Nonlinear Difference Frequency Generation Research Articles

Numerical study of tunable terahertz radiation from differential frequency generation in high-<i>Q</i> geometrically perturbed grating waveguide structures

Nonlinear difference frequency generation (DFG) is a key mechanism for realizing terahertz (THz) sources. Utilization of DFG within micro- and nano-structures can circumvent the phase-matching limitations while supporting device miniaturization and integrability, thus the DFG is made a significant area of research. Enhancing the local electric fields through resonant modes in micro- and nano-structures has become a promising approach to achieving efficient and tunable THz sources across a broad wavelength range. In this work, the mechanism of DFG in high-Q-factor grating-waveguide structures for efficientlytuning THz radiation over a wide spectral range is investigated by using numerical simulations based on the finite element method (COMSOL Multiphysics). Theoretical analysis reveals that modulating the positional perturbation of one of the adjacent gratings effectively doubles the grating period, causing Brillouin zone to fold. This folding shifts the dispersion curve of the guided mode (GM) within the waveguide layer above the light cone, forming a guided mode resonance (GMR) with an ultra-high Q-factor, thereby significantly enhancing THz generation in a broad spectral range. Taking a cadmium sulfide (CdS) grating-waveguide structure for example, numerical simulations demonstrate that the THz conversion efficiency reaches an order of 10<sup>–8</sup>W<sup>–1</sup> when both fundamental frequency beams have an intensity of 100 kW/cm<sup>2</sup>, which is 10<sup>9</sup> times higher than the conversion efficiency of a CdS film of the same thickness. Moreover, the fundamental frequency resonance wavelength can be widely tuned by adjusting the incident angle. High-Q-factor resonance modes enable various fundamental frequency combinations by changing the incident angles of the two fundamental frequency beams, facilitating the generation of THz waves with arbitrary frequencies. This approach ultimately enables a highly efficient and tunable THz source in a wide spectral range, providing valuable insights for generating THz sources on micro- and nanophotonic platforms.

Precise passive synchronization of dissipative soliton resonance lasers via cascaded cross-phase- and cross-absorption-modulation for mid-infrared mode-locked pulse generation

We present the first demonstration of utilizing cascaded cross-phase and cross-absorption modulation effects for synchronizing the pulse parameters of two mode-locked fiber lasers operating in the dissipative soliton resonance regime. By utilizing the cross-absorption modulation effect we achieve a significant improvement in pulse repetition frequency synchronization dynamic range (13.5 cm cavity optical path mismatch, or 1.87 kHz pulse repetition frequency mismatch) while simultaneously achieving passive pulse duration synchronization through injection of synchronization pulses into the gain fiber of one of the Slave lasers. This approach leads to a record pulse repetition frequency synchronization dynamic range. Subsequently, the synchronized DSR lasers at 1.06 µm and 1.56 µm are employed in a nonlinear difference frequency generation stage to generate mode-locked mid-infrared pulses with a pulse repetition rate of ∼ 2 MHz and an exceptional fractional instability of 3.60 × 10-13, measured for a 1000 s integration time.

Digitally generated high-resolution mid-infrared dual-comb spectroscopy system based on electro-optic modulation.

In this Letter, we propose a high-resolution dual-comb spectroscopy (DCS) in the mid-infrared (MIR) region. A broadband electro-optic frequency comb (EOFC) with a line spacing of 13 GHz is generated in the near-infrared region. The injection locking technique is employed to lock the distributed feedback (DFB) laser to each comb line of the 34 comb lines as the seed laser for the subsequent electro-optic modulation. A dual radio frequency (RF) comb source with a 50 MHz line spacing and a 13 GHz bandwidth drives a single IQ Mach-Zehnder modulator (IQ-MZM), functioning as a single-sideband (SSB) generator and producing a DCS with high spectrum flatness and resolution flexibility. The generated DCS is converted to the MIR region via a nonlinear difference frequency generation (DFG) system. A DCS with a bandwidth of 442 GHz and a resolution of 50 MHz is achieved in the 3.3 µm region, and the figure of merit reaches 2.94×106 H z 12 in a 183.6 ms measurement time.

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.

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.

Generation of terahertz waves based on nonlinear frequency conversion with stimulated Raman adiabatic passage.

In recent years, high-power, tunable terahertz (THZ) radiation sources have become the key areas of research in the world. The method of THZ waves by nonlinear optical difference frequency generation (DFG) has the advantages of wide tuning, high power, room temperature operation, and compact structure. However, the conversion efficiency of the current difference frequency method is low, which needs a trade-off between conversion efficiency and tuning range. We apply the nonlinear optical cascade difference frequency conversion theory based on stimulated Raman adiabatic passage (STIRAP) and propose a theoretical scheme to generate THZ waves. Numerical simulation investigates the cascaded difference frequency process of generating THZ waves with the help of the nonlinear medium lithium niobate (LN) crystal. The theoretical analysis shows that the maximum quantum conversion efficiency from signal laser to THZ waves is 43.2 % when the wavelength of the tuned signal laser varies between 1.044 - 1.065 µm with the fixed two pump laser wavelengths constant. The tunable THZ waves of 0.48 - 5.0 THz can be obtained and the maximum output intensity of THZ waves is 2.17 MW/cm2, and the method is robust to temperature variations. It also provides a novel idea for the cascaded difference frequency generation of THZ waves.

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.

Optics-to-THz conversion of vortex beams using nonlinear difference frequency generation

In this paper, using a modified model of slowly varying amplitudes, a process of optics-to-THZ-conversion of vortex beams based on the nonlinear difference frequency generation in a medium with second-order susceptibility is considered. A theoretical substantiation of the law of topological charge conversion of vortex beams is given – the topological charge of the output THz vortex beam is equal to the difference of the topological charges of the input optical vortex beams. A simulation model of the processes under consideration is implemented.

Passively Q switched dual channel Tm:YLF laser by intracavity spectral beam combination with volume Bragg gratings.

A novel dual channel Tm:YLF laser system was developed where two degenerate laser cavities were coupled by spectrally beam combining their emission and by implementing a common output coupler. Under continuous wave running conditions, each channel's slope efficiency was greater than 45% and the maximum combined output power was 11 W. Passive Q-switching was achieved using an 80%, Cr:ZnSe saturable absorber. The output pulses had a maximum energy of 5.8 mJ and duration of 90 ns (~65 kW of peak power) at 5.7 W of absorbed pump power. Each channel showed less than 1 nm of spectral width with central wavelengths around 1880 nm and 1908 nm correspondingly. The system had adjustable spectral difference between the channels ranging from 5 to 20 nm which corresponds to 0.4 - 1.7 THz if the system is used for nonlinear difference frequency generation.

Nonlinear negative refraction by difference frequency generation

Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here, we demonstrate theoretically and experimentally a scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin Beta barium borate slice serves as a negative refraction layer bending the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.

Toward Continuous-Wave Regime Teleportation for Light Matter Quantum Relay Stations

We report a teleportation experiment involving narrowband entangled photons at 1560 nm and qubit photons at 795 nm emulated by faint laser pulses. A nonlinear difference frequency generation stage converts the 795 nm photons to 1560 nm in order to enable interference with one photon out of the pairs, i.e., at the same wavelength. The spectral bandwidth of all involved photons is of about 25 MHz, which is close to the emission bandwidth of emissive quantum memory devices, notably those based on ensembles of cold atoms and rare earth ions. This opens the route towards the realization of hybrid quantum nodes, i.e., combining quantum memories and entanglement-based quantum relays exploiting either a synchronized (pulsed) or asynchronous (continuous- wave) scenario.

Terahertz wave generation by plasmonic-enhanced difference-frequency generation

We propose an efficient and compact plasmonic surface-enhanced terahertz generation scheme based on nonlinear difference-frequency generation inside a metal–insulator–metal structure. Gold nanowire arrays are planted on top of the surface of a lithium niobate (LN) substrate with second-order nonlinearity to enhance both the nonlinear wavelength conversion and waveguide terahertz waves at the same time. Our numerical simulations show that our structures are capable of generating both tunable continuous and ultrafast-pulsed terahertz sources. We also discuss further improvements on the conversion efficiency by combining with Ti-diffusing LN waveguides.

Efficient Nonlinear Generation of THz Plasmons in Graphene and Topological Insulators

Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation (DFG) of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a broad range of frequencies.

Investigation of high power terahertz emission in gap crystal based on collinear difference frequency generation

Among many terahertz wave generation methods, nonlinear optical collinear difference frequency generation (CDFG) is always regarded as a promising way to achieve the high power, broadband, continual tunable terahertz wave emission. Theoretical analysis shows that a big coherent length (on millimeter scale) in isotropic GaP crystal could be realized by the laser wavelength near 1064 nm in the CDFG process, which meets the condition of high power and broadband terahertz generation. In the experiment, a high power and broadband terahertz wave is achieved from GaP crystal, with its tunable terahertz range 95.9-773.4 μm (0.39-3.13 THz) and the highest terahertz peak power 7 W at 2 THz. The experimental result is generally consistent well with its theoretical calculation.

Nonlinear difference-frequency generation in the mid-infrared spectral range in waveguides with a modulated permittivity profile

A method for implementing quasi-phase matching for nonlinear difference-frequency generation in planar waveguides with a modulated permittivity profile is analyzed. For a pump wave power equal to 10 W, the difference-frequency wave power in the 11–24 μm wavelength range can be as high as 0.6 μW for edge output and 0.12 mW/mm2 for vertical output.

Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities

We present a comprehensive study of second-order nonlinear difference frequency generation in triply resonant cavities using a theoretical framework based on coupled-mode theory. We show that optimal "quantum-limited" conversion efficiency can be achieved at any pump power when the powers at the pump and idler frequencies satisfy a critical relationship. We demonstrate the existence of a broad parameter range in which all triply-resonant DFG processes exhibit monostable conversion. We also demonstrate the existence of a geometry-dependent bistable region.

Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production.

Cascaded nonlinear optical interactions are analyzed for their potential to overcome quantum-defect related limitations on the efficiency of terahertz wave difference-frequency generation. The dispersion of ZnTe permits phase-matched production of a series of Stokes lines from two initial near-infrared beams. As the pump beams run down the Stokes ladder, the number of terahertz photons continually increases. A potential improvement by a factor of 5 is demonstrated in a 0.26-cm-long crystal by use of 25-MW/mm2 pumps at a wavelength of 824 nm.

Quasi-phase-matched (QPM) difference frequency generation in a mirrorless counterpropagating configuration

We present a theoretical analysis of second-order nonlinear difference frequency generation (DFG) in a generalized mirrorless quasi-phase-matching (QPM) frame, aimed at a comparison of counterpropagating DFG configuration (CDFG) to other DFG schemes, in view of all-optical processing applications. Field nonlinear coupling equations have been numerically solved under the hypothesis of phase-matched interaction. The evolution of propagating fields within the material and the wavelength conversion efficiency have been calculated in dependence of operating parameters. The increased complexity in the evolution of amplitude and phase for fields interacting in CDFG with respect to forward-propagating DFG (FDFG) is at the basis of a dramatic increase in the wavelength conversion efficiency under particular settings of device parameters.

Evolution of classical light statistics in coherent difference-frequency generation

Classical solution of coherent nonlinear difference-frequency generation process based on the averaging of stochastic quantities over the initial photocount distributions in pump and signal input radiations is presented in this paper. The evolution of second-order light statistics in difference-frequency generation with coherent and chaotic input radiations is calculated for arbitrary values of the time or space parameter.

Third order nonlinear optical difference frequency generation in KH2PO4, TiO2, LiNbO3, CaCO3, ZnO and CdS

Third-order nonlinear optical susceptibilities of different crystals have been measured relative to LiNbO3 by observing collinear phase-matched difference frequency generationω1=2ω2−ω4. The two incident light waves have been produced by a ruby laser (ω2,λ2=694.3 nm) and by induced Raman scattering (ω4,λ4=765.8 nm). With noncollinear phase-matching the number of nonlinear processes and the possibilities to determine nonlinear coefficients is much larger than in the collinear case. Therefore the theory of Raman-type third order interactions has been extended to noncollinear propagation of the interacting waves. The theory has been tested experimentally for CdS.