Difference Frequency Generation Research Articles

Interfacial epitaxy of multilayer rhombohedral transition-metal dichalcogenide single crystals.

Rhombohedral-stacked transition-metal dichalcogenides (3R-TMDs), which are distinct from their hexagonal counterparts, exhibit higher carrier mobility, sliding ferroelectricity, and coherently enhanced nonlinear optical responses. However, surface epitaxial growth of large multilayer 3R-TMD single crystals is difficult. We report an interfacial epitaxy methodology for their growth of several compositions, including molybdenum disulfide (MoS2), molybdenum diselenide, tungsten disulfide, tungsten diselenide, niobium disulfide, niobium diselenide, and molybdenum sulfoselenide. Feeding of metals and chalcogens continuously to the interface between a single-crystal Ni substrate and grown layers ensured consistent 3R stacking sequence and controlled thickness from a few to 15,000 layers. Comprehensive characterizations confirmed the large-scale uniformity, high crystallinity, and phase purity of these films. The as-grown 3R-MoS2 exhibited room-temperature mobilities up to 155 and 190 square centimeters per volt second for bi- and trilayers, respectively. Optical difference frequency generation with thick 3R-MoS2 showed markedly enhanced nonlinear response under a quasi-phase matching condition (five orders of magnitude greater than monolayers).

Peregrine solitons and resonant radiation in cubic and quadratic media.

We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue waves. In cubic media, it turns out that the emission of radiation from a Peregrine soliton can be attributed to the presence of higher-order dispersion, but is affected by the intrinsic local longitudinal variation of the soliton wavenumber. In quadratic media, we reveal that a two-color Peregrine rogue wave can resonantly radiate dispersive waves even in the absence of higher-order dispersion, subjected to a phase-matching mechanism that involves the second-harmonic wave, and to a concomitant difference-frequency generation process. In both cubic and quadratic media, we provide simple analytic criteria for calculating the radiated frequencies in terms of material parameters, showing excellent agreement with numerical simulations.

Unified Stokes-Mueller polarimetry for multi-photon processes at varying wavelengths.

Existing polarimetry, mainly focusing on harmonic generations, overlooks the differences in retardance (DRs) caused by illuminations with different wavelengths in nonlinear processes, consequently falling short in accuracy beyond frequency doubling. In this Letter, with DRs considered, we propose a universal nonlinear Stokes-Mueller (NSM) polarimetry design involving illuminations with different wavelengths. Then, we optimize the NSM measurement model, applied to sum-frequency generation (SFG) and difference frequency generation. To demonstrate the necessity of consideration of DRs, the processes of polarization measurement for SFG are simulated, where the condition number decreases by 51.2%, and the root mean square error of the nonlinear Mueller matrix decreases by 20.48%.

Millimeter-wave generation with a room-temperature nonlinear quantum cascade laser

Millimeter-wave difference frequency generation is reported for a dual-wavelength mid-infrared quantum cascade laser operating at room temperature. To overcome a low mid-infrared-to-terahertz conversion efficiency below 1 THz, a long-wavelength, high-performance mid-infrared quantum cascade laser structure with higher nonlinear susceptivity is adopted. By designing the efficient allocation of mid-infrared pumps to two sections of fabricated distributed feedback grating, a closely separated dual-wavelength (λ1 ∼ 13.53 μm and λ2 ∼ 13.39 μm) laser oscillation was obtained. Consequently, a millimeter-wave emission at a frequency of 231 GHz was successfully observed at room temperature.

Theoretical investigation on the second order nonlinear optical properties of heptagon bridged bi-porphyrin derivatives

Porphyrins and their derivatives have drawn extensive attention as promising nonlinear optical (NLO) materials especially for biological applications owing to its large aromatic conjugation and special biological activity and compatibility. However, it is still critical to strategically design porphyrin derivatives materials with high performance in second order NLO applications and disclose the structure property correlation. In the present work, a series of dual-metallic-porphyrin derivatives are designed by incorporating a heptagon between two porphyrins with further addition of heteroatoms and metals. The doping of B and N along the dipole direction induces large static first hyperpolarizability, and strong charge transfer occurs with further introduction of Mg, thus ultimately achieving excellent second order NLO properties including strong sum frequency generation and difference frequency generations under external fields. The doping of heteroatoms and metals synergistically tunes the electronic structure of porphyrin-based derivatives and brings about high performance in biological nonlinear optics.

Characterizing mid-infrared micro-ring resonator with frequency conversion

Due to the high cost, low-performance lasers and detectors in the mid-infrared (MIR) band, the development of MIR-integrated devices is very slow. Here, we demonstrate an effective method to characterize the parameters of MIR devices by using frequency conversion technology. We designed and fabricated rib waveguides and the micro-ring resonators (MRRs) on a silicon-on-sapphire platform. The MIR laser for the test is generated by difference frequency generation, and the transmission spectrum of the MIR-MRRs is detected by sum frequency generation. The experimental results show that the waveguide transmission loss is 4.5 dB/cm and the quality factor of the micro-ring reaches 38000, which is in good agreement with the numerical simulations. This work provides a useful method to characterize MIR integrated devices based on the frequency conversion technique, which can boost the development of MIR integrated optics in the future.

Mid-infrared computational temporal ghost imaging

Ghost imaging in the time domain allows for reconstructing fast temporal objects using a slow photodetector. The technique involves correlating random or pre-programmed probing temporal intensity patterns with the integrated signal measured after modulation by the temporal object. However, the implementation of temporal ghost imaging necessitates ultrafast detectors or modulators for measuring or pre-programming the probing intensity patterns, which are not available in all spectral regions especially in the mid-infrared range. Here, we demonstrate a frequency downconversion temporal ghost imaging scheme that enables to extend the operation regime to arbitrary wavelengths regions where fast modulators and detectors are not available. The approach modulates a signal with temporal intensity patterns in the near-infrared and transfers the patterns to an idler via difference-frequency generation in a nonlinear crystal at a wavelength where the temporal object can be retrieved. As a proof-of-concept, we demonstrate computational temporal ghost imaging in the mid-infrared with operating wavelength that can be tuned from 3.2 to 4.3 μm. The scheme is flexible and can be extended to other regimes. Our results introduce new possibilities for scan-free pump-probe imaging and the study of ultrafast dynamics in spectral regions where ultrafast modulation or detection is challenging such as the mid-infrared and THz regions.

Relative strengths of sum and difference frequency generation in perturbative high harmonic wave mixing

High harmonic generation (HHG) modulated by a weak laser field allows the perturbative wave mixing process which involves sum and difference frequency generations (SFG and DFG). The relative strengths of SFG and DFG have been extensively discussed in the literature but are still ambiguous. Here we experimentally study the relative strengths between SFG and DFG channels by applying a frequency-offset second-harmonic perturbing laser field collinearly in a thin gaseous nonlinear medium. It shows that SFG is favored for low harmonic orders, but DFG dominates for high-energy photons, when only short trajectories of high harmonics are considered. A semi-classical model incorporating both modulations to the tunneling ionization and the electron propagation steps by the perturbing laser field for a train of attosecond pulses explains the experimental results.

Enhanced second-order nonlinear susceptibility in type-II asymmetric quantum well structures

Asymmetric quantum wells (AQWs) utilizing interband transitions enhance second-order susceptibility over a wide wavelength range compared to natural crystals. The nonlinear susceptibility is further enhanced in AQWs with type-II band alignment as compared to type-I band alignment, a result of the larger interband charge shift. This enhancement is demonstrated in this work by analyzing three type-I and type-II AQW designs based on the lattice-matched InP/AlGaInAs materials systems using the envelope wavefunction approximation. The calculated interband second-order susceptibility tensor elements in type-II structures range between 20 and 1.60 × 103 pm/V for nearly resonant optical rectification and difference frequency generation applications at near-infrared and terahertz wavelengths, an improvement of nearly 1 order of magnitude over the type-I structures and 1–2 orders of magnitude over natural crystals such as LiNbO3, KTiOPO4 (KTP), or GaAs. A factor of 2–3 further enhancement of the tensor elements is achieved by optimizing the well widths and band offsets of the type-II asymmetric quantum wells. The type-II structure can be implemented in other material systems spanning the longwave infrared to visible wavelengths, enhancing nonlinear susceptibility for various applications, including photonic integrated circuits.

Synchronous mode-locking of solid-state lasers by difference frequency generation.

This Letter introduces a novel, to the best of our knowledge, method for achieving mode-locking and synchronization of mode-locked output pulses from two lasers. The proposed technique leverages parametric gain from difference frequency generation. Specifically, a Nd:YAG laser is mode-locked by single-pass mode-locked pulses from a mode-locked Ti:sapphire laser using an intracavity nonlinear crystal. When the continuous-wave laser is not actively pumped, the system functions as a synchronously pumped optical parametric oscillator. This novel approach has the potential to enable new devices, especially for pump-probe applications or for generation of mode-locked pulses in spectral regions where conventional mode-locked devices are typically not available.

Frequency Conversion of Femtosecond Ti:Sapphire Laser Pulse to the Long-Wave Mid-IR Range with BaGa2GeSe6 Crystal

Generation of ultrashort mid-IR pulses spanning from 8.5 to 10.5 μm with high energy (up to 4.5 μJ) was experimentally demonstrated through difference frequency generation in BaGa2GeSe6 crystal pumped by 100-fs 0.95-μm Ti:sapphire laser pulses. Optical damage threshold and two-photon absorption coefficient were determined for this pump pulses. Frequency conversion efficiency reached 0.24% at 1.85 mJ pump pulse energy and was decreased at higher one. Estimations indicate that application of 15 mm in diameter wide-aperture BaGa2GeSe6 sample will allow one to increase pump pulse energy up to ~10 mJ, and to increase the mid-IR pulse energy up to 24 μJ at the same efficiency.

Optimal vector phase-matching conditions in biaxial crystalline materials determined by the extreme surfaces method: the case of orthorhombic crystals

The optimal geometries of vector phase matching are determined for the cases of second harmonic generation, sum frequency generation, and difference frequency generation in a number of orthorhombic nonlinear optical crystals: KTP, KTA, KB5, KNbO3, LBO, CBO, and LRB4. The extreme surface method was used to define the wave vector directions of highest possible generation efficiency. As shown, in a significant number of cases vector phase matching ensures higher efficiencies than the scalar one.

Picosecond Spin Current Generation from Vicinal Metal-Antiferromagnetic Insulator Interfaces.

We report the picosecond spin current generation from the interface between a heavy metal and a vicinal antiferromagnet insulator Cr_{2}O_{3} by laser pulses at room temperature and zero magnetic field. It is converted into a detectable terahertz emission in the heavy metal via the inverse spin Hall effect. The vicinal interfaces are apparently the source of the picosecond spin current, as evidenced by the proportional terahertz signals to the vicinal angle. We attribute the origin of the spin current to the transient magnetic moment generated by an interfacial nonlinear magnetic-dipole difference-frequency generation. We propose a model based on the in-plane inversion symmetry breaking to quantitatively explain the terahertz intensity with respect to the angles of the laser polarization and the film azimuth. Our work opens new opportunities in antiferromagnetic and ultrafast spintronics by considering symmetry breaking.

Optical to terahertz frequency conversion using near zero-index nonlinear hybrid waveguides

Terahertz communications has emerged as an excellent candidate for the next generation of wireless communication networks. Despite of significant advances, one still looks for a high-efficiency terahertz source using nonlinear optics, such as optical refraction and difference-frequency generation. Concurrently, recent years have witnessed significant progress in metamaterials-assisted nonlinear optical processes. In this study, we propose a theoretical approach using near zero-index nonlinear hybrid waveguides to realize a high generation efficiency of terahertz waves via on-chip difference-frequency generation. Remarkably, thanks to the simultaneous realization of near zero-index both at terahertz and telecom frequencies, such a nonlinear hybrid waveguide can overcome two major bottlenecks in the conversion from optical wave to terahertz waves: phase mismatch and weak nonlinear optical-terahertz waves interactions, resulting in a high conversion as 2.2 × 10−3W−1 just within the propagation length of several terahertz wavelengths. Our results demonstrate the feasibility of an on-chip terahertz source, offering unique properties such as high integration and ultra-low power consumption for terahertz communication systems.

An integrated 3C-silicon carbide-on-insulator photonic platform for nonlinear and quantum light sources

Silicon carbide (SiC) polytypes are emerging for integrated nonlinear and quantum photonics due to their wide-bandgap energies, second-order optic nonlinearity and process compatibility with complementary metal-oxide-semiconductor technologies. Among polytypes, 3C-SiC is the only one epitaxially grown on wafer-scale silicon substrates. However, on-chip nonlinear and quantum light sources leveraging the second-order nonlinearity of 3C-SiC have not been reported to our knowledge. Here, we design and fabricate an elliptical microring on 3C-SiC. We demonstrate a nonlinear light source with a second-harmonic generation efficiency of 17.4±0.2%W−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$17.4\\pm 0.2 \\% {W}^{-1}$$\\end{document} and difference-frequency generation with a signal-idler bandwidth of 97 nm. We demonstrate a spontaneous parametric down-conversion source with a photon-pair generation rate of 4.8 MHz and a coincidence-to-accidental ratio of 3361±84\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3361\\pm 84$$\\end{document}. We measure a low heralded single-photon second-order coherence gH2=0.0007\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${g}_{H}^{\\left(2\\right)}=0.0007$$\\end{document}. We observe time-bin entanglement with a visibility of 86.0±2.4%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$86.0\\pm 2.4 \\%$$\\end{document} using this source. Our work paves a way toward SiC-based on-chip nonlinear and quantum photonic circuits.

Sum and difference frequency generation in a valley-photonic-crystal-like topological system

Nonlinear sum frequency generation (SFG) and difference frequency generation (DFG) are fundamental methods to obtain new light sources for various applications. However, most of the on-chip SFG and DFG are based on conventional resonators, lacking robustness against fabrication defects. Here, we demonstrate topologically protected SFG and DFG in a second-order topological photonic system. The mechanism is based on the nonlinear interaction between three high-Q corner modes inside dual topological band gaps. The frequency matching condition for SFG and DFG is precisely satisfied by designing a valley-photonic-crystal-like topological system, which provides more freedoms to tune the corner modes. The topological SFG and DFG are achieved with high conversion efficiency, and the underlying topological physics is revealed. This work opens up avenues toward topologically protected nonlinear frequency conversion, and can find applications in the fields of on-chip single-photon detections and optical quantum memories with robustness against defects.

Ultra-broadband spectroscopy using a 2–11.5 µm IDFG-based supercontinuum source

Supercontinuum sources based on intrapulse difference frequency generation (IDFG) from mode-locked lasers open new opportunities in mid-infrared gas spectroscopy. These sources provide high power and ultra-broadband spectral coverage in the molecular fingerprint region with very low relative intensity noise. Here, we demonstrate the performance of such a light source in combination with a multipass cell and a custom-built Fourier transform spectrometer (FTS) for multispecies trace gas detection. The light source provides a low-noise, ultra-broad spectrum from 2–11.5 µm with ∼3 W output power, outperforming existing mid-infrared supercontinuum sources in terms of noise, spectral coverage, and output power. This translates to an excellent match for spectroscopic applications, establishing (sub-)ppb sensitivity for molecular hydrocarbons (e.g., CH4, C2H4), oxides (e.g., SO2, NOx), and small organic molecules (e.g., acetone, ethyl acetate) over the spectral range of the supercontinuum source with a measurement time varying from seconds to minutes. We demonstrate a practical application by measuring the off-gas composition of a bioreactor containing an acidic ammonia-oxidizing culture with the simultaneous detection of multiple nitrogen oxides (NO, NO2, N2O, etc.). As the different species absorb various parts of the spectrum, these results highlight the functionality of this spectroscopic system for biological and environmental applications.

Interplay between gain and loss in arrays of nonlinear plasmonic nanoparticles: toward parametric downconversion and amplification.

With the help of a theoretical model and finite-difference time-domain (FDTD) simulations based on the hydrodynamic-Maxwell model, we examine the effect of difference-frequency generation (DFG) in an array of L-shaped metal nanoparticles (MNPs) characterized by intrinsic plasmonic nonlinearity. The outcomes of the calculations reveal the spectral interplay between gain and loss in the vicinity of the fundamental frequency of the localized surface plasmon resonances. Subsequently, we identify different array thicknesses and pumping regimes facilitating parametric amplification and spontaneous parametric downconversion. Our results suggest that the parametric amplification regime becomes feasible on a scale of hundreds of nanometers and spontaneous parametric downconversion on the scale of tens of nanometers, opening up new exciting opportunities for developing building blocks of photonic metasurfaces.

Ultra-broadband and ultra-high conversion efficiency difference frequency generation in a dual-layer thin-film LiNbO3 waveguide with reversed ferroelectric domain orientations

Although there is a great breakthrough in second harmonic generation based on the birefringence and quasi phase matching (QPM) concepts, the development of an efficient difference frequency generation (DFG) based on modal phase matching (MPM) is still in its infancy at present. In this paper, we propose an ultra-broadband and ultra-high conversion efficiency mid-infrared DFG on the basis of MPM in a dual-layer waveguide consisting of two reversed poled LiNbO3 thin-films on sapphire. The ultra-high conversion efficiency is ascribed to significantly enhanced nonlinear interaction realized by making use of spatial profile of optical nonlinearity of LN crystal produced by two reversed ferroelectric domain orientations in the dual-layer waveguide. The proposed DFG device has been modeled on the basis of a 0.98 μm pump wave and a 1.34–1.44 μm signal wave, the frequency difference of which generates a mid-infrared idler wave centered at 3.32 μm wavelength. The results show that the device exhibits excellent DFG performance, including an ultra-high nonlinear conversion efficiency 434.6 % W−1 cm−2 and an ultra-broad tuning band 340 nm meanwhile, which far exceed the performance of conventional MPM devices, even the QPM ones.

Direct sampling of femtosecond electric-field waveforms from an optical parametric oscillator

Detecting the electric-field waveform of an optical pulse from the terahertz to the visible spectral domain provides a complete characterization of the average field waveform and holds great potential for quantum optics, time-domain (including frequency-comb) spectroscopy, high-harmonic generation, and attosecond science, to name a few. The field-resolved measurements can be performed using electro-optic sampling, where a laser pulse is characterized through an interaction with another pulse of a much shorter duration. The measured pulse train must consist of identical pulses, including their equal carrier-envelope phase (CEP). Due to the limited coverage of broadband laser gain media, creating CEP-stable pulse trains in the mid-infrared typically requires nonlinear frequency conversion, such as difference frequency generation, optical parametric amplification, or optical rectification. These techniques operate in a single-pass geometry, often limiting efficiency. In this work, we demonstrate field-resolved analysis of the pulses generated in a resonant system, an optical parametric oscillator (OPO). Due to the inherent feedback, this device exhibits a relatively high conversion efficiency at a given level of input power. By electro-optic sampling, we prove that a subharmonic OPO pumped with CEP-stable few-cycle fiber-laser pulses generates a CEP-stable mid-infrared output. The full amplitude and phase information renders dispersion control straightforward. We also confirm the existence of an exotic “flipping” state of the OPO directly in the time domain, where the electric field of consecutive pulses has the opposite sign.