Phase-matching Condition Research Articles

Optical properties of barium borate crystal in the THz range revisited

Low-temperature phase (β-form) barium borate (BBO) is one of the most important nonlinear crystals that has been widely used for optical second-harmonic generation (SHG), especially with femtosecond sources. There was growing interest in its applications in the direct generation of terahertz (THz) radiations, but it was hindered by the lack of knowledge of its basic properties in the THz range. In a recent study based on first-principles quantum chemistry calculation, we found that the theoretically calculated refractive indices of β-BBO in the THz frequency range do not agree with the previously reported values. To explore the discrepancy between measured and calculated results, we grew and cut β-BBO crystals and performed independent experimental measurements on the refractive indices of BBO crystals. The new data show that the order of ordinary and extraordinary index of β-BBO in the THz range is opposite, contrary to several papers previously reported. Based on the newly acquired material properties, simple geometries fulfilling phase matching (PM) conditions with n o (THz)=n o g r (800nm) for efficient generation of THz radiation through optical rectification in β-BBO are proposed.

Research on Noise Suppression in High-Speed Optical Communication Systems

With the rapid advancement of optical fiber communication technology, the speed and distance of information transmission have increased unprecedentedly. Multi-core fibers (MCF), which contain multiple cores, enable high-capacity and high-density information transmission. However, during signal transmission, four-wave mixing (FWM) and intercore crosstalk (ICXT) noise are generated, significantly impacting signal propagation quality. Based on the characteristics of FWM and ICXT noise, two effective noise suppression schemes are proposed. The first scheme involves reducing noise power by increasing the wavelength interval or using non-equally spaced wavelengths to mitigate phase-matching conditions. The second scheme focuses on altering the structure of the MCF; in weakly coupled MCFs, longitudinal random bending, torsion, and structural fluctuations randomly affect the power coupling coefficient. According to the noise power formula, reducing the effective fiber length, increasing the cores effective area, and using a band with a low nonlinear effect on the MCF can effectively minimize noise generation. Finally, we evaluate the proposed scheme and analyze and discuss the results.

Nonlinear Raman-Nath diffraction in submicron-thick periodically poled lithium niobate thin film

Nonlinear Raman-Nath diffraction (NRND) is a unique diffraction pattern formed when a high-intensity laser interacts with a nonlinear microstructure bulky medium relying only on the transverse phase matching condition. Here, we report on the first experimental observation of NRND in a submicron-thick periodically poled lithium niobate thin film (PPLNTF) by geometric reflection pumped via a near-infrared femtosecond pulse laser. We further observe the evolution of the diffracted signals after broadening of the pump laser via a fused silica plate. We systematically analyze the spectral properties of multi-order second harmonic generation (SHG) diffracted signals exhibiting asymmetric distributions and explicitly clarify their phase matching conditions, simultaneously considering the impacts of the incident pump wavelength, the sample poling period, and the incident angle on the properties of the angular distribution diffracted beams. The realization of NRND phenomena with appreciable on-chip efficiency at a submicron interaction length is mainly attributed to the significant contribution of domain walls to enhance the nonlinear effects along with the modulation of second-order nonlinear susceptibilities χ(2). This NRND scheme provides a high-resolution, non-destructive on-chip microstructure diagnostic method, and even has the potential to develop novel on-chip integrated optoelectronic devices for applications such as precision metrology, biosensing, and spectral analysis.

Optical properties and phase matching conditions of KTiOPO4 crystals at terahertz frequencies in the temperature range of 5.8 to 300 K

In this paper, the optical properties and phase matching (PM) conditions of KTiOPO4 (KTP) crystals in the temperature range of 5.8–300 K are studied by terahertz (THz) time-domain spectroscopy. It is found that the absorption coefficient of KTP decreases with the decrease of temperature, and that of the Z axis at 1.2 THz decreases from 19.56cm−1 at 300 K to 7.83cm−1 at 5.8 K. Along the Z axis, the refractive index decreases with the decrease of temperature and changes the most, while along the X and Y axes the refractive index is relatively stable with temperature. The optical properties along the Z axis are sensitive to temperature, mainly because the movement of K+ is located in the Z axis and slows down with the decrease of temperature. KTP crystals are found to have obvious birefringence characteristics in the frequency range of 0.3–1.6 THz, with the birefringence of approximately 0.67 at 300 K and 0.58 at 5.8 K. The PM angle is calculated using the refractive index dispersion equation to satisfy the PM condition of frequency transformation. When the temperature is lowered from 300 K to 5.8 K, the maximum change in PM angle is 1.08°, while the minimum change is 0.10° at the same output wavelength. Due to the small absorption coefficient and the birefringence characteristics at low temperatures, and the relatively stable change of PM angle with temperature, the potential of KTP crystals to efficiently generate THz radiation at low temperatures can be fully realized.

Spatial filtering and optimal generation of high-flux soft x-ray high harmonics using a Bessel–Gauss beam

In recent years, significant advancements in high-repetition-rate, high-average-power mid-infrared laser pulses have enabled the generation of tabletop high-flux coherent soft x-ray harmonics for photon-hungry experiments. However, for practical applications, it is crucial to effectively filter out the driving beam from the high harmonics. In this study, we leverage the distinctive properties of a Bessel–Gauss (BG) beam to introduce a novel approach for spatial filtering, specifically targeting soft x-ray harmonics, releasing with a high-photon flux simultaneously. Our simulations reveal that by finely adjusting the focus geometry and gas pressure, the BG beam naturally adopts an annular shape, emitting high harmonics with minimal divergence in the far field. To achieve complete spatial separation of the driving beam and harmonic emissions, we pinpoint the optimal gas pressure and focusing geometry, particularly under overdriven laser intensities, for achieving good phase matching of harmonic emissions from short-trajectory electrons within the gas medium when the exact ionization level is higher than the “critical” value. Additionally, we establish scaling relations for sustaining optimal phase-matching conditions crucial for spatially separating the driving laser and the high-harmonic field, especially as the wavelength of the driving laser increases. Furthermore, our analysis demonstrates a substantial enhancement of harmonic yields by at least one order of magnitude compared to a truncated Gaussian annular beam. We also show that under accessible experimental conditions, soft x-ray photon flux up to 1010 photons/s at 250 eV can be achieved. The utilization of the BG beam opens up a promising pathway for the development of high-flux attosecond soft x-ray light sources, poised to serve a wide range of applications.

Cascaded high harmonic generation in mixture of argon and helium: Achieving a broad photon spectrum

In this study, we explore high harmonic generation (HHG) in pure argon (Ar) gas and a mixture of argon and helium (He). We investigate phase-matching conditions and interference effects in both single and mixed-gas systems. By varying the gas pressure in the Ar–He mixture, we optimize the harmonic spectrum, achieving a broad range from H17 to H43, corresponding to photon energies of 25 eV to 75 eV. We attribute the spectrum broadening to a cascaded HHG process: argon-generated extreme ultraviolet photons excite helium's outer electrons, which are then driven by the fundamental laser field to contribute to HHG. This finding aligns with previous studies, showing that mixing gases with low and high ionization potentials can enhance HHG. The results offer a broad HHG spectrum ideal for ultra-fast spectroscopy and high-resolution imaging applications.

Phase-matching enhanced quantum phase and amplitude estimation of a two-level system in a squeezed reservoir

Abstract Squeezed reservoir engineering is a powerful technique in quantum information that combines the features of squeezing and reservoir engineering to create and stabilize non-classical quantum states. In this paper, we focus on the previously neglected aspect of the impact of the squeezing phase on the precision of quantum phase and amplitude estimation based on a simple model of a two-level system (TLS) interacting with a squeezed reservoir. We derive the optimal squeezed phase-matching conditions for phase ϕ and amplitude θ parameters, which are crucial for enhancing the precision of quantum parameter estimation. The robustness of the squeezing-enhanced quantum Fisher information against departures from these conditions is examined, demonstrating that minor deviations from phase-matching can still result in remarkable precision of estimation. Additionally, we provide a geometric interpretation of the squeezed phase-matching conditions from the classical motion of a TLS on the Bloch sphere. Our research contributes to a deeper understanding of the operational requirements for employing squeezed reservoir engineering to advance quantum parameter estimation.

Abrupt X-to-O-wave structural field transition in presence of anomalous dispersion

All linear, propagation-invariant, paraxial pulsed beams are spatiotemporally X-shaped (conical waves) in the absence of group-velocity dispersion (GVD) or in the presence of normal GVD. It is known, however, that such conical waves become O-shaped in the presence of anomalous GVD, resulting in a field profile that is circularly symmetric in space and time. To date, experiments generating conical waves in which the wavelength of a high-energy pump laser is tuned across the zero-dispersion wavelength of a nonlinear medium have not revealed the expected X-to-O-wave structural field transition. We report here an unambiguous observation of a fixed-central-wavelength X-to-O-wave structural field transition occurring in linear dispersion-free wave packets in the anomalous GVD regime, without needing to change the sign or magnitude of the GVD. Instead, by tuning the group velocity of a space–time wave packet (STWP) across a threshold value that we call the “escape velocity,” we observe an abrupt transition in the STWP from an O-shaped to an X-shaped spatiotemporal profile. This transition is associated with an abrupt change in the associated spatiotemporal spectrum of the STWP: from closed elliptical spatiotemporal spectra below the escape velocity to open hyperbolic spectra above it. These results may furnish new opportunities for engineering the phase-matching conditions in nonlinear and quantum optics.

Precise wavelength alignment of second-harmonic generation in thin-film lithium niobate resonators.

Second-harmonic generation (SHG) plays a significant role in modern photonic technology. Integrated photonic resonators fabricated with thin-film lithium niobate can achieve ultrahigh efficiencies by combining small mode volumes with high material nonlinearity. Cavity-enhanced SHG requires accurate phase and frequency matching conditions, where fundamental and second-harmonic wavelengths are both on resonance. However, this double-resonance condition can typically be realized only at a fixed random wavelength due to the high sensitivity of photonic resonances to the device geometry and fabrication variations. Here, we propose a novel method that can achieve the double-resonance condition over a large wavelength range. We combine thermal-optic and electro-optic (EO) effects to realize the separate tuning of fundamental and second-harmonic resonances. We demonstrated that the optimum SHG efficiency can be maintained over a wavelength range that exceeds the limit achievable with only thermal tuning. With this flexible tuning capability, we further show the precise alignment of SHG wavelengths of two separate thin-film lithium niobate resonators without sacrificing efficiencies.

Quasi-phase-matching enabled by van der Waals stacking

Quasi-phase matching (QPM) is a technique extensively utilized in nonlinear optics for enhancing the efficiency and stability of frequency conversion processes. However, the conventional QPM relies on periodically poled ferroelectric crystals, which are limited in availability. The 3R phase of molybdenum disulfide (3R-MoS2), a transition metal dichalcogenide (TMDc) with the broken inversion symmetry, stands out as a promising candidate for QPM, enabling efficient nonlinear process. Here, we experimentally demonstrate the QPM at nanoscale, utilizing van der Waals stacking of 3R-MoS2 layers with specific orientation to realize second harmonic generation (SHG) enhancement beyond the non QPM limit. We have also demonstrated enhanced spontaneous parametric down-conversion (SPDC) via QPM of 3R-MoS2 homo-structure, enabling more efficient generation of entangled photon pairs. The tunable capacity of 3R-MoS2 van der Waals stacking provides a platform for tuning phase-matching condition. This technique opens interesting possibilities for potential applications in nonlinear process and quantum technology.

Antiferromagnetic Spin Wave Amplification by Scattering in the Presence of Non-Uniform Dzyaloshinskii-Moriya Interaction.

In this study, we suggest a method to amplify spin waves (SWs) in antiferromagnets (AFMs). By introducing a non-uniform Dzyaloshinskii-Moriya (DM) interaction, the potential barrier forms a resonant cavity. SWs with an opposite chirality undergo scattering and are resonantly amplified at a phase-matching condition. The calculation is performed in the insulating AFMs where the electric-field-induced DM interaction and pseudo-dipole anisotropy broaden the parabolic-like SW band for multiple resonant modes. Using a transfer matrix method, we also show numerically that scattering between SWs contributes significantly to the SW amplification. Since the electric field selectively amplifies the SWs with resonant frequencies, the proposed device works as an SW transistor and rectifier. This finding will contribute to insulating AFM-based magnon devices where Joule heating is, in principle, avoided.

Optical parametric amplification and oscillation in nonlinear chiral media.

We discuss the nonlinear process of optical parametric amplification inside a chiral crystal. We show that circular birefringence, induced by chirality, leads to two different nonlinear processes with different phase-matching conditions that are associated with the opposite states of circular polarizations. A single nonlinear process occurs only when the states of polarization of the incident pump and signal beams are both circular and orthogonal. When these beams are linearly polarized initially, their state of polarization evolves in an elliptical fashion because of the two competing nonlinear processes taking place in parallel. We also discuss the properties of singly and doubly resonant optical parametric oscillators made by placing a chiral nonlinear crystal inside an optical cavity.

Josephson traveling wave parametric amplifiers with plasma oscillation phase matching

High gain and large bandwidth of traveling-wave parametric amplifier exploiting the nonlinearity of Josephson Junctions can be achieved by fulfilling the so-called phase-matching condition. This condition is usually addressed by placing resonant structures along the waveguide or by periodic modulations of its parameters, creating gaps in the waveguide’s dispersion. Here, we propose to employ the Josephson junctions, which constitute the centerline of the amplifier, as resonant elements for phase matching. By numerical simulations in JoSIM (and WRspice) software, we show that Josephson plasma oscillations can be utilized to create wave vector mismatch sufficient for phase matching as well as to prevent the conversion of the pump energy to higher harmonics. The proposed traveling wave parametric amplifier design has a gain of 15 dB and a 3 GHz bandwidth, which is comparable to the state-of-the-art TWPAs.

Nonlinear optical properties of some nanosized ammonium dihydrogen phosphate crystals incorporated in aluminum oxide nanopores

This study explores the nonlinear optical properties of aluminum oxide (Al2O3) matrices embedded in ammonium dihydrogen phosphate (ADP) nanocrystals using third-harmonic generation (THG) techniques. The successful integration of ADP crystallites within the nanopores of the Al2O3 matrix was confirmed using x-ray structural analysis and electron microscopy. The optical absorption characteristics were examined over a wide wavelength range, revealing that the reflection and transmission spectra were notably affected by pore size and surface scattering effects. THG measurements conducted with a high-intensity infrared laser demonstrated a pronounced third-order nonlinear response, whereas second-harmonic generation was not observed. The absence of SHG can be attributed to phase mismatch and inherent material properties, including centrosymmetry and surface roughness. The comparative and Reintjes models were used to calculate the third-order nonlinear optical susceptibilities. Among these, the Reintjes model provided the most accurate fit for the experimental data. This research underscores the considerable influence of nanopore size on THG efficiency, highlighting the importance of light scattering and phase-matching conditions. These findings contribute to a growing body of knowledge regarding nonlinear optical phenomena in nanocomposite materials and offer valuable insights for future applications in photonic devices. This comprehensive analysis highlights the potential of Al2O3 matrices with embedded ADP nanocrystals to advance the field of nonlinear optics in nanocomposite materials and offers insights for prospective applications in photonic devices.

High-performance and scalable polarization splitter-rotator based on photonic crystal nanobeam reflection.

The polarization splitter-rotator (PSR) is a key device for polarization processing in polarization diversity systems, which has wide applications in achieving polarization independence and mixed multiplexing. However, it remains a significant challenge to simultaneously achieve a better balance in bandwidth, crosstalk (CT), polarization extinction ratio (PER), and compact footprint of the PSR. In this article, a photonic crystal nanobeam (PCN) structure is introduced to PSR for large bandwidth and compact size, with a device length of only 104 µm. Additionally, to achieve lower CT, a bridge waveguide is introduced for primary filtering. Simulation results show that the insertion loss (IL) is less than 0.55 dB, CT less than -35 dB, and PER greater than 35 dB within a bandwidth exceeding 110 nm, while maintaining a large process tolerance. Furthermore, the proposed PSR design breaks through the limitations of traditional schemes by extending its functionality effectively. To further improve integration, a novel approach to PSR using mode hybridization followed by spatial beam splitting is proposed. By controlling the phase-matching condition of various modes in different waveguides, the designed spatial beam splitting achieves lower CT and better compactness. Simulation results verify that the IL of the improved scheme is less than 1 dB, CT less than -24 dB, and PER greater than 22 dB within an 85 nm bandwidth, while reducing the overall length to less than 20 µm.

Light bullets under conditions of third harmonics generation

Abstract An analytical study of the possibility of a two-color light bullet forming during generation of the third harmonics in a graded index waveguide with the focusing Kerr nonlinearity is carried out. It is shown that under conditions of phase and group matching, as well as the absence of group velocity dispersion at the third harmonic frequency, a stable light bullet can be formed under certain restrictions. This applies to the lower limit on the temporal duration of the light bullet and to the upper limit on its power. The most stringent condition is the double restriction on the transverse radius of the light bullet.

Topological parametric gain and two-color edge states in equidistant lithium niobate waveguide arrays.

We analyze parametric χ2 processes in equidistant finite-size arrays of thin-film lithium niobate waveguides, where the fundamental harmonic (FH) field supports topological edge states due to the specific interplay between inter- and intra-modal couplings of two families of guided modes, while the second-harmonic (SH) field only supports bulk modes. Regimes of topological parametric gain are identified, where the gain only occurs in the edge states of the FH field, regardless of the spatial distribution of the pump SH field. The topological gain of the FH component generally triggers localization of the SH field near an edge of the array in the optical parametric oscillation dynamics. In small-size arrays, parametric gain at both edges can be observed even when pumped at one side. This process can lead to an anomalous "tunneling" of the SH field to the opposite edge. We also analyze the existence and stability of two-color nonlinear edge states (solitons), in which both FH and SH fields are localized at an edge of the array. Depending on the phase-matching condition, such solitons either emerge from the linear FH edge state without a power threshold or exist above a certain power threshold dictated by the coupling strength in the SH field.

Enhanced high-harmonic generation in a polarization-insensitive all-dielectric metasurface exploiting dual-Fano resonance

Nonlinear optics demands efficacious techniques for nonlinear properties engineering. Metasurfaces, as a flat technology with easy fabrication in various arrangements and without the need for phase-matching conditions, are suitable platforms for nonlinear optics. This study proposes a silicon metasurface with special geometry that provides high conversion efficiency by exploiting Fano resonances and the excitation of magnetic and toroidal dipoles. The results indicate the high efficiencies of third harmonic generation of 5.17×10−3 W−2 and fifth harmonic generation of 7.92×10−9 W−4 under 1 GW/cm2 pump intensity in the near-infrared regime. More specifically, linear and nonlinear optical responses of the structure are completely polarization-independent.

Direct generation of a narrowband EUV vortex with ring Pearcey-Gaussian-vortex-beam-driven harmonics.

The generation of tunable extreme-ultraviolet (EUV) vortex beams is highly sought after for optoelectronic applications in the EUV region. In this study, we investigate the generation of vortex high-order harmonics using a ring Pearcey-Gaussian vortex beam as the driving source. We analyze the beam's spatial structure through phase-matching conditions and simulate high-order harmonic generation by solving the Maxwell wave equations. The beam's self-focusing characteristics and low-diffraction properties after focusing significantly enhance harmonics near the 53rd order, indicating the generation of a narrowband EUV vortex. Our findings underscore the advantages of using a ring Pearcey-Gaussian vortex beam for narrowband EUV vortex generation, paving the way for creating tunable vortex high-order harmonics or attosecond pulses with innovative vortex beams.

Unidirectional and highly dispersive grating emitters for silicon photonic beam steerers.

Grating emitters are the key component used in silicon photonic beam steerers to create light emission and allow dispersion-based steering. Conventional grating emitters are inefficient due to bidirectional emission, and their angular dispersion is only on the order of 0.1°/nm. In this paper, we develop unidirectional grating emitters by choosing a top cladding material with a refraction index higher than that of the bottom cladding. The refractive index difference allows the phase-matching condition to be satisfied only for the upward diffraction. We demonstrate experimentally grating emitters with a directionality of 83% and an angular dispersion of 0.79°/nm. These grating emitters have a simple device structure compatible with the standard silicon photonic platform.