Difference Frequency Generation Process Research Articles

Modelling of long-wave mid-infrared ultrashort pulse generation via difference frequency generation

In this paper, a model of generating mid-infrared (MIR) ultrashort laser pulse through difference frequency generation (DFG) is established. The pulse evolution relationship among the pump, signal, and idler pulses during the DFG process, as well as the effects of crystal length, pulse energy of the pump and signal lights, pulse width, and other factors on the characteristics of the MIR pulse are explored. Furthermore, through simulations from the time domain to the frequency domain, the spectral characteristics and angular distribution of MIR were analyzed. DFG experimental data are also presented to support the model.

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.

Unidirectional ring laser operation and tunable single-frequency emission using differential parametric gain.

In this Letter, a novel approach for unidirectional operation of a 1064 nm solid-state ring laser is demonstrated based on difference frequency mixing. Unidirectional operation is achieved exploiting the directional parametric gain from a single-pass diode laser, facilitated through a periodically poled LiNbO3 crystal. In addition to achieving unidirectional operation, the nonlinear process further enables the generation of single-frequency mid-infrared light. Using a single-pass tapered diode laser, tunable in the range from 780 to 815 nm, the generated mid-infrared signal covers the 2.9 to 3.5 µm range while optimizing the phase-match condition of the difference frequency generation process.

Precise parameter control of multicycle terahertz generation in PPLN using flexible pulse trains.

The low (sub %) efficiencies so-far demonstrated for nonlinear optical down-conversion to terahertz (THz) frequencies are a primary limiting factor in the generation of high-energy, high-field THz-radiation pulses (in particular narrowband, multicycle pulses) needed for many scientific fields. However, simulations predict that far higher conversion efficiencies are possible by use of suitably-optimized optical sources. Here we implement a customized optical laser system producing highly-tunable trains of infrared pulses and systematically explore the experimental optimization of the down-conversion process. Our setup, which allows tuning of the energy, duration, number and periodicity of the pulses in the train, provides a unique capability to test predictions of analytic theory and simulation on the parameter dependences for the optical-to-THz difference-frequency generation process as well as to map out, with unprecedented precision, key properties of the nonlinear crystal medium. We discuss the agreements and deviations between simulation and experimental results which, on the one hand, shed light on limitations of the existing theory, and on the other hand, provide the first steps in a recipe for development of practical, high-field, efficiency-optimized THz sources.

Generation of terahertz waves based on nonlinear frequency conversion with double rapid adiabatic passage technique

In this paper, a nonlinear optical cascaded difference frequency generation model based on double rapid adiabatic passage technique is established, and a theoretical scheme for generating THz waves based on the above model is proposed. In this model, when the incident signal laser interacts with a pump laser, the signal laser can be completely converted into the output laser by special processing of the coupling wave equation and making reasonable assumptions. Numerical simulation results show that THz waves with a centre frequency of 260 GHz can be obtained. The maximum quantum conversion efficiency of the signal laser to THz waves is about 43.4%. Under the premise of keeping the wavelength of the pump laser unchanged, the tunable THz waves of 0.26–2.94 THz can be obtained when tuning the wavelength of the signal laser to change in the range of 1.054–1.064 μm. Compared with the scheme using stimulated Raman adiabatic passage technique, the scheme can still generate terahertz waves during the application of a pump laser to two simultaneous difference frequency generation processes, and the intensity of the pump laser can be reduced from Gigawatt level to Megawatt level. This scheme is robust to the temperature variation and provides a new method for generating terahertz wave band for high-speed wireless transmission.

Phase-matching in terahertz quantum cascade laser sources based on Cherenkov difference-frequency mixing

Terahertz quantum cascade laser sources based on intra-cavity Cherenkov difference-frequency generation in dual-wavelength mid-infrared quantum cascade lasers are currently the only monolithic semiconductor laser technology that can deliver continuous-wave coherent terahertz output at room temperature. Because the Cherenkov difference-frequency generation process enables terahertz radiation generation and extraction across a wide range of frequencies, it is often assumed that phase-matching conditions for this process are automatically fulfilled. We theoretically analyze and experimentally demonstrate that phase-matching plays an important role in these devices, and significant improvements in terahertz power output can be achieved by adjusting the waveguide configuration of the quantum cascade lasers to provide better phase-matching.

Simultaneous RGB generation in domain engineered QPM devices using type 0 DFG process

We have theoretically demonstrated the simultaneous generation of red (R), green (G), and blue (B) wavelengths by employing the type-0 quasi-phase-matched (QPM) difference frequency generation (DFG) process in congruent LiNbO3 crystal. Various domain-engineered QPM structures are presented and analysed, aiming to achieve an excellent spectral response. The RGB emissions were observed to vary from 632 nm to 656 nm for red, 504 nm to 532 nm for green, and 449 nm to 484 nm for blue, respectively, for different configurations of input pump, operating temperature, and phase matching periods. A maximum shift of about 10 nm to 20 nm was noticed in the spectral position of the DFG peaks when the operating temperature varies from 25 °C to 60 °C. We have also investigated the effect of pump detuning and random domain fluctuations over the phase matching point on the DFG spectrum. Further, we have addressed the advantages of introducing a phase shifter (PS) domain in the periodically poled lithium niobate (PPLN) to produce excellent equal intensity RGB peaks in a single device for their potential application in a laser-based projection display system.

Few-mode optical parametric amplification in a multiple quasi-phase-matched thin-film lithium niobate waveguide

Mode-division multiplexing (MDM) technology, an effective approach to boost the transmission capacity, has seen momentous progress in the past decade. Wideband, low-noise, and power-efficient optical amplifiers for the MDM systems are highly desired. We propose and theoretically demonstrate a broadband few-mode optical parametric amplifier (OPA) using a multimode thin-film periodically poled lithium niobate (PPLN) waveguide with multiple quasi-phase matching (QPM). The few-mode OPA relies on intramodal and intermodal difference-frequency generation (DFG) processes, obtaining strong parametric amplification of MDM signals using a single-frequency fundamental-mode pump. Differential modal gain (DMG) is optimized by adjusting the effective length of parametric interaction for each mode. In addition, parasitic DFG processes to cause nonlinear modal crosstalk is suppressed due to the large phase mismatch ensured by the multiple QPM design. The results show that amplification of signals carrying three modes with >11.2-dB gain per mode over 41 nm bandwidth covering extended C band can be achieved with a 600-mW pump, while the DMG is less than 1.1 dB and nonlinear modal crosstalk is negligible.

Tunable phase-mismatched mid-infrared difference-frequency generation between 6 and 17 µm in CdTe.

In parametric conversion, phase-matching techniques such as birefringence and quasi phase-matching (PM) with the designed crystal angle or periodically poled polarities are employed to fulfill the requirement of momentum conservation. However, directly using phase-mismatched interactions in nonlinear media with large quadratic nonlinear coefficient remains unheeded. Here, for the first time to the best of our knowledge, we study the phase-mismatched difference-frequency generation (DFG) in an isotropic cadmium telluride (CdTe) crystal, with the comparison of other DFG processes based on birefringence-PM, quasi-PM, and random-quasi-PM. Long-wavelength mid-infrared (LWMIR) phase-mismatched DFG with an ultra-broadband spectral tuning range of 6-17 µm based on CdTe is demonstrated. Thanks to the giant quadratic nonlinear coefficient (∼109 pm/V) and good figure of merit in the parametric process, the output power up to 100 µW is obtained, which is comparable to or even better than the DFG output from a polycrystalline ZnSe with the same thickness facilitated by random-quasi-PM. A proof-of-concept demonstration in gas sensing of CH4 and SF6 is conducted based on the phase-mismatched DFG as a typical application. Our results demonstrate the feasibility of phase-mismatched parametric conversion in producing useful LWMIR power and ultra-broadband tunability in a simple and convenient way without the necessity of controlling the polarization, phase-matching angle, or pole periods, which could find applications in the fields of spectroscopy and metrology.

Generation of 17-32 THz radiation from a CdSiP2 crystal.

A phase-resolved electric field pulse is produced through the second-order nonlinear process of intra-pulse difference frequency generation (DFG) in a (110) CdSiP2 chalcopyrite crystal. The generated electric field pulse exhibits a duration of several picoseconds and contains frequency components within the high-frequency terahertz regime of ∼17-32 THz. The intra-pulse DFG signal is shown to be influenced by single-phonon and two-phonon absorption, the nonlinear phase-matching criterion, and temporal spreading of the excitation electric field pulse. To date, this is the first investigation in which a CdSiP2 chalcopyrite crystal is used to produce radiation within the aforementioned spectral range.

Generation of 2 μm few-cycle laser pulse with dual laser filaments nonlinear processes

For the first time, we propose a new scheme for generating few-cycle 2 μm seed laser pulse in an optical parametric chirped pulse amplifier (OPCPA) front-end. The 2 μm ultrafast seed laser pulse is generated via a difference frequency generation (DFG) process between the visible and near-IR supercontinuum from two different filamentation processes inside the transparent YAG crystals. The generated DFG pulse spectrum has a broad spectrum range of 1200 nm from 1500 nm to 2700 nm. By further scaling up the pulse energy of the seed laser pulse via a non-collinear optical parametric amplification (OPA) stage, the single pulse energy is boosted to 15.6 μJ. After dispersion compensation, the pulse duration is compressed to 14.3 fs with its spectrum covering from 1600 nm to 2600 nm.

Triply-resonant sum frequency conversion with gallium phosphide ring resonators.

We demonstrate quasi-phase matched, triply-resonant sum frequency conversion in 10.6-µm-diameter integrated gallium phosphide ring resonators. A small-signal, waveguide-to-waveguide power conversion efficiency of 8 ± 1.1%/mW; is measured for conversion from telecom (1536 nm) and near infrared (1117 nm) to visible (647 nm) wavelengths with an absolute power conversion efficiency of 6.3 ± 0.6%; measured at saturation pump power. For the complementary difference frequency generation process, a single photon conversion efficiency of 7.2%/mW from visible to telecom is projected for resonators with optimized coupling. Efficient conversion from visible to telecom will facilitate long-distance transmission of spin-entangled photons from solid-state emitters such as the diamond NV center, allowing long-distance entanglement for quantum networks.

Non-Hermitian quantum-like cascaded nonlinear optical frequency conversion and splitting in dissipative media

It is shown that cascaded nonlinear optical frequency conversion over an intermediate wavelength, subjected to dissipation, behaves similarly to population transfer via a decaying state in a three-state non-Hermitian quantum system. The intermediate dissipation leads to a fixed phase relationship between the input signal wave and the wave at the target frequency, what finally stabilizes both waves preventing any spatial oscillation of their powers. The cascaded conversion acts as a stable wave splitter between the input and target waves, the latter being nearly immune to power fluctuations of the pumps. A case of a simultaneous cascade of the sum frequency generation and the difference frequency generation processes is discussed as an example. A possible implementation, based on aperiodically engineered quasi-phase-matching in lithium niobate, is proposed.

Classical model of spontaneous parametric down-conversion

We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic "vacuum" seed field. We analytically show that the second-order spatiotemporal correlations of the field generated from the DFG process replicate those of the signal field from SPDC. Specifically, for low gain, the model is consistent with the quantum calculation of the signal photon's reduced density matrix; and for high gain, the model's predictions are in good agreement with our experimental measurements of the far-field intensity profile, orbital angular momentum spectrum, and wavelength spectrum of the SPDC field for increasing pump strengths. We further theoretically show that the model successfully captures second-order SU(1,1) interference and induced coherence effects in both gain regimes. Intriguingly, the model also correctly predicts the linear scaling of the interference visibility with object transmittance in the low-gain regime -- a feature that is often regarded as a quintessential signature of the nonclassicality of induced coherence. Our model may not only lead to novel fundamental insights into the classical-quantum divide in the context of SPDC and induced coherence, but can also be a useful theoretical tool for numerous experiments and applications based on SPDC.

Numerical study of terahertz radiations from difference frequency generation with large spectral tunability and significantly enhanced conversion efficiencies boosted by 1D leaky modes

The nonlinear optical process of difference frequency generation (DFG) is a prominent technique to produce continuous-wave terahertz radiations while its low conversion efficiency calls for substantial enhancement using artificial structures. All-dielectric nanostructures supporting the quasi-bound states in the continuum (QBIC) appear as a promising approach to this end. To achieve the utmost of enhancement, both input lightwaves of the DFG should work at the QBIC conditions and in many cases a spectral tunability of the input wavelength is necessary. All these requirements go beyond the capability of conventional QBIC which can only happen within a narrow bandwidth for a given structure. In this work, we numerically demonstrate that these restrictions can be eliminated by using our recently proposed concept of one-dimensional leaky modes with ultrahigh Q factors and large operation bandwidth. Using an elaborately designed structures in the form of binary waveguide gratings (BWGs) made from LiNbO3 thin film, we demonstrate that a conversion efficiency enhanced by the order of 1011 can be achieved using the BWGs made from LiNbO3, compared to the case of a bare LiNbO3 thin film. Furthermore, enhanced THz generations over a large spectral range can be easily achieved by changing the incident angle of one input light beam while tuning its wavelength to match the requirement for the leaky resonance excitation at that angle.

Up-conversion detection of mid-infrared light carrying orbital angular momentum

Frequency up-conversion is an effective method of mid-infrared (MIR) detection by converting long-wavelength photons to the visible domain, where efficient detectors are readily available. Here, we generate MIR light carrying orbital angular momentum (OAM) from a difference frequency generation process and perform up-conversion on it via sum frequency conversion in a bulk quasi-phase-matching crystal. The maximum quantum conversion efficiencies from MIR to visible are 34.0%, 10.4%, and 3.5% for light with topological charges of 0, 1, and 2, respectively, achieved by utilizing an optimized strong pump light. We also verify the OAM conservation with a specially designed interferometer, and the results agree well with the numerical simulations. Our study opens up the possibilities for generating, manipulating, and detecting MIR light that carries OAM, and will have great potential for optical communications and remote sensing in the MIR regime.

Mixing second- and third-order nonlinear interactions in nanophotonic lithium-niobate waveguides

In this paper, we have investigated the interplay between the second and third-order nonlinearities in lithium-niobate waveguides with strong waveguide dispersion using uniform and linearly-chirped poling patterns at input powers in the pico-joule range. We have implemented the accurate unidirectional pulse propagation model to take into account all the possible nonlinear interactions inside these structures. In particular, the poling period has been designed to quasi-phase-match single and multiple sum- and difference-frequency generation processes. We have shown how the poling period can be used as an additional degree of freedom to tailor the output spectra of chip-based nonlinear waveguides in an unprecedented way.

An integrated photonic circuit for color qubit preparation by third-order nonlinear interactions

This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching color qubit preparation fidelity close to unity. We present the generalized rotation operator related to the DFG process, a methodology for the device design, and qubit preparation fidelity results as a function of user-accessible parameters.

Enhanced intrapulse difference frequency generation in the mid-infrared by a spectrally dependent polarization state.

We present a technique to optimize the intrapulse difference frequency generation efficiency for mid-infrared generation. The approach employs a multi-order wave plate that is designed to selectively rotate the polarization state of the incoming spectral components on the relevant orthogonal axes for subsequent nonlinear interaction. We demonstrate a significant increase of the mid-infrared average power generated, of a factor ≥2.5 compared with the conventional scheme, owing to an optimally distributed number of photons enrolled in the difference frequency generation process.

Structure design and numerical simulation of chirped periodically polarized lithium niobate crystal for broadband mid-infrared laser generation

Mid-infrared band 3–5 <inline-formula><tex-math id="M1">\begin{document}${\text{μm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M1.png"/></alternatives></inline-formula> laser light source has important applications in many fields such as medical treatment, basic science, communication, and industry. Owing to the limitation to available efficient gain media in the mid-infrared band, the traditional methods of generating and amplifying lasers , such as regenerative amplification, are no longer applicable. In order to produce broadband and high-energy mid-infrared laser, in this work we combine quasi-phase matching technology and chirped periodically polarized lithium niobate (CPPLN) crystal for theoretical analysis and numerical design. The second-order nonlinear difference-frequency generation (DFG) process is used to implement the generation of mid-infrared laser via CPPLN. In the differential frequency process, the pump light used is 800 nm in wavelength and the wavelength range of signal light is 0.95–1.6 <inline-formula><tex-math id="M2">\begin{document}${\text{μm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M2.png"/></alternatives></inline-formula>. By calculating the dispersion curve of CPPLN crystal, the phase mismatch of difference frequency generation processes with different light signals is obtained. Under the condition of quasi-phase matching, the CPPLN with deliberately poling structures is designed and used to provide phase mismatch compensation in a broad bandwidth. The designed structure can meet the generation of mid infrared laser in a 1.6–5<inline-formula><tex-math id="M3">\begin{document}$ {\text{μm}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M3.png"/></alternatives></inline-formula> band according to the numerical simulations. The conversion efficiencies of mid-infrared laser with different wavelengths at different positions in the crystal are obtained by using nonlinear coupled wave equations and fourth-order Runge-Kutta method. The results show that the mid-infrared laser in a wavelength range of 1.6–5 <inline-formula><tex-math id="M4">\begin{document}$ {\text{μm}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220016_M4.png"/></alternatives></inline-formula> can be produced efficiently in a single CPPLN crystal, with an average conversion efficiency of about 15%. The theoretical analysis and numerical simulation for the designed CPPLN crystal can provide good schematic reference and theoretical support for further experimental exploration on generation of mid-infrared laser.