Phase-matching Condition Research Articles

Soliton-sinc optical pulse propagation in the presence of high-order effects.

We investigate the propagation dynamics of the soliton-sinc, a kind of novel hybrid pulse, in the presence of higher-order effects with emphasis on the third-order dispersion (TOD) and Raman effects. At variance with the fundamental sech soliton, the traits of the band-limited soliton-sinc pulse can effectively manipulate the radiation process of dispersive waves (DWs) induced by the TOD. The energy enhancement and the radiated frequency tunability strongly depend on the band-limited parameter. A modified phase-matching condition is proposed for predicting the resonant frequency of the DWs emitted by soliton-sinc pulses, which is verified by the numerically calculated results. In addition, Raman-induced frequency shift (RIFS) of the soliton sinc pulse increases exponentially with a decrease of the band-limited parameter. Finally, we further discuss the simultaneous contribution of the Raman and TOD effects to the generation of the DWs emitted from the soliton-sinc pulses. The Raman effect can then either reduce or amplify the radiated DWs depending on the sign of the TOD. These results show that soliton-sinc optical pulses should be relevant for practical applications such as broadband supercontinuum spectra generation as well as nonlinear frequency conversion.

Ultrawide dynamic modulation of perfect absorption with a Friedrich–Wintgen BIC

Dynamical control of perfect absorption plays an indispensable role in optical switch and modulators. However, it always suffers from the limited modulation range, small depth, and susceptible absorption efficiencies. Here, we propose a new strategy based on Friedrich–Wintgen bound states in the continuum (F–W BICs) to realize a tunable perfect absorber with large dynamic modulation range. For proof of concept, we demonstrate a pentaband ultrahigh absorption system consisting of graphene gratings and graphene sheets through elaborately tuning F–W BIC. The nature of the F–W BIC arises from the destructive interference between Fabry–Perot resonance and guided mode resonance modes in the coherent phase-matching condition. The radiation channels are avoided from crossing. The BIC can be dynamically modulated by engineering the Fermi level of graphene gratings, which breaks the traditional modulation methods with an incidence angle. Remarkably, the perfect absorber with this F–W BIC approach achieves the largest modulation range of up to 3.5 THz. We believe that this work provides a new way to dynamically engineer perfect absorption and stimulates the development of multiband ultracompact devices.

Photon Acceleration from Optical to XUV.

The propagating density gradients of a plasma wakefield may frequency upshift a trailing witness laser pulse, a process known as "photon acceleration." In uniform plasma, the witness laser will eventually dephase because of group delay. We find phase-matching conditions for the pulse using a tailored density profile. An analytic solution for a 1D nonlinear plasma wake with an electron beam driver indicates that, even though the plasma density decreases, the frequency shift reaches no asymptotic limit, i.e., is unlimited provided the wake can be sustained. In fully self-consistent 1D particle-in-cell (PIC) simulations, more than 40 times frequency shifts were demonstrated. In quasi-3D PIC simulations, frequency shifts up to 10 times were observed, limited only by simulation resolution and nonoptimized driver evolution. The pulse energy increases in this process, by a factor of 5, and the pulse is guided and temporally compressed by group velocity dispersion, resulting in the resulting extreme ultraviolet laser pulse having near-relativistic (a_{0}∼0.4) intensity.

Phase matching in quantum search algorithm

We systematically generalize the Grover algorithm in a density matrix formalism by exploiting the underlying two-dimensional subspace of the problem. Using this, we derive analytic expressions for the success probability after arbitrary iterations of the generalized Grover operator with two generic phase angles . We show for the phase matching condition with three iterations, success probability can be achieved only with knowledge about the lower bound , where λ is the ratio of marked to total number of states in the database. This result will improve the quantum search algorithm when applied to databases with unknown number of marked states in the specified regime of λ, at the cost of decreased efficiency in the smaller λ region.

Resonant radiation emitted by solitary waves via cascading in quadratic media.

We present a systematic investigation of the resonant radiation emitted by localized soliton-like wave-packets supported by second-harmonic generation in the cascading regime. We emphasize a general mechanism which allows for the resonant radiation to grow without the need for higher-order dispersion, primarily driven by the second-harmonic component, while radiation is also shed around the fundamental-frequency component through parametric down-conversion processes. The ubiquity of such a mechanism is revealed with reference to different localized waves such as bright solitons (both fundamental and second-order), Akhmediev breathers, and dark solitons. A simple phase matching condition is put forward to account for the frequencies radiated around such solitons, which agrees well with numerical simulations performed against changes of material parameters (say, phase mismatch, dispersion ratio). The results provide explicit understanding of the mechanism of soliton radiation in quadratic nonlinear media.

Wavefront shaping with nonlinear four-wave mixing

Wavefront manipulations have enabled wide applications across many interdisciplinary fields ranging from optics and microwaves to acoustics. However, the realizations of such functional surfaces heavily rely on micro/nanofabrication to define the structured surfaces, which are fixed and only work within a limited spectrum. To address these issues, previous attempts combining tunable materials like liquid crystal or phase-change ones onto the metasurfaces have permitted extra tunability and working spectra, however, these additional layers bring in inevitable loss and complicate the fabrication. Here we demonstrate a fabrication-free tunable flat slab using a nonlinear four-wave mixing process. By wavefront-shaping the pump onto the flat slab, we can successfully tune the effective nonlinear refraction angle of the emitting FWM beams according to the phase-matching condition. In this manner, a focusing and a defocusing nonlinear of FWM beam through the flat slab have been demonstrated with a converging and a diverging pump wavefronts, respectively. Furthermore, a beam steering scheme over a 20° angle has been realized through a non-degenerate four-wave mixing process by introducing a second pump. These features open up a door to manipulating light propagation in an all-optical manner, paving the way to more functional and tunable flat slab devices in the applications of imaging and all-optical information.

Manipulating dispersive wave emission via temporal sinusoidal phase modulation.

We report the dispersive wave (DW) emission from the Gaussian pulse with temporal sinusoidal phase (TSP) modulation. The TSP-induced chirp can enhance or cancel the chirp generated by self-phase modulation by properly selecting the modulation parameters of TSP, which can influence the nonlinear propagation of the TSP-modulated pulse. It is shown that the TSP can effectively control the resonant frequency and energy conversion efficiency of the DW emission. We give a modified phase-matching condition to predict the resonant frequencies, which agree with the simulation results obtained by numerically solving the nonlinear Schrödinger equation. The enhanced conversion efficiency of the DWs can be increased up to 28% with only TSP modulation. Our results can extend the application of temporal phase modulation technology for wavelength conversion, and broadband supercontinuum generation.

Nonlinear photonics with metasurfaces

Nonlinear optics is a well-established field of research that traditionally relies on the interaction of light with macroscopic nonlinear media over distances significantly greater than the wavelength of light. However, the recently emerged field of optical metasurfaces provides a novel platform for studying nonlinear phenomena in planar geometries. Nonlinear optical metasurfaces introduce new functionalities to the field of nonlinear optics extending them beyond perturbative regimes of harmonic generation and parametric frequency conversion, being driven by mode-matching, resonances, and relaxed phase-matching conditions. Here we review the very recent advances in the rapidly developing field of nonlinear metasurface photonics, emphasizing multi-frequency and cascading effects, asymmetric and chiral frequency conversion, nonperturbative nonlinear regimes, and nonlinear quantum photonics, empowered by the physics of Mie resonances and optical bound states in the continuum.

Compact and high-performance polarization beam splitter based on triple-waveguide coupler

Polarization beam splitter (PBS) is a fundamental component of integrated photonics to manipulate wave polarization state, and most PBS devices were designed on the popular SOI. As an alternative, a PBS may be implemented on the basis of thin-film LiNbO3-on-insulator (LNOI), a promising platform for developing various compact or ultra-compact photonic active and passive devices. However, smaller modal birefringence of the LNOI waveguide makes it not easy to implement a PBS of high-performance. Here, we propose a compact, high-performance PBS on the basis of a triple-waveguide coupler consisted of two LNOI ridge waveguides and an amorphous silicon (α-Si) nanostrip assisted waveguide. By making use of the α-Si nanostrip, the PBS works in the case that the TM polarization mode meets the phase matching condition while the TE polarization mode does not. Numerical results show that the PBS is compact with a length of only 31 μm. The device can achieve an ultra-high polarization extinction ratio (>29.4 dB) and an ultra-low insertion loss (<0.066 dB) in the operating wavelength range of 1500–1600 nm for the TE polarization mode, and a polarization extinction ratio of > 20 dB and an insertion loss of < 0.16 dB over a ∼ 60 nm bandwidth from 1527 nm to 1587 nm for the TM polarization mode. Moreover, the device has a larger feature size that facilitates fabrication. Overall, this device has the advantages of compact size, higher polarization extinction ratio, lower insertion loss, and larger feature size, which is suitable for on-chip applications.

Growth and Optical Properties of Large-Sized NaVO2(IO3)2(H2O) Crystals for Second-Harmonic Generation Applications

Large-sized crystals of the quaternary iodate NaVO2(IO3)2(H2O) (NVIO) with centimeter-scale dimensions (23 mm × 18 mm × 6 mm as a representative) have been successfully grown by the top-seeded hydrothermal method. Linear optical properties have been measured, including the optical transmission spectrum and refractive index. The NVIO crystal possesses an optical window with high transmittance (above 80%) over the range of 500-1410 nm and exhibits strong optical anisotropy with large birefringence Δn (nz - nx) of 0.1522 at 1064 nm and 0.1720 at 532 nm. Based on the measured refractive indices, the phase-matching conditions for second-harmonic generation (SHG) have been calculated, and SHG devices have further been fabricated along the calculated type I and type II phase-matching directions of (θ = 39.0°, φ = 3.8°) and (θ =53.8°, φ = 1.3°). Laser experiments of extra-cavity frequency doubling have been performed on these NVIO devices. It has been confirmed that the effective SHG conversion from 1064 to 532 nm could be achieved with an energy conversion efficiency of 8.1%. Our work demonstrates that large-sized NVIO crystals are promising in the frequency-doubling application.

Dispersive higher harmonic generation and enhancement in mechanical metamaterials

Higher harmonic generation (HHG) of elastic waves is beneficial for various applications, including engineering nondestructive testing, imaging, therapy, etc. Due to the ubiquity of dispersion in most materials and structures, however, it is usually difficult to simultaneously satisfy the conditions of phase-matching and non-zero energy flux that are needed for high-efficient HHG. Here we propose a mechanical metamaterial with coupled translation-rotation motion and explore its rich dispersion property for the enhancement of two HHGs in arbitrary regions of the acoustic band, i.e., the dispersive second harmonic generation (SHG) and the dispersive third harmonic generation (THG). Besides the phase-matching condition for enhancing SHG, we analytically obtain two phase-matching conditions for THG and reveal that THG is a complex process involving the interaction of multiple waves. By tailoring the dispersion of the metamaterial, the enhanced dispersive SHG and HHG are shown to be able to propagate at an arbitrarily slow group velocity, or even zero velocity, giving rise to localization. The analytical predictions are validated by numerical simulations and experimental tests. This work shows that by combining nonlinearity, mechanical metamaterials can be designed to have advanced capabilities of wave manipulation.

Emission and sensing of high-frequency terahertz electric fields using a GaSe crystal.

A GaSe crystal cut along the (001) crystallographic plane is investigated for the emission and detection of high-frequency (i.e. up to ∼20 THz) electric fields. To date, a comprehensive analysis on high-frequency difference frequency generation and electro-optic sensing in GaSe has not been performed and should consider aspects such as electric field polarization orientation, symmetries inherent to the crystal structure, and the various possible generation and detection phase-matching arrangements. Herein, terahertz radiation generation is investigated for various excitation electric field polarizations as the GaSe crystal is rotated in the (001) plane. Subsequently, the crystal is rotated out-of-plane to investigate the difference frequency generation and electro-optic sampling phase-matching conditions for various arrangements. The measured terahertz radiation spectra show peak generation at the frequencies of 10, 16, and 18 THz (dependent on the GaSe crystal orientation), in agreement with the frequencies exhibiting perfect phase-matching. GaSe has the potential to emerge as the primary crystal for the emission and detection of high-frequency electric fields, such that this comprehensive analysis is necessary for the widespread adoption and practical implementation of GaSe as a high-frequency source crystal.

Refractive Index Measurement Using SOI Photodiode with SP Antenna toward SOI CMOS-Compatible Integrated Optical Biosensor.

This paper proposes a new optical biosensor composed of a silicon-on-insulator (SOI) p-n junction photodiode (PD) with a surface plasmon (SP) antenna. When the phase-matching condition between two lateral wavelengths of the diffracted light from the SP antenna and the waveguiding mode in the SOI PD is satisfied, we observe sharp peaks in the spectroscopic light sensitivity. Since the peak wavelength depends on the RI change around the SP antenna corresponding to the phase-matching condition, the SOI PDs with an SP antenna can be applied to the optical biosensor. The RI detection limit is evaluated in the measurements with bulk solutions, and 1.11 × 10-5 RIU (refractive index unit) can be obtained, which is comparable to that of a surface plasmon resonance (SPR) sensor, which is well known as a representative optical biosensor. In addition, the response for intermolecular bonds is estimated by the electromagnetic simulations using the finite-difference time-domain (FDTD) method to clarify its ability to detect biomolecular interactions. The results of this paper will provide new ground for high-throughput label-free biosensing, since a large number of SOI PDs with an SP antenna can be easily integrated on a single chip via an SOI complementary metal-oxide-semiconductor (CMOS) fabrication process.

First measurements of second-order frequency conversion phase-matching conditions in the new CTAS crystal

We report that Ca3TaAl3Si2O14 is a positive uniaxial crystal and provides second-order frequency conversion. Indeed, we performed direct measurements of phase-matching conditions for second-harmonic generation and sum-frequency generation up to 3.5 µm. The simultaneous fitting of recorded data provided the Sellmeier equations of the two principal refractive indices and the magnitude of the nonlinear coefficient.

Chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity

The present study is devoted to investigate the chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity. Thus, the mathematical model consists of coupled nonlinear Schrödinger equation (NLSE) that describes pulse propagation in a medium of fiber Bragg gratings (BGs). To reach an integrable form for this intricate model, the phase-matching condition is applied to derive equivalent equations that are handled analytically. By means of auxiliary equation method which possesses Jacobi elliptic function (JEF) solutions, various forms of soliton solutions are extracted when the modulus of JEF approaches 1. The generated chirped gap solitons have different types of structures such as bright, dark, singular, W-shaped, kink, anti-kink and Kink-dark solitons. Further to this, two soliton waves namely chirped bright quasi-soliton and chirped dark quasi-soliton are also created. The dynamic behaviors of chirped gap solitons are illustrated in addition to their corresponding chirp. It is noticed that self-phase modulation and dispersive reflectivity have remarkable influences on the pulse propagation. These detailed results may enhance the engineering applications related to the field of fiber BGs.

Resonant Kushi-comb-like multi-frequency radiation of oscillating two-color soliton molecules

Nonlinear waveguides with two distinct domains of anomalous dispersion can support the formation of molecule-like two-color pulse compounds. They consist of two tightly bound subpulses with frequency loci separated by a vast frequency gap. Perturbing such a two-color pulse compound triggers periodic amplitude and width variations, reminiscent of molecular vibrations. With increasing strength of perturbation, the dynamics of the pulse compound changes from harmonic to nonlinear oscillations. The periodic amplitude variations enable coupling of the pulse compound to dispersive waves, resulting in the resonant emission of multi-frequency radiation. We demonstrate that the location of the resonances can be precisely predicted by phase-matching conditions. If the pulse compound consists of a pair of identical subpulses, inherent symmetries lead to degeneracies in the resonance spectrum. Weak perturbations lift existing degeneracies and cause a splitting of the resonance lines into multiple lines. Strong perturbations result in more complex emission spectra, characterized by well separated spectral bands caused by resonant Cherenkov radiation and additional four-wave mixing processes.

Coupling interactions of anisotropic hyperbolic phonon polaritons in double layered orthorhombic molybdenum trioxide

The natural hyperbolic phonon polariton material-orthorhombic molybdenum trioxide (α-MoO&lt;sub&gt;3&lt;/sub&gt;) has recently attracted much interest , due to the associated ultra-confinement of light and enhanced light-matter interactions. We theoretically propose and study the in-plane anisotropic phonon polaritons (APhPs) in the Kretschmann structure with monolayer and dual layers α-MoO&lt;sub&gt;3&lt;/sub&gt;. The excitation of phonon polaritons and the corresponding dispersion properties in this multilayer system are studied by using a generalized 4×4 transfer matrix method (TMM). The frequency dispersions with geometrical parameters are also discussed in detail. The results confirm that the interlayer coupling can be modulated by stacking the multilayer films and regulating the thickness of each layer. More interestingly, when the distance between double α-MoO&lt;sub&gt;3&lt;/sub&gt; layers is much smaller than the propagation length of PhPs, a strong coupling phenomenon occurs, and the photon tunneling probability and intensity can be greatly improved. When the incident angle is greater than the total internal reflection angle, the phase matching condition for SPhP excitation can be satisfied. Within the 40° incident angle, the SPhP blue-shifts rapidly with the increase of incident angle. But then the dispersion curve no longer changes with increase of incidence angle. The enlargement of the interstitial layer can also lead the Fabry-Perot (FP) resonance mode to be excited. The APhP in layered heterostructure is an important part of today's nanophotonic technology, our study can help optimize and design tunable optoelectronic devices based on hyperbolic materials.

Spin-orbit interaction through Brillouin scattering in nanofibers

Spin-orbit interactions (SOI), describing the transfer of a spin degree of freedom to an orbital angular momentum (OAM), have been widely explored in recent opto-acoustic studies for applications mainly in spintronics and for topological insulators [1]. We report the observation of SOI by Brillouin scattering in an optical nanofiber. Specifically, we describe the transfer of a spin degree of freedom from light incident to the nanofiber to an acoustic vortex with a topological charge of order 2 in the form of OAM. Coupled with the phase matching condition for the energy conservation during Brillouin scattering, it results in a backscattered wave with a spin opposite to the incident wave. This observation allows considering applications of opto-acoustic Brillouin memory based on polarization conversion through a SOI [2].

Efficient second- and higher-order harmonic generation from LiNbO3 metasurfaces.

Lithium niobate (LiNbO3) is a material that has drawn great interest in nonlinear optics because of its large nonlinear susceptibility and wide transparency window. However, for complex nonlinear processes such as high-harmonic generation (HHG), which involves frequency conversion over a wide frequency range, it can be extremely challenging for a bulk LiNbO3 crystal to fulfill the phase-matching conditions. LiNbO3 metasurfaces with resonantly enhanced nonlinear light-matter interaction at the nanoscale may circumvent such an issue. Here, we experimentally demonstrate efficient second-harmonic generation (SHG) and HHG from a LiNbO3 metasurface enhanced by guided-mode resonance. We observe a high normalized SHG efficiency of 5.1 × 10-5 cm2 GW-1. Moreover, with the alleviated above-gap absorption of the material, we demonstrate HHG up to the 7th order with the shortest generated wavelength of 226 nm. This work may provide a pathway towards compact coherent white-light sources with frequency spanning into the deep ultraviolet region for applications in spectroscopy and imaging.

Chirped gap solitons in fiber Bragg gratings with polynomial law of nonlinear refractive index

The objective of the present study is to examine the behaviors of chirped optical solitons in fiber Bragg gratings (BGs) with dispersive reflectivity. The form of nonlinear refractive index represents polynomial law nonlinearity. By virtue of phase-matching condition, the discussed model of coupled nonlinear Schrödinger equation is reduced to an integrable form. Consequently, chirped optical solitons having various profiles such as W-shaped, bright, dark, kink and anti-kink solitons are derived. Further to this, the chirp associated with these soliton structures are extracted. The impact of dispersive reflectivity, self-phase modulation and cross-phase modulation on the pulse propagation is investigated and it is induced that the changes of self-phase modulation and cross-phase modulation cause a marked rise in soliton amplitude which is subject to minor variations by dispersive reflectivity. The physical evolutions of chirped optical solitons are described along with the corresponding chirp to pave the way for possible applications in the field of fiber BGs.