Phase Matching Effects Research Articles

Pure-quartic soliton in a birefringence-managed fiber laser

Pure-quartic soliton (PQS) fiber lasers with a great variety of operating regimes have aroused considerable interest in high-energy ultrashort pulses and novel soliton patterns. Here, we numerically investigate the generation and dynamic properties of birefringence-managed pure-quartic soliton (BMPQS) in a positive fourth-order dispersion (FOD) fiber laser consisting of single-mode fibers and a section of polarization-maintaining fiber. The formation mechanism of the chirp-free BMPQS is dominated by the phase-matching effect, which arises from the co-actions of the birefringence, positive FOD, and nonlinear effects. It is observed that a higher FOD coefficient leads to energy transfer between the spectral sidebands inside the BMPQS. Moreover, the evolution of the BMPQS with the increase of the pump power confirms the phase-matching theory. Finally, the BMPQS molecule can be obtained with further increasing the pump power. This work offers a new avenue to create chirp-free pulses in positive FOD fiber lasers and enriches the sub-families of PQSs.

The single-cycle biphotons generated by SPDC in chirped QPM PPKTP crystal

In this paper, we have studied the process of monochromatic pump light in linearly chirped Periodically Poled [Formula: see text] (PPKTP) nonlinear crystal to generate single-cycle biphotons under Quasi-Phase-Matching (QPM) conditions through a Spontaneous Parametric Down-Conversion (SPDC). A detailed analysis of the phase mismatching function reveals that in PPKTP crystals, for the proper frequency range, the phase mismatching [Formula: see text] is stable and relatively close to 0 due to the relatively stable refractive index, and therefore has a good phase matching effect. Even when the chirp rate becomes small, it is able to produce single-cycle biphotons due to the near-perfect phase matching. Of course, as the chirp rate increases, the frequency response range becomes wider, the temporal width is narrower, and the number of cycles is smaller.

Flexible Anionic Groups-Activated Structure Dissymmetry for Strong Nonlinearity in Ln2 Ae3 MIV 3 S12 Family.

Structural dissymmetry and strong second-harmonic generation (SHG) responses are key conditions for nonlinear optical (NLO) crystals, and targeted combinatorial screening of suitable anionic groups has become extremely effective. Herein, optimal combination of flexible SnSn (n=5, 6) groups and highly electropositive cations (lanthanides (Ln3+ ) and alkaline earth (Ae2+ : Sr, Ca) metals) affords the successful synthesis of 12 NLO thiostannates including Ln2 Sr3 Sn3 S12 (Pmc21 ) and Ln2 Ca3 Sn3 S12 (P-62m); whereas 17 rigid GeS4 or SiS4 tetrahedra-constructed Ln2 Ae3 Ge3 S12 and Ln2 Ae3 Si3 S12 crystallize in the centrosymmetric (CS) Pnma. This unprecedented CS to noncentrosymmetric (NCS) structural transformation (Pnma to P-62m to Pmc21 ) in the Ln2 Ae3 MIV 3 S12 family indicates that chemical substitution of the tetrahedral GeS4 /SiS4 units with SnSn breaks the original symmetry to form the requisite NCS structures. Remarkably, strong polarization anisotropy and hyperpolarizability of the Sn(4+) S5 unit afford huge performance improvement from the nonphase-matching (NPM) SHG response (1.4×AgGaS2 and Δn=0.008) of La2 Ca3 Sn3 S12 to the strong phase-matching (PM) SHG effect (3.0×AgGaS2 and Δn=0.086) of La2 Sr3 Sn3 S12 . Therefore, Sn(4+) S5 is proven to be a promising "NLO-active unit." This study verifies that the coupling of flexible SnSn building blocks into structures opens a feasible path for designing targeted NCS crystals with strong nonlinearity and optical anisotropy.

Nonlinear nonlocal metasurfaces

Optical metasurfaces have recently emerged as the game changer in light manipulation and opened up new perspectives in many subfields of optics and photonics. Recent developments in nonlocal metasurfaces, in which the nanoscale building blocks respond to the incoming light collectively rather than as individual objects, are especially promising for enhancing and controlling the nonlinear optical phenomena. In this article, we provide a brief overview of the basic principles of nonlocal metasurfaces in the context of their nonlinear optical functionalities. We discuss the origin and the regimes of the nonlocal response, covering the aspects of multiple scattering, radiation damping, quality factor, local-field enhancement, and temporal dynamics. Some important aspects are illustrated by computational examples. We also give our personal viewpoint on the selected ideas and research directions in nonlocal and nonlinear metasurfaces, including the role of spatial symmetry in nonlocal interactions, the effects of phase and momentum matching in frequency conversion, as well as the possibilities offered by new material platforms and novel concepts, such as bound states in the continuum, parity–time symmetry, and time-variant metasurfaces.

(C4H10NO)PbX3 (X = Cl, Br): Design of Two Lead Halide Perovskite Crystals with Moderate Nonlinear Optical Properties.

Introducing electronegative species into organic constituents was considered to be one effective strategy for adjusting crystal symmetry and designing new nonlinear optical (NLO) materials. By substitution of C4 in piperidine (C5H11N) with electronegative oxygen, organic morpholine (C4H9NO) was easily obtained. Therefore, to design NLO crystals, we focused on combinations of stereochemically active lone-pair (SCALP) cation (Pb2+)-based chloride and bromide with morpholine molecules. In this work, two lead halide hybrid perovskite (C4H10NO)PbX3 (X = Cl, Br, abbreviated as MPbCl3 and MPbBr3, respectively) single crystals with moderate nonlinear optical properties were synthesized by a slow evaporation method. The two title crystals belong to orthorhombic space group P212121 with one-dimensional (1D) chainlike perovskite structures. Theoretical calculations revealed that the second harmonic generation (SHG) responses mainly originate from distorted {PbX6} octahedrons of the inorganic framework. Remarkably, moderate phase-matching SHG effects of about 0.70 and 0.81 times KH2PO4, large birefringences of 0.098 and 0.111 at 1064 nm, and large laser damage thresholds (LDTs) of 19.94 and 46.82 MW/cm2 were estimated for MPbCl3 and MPbBr3, respectively. This work provides a novel strategy for new purpose-designed hybrid NLO crystals by adjustment and modulation of chemical modification.

Resonance absorption of the inner shell during high-order harmonic generation.

In this work, we report the observation of resonance absorption of the inner shell during the high-order harmonic generation (HHG) from xenon (Xe) and krypton (Kr). The absorption peaks show a periodic variation with the change of carrier-envelope phase of driving laser pulses and the delay of two-color laser field, which indicates the absorption peaks come from the collective multielectron effects during the HHG. With the increase of gas pressure, the depth of absorption peak will continue to increase, while due to the phase matching effect, there will be an optimal pressure for the intensity of harmonic signal. Our experimental results pave the way to uncover the physical mechanism of the collective multielectron effects involving inner-shell electrons in the HHG process.

Phase-matching-induced near-chirp-free solitons in normal-dispersion fiber lasers

Direct generation of chirp-free solitons without external compression in normal-dispersion fiber lasers is a long-term challenge in ultrafast optics. We demonstrate near-chirp-free solitons with distinct spectral sidebands in normal-dispersion hybrid-structure fiber lasers containing a few meters of polarization-maintaining fiber. The bandwidth and duration of the typical mode-locked pulse are 0.74 nm and 1.95 ps, respectively, giving the time-bandwidth product of 0.41 and confirming the near-chirp-free property. Numerical results and theoretical analyses fully reproduce and interpret the experimental observations, and show that the fiber birefringence, normal-dispersion, and nonlinear effect follow a phase-matching principle, enabling the formation of the near-chirp-free soliton. Specifically, the phase-matching effect confines the spectrum broadened by self-phase modulation and the saturable absorption effect slims the pulse stretched by normal dispersion. Such pulse is termed as birefringence-managed soliton because its two orthogonal-polarized components propagate in an unsymmetrical “X” manner inside the polarization-maintaining fiber, partially compensating the group delay difference induced by the chromatic dispersion and resulting in the self-consistent evolution. The property and formation mechanism of birefringence-managed soliton fundamentally differ from other types of pulses in mode-locked fiber lasers, which will open new research branches in laser physics, soliton mathematics, and their related applications.

PbBe2B2O6: an ultraviolet nonlinear-optical crystal with unprecedented π–π interacting BeBO5 group

π-Conjugated-group systems are fascinating and have been pursued for nonlinear materials owing to their superior optical and electronic properties, but are so far quite limited. Here, we report a new ultraviolet (UV) nonlinear-optical (NLO) beryllium borate crystal PbBe2B2O6 that manifests an unprecedented π-π interacting BeBO5 group, constructed by interconnected π-conjugated BeO3 and BO3 units. The PbBe2B2O6 crystal has a short UV cutoff wavelength of 249 nm, phase-matching behavior in the whole transmission region from UV to IR light region (249-3166 nm), and remarkably the largest NLO effect (18.5 × KDP) among the π-conjugated UV NLO crystal materials. Theoretical calculation unravels that the highly NLO-active BeBO5 group has strong π-π interactions. This work offers an innovative source of BeO3-participating NLO materials and expands the frontier of NLO research.

Birefringence-Managed Normal-Dispersion Fiber Laser Delivering Energy-Tunable Chirp-Free Solitons

Chirp-free solitons have been mainly achieved with anomalous-dispersion fiber lasers by the balance of dispersive and nonlinear effects, and the single-pulse energy is constrained within a relatively small range. Here, we report a class of chirp-free pulse in normal-dispersion erbium-doped fiber lasers, termed birefringence-managed soliton, in which the birefringence-related phase-matching effect dominates the soliton evolution. Controllable harmonic mode locking from 5 order to 85 order is obtained at the same pump level of ~10 mW with soliton energy fully tunable beyond ten times, which indicates a new birefringence-related soliton energy law, which fundamentally differs from the conventional soliton energy theorem. The unique transformation behavior between birefringence-managed solitons and dissipative solitons is directly visualized via the single-shot spectroscopy. The results demonstrate a novel approach of engineering fiber birefringence to create energy-tunable chirp-free solitons in normal-dispersion regime and open new research directions in fields of optical solitons, ultrafast lasers, and their applications.

Synthesis, Crystal Structure, and Nonlinear Optical Property of an Anhydrous Sulfate KTb(SO4)2.

A new alkali metal-rare earth metal anhydrous sulfate, KTb(SO4)2 (KTSO), was synthesized by a hydrothermal method. It crystallized in the non-centrosymmetric (NCS) orthorhombic space group P212121 with cell parameters a = 5.43950(10), b = 8.8579(3), c = 13.3962(4), Z = 2. Its structure is composed of [KO11], [TbO8], and [SO4] groups, which are interconnected to constitute a one-dimensional (1D) chain, and then further linked to construct a three-dimensional (3D) network structure through [SO4] units. The results of the powder frequency doubling test show that KTb(SO4)2 has a phase-matching second-order nonlinear optical effect of 0.3 times that of KH2PO4 (KDP). The measured birefringence of the crystal (0.01) agrees well with the calculated value (0.019). Meanwhile, its infrared and ultraviolet spectrum and thermal properties were studied, respectively. Its optical properties and band gap structure are studied by theoretical calculation. This work provides a NCS structure of anhydrous sulfates and offers guidance for further exploration of new anhydrous sulfates.

Growth and XRD, Elemental, Mechanical, Dielectric, Optical and Photoconductivity, and Surface Morphological Characterizations of 2-[4-(Trifluoromethyl) phenyl]-1H-benzimidazole (TFMPHB) Crystals for Electronic, Mechanical Applications

Nonlinear optical crystalline material is the fascinating tool for the optoelectronic devices and for phase-matched equipments, frequency matching circuits and etc. Present study portrays the synthesize and utility of macro and nano scaled crystals of 2-[4-(trifluoromethyl) phenyl]-1H-benzimidazole (TFMPHB) by slow evaporation solution growth method and by milling conversion. As-prepared crystals were studied by XRD, CHNSO analysis, dielectric and tribology-mechanical, NLO, and photoconductivity. The orthorhombic phase structure with the average crystalline size of 21 nm was observed. The elemental composition of crystals was analyzed for the presence of elements. Tribological studies of macro and nano TFMPHB crystals were favorable for mechanical applications. Further, the high dielectric constant (363 K) at low frequency was suitable for microelectronic devices; NLO is analyzed with phase matching effect over particle size, and photoconductivity study also reported for the entitled crystalline specimen. The structural parameters by AFM and SEM, absorbance nature by UV spectra, and modeling data by computational methods are also reported.

Second-harmonic generation of temporally low-coherence light

In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.

Nano-plasmonic near field phase matching of attosecond pulses

Nano-structures excited by light can enhance locally the electric field when tuned to plasmonic resonances. This phenomenon can be used to boost non-linear processes such as harmonic generation in crystals or in gases, Raman excitation, and four wave mixing. Here we present a theoretical investigation of the near-field phase matching of attosecond pulses emitted by high-order harmonic generation (HHG) of an atom immersed in a multi-cycle femtosecond infrared laser field and a spatially inhomogeneous plasmonic field. We demonstrate that the spatial inhomogeneity factor of the plasmonic field strongly affects the electron trajectory and recombination time which can be used to control the attosecond emission. For further insight into the plasmonic field effect, we monitor the phase of each quantum path as a function of the inhomogeneity strength. Moreover, we investigate the attosecond emission as a function of near-field phase matching effects. This is achieved by calculating the coherent field superposition of attosecond pulses emitted from various intensities or field inhomogeneities. Finally, far-field and near-field phase matching effects are combined to modulate the harmonic spectral phase towards the emission of a single attosecond pulse.

Phase matching effects in high harmonic generation at the nanometer scale.

Plasmon resonances are known to amplify the electromagnetic fields near metallic nanostructures, providing a promising scheme to generate extreme-ultraviolet harmonics using low power drivings. During high-order harmonic generation (HHG), the driving and harmonic fields accumulate a phase difference as they propagate through the target. In a typical set-up -a laser focused into a gas jet- the propagation distances amount to several wavelengths, and the cumulative phase-mismatch affects strongly the efficiency and properties of the harmonic emission. In contrast, HHG in metallic nanostructures is considered to overcome these limitations, as the common sources of phase mismatch -optical density and focusing geometry- are negligible for subwavelength propagation distances. We demonstrate that phase matching still plays a relevant role in HHG from nanostructures due to the non-perturbative character of HHG, that links the harmonic phase to the intensity distribution of the driving field. Our computations show that widely used applications of phase matching control, such as quantum path selection and the increase of contrast in attosecond pulse generation, are also feasible at the nanoscale.

Phase matching alters spatial multiphoton processes in dense atomic ensembles.

Multiphoton processes in dense atomic vapors such as four-wave mixing or coherent blue light generation are typically viewed from single-atom perspective. Here we study the surprisingly important effect of phase matching near two-photon resonances that arises due to spatial extent of the atomic medium within which the multiphoton process occurs. The non-unit refractive index of the atomic vapor may inhibit generation of light in nonlinear processes, significantly shift the efficiency maxima in frequencies and redirect emitted beam. We present these effects on an example of four-wave mixing in dense rubidium vapors in a double-ladder configuration. By deriving a simple theory that takes into account essential spatial properties of the process, we give precise predictions and confirm their validity in the experiment. The model allows us to improve on the geometry of the experiment and engineer more efficient four-wave mixing.

Detailed discussion of the optimum baud rate of nonlinearity in WDM transmission

Different numbers of sub-channels correspond to different baud rates per sub-channel when the total baud rate is fixed. The optimum baud rate of nonlinearity in WDM systems is investigated in this paper. We find that the phase matching effect produces an optimum baud rate of nonlinearity, which is related to the chromatic dispersion accumulation of a single span. Then other factors that influence the optimum baud rate are analyzed. By mathematical derivation and simulation verification, larger number of spans and larger spectrum gap between sub-channels both make the optimum value decrease. We also find that different modulation formats barely change the optimum baud rate if other system settings are the same and all sub-channels have the same modulation format.

Propagation of intense and short circularly polarized pulses in a molecular gas: From multiphoton ionization to nonlinear macroscopic effects

We present a detailed analysis of the propagation dynamics of short and intense circularly polarized pulses in an aligned diatomic gas. Compared to linearly polarized intense pulses, high harmonic generation (HHG) and the coherent generation of attosecond pulses in the intense-circular-polarization case are a new research area. More specifically, we numerically study the propagation of intense and short circularly polarized pulses in the one-electron ${\mathrm{H}}_{2}{}^{+}$ molecular gas, using a micro-macro Maxwell--Schr\odinger model. In this model, the macroscopic polarization is computed from the solution of a large number of time-dependent Schr\odinger equations, the source of dipole moments, and using a trace operator. We focus on the intensity and the phase of harmonics generated in the ${\mathrm{H}}_{2}{}^{+}$ gas as a function of the pulse-propagation distance. We show that short coherent circularly polarized pulses of same helicity can be generated in the molecular gas as a result of cooperative phase-matching effects.

Collection and spectral control of high-order harmonics generated with a 50 W high-repetition rate Ytterbium femtosecond laser system

We generate high-order harmonics with a 50 W, Yb femtosecond fiber laser system operating at 100 kHz in a tight focusing configuration. We achieve a high photon flux even with pulses longer than 500 fs. We collect the diverging extreme ultraviolet (XUV) harmonic beam in a 35 mrad wide solid angle by using a spectrometer designed to handle the high thermal load under vacuum and refocus the XUV beam onto a detector where the beam is characterised or can alternatively be used for experiments. This setup is designed for a 50 eV XUV bandwidth and offers the possibility to perform XUV-IR pump probe experiments with both temporal and spectral resolution. The high-order harmonics were generated and optimized at 100 kHz by using several gas target geometries (a gas jet and a semi-infinite gas cell) and several gases (argon, krypton, xenon) that provide XUV beams with different characteristics. After the spectrometer and for high-order harmonic generation (HHG) in xenon, we detect more than 4 × 1010 photons per second over four harmonics, that is a useful XUV power on target of 0.1 μW. This corresponds to the emission of more than 1 μW per harmonic at the source and we achieved a similar flux with both the semi-infinite cell and the jet. In addition, we observe a strong spectral selectivity when generating harmonics in a semi-infinite gas cell as few harmonics clearly dominate the neighbouring harmonics. We attribute this spectral selectivity to phase matching effects.

Pulsed Rydberg four-wave mixing with motion-induced dephasing in a thermal vapor.

We report on time-resolved pulsed four-wave mixing (FWM) signals in a thermal Rubidium vapor involving a Rydberg state. We observe FWM signals with dephasing times up to 7 ns, strongly dependent on the excitation bandwidth to the Rydberg state. The excitation to the Rydberg state is driven by a pulsed two-photon transition on ns timescales. Combined with a cw de-excitation laser, a strongly directional and collective emission is generated according to a combination of the phase matching effect and averaging over Doppler classes. In contrast to a previous report (Huber et al. in Phys Rev A 90: 053806, 2014) using off-resonant FWM, at a resonant FWM scheme we observe additional revivals of the signal shortly after the incident pulse has ended. We infer that this is a revival of motion-induced constructive interference between the coherent emissions of the thermal atoms. The resonant FWM scheme reveals a richer temporal structure of the signals, compared to similar, but off-resonant excitation schemes. A simple explanation lies in the selectivity of Doppler classes. Our numerical simulations based on a four-level model including a whole Doppler ensemble can qualitatively describe the data.

Shear horizontal acoustic waves propagating along two isotropic solid plates bonded with a non-dissipative adhesive layer: Effects of the rough interfaces

The aim of this paper is to provide an analytical contribution which presents the application of shear-horizontal (SH)-guided waves for the characterisation of a bi-layered structure which consists of two isotropic plates adhesively bonded using a non-dissipative thin layer of glue. The thickness of the layer of glue is assumed to be non-negligible, and the interfaces between this layer of glue and the plates are both assumed to be roughened (parallel ridges with complex shape and depth profiles). The basis of the theoretical approach is an extension of the integral formulation, in the frame of SH modal couplings due to the roughness, which has been developed previously for SH-wave propagation over a single plate with a rough surface. This approach assumes that the average roughness height is a small fraction of the thicknesses of the waveguides (the plates) everywhere. The changes, due to the roughness, in the characteristics of the fields created by a harmonic source set at the entrance edge of the structure are expressed through the mapping of the displacement and stress perturbations. Preliminary tests of the effectiveness of the model are given; they rely on the phase-matching effects of periodic profiles and pseudo-random experimental profile.