisotropy.

We demonstrate that the spatially diffractive properties of cylindrical vector beams could be controlled via linear interactions with anisotropic crystals. It is the first time to show experimentally that the diffraction of the vector beams can be either suppressed or enhanced significantly during propagation, depending on the sign of anisotropy. Importantly, it is also possible to create a linear non-spreading and shape-preserving vector beam, by vanishing its diffraction during propagation via strong anisotropy in a crystal. The manageable diffractive effect enables manipulating propagation dynamics of the circular Airy vector beams, i.e., their propagation trajectories can be dynamically controlled by weakening or enhancing self-acceleration of the Airy beam. We further demonstrate that the cylindrical vector beams with initially zero orbital angular momentum can be rotated either clockwise or anticlockwise, relying on the sign of the anisotropy.

Sensitization and deactivation effects of Nd3+on the Ho3+ : 3.9 µm emission in a PbF2 crystal.

The use of Nd3+ codoping for sensitizing the Ho3+ ion and enhancing the ∼3.9 µm emission from Ho3+:I55→I65 was investigated in the PbF2 crystal for the first time, to the best of our knowledge. The ∼3.9 µm fluorescence emission properties and energy transfer mechanism of the as-grown crystals were investigated. The results show that the Nd3+ ion can act as a sensitizer to the Ho3+ ion, providing an efficient excitation channel, making the Ho3+/Nd3+:PbF2 crystal propitious to be pumped by commercialized InGaAs laser diodes (LDs). Moreover, an enhanced ∼3.9 µm emission was obtained in the Ho3+/Nd3+:PbF2 crystal due to the codoping of Nd3+ ions, leading to an efficient energy transfer from a lower laser level of Ho3+:I65 to Nd3+:I15/24, while having little influence on the higher laser level of Ho3+:I55. These advantageous spectroscopic characteristics indicate that the Ho3+/Nd3+:PbF2 crystal might have potential application in ∼3.9 µm mid-infrared lasers under a conventional 808 nm LD pump.

Directional release of the stored ultrashort light pulses from a tunable Bragg-grating microcavity.

We demonstrate numerically the ability for directionally releasing the stored ultrashort light pulse from a microcavity by means of two-pulse nonlinear interaction in a cascading Bragg grating structure. The setting is built by a chirped grating segment which is linked through a uniform segment, including a tunable microcavity located at the junction between the two components. Our simulations show that stable trapping of an ultrashort light pulse can be achieved in the setting. The stored light pulse in a microcavity can be possibly released, by nonlinearly interacting with the lateral incident control pulse. Importantly, by breaking the symmetry of potential cavity, the stably trapped light pulse can be successfully released from the microcavity to the expected direction. Owing to the induced optical nonlinearity, the released ultrashort light pulses could preserve their shapes, propagating in a form of Bragg grating solitons through the uniform component, which is in contrast to the extensively studied light pulse trappings in photonic crystal cavities which operate at the linear regime.

Dispersion Management of Propagating Waveguide Modes on the Water Surface.

We report on the theoretical and experimental study of the generation of propagating waveguide modes on the water surface. These propagating modes are modulated in the transverse direction in a manner that satisfies boundary conditions on the walls of the water tank. It is shown that the propagating modes possess both anomalous and normal dispersion regimes, in contrast to the extensively studied zero mode that, in the case of deep water, only has normal dispersion with a fixed frequency independent dispersion coefficient. Importantly, by using a carrier frequency at which the group velocity dispersion crosses zero, a linear nonspreading and shape-preserving wave packet is observed. By increasing the wave steepness, nonlinear effects become pronounced, thereby enabling the first observation of linearly chirped parabolic water wave pulses in the anomalous dispersion regime. This parabolic wave maintains its linear frequency chirp and does not experience wave breaking during propagation.

Passively Q-switched dual-wavelength green laser with an Yb:YAG/Cr4+:YAG/YAG composite crystal.

A compact dual-wavelength passively Q-switched green laser by intra-cavity frequency doubling of a Yb:YAG/Cr4+:YAG/YAG composite crystal was demonstrated for the first time to our best knowledge. The maximum green laser output power of 1.0 W was obtained under the pump power of 9.7 W, and the corresponding slope efficiency is 15.2%. The shortest pulse width, largest pulse energy, and highest peak power were achieved to be 5.54 ns, 246.1µJ, and 40.76 KW, respectively. Dual-wavelength laser oscillation simultaneously at 515 nm and 524.5 nm has been achieved. This passively Q-switched dual-wavelength green laser can be used as a laser source for Terahertz generation.

Diffractive Focusing of Waves in Time and in Space.

We study the general wave phenomenon of diffractive focusing from a single slit for two types of waves and demonstrate several properties of this effect. Whereas in the first situation, the envelope of a surface gravity water wave is modulated in time by a rectangular function, leading to temporal focusing, in the second example, surface plasmon polariton waves are focused in space by a thin metal slit to a transverse width narrower than the slit itself. The observed evolution of the phase carrier of the water waves is measured for the first time and reveals a nearly flat phase as well as an 80% increase in the intensity at the focal point. We then utilize this flat phase with plasmonic beams in the spatial domain, and study the case of two successive slits, creating a tighter focusing of the waves by putting the second slit at the focal point of the first slit.