Phase-matched Generation Research Articles

Noncollinear phase-matching of high harmonic generation in solids

We propose and experimentally demonstrate a scheme allowing reaching noncollinear phase-matching of high harmonic generation in solids, which may potentially lead to an enhancement of the generation efficiency. The principle is based on high-order frequency mixing of two light waves with identical frequencies but different directions of wavevectors. In this process, Nth harmonic frequency is produced by frequency mixing of N + 1 photons from a wave with high amplitude of electric field and a single photon from a wave with low field amplitude, which are propagating noncollinearly in optically isotropic media. We experimentally verify the feasibility of this scheme by demonstrating phase-matched generation of third and fifth harmonic frequency in sapphire.

Resonant generation of propagating second-harmonic spin waves in nano-waveguides

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field of magnonics, which considers the use of spin waves in magnetic nanostructures to implement wave-based signal processing and computing. However, due to the strong frequency dependence of the phase velocity of spin waves, resonant phase-matched generation of second-harmonic spin waves has not yet been achieved in practice. Here, we show experimentally that such a process can be realized using a combination of different modes of nano-sized spin-wave waveguides based on low-damping magnetic insulators. We demonstrate that our approach enables efficient spatially-extended energy transfer between interacting waves, which can be controlled by the intensity of the initial wave and the static magnetic field.

Pulsewidth-switchable ultrafast source at 114 nm.

Femtosecond laser sources with high repetition rate in the ultraviolet (UV) and vacuum UV (VUV) are fundamental tools enabling tabletop time-resolved and angle-resolved photoemission spectroscopy in solids. We describe a VUV source at 114 nm (10.8 eV) based on an industrial grade ytterbium-doped ultrafast laser, a nonlinear pulse width selection stage, and two cascaded frequency tripling stages, first in crystals, second in xenon. The role of ionization in gas-based perturbative third harmonic generation phase-matching is analyzed using a simple theory, numerical simulations, and experimental data. The source features high photon flux, high repetition rate, and adjustable time resolutions. Thereby, in combination with a state-of-the-art angle-resolved photoemission spectroscopy (ARPES) apparatus it enables the study of the electronic dynamics of the whole Brillouin zone in a large number of materials.

Phase-locked degenerate backward wave optical parametric oscillator

We report a self-phase-locked and degenerate backward wave optical parametric oscillator (BWOPO) generating a counterpropagating signal and an idler in the spectral band of optical communication. The device is based on a periodically poled Rb-doped KTiOPO4 crystal with a poling period of 433 nm. To the best of our knowledge, this is the shortest quasi-phase matching period reported in the bulk of a ferroelectric crystal. The spectral and coherence properties of the BWOPO at degeneracy are investigated. We observe a single pass conversion efficiency of 40%. At degeneracy, the counterpropagating signal and idler generate phase-matched sum-frequency generation in both directions. We confirm the phase-locked state at degeneracy by interfering the pump with the frequency-doubled backward wave. The phase-locked state is stable during the entire duration of the experiment without active stabilization.

Phase-Matched High-Harmonic Generation under Nonadiabatic Conditions: Model and Experiment

Nonadiabatic phase matching of high-harmonic generation (HHG) driven by few-cycle laser pulses is essential for extending harmonic energy and generating isolated attosecond pulses. However, understanding nonadiabatic HHG is challenging due to the complex interplay of various optical phases driven by temporally and spatially varying laser fields. Theoretical calculations typically rely on computationally demanding 3-dimensional simulations, which can make it difficult to extract the essential features of nonadiabatic HHG. In this work, we develop a computationally efficient 2-dimensional model that directly considers various phase contributions of HHG. Our model can well explain the experimentally observed pressure- and intensity-dependent behaviors of different harmonic orders. By appropriately parameterizing the single-atom response, our model can also estimate the variation of HHG spectra under different driving conditions. Our model can provide an efficient tool for the design and optimization of HHG-based applications.

Design of Semiconductor Contact Grating Terahertz Source with Enhanced Diffraction Efficiency

We report a semiconductor contact grating terahertz source design based on a rectangular profile for phase-matched terahertz generation in the long infrared pump wavelength range. The calculations show that the best diffraction efficiency can be achieved by a filling factor significantly smaller than 50%. Furthermore, the possibility of diffraction efficiency enhancement was investigated by applying three different antireflective coating structures. Numerical simulations have indicated that at 2.06 μm and 3.0 μm pump wavelength, diffraction efficiencies greater than 91% and 89% can be achieved by adding an appropriate antireflective coating to the GaP and GaAs contact grating structure, respectively. In addition, numerical simulations were performed to investigate the influence of wall angles on diffraction efficiency. The results reveal that the wall angle does not significantly affect the diffraction efficiency: while keeping the wall angle deviation from the vertical below 25 degrees, the efficiency drop remains below 5% for otherwise optimal grating parameters.

Na4 B8 O9 F10 : A Deep-Ultraviolet Transparent Nonlinear Optical Fluorooxoborate with Unexpected Short Phase-Matching Wavelength Induced by Optimized Chromatic Dispersion.

Exploring significant ultraviolet/deep-ultraviolet nonlinear optical (NLO) materials is hindered by rigorous and contradictory requirements, especially, possessing a moderate optical birefringence to meet phase-matching (PM). Except for suitable birefringence, small chromatic dispersion is also crucial to blue-shift the PM wavelength. Here, the introduction of a fluorinated tetrahedral boron-centred chromophore strategy was proposed to optimize the chromatic dispersion. Herein, the [BF4 ]- unit with a large HOMO-LUMO band gap was introduced to the Na-B-O-F system and Na4 B8 O9 F10 was designed and synthesized successfully for the first time. Na4 B8 O9 F10 with an optimized chromatic dispersion can achieve a short second harmonic generation PM wavelength of 240 nm with a relatively small birefringence (0.036@1064 nm). Notably, Na4 B8 O9 F10 is the first acentric crystal with [BF4 ]- units among the reported metal-fluorooxoborate systems, involving isolated [BF4 ]- and novel [B7 O10 F6 ]5- fundamental building blocks.

Na4B8O9F10: A Deep‐Ultraviolet Transparent Nonlinear Optical Fluorooxoborate with Unexpected Short Phase‐Matching Wavelength Induced by Optimized Chromatic Dispersion

AbstractExploring significant ultraviolet/deep‐ultraviolet nonlinear optical (NLO) materials is hindered by rigorous and contradictory requirements, especially, possessing a moderate optical birefringence to meet phase‐matching (PM). Except for suitable birefringence, small chromatic dispersion is also crucial to blue‐shift the PM wavelength. Here, the introduction of a fluorinated tetrahedral boron‐centred chromophore strategy was proposed to optimize the chromatic dispersion. Herein, the [BF4]− unit with a large HOMO–LUMO band gap was introduced to the Na−B−O−F system and Na4B8O9F10 was designed and synthesized successfully for the first time. Na4B8O9F10 with an optimized chromatic dispersion can achieve a short second harmonic generation PM wavelength of 240 nm with a relatively small birefringence (0.036@1064 nm). Notably, Na4B8O9F10 is the first acentric crystal with [BF4]− units among the reported metal–fluorooxoborate systems, involving isolated [BF4]− and novel [B7O10F6]5− fundamental building blocks.

A Multi-Band Photonic Source by Means of Phase-Matched Nonlinear Generation Processes

A technique for multi-band generation is investigated to simultaneously achieve phase-matching in multiple second-order nonlinear processes. By coupling a near-infrared excitation pulse into a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> planar waveguiding platform, modal phase-matched second harmonic radiation is generated at wavelengths of 403 ± 0.6 nm and Cherenkov-emitted terahertz radiation is generated at frequencies up to ~3.5 THz. For the second harmonic generation process and the terahertz radiation generation process, the conversion efficiencies are measured as 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> %/(GW-cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> ) and 1.9 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> %/(GW-cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> ), respectively. The investigated multi-band generation technique permits a single structure to produce radiation within multiple spectral bands, such that this technique could be used to increase the density of photonic sources on a photonic integrated chip.

Phase-Matching for Generation of Isolated Attosecond XUV and Soft-X-Ray Pulses with Few-Cycle Drivers

Isolated attosecond pulses (IAPs) produced through laser-driven high-harmonic generation (HHG) hold promise for unprecedented insight into biological processes via attosecond x-ray diffraction with tabletop sources. However, efficient scaling of HHG towards x-ray energies has been hampered by ionization-induced plasma generation impeding the coherent buildup of high-harmonic radiation. Recently, it has been shown that these limitations can be overcome in the so-called 'overdriven regime' where ionization loss and plasma dispersion strongly modify the driving laser pulse over small distances, albeit without demonstrating IAPs. Here, we report on experiments comparing the generation of IAPs in argon and neon at 80 eV via attosecond streaking measurements. Contrasting our experimental results with numerical simulations, we conclude that IAPs in argon are generated through ionization-induced transient phase-matching gating effective over distances on the order of 100 $\mu$m. We show that the decay of the intensity and blue-shift due to plasma defocussing are crucial for allowing phase-matching close to the XUV cutoff at high plasma densities. We perform simulations for different gases and wavelengths and show that the mechanism is important for the phase-matching of long-wavelength, tightly-focused laser beams in high-pressure gas targets, which are currently being employed for scaling isolated attosecond pulse generation to x-ray photon energies.

On the effect of third-order dispersion on phase-matched terahertz generation via interfering chirped pulses

High-energy narrowband terahertz (THz) pulses, relevant for a plethora of applications, can be created from the interference of two chirped-pulse drive lasers. The presence of third order dispersion, an intrinsic feature of many high-energy drive lasers, however, can significantly reduce the optical-to-THz conversion efficiency and have other undesired effects. Here, we present a detailed description of the effect of third-order dispersion (TOD) in the pump pulse on the generation of THz radiation via phase-matching of broadband highly chirped pulse trains. Although the analysis is general, we focus specifically on parameters typical to a Ti:Sapphire chirped-pulse amplification laser system for quasi-phase-matching in periodically-poled lithium niobate (PPLN) in the range of THz frequencies around 0.5 THz. Our analysis provides the tools to optimize the THz generation process for applications requiring high energy and to control it to produce desired THz waveforms in a variety of scenarios.

Magnetosonic wave-aided terahertz emission by nonlinear mixing of lasers in plasmas

AbstractA scheme of phase-matched terahertz generation by beating two co-propagating lasers in magnetized plasma, in the presence of a magnetosonic wave (MSW), is developed. The beat frequency ponderomotive force of the lasers imparts an oscillatory drift to electrons. The electron drift velocity couples with the electron density perturbation associated with the MSW to produce an irrotational nonlinear current $\left(\nabla \times {\vec J}\;{}^{\rm NL}\ne 0\right)$. The beat current density resonantly excites a THz (Terahertz) radiation when the phase-matching conditions are satisfied. The MSW mediates the phase matching. At 9.6 and 10.6 µm wavelengths, and background magnetic field of 285 kG, one may achieve normalized THz wave amplitude of the order of 10−3 and one obtains the ratio of THz power to pump power of the order of 10−6.

Pump-probe multi-species CARS in a hollow-core PCF with a 20 ppm detection limit under ambient conditions.

We report coherent anti-Stokes Raman spectroscopy (CARS) in a gas-filled single-ring hollow-core photonic crystal fiber (SR-PCF) using a pump-probe configuration. The long collinear path length offered by an SR-PCF strongly enhances the efficiency of the Raman interactions. Pressure tuning the zero-dispersion wavelength (ZDW) of the SR-PCF allows the Raman coherence prepared by seeded pumping at 515nm to be used in the visible for phase-matched generation of an anti-Stokes signal from a probe in the ultraviolet. The unique dispersion profile in the vicinity of the ZDW enables simultaneous phase matching of all known Raman transitions. We demonstrate that simultaneous multi-species CARS with a detection limit of 20ppm is possible with only 20kW of peak pump power delivered by a single laser source.

Phase-matched nonlinear wave-mixing processes in XUV region with multicolor lasers.

We report here experimental results of perturbative nonlinear optical wave-mixing processes in the extreme ultraviolet region by using two-color and three-color laser fields. Besides the usual odd-harmonic spectrum of high harmonic generation, new spectral components are observed when multiple incommensurate lasers (one driving plus one or two control field) interact with neutral krypton gas. To demonstrate the wave-mixing process underlying such an observation, we first couple the driving field with either the signal or the idler field of an optical parametric amplifier in the gaseous ensemble to generate certain mixing frequencies. The two control fields are then simultaneously combined with the driving field to produce broad and distinguishable mixing peaks that clearly reveal the contribution of each control laser. Finally, the variation of the intensity of the mixing waves with the intensity of each control field, the gas density, and the relative focus position is examined for signatures of phase-matched generation of the mixing fields in this spectral region.

Noncritically phase-matched fourth-harmonic generation of Nd:glass lasers and design of final optics assembly

The noncritically phase-matched (NCPM) fourth-harmonic generation (FHG) with partially deuterated dihydrogen phosphate (KD*P) crystal at an Nd:glass laser radiation wavelength of 1053.1nm has been confirmed. NCPM FHG has been achieved in 70% and 65% deuterated KD*P crystal at the temperature of 17.7°C and 29.3°C, respectively. The angular acceptance of 70% and 65% deuterated KD*P crystals fixed at their NCPM temperature were measured, which were 53 and 55mrad, respectively. The application of the NCPM FHG in a high-power laser facility for inertial confinement fusion is also discussed. Based on the theoretical analysis, the NCPM KD*P can be placed after the focus lens; thus, the laser-induced damage of a fused-silica lens at ultraviolet can be avoided.

Influence of absorption on phase-matched generation of coherent extreme ultraviolet radiation in a long interaction geometry

Abstract The pressure dependent high-order harmonic generation in a semi-infinite gas cell with two different absorbing gaseous media (argon and helium) is analyzed to reveal the influence of absorption on the radiation process in the extreme ultraviolet region. The absorption cross section of a particular wavelength in this region is measured. Moreover, in consideration of macroscopic response, the geometrical phase mismatch and the dipole phase mismatch which are independent to the pressure are clearly studied. A Young's double slit experiment is also performed to indicate a high spatial coherence of the harmonic radiation. This measurement shows that a narrow bandwidth, bright, and highly coherent high harmonic source can be generated in gas cell filled with absorbing gases which could be useful for coherent diffractive imaging.

Fast-light-assisted four-wave mixing in the photonic bandgap.

In this Letter, the enhanced four-wave mixing (FWM) in the photonic bandgap of fiber Bragg grating (FBG) has been achieved with an extra phase introduced by fast-light effect in the bandgap. The experiment for phase-matched FWM generation in the bandgap in a special-designed FBG was carried out, as well as simulations. The enhanced energy conversion with such a FWM in the bandgap has been demonstrated but the transmissivity has not. The experimental results show agreement with the simulations.

Phase matching characteristics of deuterated ammonium dihydrogen phosphate crystals

Refractive indices for crystals ammonium dihydrogen phosphate (ADP), 30% deuterated ADP (DADP), 50% DADP, and 70% DADP are measured from 253 to 1529 nm with 5 × 10-6 accuracy. Numerical fits to modified double-pole Sellmeier equation are made. Second-harmonic generation, third-harmonic generation phase matching (PM) angles, and noncritical PM (NCPM) wavelengths are calculated using the Sellmeier parameters. The deuterated crystals show smaller PM angles than pure crystal. Fourth-harmonic generation process can be realized by DADP in smaller deuterium content than deuterated potassium dihydrogen phosphate (DKDP). The measured NCPM wavelengths are consistent with the calculated value. PM characteristics are compared between DADP and DKDP.

THz generation by optical rectification of near-infrared laser pulses in the organic nonlinear optical crystal HMQ-TMS

We show that the organic electro-optic crystal HMQ-TMS [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 2,4,6-trimethylbenzenesulfonate] has favorable properties for the parametric generation of THz waves in a collinear type-0 phase-matching scheme, i.e., a low absorption coefficient at wavelengths from 800 to 1500 nm (α 0.5 mm). We demonstrate efficient generation of broadband THz pulses through optical rectification of sub-picosecond laser pulses in a 0.2 mm thick HMQ-TMS crystal at the wavelength of 1000 nm. The energy conversion efficiency achieved in this crystal was 41 times higher than the one achieved in a 0.3 mm thick GaP crystal, which is an often used material for collinearly phase-matched THz generation at this laser wavelength. The peak amplitudes of the THz signal obtained with the HMQ-TMS crystal were 5.4 times larger in the time-domain and 7.1 times larger in the frequency-domain than the ones obtained with the GaP crystal.

Phase-Matched High-Order Harmonics from N2 Using kHz Femtosecond Laser Pulses

We report the phase-matched high-harmonic generation from N2 driven by kHz femtosecond laser pulses. By varying the position of the laser focus in the gas tube, we observe the radiation of different harmonics. Our results provide a potential source for studying ultrafast molecular dynamics.