Phase-matching Scheme Research Articles

Recent progress in terahertz difference-frequency quantum cascade laser sources

Abstract Terahertz quantum cascade laser (QCL) sources based on intra-cavity difference frequency generation are currently the only electrically pumped monolithic semiconductor light sources operating at room temperature in the 1–6-THz spectral range. Relying on the active regions with the giant second-order nonlinear susceptibility and the Cherenkov phase-matching scheme, these devices demonstrated drastic improvements in performance in the past several years and can now produce narrow-linewidth single-mode terahertz emission that is tunable from 1 to 6 THz with power output sufficient for imaging and spectroscopic applications. This paper reviews the progress of this technology. Recent efforts in wave function engineering using a new active region design based on a dual-upper-state concept led to a significant enhancement of the optical nonlinearity of the active region for efficient terahertz generation. The transfer of Cherenkov devices from their native semi-insulating InP substrates to high-resistivity silicon substrates resulted in a dramatic improvement in the outcoupling efficiency of terahertz radiation. Cherenkov terahertz QCL sources based on the dual-upper-state design have also been shown to exhibit ultra-broadband comb-like terahertz emission spectra with more than one octave of terahertz frequency span. The broadband terahertz QCL sources operating in continuous-wave mode produces the narrow inter-mode beat-note linewidth of 287 Hz, which indicates frequency comb operation of mid-infrared pumps and thus supports potential terahertz comb operation. Finally, we report the high-quality terahertz imaging obtained by a THz imaging system using terahertz QCL sources based on intra-cavity difference frequency generation.

Analytical solution of second-harmonic generation in a lithium-niobate-birefringence thin-film waveguide via modal phase matching

We present a systematic theoretical investigation of second-harmonic generation (SHG) in a subwavelength lithium niobate (LN) single-crystal thin-film waveguide with birefringence in permittivity and refractive index and strong anisotropy in the nonlinear susceptibility ${\ensuremath{\chi}}^{(2)}$. In a macroscopic birefringence LN crystal, the birefringence phase matching scheme that makes use of the refractive index management between the extraordinary light (EL) and ordinary light (OL) is dominantly used to ensure high-efficiency SHG. Yet, this scenario needs significant modification in a subwavelength LN thin film, where one should instead consider the waveguide modes of fundamental wave (FW) and second-harmonic wave (SHW) to participate in the SHG process. To this end, we first analytically solve and calculate the dispersion and modal profile of optical waveguide modes supported in the birefringence LN planar waveguide in a broad bandwidth ranging from ultraviolet to infrared regimes for TM (EL-like) and TE (OL-like) polarization states and at different waveguide thicknesses. Then we systematically examine the phase matching conditions that are necessary for high-efficiency energy conversion from FW waveguide mode to SHW waveguide mode via SHG. We find several modal phase matching schemes by exploiting the versatile freedoms of the FW and SHW waveguide mode number and polarization, and the waveguide thickness and symmetry. Yet modal phase matching only takes place at very limited discrete wavelengths of FW pump light. Under the modal phase matching condition, we derive the nonlinear coupled mode theory from Maxwell's equations and calculate the conversion efficiency of SHG, and find that the efficiency of SHG is determined by the nonlinear coupling coefficients that are closely associated with the modal profile overlap extent and mode transition strength between FW mode and SHW mode, and the involved nonlinear coefficient components of ${\ensuremath{\chi}}^{(2)}$. Finally, we have analytically derived the explicit formula that allows for direct calculation of the SHG efficiency as a function of the interaction length of FW mode and SHW mode, the nonlinear coupling coefficient, and the FW pump intensity, for both the small signal and general large signal situations. Our analytical theory and formulation can greatly facilitate the deep understanding of nonlinear optical interaction physics and provide a convenient tool for accurate quantitative evaluation of the SHG energy conversion efficiency of a pump laser in nanoscale LN single-crystal thin films. This analytical theory can also benefit for the design of nanoscale nonlinear optical devices based on the material platform of LN and other nonlinear crystal thin films.

Design of High Average Power OPCPA Based on Simultaneous Temperature and Wavelength Insensitive Phase Matching

Optical parametric chirped-pulse amplification (OPCPA) provides an efficient route to push ultrafast pulses toward ultrahigh peak powers. However, in high average power regime, the unavoidable thermal effects in nonlinear crystals will intrinsically destroy the phase-matching (PM) condition, which fundamentally limit average power scaling. Here, we present a theoretical design of high average power OPCPA based on simultaneous temperature and wavelength insensitive PM. By regulating the temperature set for PM as well as the wavelength of interacting waves in lithium triborate crystal, the noncollinear angles for temperature insensitive PM and wavelength insensitive PM will coincide and thus ensures simultaneous temperature and wavelength insensitive PM condition. We investigate the performances of the proposed PM scheme in comparison with traditional wavelength insensitive noncollinear PM. Because of the larger temperature bandwidth, higher average power can be anticipated in OPCPA with the proposed PM scheme. Besides, the large spectral bandwidth also allows the amplification of sub-10 fs pulses in the visible spectral range. The proposed PM scheme will provide a promising approach in generating ultrashort pulses with high peak and average powers.

Anisotropic narrowing of biphoton wave packet distribution in spontaneous parametric down-conversion with biaxial crystal

We investigate theoretically the strong anisotropy in the wave packet distribution of biphoton pairs generated via spontaneous parametric down-conversion (SPDC) process with biaxial crystals. From the angle relationship in biaxial crystals, we deduce the wave function of type I SPDC by considering the longitudinal detuning under paraxial approximation. Taking BiB3O6 (BIBO) as an example, we numerically simulate the single-particle and coincidence distributions in two observation planes under the optimum phase-matching scheme. In contrast to uniaxial crystals, a stronger anisotropy effect and a higher entanglement of the photon pair states are obtained, which are attributed to the complex structure of biaxial crystals. These results are important for the generation of highly entangled biphoton pairs, especially for multi-photon pairs generation.

Theoretical analysis of stimulated polariton scattering from the A1-symmetry modes of KNbO3 crystal

Stimulated polariton scattering (SPS) based on noncollinear phase matching scheme from the A1-symmetry modes of KNbO3 crystal is investigated for generating terahertz (THz) wave. Frequency tuning characteristics of THz wave by varying the phase matching angle and pump wavelength are analyzed. The expression of the effective parametric gain length under the noncollinear phase matching condition is deduced. Parametric gain and absorption characteristics of THz wave in KNbO3 are theoretically simulated. The characteristics of KNbO3 for parametric oscillator (TPO) are compared with those of MgO:LiNbO3. The analysis results indicate that KNbO3 is an excellent optical crystal for TPO to enhance the output of THz wave.

Extended phase matching of high harmonic generation by plasma-induced defocusing

High-harmonic generation (HHG) of femtosecond lasers produces unique short-wavelength light pulses with femtosecond to attosecond duration. However, free electrons in the partially ionized gas medium are known to prevent phase matching and limit upconversion to low-energy harmonics only. We have demonstrated experimentally and theoretically an unconventional phase-matching scheme: extending the HHG phase matching cutoff by controlling the rapid self-defocusing effect of the driving laser. This method takes advantage of the additional intrinsic atomic dipole phase mismatch introduced by the rapid laser defocusing. This phase can be precisely controlled by adjusting the aperture of a simple iris, which truncates the input beam, to correctly compensate free-electron dispersion, resulting in tunable harmonic energy and phase matching cutoff extension. Based on this approach, we report experimental observation of extending the harmonic cutoff energy in Ar to ∼65 eV with a 400-fold increase in conversion efficiency using a tightly focused truncated Gaussian beam in a short high-pressure gas cell. This new defocusing-assisted phase matching in a highly ionized gas medium can be applied to different targets, laser wavelengths, and pulse durations to extend harmonic upconversion to higher cutoff energy with higher efficiency.

Temperature-insensitive second-harmonic generation based on noncollinear phase matching in a lithium triborate crystal

In high-average-power second-harmonic generation (SHG) devices, the unavoidable thermal distortion induces a nonuniform phase mismatch that poses an inherent limitation on the conversion efficiency. Here we introduce a temperature-insensitive noncollinear (TIN) phase-matching scheme, which can significantly improve the performance of high-power SHG devices and is versatile to a broad range of laser wavelengths. In the proof-of-principle experiment with a lithium triborate crystal and a 1053 nm nanosecond laser, we demonstrate a large temperature bandwidth of ∼50 K×cm1/2 and a high SHG efficiency of ∼56%. This temperature bandwidth is 13 times that of the conventional collinear phase matching. We also numerically investigate the performance of the proposed TIN phase-matching scheme in high-power lasers. The demonstrated large temperature bandwidth allows efficient SHG in the high-power regime of 5–10 kW. The simplicity, high efficiency, and wavelength versatility will make the TIN phase matching attractive for wide applications in high-power lasers.

Surface enhanced nonlinear Cherenkov radiation in one-dimensional nonlinear photonic crystal.

We study the configuration of efficient nonlinear Cherenkov radiation generated at the inner surface of a one-dimensional nonlinear photonic crystal, which utilizes the combination of both quasi-phase matching and total internal reflection by the crystal surface. Multi-directional nonlinear Cherenkov radiation assisted by different orders of reciprocal vectors is demonstrated experimentally. At specific angles, by associating with quasi-phase matching, the incident fundamental wave and total internal reflection wave format completely the phase-matching scheme, leading to great enhancement of harmonic wave intensity.

Efficient Second Harmonic Generation by Mode Phase Matching in a Silicon Waveguide

Bulk silicon possesses no second-order susceptibility (χ(2)), inhibiting second-order nonlinear processes in the emerging silicon photonic platform. Here, we propose a method to overcome this limitation by enabling a third-order (χ(3)) nonlinear mixing scheme between optical waves and an externally applied static electric field inside a silicon waveguide. We show in theory that facilitated by a modal phase-matching scheme efficient second-harmonic generation can be realized under an applied voltage of 65 V, giving rise to an equivalent χ(2) = 4.7 pm/V. We also show that unlike the classical second-harmonic generation, the wavelengths of phase-matched pump and second-harmonic waves are pump-power dependent due to the χ (3) nature of this process.

High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification.

A design for efficient generation of mid-infrared pulses at 3.2 μm is presented, which is based on numerical simulations of the broadband-pumped dual-chirped optical parametric amplification (DC-OPA) in LiNbO3 doped with 5 mol.% MgO (MgO:LiNbO3). The broadband seed can be generated by difference frequency generation in KTA using spectrally-broadened Ti:Sapphire lasers. The broad DC-OPA phase-matching bandwidth-spanning from 2.4 μm to 4.0 μm-is achieved by chirping both the broadband Ti:Sapphire pump pulses and the seed pulses in such a way that the individual temporal slice of pump spectrum is able to phase match that of seed spectrum. This phase matching scheme allows the use of longer crystals without gain narrowing or loss of conversion efficiency. The theoretical conversion efficiency from the pump to the idler reaches 19.1 %, enabling generation of a few hundred mJ of mid-IR energy with an available large-aperture MgO:LiNbO3 crystal. Furthermore, the commercially available acousto-optic programmable dispersive filter (AOPDF) ensures compression of such a broad bandwidth down to 20 fs (two optical cycles at 3.2 μm).

Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell.

Entangled photon pairs, termed as biphotons, have been the benchmark tool for experimental quantum optics. The quantum-network protocols based on photon–atom interfaces have stimulated a great demand for single photons with bandwidth comparable to or narrower than the atomic natural linewidth. In the past decade, laser-cooled atoms have often been used for producing such biphotons, but the apparatus is too large and complicated for engineering. Here we report the generation of subnatural-linewidth (<6 MHz) biphotons from a Doppler-broadened (530 MHz) hot atomic vapour cell. We use on-resonance spontaneous four-wave mixing in a hot paraffin-coated 87Rb vapour cell at 63 °C to produce biphotons with controllable bandwidth (1.9–3.2 MHz) and coherence time (47–94 ns). Our backward phase-matching scheme with spatially separated optical pumping is the key to suppress uncorrelated photons from resonance fluorescence. The result may lead towards miniature narrowband biphoton sources.

Multiparameter spatio-thermochemical probing of flame–wall interactions advanced with coherent Raman imaging

Ultrabroadband coherent anti-Stokes Raman spectroscopy (CARS) has been developed for one-dimensional imaging of temperature and major species distributions simultaneously in the near-wall region of a methane/air flame supported on a side-wall-quenching (SWQ) burner. Automatic temporal and spatial overlap of the ∼7fs pump and Stokes pulses is achieved utilizing a two-beam CARS phase-matching scheme, and the crossed ∼75ps probe beam provides excellent spatial sectioning of the probed location. Concurrent detection of N2, O2, H2, CO, CO2, and CH4 is demonstrated while high-fidelity flame thermometry is assessed from the N2 pure rotational S-branch in a one-dimensional-CARS imaging configuration. A methane/air premixed flame at lean, stoichiometric, and rich conditions (Φ=0.83, 1.0, and 1.2) and Reynolds number=5000 is probed as it quenches against a cooled steel side-wall parallel to the flow providing a persistent flame–wall interaction. An imaging resolution of better than 40µm is achieved across the field-of-view, thus allowing thermochemical states (temperature and major species) of the thermal boundary layer to be resolved to within ∼30µm of the interface.

Antiphase domain tailoring for combination of modal and 4¯ -quasi-phase matching in gallium phosphide microdisks.

We propose a novel phase-matching scheme in GaP whispering-gallery-mode microdisks grown on Si substrate combining modal and 4¯ -quasi-phase-matching for second-harmonic-generation. The technique consists in unlocking parity-forbidden processes by tailoring the antiphase domain distribution in the GaP layer. Our proposal can be used to overcome the limitations of form birefringence phase-matching and 4¯ -quasi-phase-matching using high order whispering-gallery-modes. The high frequency conversion efficiency of this new scheme demonstrates the competitiveness of nonlinear photonic devices monolithically integrated on silicon.

Theoretical analysis of terahertz parametric oscillator using KTiOPO4 crystal

Terahertz parametric oscillator (TPO) using KTiOPO4 (KTP) crystal with a noncollinear phase-matching scheme is investigated. Frequency tuning characteristics of terahertz wave (THz-wave) by varying the phase-matching angle and pump wavelength are analyzed. The expression of the effective parametric gain length under the noncollinear phase matching condition is deduced. Parametric gain and absorption characteristics of THz-wave in KTP are theoretically simulated for the first time. The characteristics of KTP for TPO are compared with MgO:LiNbO3. The analyses indicate that KTP is more suitable than MgO:LiNbO3 for TPO.

Investigation on Terahertz Generation by GaP Ridge Waveguide Based on Cascaded Difference Frequency Generation

Terahertz (THz) generation by a GaP ridge waveguide with a collinear modal phase-matching scheme based on cascaded difference frequency generation (DFG) processes is theoretically analyzed. The cascaded Stokes interaction processes and the cascaded anti-Stokes interaction processes are investigated from coupled wave equations. THz intensities and quantum conversion efficiency are calculated. Compared with non-cascaded DFG processes, THz intensities from 11-order cascaded DFG processes are increased to 5.48. The quantum conversion efficiency of 177.9% in cascaded processes can be realized, exceeding the Manley-Rowe limit.

Terahertz generation by DSTMS based on cascaded difference frequency generation

Terahertz (THz) wave generation by organic crystal 4-N, N-dimethylamino-4′-N′-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS) with a collinear phase-matching scheme based on cascaded difference frequency generation (DFG) processes is theoretical analyzed. The cascaded Stokes interaction processes and the cascaded anti-Stokes interaction processes are investigated from coupled wave equations. THz intensities and quantum conversion efficiency are calculated. Compared with non-cascaded DFG processes, THz intensities from 17-order cascaded DFG processes are increased to 6.7. The quantum conversion efficiency of 298.5% in cascaded processes can be realized, which exceeds the Manley–Rowe limit.

Recent Progress in Widely Tunable Single-Mode Room Temperature Terahertz Quantum Cascade Laser Sources

We present the operating principle, design, and performance of external-cavity (EC) and monolithic terahertz (THz) tuners based on intracavity difference-frequency generation (DFG) in midinfrared (mid-IR) quantum cascade lasers (QCLs). A DFG-QCL gain chip employed in a Littrow-type THz EC system was optimized for wide tunability in 1–6 THz range using broad mid-IR gain bandwidth active region with integrated optical nonlinearity and Cherenkov THz phase-matching scheme. The EC system demonstrated ultrabroadband single-mode tuning from 1.2 to 5.9 THz. Beam steering in THz far field due to refractive index dispersion of InP substrate has been successfully suppressed by bonding the QCL chip on a high-resistivity silicon substrate. We also discuss the design of compact widely tunable monolithic THz DFG-QCL sources. Devices use two electrically isolated grating sections for independent electronic tuning of the two mid-IR pump frequencies. THz DFG frequency tuning from 3.44 to 4.02 THz, corresponding to 580 GHz or 15% of center frequency, is obtained.

Investigation of Terahertz Generation from Bulk and Periodically Poled LiTaO3Crystal with a Cherenkov Phase Matching Scheme

Terahertz (THz) wave generation from bulk and periodically poled $LiTaO_3$ (PPLT) with a Cherenkov phase matching scheme is numerically investigated. It is shown that by using the crystal birefringence of bulk $LiTaO_3$ and a grating vector of PPLT, THz waves can be efficiently generated by difference frequency generation (DFG) with a Cherenkov phase matching scheme. The frequency tuning characteristics of the THz wave via varying wavelength of difference frequency waves, phase matching angle, poling period of PPLT and working temperature are theoretically analyzed. The parametric gain coefficient in the low-loss limit and the absorption coefficient of the THz wave during the DFG process in the vicinity of polariton resonances are numerically analyzed. A THz wave can be efficiently generated by utilizing the giant second order nonlinearities of $LiTaO_3$ in the vicinity of polariton resonances.

Terahertz generation in mid-infrared quantum cascade lasers with a dual-upper-state active region

We report the performance of room temperature terahertz sources based on intracavity difference-frequency generation in mid-infrared quantum cascade lasers with a dual-upper-state (DAU) active region. DAU active region design is theoretically expected to produce larger optical nonlinearity for terahertz difference-frequency generation, compared to the active region designs of the bound-to-continuum type used previously. Fabricated buried heterostructure devices with a two-section buried distributed feedback grating and the waveguide designed for Cherenkov difference-frequency phase-matching scheme operate in two single-mode mid-infrared wavelengths at 10.7 μm and 9.7 μm and produce terahertz output at 2.9 THz with mid-infrared to terahertz conversion efficiency of 0.8 mW/W2 at room temperature.

Terahertz wave parametric oscillations at polariton resonance using a MgO:LiNbO3 crystal.

Terahertz wave (THz-wave) parametric oscillations with a noncollinear phase-matching scheme at polariton resonance using a MgO:LiNbO3 crystal with a surface-emitted configuration are investigated. We investigate frequency tuning characteristics of a THz-wave via varying the wavelength of the pump wave and phase-matching angle. The effective parametric gain length under the noncollinear phase-matching condition is calculated. Parametric gain and absorption characteristics of a THz-wave in the vicinity of polariton resonances are analyzed.