Difference Frequency Generation Research Articles

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.

Frequency Сonversion 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.

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.

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.

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.

External chirality enhancing downconversion in a waveguide-coupled nonlinear plasmonic metasurface.

Metasurfaces, typically constructed from spatial arrangements of localized building blocks, can enhance light-matter interactions through local field enhancement or by coherent coupling to extended photonic modes. Recent works have explored how guided mode resonances influence the performance of nonlinear metasurfaces. Here we investigate the modal impact on difference-frequency generation in a waveguide-coupled metasurface platform. The system is constructed from gold split-ring resonators on a high-index TiO2 waveguide. We find that a symmetric configuration of the metasurface's localized modes and the extended waveguide modes lead to a modest enhancement of the downconversion process. However, when the mirror symmetry of the localized modes with respect to the guided mode propagation breaks, it introduces external chirality. This enables coupling to a higher quality mode, resulting in a 70-fold enhancement of the difference-frequency generation. The capacity to manipulate the nonlocal modes through the design offers broader control over the interaction and new avenues to tailor the nonlinear processes.

Extending the propagation length of graphene plasmons via nonlinear frequency conversion

Graphene plasmons (GPs) are broadband and electrically tunable mid-infrared (MIR)/terahertz (THz) excitations, exhibiting high confinement factors exceeding two orders of magnitude. Such highly confined modes are extremely attractive for nonlinear frequency conversion owing to the large inherent field enhancement. However, this high confinement is also accompanied by losses, and together with the centrosymmetric nature of graphene practical usage of its properties in second-order nonlinear processes remains hindered. In this paper, we introduce an approach for realizing quasi-phase-matching (QPM) of propagating GPs, by placing the graphene on an orientationally patterned GaAs substrate—a transparent material in the MIR/THz range with a large second-order nonlinear coefficient. We analyze the complete frequency/Fermi-level space for QPMed second-harmonic generation of GPs in the MIR and THz and demonstrate GP amplification and loss compensation. We find that our approach provides extended GP propagation lengths that are more than twice larger than the state-of-the-art cryogenic temperature propagation lengths. The approach is general to all second-order nonlinear processes, such as sum and difference frequency generation, thus opening a path for efficient and electrically tunable QPM nonlinear processes at the atomic scale.

Continuous-wave long-wavelength infrared difference-frequency generation in ZGP driven by near-infrared fiber lasers.

We report the continuous-wave (cw) difference-frequency generation (DFG) in a ZnGeP2 (ZGP) crystal that produces tunable long-wavelength infrared (LWIR) lasing. Particularly, we experimentally demonstrate the feasibility to drive DFG in ZGP by all-fiber near-infrared fiber lasers consisting of a 1.3 µm tunable cw random Raman fiber laser (RRFL) and a 1.5 µm erbium-doped fiber amplifier seeded by a tunable distributed feedback (DFB) laser, making the whole system compact and robust. As a result, the demonstrated LWIR DFG presents a broadband spectral tuning range spanning from 9.5 to 11.5 µm, and the output powers in the spectral range of 9.5-11 µm are larger than 40 µW pumped by watt-level fiber lasers. Meanwhile, as a typical application, a proof-of-concept demonstration of gas sensing of SF6 is executed based on the generated cw LWIR source. Our work demonstrates that the combination of ZGP crystal and fiber lasers can provide an effective and robust approach for the generation of cw LWIR radiation with useful power and broadband wavelength tunability.

Ultra-phase-stable infrared light source at the watt level.

Ultrashort pulses at infrared wavelengths are advantageous when studying light-matter interaction. For the spectral region around 2 µm, multi-stage parametric amplification is the most common method to reach higher pulse energies. Yet it has been a key challenge for such systems to deliver waveform-stable pulses without active stabilization and synchronization systems. Here, we present a different approach for the generation of infrared pulses centered at 1.8 µm with watt-level average power utilizing only a single nonlinear crystal. Our laser system relies on a well-established Yb:YAG thin-disk technology at 1.03 µm wavelength combined with a hybrid two-stage broadening scheme. We show the high-power downconversion process via intra-pulse difference frequency generation, which leads to excellent passive stability of the carrier envelope phase below 20 mrad-comparable to modern oscillators. It also provides simple control over the central wavelength within a broad spectral range. The developed infrared source is employed to generate a multi-octave continuum from 500 nm to 2.5 µm opening the path toward sub-cycle pulse synthesis with extreme waveform stability.

High-SNR mid-infrared dual-comb spectroscopy using active phase control cooperating with CWs-dependent phase correction.

Mid-infrared (MIR) dual-comb spectroscopy (DCS) is a highly effective method for molecular metrology of rovibrational transition spectra in a quick accurate manner. However, due to limited comb frequency instability, manipulating coherence between two frequency combs to accomplish high-quality spectral analysis in the MIR region is a huge challenge. Here, we developed a comb-teeth resolved MIR DCS based on active phase control cooperating with a CWs-dependent (CWD) interferogram timing correction. Firstly, four meticulously engineered actuators were individually integrated into two near-infrared (NIR) seed combs to facilitate active coherence maintenance. Subsequently, two PPLN waveguides were adopted to achieve parallel difference frequency generations (DFG), directly achieving a coherent MIR dual-comb spectrometer. To improve coherence and signal-to-noise ratio (SNR), a CWD resampled interferogram timing correction was used to optimize the merit of DCS from 7.5 × 105 to 2.5 × 106. Meanwhile, we carried out the measurement of MIR DCS on the methane hot-band absorption spectra (v3 band), which exhibited a good agreement with HITRAN by a standard deviation on recording residual of 0.76%. These experimental results confirm that this MIR DCS with CWD interferogram timing correction has significant potential to characterize the rovibrational transitions of MIR molecules.

Simultaneous generation and manipulation of terahertz waves based on nonlinear leaky-waveguide antennas with integrated bianisotropic metasurfaces.

We hereby propose and theoretically investigate a new scheme for simultaneous generation and manipulation of terahertz (THz) waves through difference frequency generation facilitated by a metasurface-assisted nonlinear leaky waveguide antenna. The proposed structure integrates a nonlinear optical waveguide, composed of multiple AlxGa1-xAs layers, with a THz leaky waveguide, wherein a bianisotropic metasurface realizes the radiating aperture. By explicitly utilizing the electric, magnetic, and magnetoelectric coupling responses of the metasurface, we demonstrate that the generated THz wave can be induced as a tightly confined, phase-matched guided mode for efficient generation of the THz wave. Additionally, this approach allows the THz wave to be transformed into a directive beam, radiating at a user-defined leakage rate and direction. Our numerical analyses suggest that THz beams ranging from 2.85 THz to 3.05 THz can be steered from 4 ∘ to 40 ∘, utilizing the inherent beam-steering capabilities of the leaky-waveguide antenna. Within this THz frequency spectrum, the phase matching condition is achieved by adjusting the optical wavelengths between 1.6μm and 1.52μm. In particular, the nonlinear conversion efficiency is 2.9 × 10-5 [1/W] at 3 THz.

Maximizing the efficiency of intrapulse difference frequency generation by pulse shaping and recycling

Maximizing the efficiency of intrapulse difference frequency generation by pulse shaping and recycling

Polarization-insensitive and polarization-controlled dual-band third-harmonic generation in silicon metasurfaces driven by quasi-bound states in the continuum

High-refractive-index nanostructures offer versatile opportunities for nonlinear optical effects, due to their ability to strongly confine field into a subwavelength scale. Herein, we propose a rhomboidal amorphous silicon metasurface to realize high-efficiency dual-band third-harmonic generation (THG), based on the supported dual quasi-bound states in the continuum (Q-BICs). Owing to the very large field confinement inside the metasurface empowered by Q-BICs, the THG efficiency up to 3.74 × 10−3 with the peak pump intensity of 30 MW/cm2 is observed. Meanwhile, thanks to the very high quality factor of Q-BICs, the ultra-narrow nonlinear process with the full width at half maximum less than 1 nm is also witnessed, suggesting the good monochromaticity. Interestingly, the dual-band THG is verified to be polarization-dependent and polarization-insensitive, respectively. The finite element method simulations exhibit that the polarization-dependent THG is attributed to the Q-BIC driven by the electric quadrupole characterized by a pair of anti-parallel electric dipoles along the x axis, which are only excited by the x-linearly polarized light. On the contrary, the polarization-insensitive THG is enabled by another Q-BIC governed by the magnetic dipole resonance with circular electric field vectors, which can be excited by any linearly polarized light. The polarization-controlled and polarization-independent dual-band THG enabled by the physics of Q-BICs would open possibilities for designing switchable nonlinear light sources. The proposed dual Q-BICs scheme undoubtedly can serve as a universal recipe for other nonlinear effects, including sum-frequency generation, difference-frequency generation, and high-order harmonics.