Difference Frequency Generation Research Articles

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators.

We conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

Sub-attosecond-precision optical-waveform stability measurements using electro-optic sampling

The generation of laser pulses with controlled optical waveforms, and their measurement, lie at the heart of both time-domain and frequency-domain precision metrology. Here, we obtain mid-infrared waves via intra-pulse difference-frequency generation (IPDFG) driven by 16-femtosecond near-infrared pulses, and characterise the jitter of sub-cycle fractions of these waves relative to the gate pulses using electro-optic sampling (EOS). We demonstrate sub-attosecond temporal jitter at individual zero-crossings and sub-0.1%-level relative amplitude fluctuations in the 10-kHz–0.625-MHz band. Chirping the nearly-octave-spanning mid-infrared pulses uncovers wavelength-dependent attosecond-scale waveform jitter. Our study validates EOS as a broadband (both in the radio-frequency and the optical domains), highly sensitive measurement technique for the jitter dynamics of optical waveforms. This sensitivity reveals outstanding stability of the waveforms obtained via IPDFG and EOS, directly benefiting precision measurements including linear and nonlinear (infrared) field-resolved spectroscopy. Furthermore, these results form the basis toward EOS-based active waveform stabilisation and sub-attosecond multi-oscillator synchronisation/delay tracking.

Simultaneous transmission of multi-format signals in the mid-infrared over free space

Mid-infrared (MIR) light within the 3–5 μm spectrum offers distinct advantages over the 1.5 μm band, particularly in adverse atmospheric conditions, rendering it a favorable option for free-space optical (FSO) communication. The transmission capacity within the 3–5 μm band is relatively low due to the immature state of its devices. In this study, we demonstrate multi-format signals FSO transmission with a total of 40 Gbps capacity in the 3 μm band, utilizing our developed MIR transmitter and receiver modules. These modules facilitate wavelength conversion between the 1.5 μm and 3 μm bands through the utilization of difference-frequency generation (DFG) effect. The MIR transmitter effectively produces three MIR signals: On-Off Keying (OOK), Binary Phase Shift Keying (BPSK), and Quadrature Phase Shift Keying (QPSK) optical signals. The generated MIR power is 7.8 dBm, covering a wavelength range from 3.5864 to 3.5885 μm. The MIR receiver regenerates the three format signals with a power of −29.6 dBm. Relevant results of regenerated signal demodulation have been collected in detail, including bit error ratio (BER), constellation diagram, and eye diagram. The required powers for the 10 Gbps OOK, BPSK, and QPSK are −37.82, −40.24, and −39.4 dBm at BER of 1 × 10−6. It is expected to further push the data capacity to the terabit-per-second level by adding more 1.5 μm band laser sources and using wider-bandwidth chirped nonlinear crystals.

Long-wavelength infrared upconversion time-stretch spectroscopy

High-speed spectroscopy in the molecular fingerprint spectral region (≈6–12 μm) is essential for the detection of ultrafast molecular dynamic processes, rapid combustion analysis, and biological diagnostics. However, ultrafast spectroscopy in the long-wavelength infrared (LWIR) region remains a challenge due to the limitations of laser sources and the lack of ultrafast and sensitive detectors in this wavelength region. Here, we demonstrate broadband LWIR time-stretch spectroscopy, which can realize a single-shot high-speed spectral measurement in a 8–10 μm region, by combining the LWIR femtosecond (fs) light generation and upconversion time-stretching detection with specific dispersive fiber. Broadband tunable fs light generated in the 8–10 μm region is upconverted to the 1.1–1.2 μm near-infrared wavelength via difference-frequency generation with the 1 μm chirped pump pulse. Time-stretch detection of the upconverted light can then be realized by adopting dispersion shifted fiber, which has a superior dispersion-to-loss ratio in the 1.1–1.2 μm wavelength region, as the dispersive medium. As a result, we experimentally demonstrate LWIR time-stretch spectroscopy in the 8–10 μm region with a spectral resolution of 1.07 cm−1, at a rate of 200 kSpectra s−1, which is only limited by the repetition rate of the 1 μm pump source. The demonstration of high-speed time-stretch spectroscopy in the LWIR region would open the possibility in exploring the transient dynamics of molecular fingerprint spectroscopy.

Concurrent phase-matchings for multi-wavelength conversion in coupled dual waveguides

Thin film lithium niobate, as a highly promising integrated photonics platform, has emerged as an ideal material platform for wavelength conversion owing to its exceptional second-order nonlinear characteristics. Here, we present the first demonstration of concurrent phase-matchings for multi-wavelength conversion in coupled thin film lithium niobate waveguides without poling technique. In the coupled dual waveguide system, employing modal phase-matching, we validate three effective phase-matching conditions for second harmonic generation, arising from additional momentum compensation due to the coupling of waveguides. Simultaneously, we confirm that phase-matching wavelengths can be tuned by adjusting the gap between waveguides. The concurrent phase-matchings in coupled dual waveguide systems can be readily extended to other nonlinear optical processes, such as difference frequency generation and spontaneous parametric down conversion. Our work contributes to advancing the exploration of efficient on-chip nonlinear optical processes within the realms of nanophotonics and quantum optics.

Time-resolved ARPES with probe energy of 6.0 eV and tunable MIR pump at 250 kHz

In this paper, we present a laser source designed specifically for time- and angle-resolved photoemission spectroscopy (TR-ARPES) investigations of light-induced electron dynamics in quantum materials. Our laser source is based on a ytterbium-doped laser that seeds an optical parametric amplifier (OPA) followed by a difference frequency generation (DFG) stage. This configuration enables the generation of tunable near-infrared and mid-infrared laser pulses (1.5 to 8 μm - 0.82 to 0.15 eV) at 250 kHz of repetition rate, serving as the pump for TR-ARPES measurements. The remaining energy of the laser is used to generate the ultraviolet 6 eV probe pulses, which prompt the material to emit photoelectrons. We demonstrate the long-term stability of the source, as well as the characterization of the beam profiles and pulse durations. Additionally, we present preliminary TR-ARPES results obtained on Bi2Te3, a prototypical 3D topological insulator. This paper illustrates the capability of our laser source to probe electronic dynamics in quantum materials.

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.

Programmable generation of counterrotating bicircular light pulses in the multi-terahertz frequency range

The manipulation of solid states using intense infrared or terahertz light fields is a pivotal area in contemporary ultrafast photonics research. While conventional circular polarization has been well explored, the potential of counterrotating bicircular light remains widely underexplored, despite growing interest in theory. In the mid-infrared or multi-terahertz region, experimental challenges lie in difficulties in stabilizing the relative phase between two-color lights and the lack of available polarization elements. Here, we successfully generated phase-stable counterrotating bicircular light pulses in the 14–39 THz frequency range circumventing the above problems. Employing spectral broadening, polarization pulse shaping with a spatial light modulator, and intra-pulse difference frequency generation leveraging a distinctive angular-momentum selection rule within the nonlinear crystal, we achieved direct conversion from near-infrared pulses into the designed counterrotating bicircular multi-terahertz pulses. Use of the spatial light modulator enables programmable control over the shape, orientation, rotational symmetry, and helicity of the bicircular light field trajectory. This advancement provides a novel pathway for the programmable manipulation of light fields, and marks a significant step toward understanding and harnessing the impact of tailored light fields on matter, particularly in the context of topological semimetals.

Background-free mid-infrared absorption spectroscopy using sub-cycle pulses

We have demonstrated highly sensitive single-shot based background-free mid-infrared (MIR) absorption spectroscopy using sub-cycle MIR pulses generated through filamentation. The MIR pulse transmitted through a sample was upconverted with a fast rising and long tailing gate pulse through four-wave difference frequency generation in a silicon membrane. By recording the upconverted spectrum of the free induction decay alone, we successfully measured the absorption spectrum as a positive signal in the wavenumber range from 500 to 4500 cm−1, which covers both the fingerprint and functional group regions. We obtained an absorption spectrum of ∼50 mM of aqueous glucose, which is not detectable with a standard Fourier transform infrared spectrometer.

Nonlinear upconverted thermal emission through difference frequency generation.

Thermal radiation management is of critical importance in energy, sensing, and heat transfer. According to Planck's law, objects at room temperature predominantly emit thermal radiation within the mid- and far-infrared bands. Here, we demonstrated the upconversion of the mid- and far-infrared thermal radiation emitted by second-order nonlinear material to the easily-detectable visible band through a difference frequency process. This nonlinear broad-spectrum upconversion is facilitated by the random quasi-phase-matching technique in the nanoparticle system. Furthermore, we show the temperature measurement of thermal spots using such nonlinear thermal radiation. This scheme paves the way for applications in thermal management and sensing.

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

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

Peregrine solitons and resonant radiation in cubic and quadratic media.

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

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

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

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

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

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

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

Characterizing mid-infrared micro-ring resonator with frequency conversion

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

Mid-infrared computational temporal ghost imaging

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

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

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

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

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

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

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