We introduce a new regime of cascaded quadratic nonlinearities which result in a continuous red shift of the optical pump, analogous to a Raman shifting process rather than self-phase modulation. This is particularly relevant to terahertz generation, where a continuous red shift of the pump can resolve current issues such as dispersion management and laser-induced damage. We show that in the absence of absorption or dispersion, the presented Raman shifting method will result in optical-to-terahertz energy conversion efficiencies that approach $100\%$ which is not possible with conventional cascaded difference-frequency generation. Furthermore, we present designs of aperiodically poled structures which result in energy conversion efficiencies of $\approx 35\%$ even in the presence of dispersion and absorption.
We explore the dynamics of a system where input spectra in the optical domain with very disparate center frequencies are strongly coupled via highly phase-matched, cascaded second-order nonlinear processes driven by terahertz radiation. The only requirement is that one of the input spectra contain sufficient bandwidth to generate the phase-matched terahertz-frequency driver. The frequency separation between the input spectra can be more than ten times larger than the phase-matched terahertz frequency. A practical application of such a system where the cascading of a narrowband pump line center…
Since the discovery of the laser, optical parametric nonlinearities have been at the core of efficient light conversion sources. Typically, thick transparent crystals or quasi-phase matched waveguides, are utilized in conjunction with phase-matching techniques to select a single parametric process. In recent years, due to the rapid developments in artificially structured materials, optical frequency mixing has been achieved at the nanoscale in subwavelength resonators arrayed as metasurfaces. Phase matching becomes relaxed for these wavelength-scale structures, and all allowed nonlinear proces…
We present an experimental study of optical frequency comb generation based on cascaded quadratic nonlinearities inside a continuous-wave-pumped optical parametric oscillator. We demonstrate comb states which produce narrow-linewidth intermode beat note signals, and we verify the mode spacing uniformity of the comb at the Hz level. We also show that spectral quality of the comb can be improved by modulating the parametric gain at a frequency that corresponds to the comb mode spacing. We have reached a high average output power of over 4 W in the near-infrared region, at ~2 μm.
We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest sol…
A highly efficient, practical approach to high-energy terahertz (THz) generation based on spectrally cascaded optical parametric amplification (THz-COPA) is introduced. The THz wave initially generated by difference frequency generation between a strong narrowband optical pump and optical seed (0.1-10% of pump energy) kick-starts a repeated or cascaded energy down-conversion of pump photons. This helps to greatly surpass the quantum-defect efficiency and results in exponential growth of THz energy over crystal length. In cryogenically cooled periodically poled lithium niobate, energy conversio…
Cascaded nonlinearities have attracted much interest, but ultrafast applications have been seriously hampered by the simultaneous requirements of being near phase-matching and having ultrafast femtosecond response times. Here we show that in strongly phase-mismatched nonlinear frequency conversion crystals the pump pulse can experience a large and extremely broadband self-defocusing cascaded Kerr-like nonlinearity. The large cascaded nonlinearity is ensured through interaction with the largest quadratic tensor element in the crystal, and the strong phase-mismatch ensures an ultrafast nonlinear…
We show that useful non-instantaneous nonlinear phase shifts can be obtained from cascaded quadratic processes in the presence of group velocity mismatch. The two-field nature of the process permits responses that can be effectively advanced or retarded in time with respect to one of the fields. There is an analogy to a generalized Raman-scattering effect, permitting both red and blue shifts of short pulses. We expect this capability to have many applications in short-pulse generation and propagation, such as the compensation of Raman-induced effects and high-quality pulse compression, which w…
Optical frequency combs are revolutionising modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturisation through microresonator-based solutions. The combs in such devices are typically generated using the third-order $χ^{(3)}$-nonlinearity of the resonator material. An alternative approach is making use of second-order $χ^{(2)}$-nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or o…
We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-$χ^{(2)}$ nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive-wave generation in the 2.5--3 $\textμ$m region and intra-pulse difference-frequency generation in the 4--5 $\textμ$m region. By engineering the quasi-phase-matched grating profiles, tunable, narrow-band MIR and broadband MIR spectra are both observed in this geometry. Final…
The use of laser pulse sequences to drive the cascaded difference frequency generation of high energy, high peak-power and multi-cycle terahertz pulses in cryogenically cooled periodically poled lithium niobate is proposed. Detailed simulations considering the coupled nonlinear interaction of terahertz and optical waves show that unprecedented optical-to-terahertz energy conversion efficiencies > 5%, peak electric fields of hundred(s) of Mega volts/meter at terahertz pulse durations of hundred(s) of picoseconds can be achieved. The proposed methods are shown to circumvent laser-induced damage …
Terahertz near fields of gold metamaterials resonant at a frequency of $0.88\,\rm THz$ allow us to enter an extreme limit of non-perturbative ultrafast THz electronics: Fields reaching a ponderomotive energy in the keV range are exploited to drive nondestructive, quasi-static interband tunneling and impact ionization in undoped bulk GaAs, injecting electron-hole plasmas with densities in excess of $10^{19}\,\rm cm^{-3}$. This process causes bright luminescence at energies up to $0.5\,\rm eV$ above the band gap and induces a complete switch-off of the metamaterial resonance accompanied by self-…
We present a method to measure quadratic Terahertz optical nonlinearities in Terahertz time-domain spectroscopy. We use a rotating linear polarizer (a polarizing chopper) to modulate the amplitude of the incident THz pulse train. We use a phase-sensitive lock-in detection at the fundamental and the second harmonic of the modulation frequency to separate the materials' responses that are linear and quadratic in Terahertz electric field. We demonstrate this method by measuring the quadratic Terahertz Kerr effect in the presence of the much stronger linear electro-optic effect in the (110) GaP cr…
We investigate the nonlinear effect of a planar superconducting metamaterial made from niobium nitride (NbN) at terahertz frequencies. As the variation of the incident intense terahertz field alters the intrinsic conductivity in the NbN, a consequent giant amplitude modulation is observed due to the strong nonlinearities. The high sensitivity of the chosen metamaterial even allows observing the nonlinear behaviors at various temperatures, but the resonance modulation induced by the nonlinear effect was distinct from that induced by the heating effect. The presented results illustrate a clever …
We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (\textit{i.e.}, the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an effective soliton number -- related to the difference between the SHG and the Kerr soliton numbers -- and show that it has to be larger than unity for successful…
We study the propagation of few-cycle optical solitary waves in a nonlinear media under the combined action of quadratic, cubic and quintic nonlinearities in a large phase-mismatched second harmonic (SHG) process. Exact bright and dark soliton solutions to the nonlinear evolution equation for cascaded quadratic media beyond the slowly varying envelope approximations is reported. The analytical solutions obtained are verified through numerical simulations.
Using system-reservoir methods to derive effective field theories for broadband nonlinear quantum optics: a case study on cascaded quadratic nonlinearities
We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find tha…
We present a theoretical description of the nonlinear response induced by an elliptically-polarized terahertz beam normally-incident on intrinsic and extrinsic metallic armchair graphene nanorib- bons. Our results show that using a straightforward experimental setup, it should be possible to observe novel polarization-dependent nonlinearities at low excitation field strengths of the or- der of 10 4 V/m. At low temperatures the Kerr nonlinearities in extrinsic nanoribbons persist to significantly higher excitation frequencies than they do for linear polarizations, and at room tem- peratures, th…
We study soliton pulse compression in materials with cascaded quadratic nonlinearities, and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible.
Highly efficient terahertz (THz) wave sources based on difference frequency generation (DFG) process in nonlinear optical crystals play an important role for the applications of THz wave. In order to find more novel nonlinear crystals, here we theoretically investigate the generation of THz wave using the isomorphs of periodically poled $\mathrm{KTiOPO_4}$ (PPKTP), including periodically poled RTP, KTA, RTA and CTA. By solving the cascaded difference frequency coupled wave equations, it is found that the intensities of the THz wave generated from the cascaded difference frequency processes are…
Third-harmonic generation can be realized via both $χ^{(3)}$ and cascaded $χ^{(2)}$ nonlinear processes in a triply-resonant microcavity. It is still unknown how these processes interfere with each other and the optimization of the conversion efficiency still remains as a question. In this work, the interplay between the direct third-harmonic generation and the cascaded process combining of the second-harmonic generation and the sum-frequency generation are investigated. It is found that the interference effect between these two processes can be used to improve the conversion efficiency. By op…
We show that 3D Dirac semimetals are promising candidates for highly efficient optical-to-terahertz conversion due to their extreme optical nonlinearities. In particular, we predict that the conversion efficiency of Cd3As2 exceeds typical materials like LiNbo3 by >5000 times over nanoscale propagation distances. Our studies show that even when no restrictions are placed on propagation distance, Cd3As2 still outperforms LiNbo3 in efficiency by >10 times. Our results indicate that by tuning the Fermi energy, Pauli blocking can be leveraged to realize a step-like efficiency increase in the optica…
Femtosecond laser pulses interacting with LiNbO3 has been widely applied in intense terahertz generation, excitation and imaging of phonon polaritons and modulating light. It is of great importance to study the nonlinearities induced by femtosecond laser pulses in LiNbO3. Here, we demonstrate that both Kerr nonlinearity and Kerr-like nonlinearity induced by terahertz wave occur under the interaction between laser pulses and LiNbO3 using optical pump-probe techniques. We show that the contribution of Kerr-like nonlinearity to pump-probe spectra varies with the interaction length because of the …
We demonstrate record conversion efficiencies of up to 0.9 percent for narrowband (1 percent relative bandwidth) THz generation by strongly-cascaded difference frequency generation. These results are achieved using a novel laser source, customized for high efficiencies, with two narrow spectral lines of variable separation and pulse duration (250 ps). THz generation in 5 percent MgO doped PPLN crystals of varying poling period was explored at cryogenic and room temperature operation as well as different crystal lengths. This work addresses an increasing demand for high-field THz pulses which h…
Optical frequency comb generation by continuous-wave-pumped cascaded quadratic nonlinearities (CQN) appears a promising alternative to well-established modelocked lasers, especially if access to the mid-infrared spectral region is needed. We report an experimental investigation of spectral properties of a CQN frequency comb, which is based on second-harmonic generation (SHG) and is pumped internally by a continuous-wave optical parametric oscillator. Our study focuses on SHG phase mismatch, which has drawn little attention in the previously reported CQN frequency comb research. The main observ…
When ultrafast noncritical cascaded second-harmonic generation of energetic femtosecond pulses occur in a bulk lithium niobate crystal optical Cherenkov waves are formed in the near- to mid-IR. Numerical simulations show that the few-cycle solitons radiate Cherenkov (dispersive) waves in the $λ=2.2-4.5\mic$ range when pumping at $λ_1=1.2-1.8\mic$. The exact phase-matching point depends on the soliton wavelength, and we show that a simple longpass filter can separate the Cherenkov waves from the solitons. The Cherenkov waves are born few-cycle with an excellent Gaussian pulse shape, and the con…
Silicon nitride (Si$_3$N$_4$) is an ever-maturing integrated platform for nonlinear optics. Yet, due to the absence of second-order ($χ^{(2)}$) nonlinearity, Si$_3$N$_4$ is mostly considered for third-order ($χ^{(3)}$) nonlinear interactions. Recently, this limitation was overcome by optical poling in both Si$_3$N$_4$ waveguides and microresonators via the photogalvanic effect, resulting in the inscription of quasi-phase-matched $χ^{(2)}$ gratings. Here, we report cascaded nonlinear effects in a normal dispersion Si$_3$N$_4$ microresonator with combined $χ^{(2)}$ and $χ^{(3)}$ nonlinearities. …
The majority of sources of coherent optical radiation rely on laser oscillators driven by population inversion. Despite their technological importance in communications, medicine, industry, and other fields, it remains a challenge to access the spectral range of 0.1-10 THz (the "terahertz gap"), a frequency band for applications ranging from spectroscopy to security and high-speed wireless communications. Here, we propose a way to produce coherent radiation spanning the THz gap by efficient second-harmonic generation (SHG) in low-loss dielectric structures, starting from technologically mature…
We investigate the optical Kerr nonlinearity and multi-photon absorption (MPA) properties of DSTMS excited by femtosecond pulses at a wavelengths of 1.43 μm, which is optimal for terahertz generation via difference frequency mixing. The MPA and the optical Kerr coefficients of DSTMS at 1.43 μm are strongly anisotropic indicating a dominating contribution from cascaded 2nd-order nonlinearity. These results suggest that the saturation of the THz generation efficiency is mainly related to the MPA process and to a spectral broadening caused by cascaded 2nd-order frequency mixing within DSTMS
Interactions of few-cycle terahertz pulses with the induced optical polarization in a quantum-well microcavity reveal that the lower and higher exciton-polariton modes together with the optically forbidden 2p-exciton state form a unique Λ-type three-level system. Pronounced nonlinearities are observed via time-resolved strong-terahertz and weak-optical excitation spectroscopy and explained with a fully microscopic theory. The results show that the terahertz pulses strongly couple the exciton-polariton states to the 2p-exciton state while no resonant transition between the two polariton levels …
The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which in this study is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatch between the pump and the second-harmonic waves. Therefore the potential for cascaded quadratic second-harmonic generation is investigated in particular for soliton compression of fs pulses. We found that excitation of temporal solitons from cascaded quadratic nonlinearities requires an effective quad…
Spatiotemporal nonlinear interactions in multimode fibers are of interest for beam shaping and frequency conversion by exploiting the nonlinear propagation of different pump regimes from quasi-continuous wave to ultrashort pulses centered around visible to infrared pump wavelengths. The nonlinear effects in multi-mode fibers depend strongly on the excitation condition, however relatively little work has been reported on this subject. Here, we present the first machine learning approach to learn and control the nonlinear frequency conversion inside multimode fibers by tailoring the excitation c…
Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and applic…
Ultrafast atomic vibrations mediate heat transport, serve as fingerprints for chemical bonds and drive phase transitions in condensed matter systems. Light pulses shorter than the atomic oscillation period can not only probe, but even stimulate and control collective excitations. In general, such interactions are performed with free-propagating pulses. Here, we demonstrate intra-cavity excitation and time-domain sampling of coherent optical phonons inside an active laser oscillator. Employing real-time spectral interferometry, we reveal that Terahertz beats of Raman-active optical phonons can …
We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength …
Heavily doped semiconductors have emerged as tunable low-loss plasmonic materials at mid-infrared frequencies. In this article we investigate nonlinear optical phenomena associated with high concentration of free electrons. We use a hydrodynamic description to study free electron dynamics in heavily doped semiconductors up to third-order terms, which are usually negligible for noble metals. We find that cascaded third-harmonic generation due to second-harmonic signals can be as strong as direct third-harmonic generation contributions even when the second-harmonic generation efficiency is zero.…
Nonlinear couplings between photons and electrons in new materials give rise to a wealth of interesting nonlinear phenomena. This includes frequency mixing, optical rectification or nonlinear current generation, which are of particular interest for generating radiation in spectral regions that are difficult to access, such as the terahertz gap. Owing to its specific linear dispersion and high electron mobility at room temperature, graphene is particularly attractive for realizing strong nonlinear effects. However, since graphene is a centrosymmetric material, second-order nonlinearities a prio…
Many applications in photonics require all-optical manipulation of plasma waves, which can concentrate electromagnetic energy on sub-wavelength length scales. This is difficult in metallic plasmas because of their small optical nonlinearities. Some layered superconductors support weakly damped plasma waves, involving oscillatory tunneling of the superfluid between capacitively coupled planes. Such Josephson plasma waves (JPWs) are also highly nonlinear, and exhibit striking phenomena like cooperative emission of coherent terahertz radiation, superconductor-metal oscillations and soliton format…
The output pulses of a commercial high-power femtosecond fiber laser or amplifier are typically around 300-500 fs with a wavelength around 1030 nm and 10s of $μ$J pulse energy. Here we present a numerical study of cascaded quadratic soliton compression of such pulses in LiNbO$_3$ using a type I phase matching configuration. We find that because of competing cubic material nonlinearities compression can only occur in the nonstationary regime, where group-velocity mismatch induced Raman-like nonlocal effects prevent compression to below 100 fs. However, the strong group velocity dispersion impli…
While two-dimensional (2D) materials have intriguing second-order nonlinearities with ultrahigh coefficient and electrical tunability, their atomic layer thicknesses hinder explorations of other optical frequency-conversions (OFCs) than second harmonic generation (SHG) due to inefficient light-coupling and unachievable phase-matching. We report, by resonantly pumping a photonic crystal cavity integrated with a few-layer GaSe, it is possible to realize multiple second-order nonlinear processes in GaSe even with microwatts continuous wave pumps, including SHGs, sum-frequency generations (SFGs), …
Although Gigahertz-scale free-carrier modulators have been previously demonstrated in silicon, intensity modulators operating at Terahertz speeds have not been reported because of silicon's weak ultrafast optical nonlinearity. We have demonstrated intensity modulation of light with light in a silicon-polymer integrated waveguide device, based on the all-optical Kerr effect - the same ultrafast effect used in four-wave mixing. Direct measurements of time-domain intensity modulation are made at speeds of 10 GHz. We showed experimentally that the ultrafast mechanism of this modulation functions a…
Optical properties of metallic nanoparticles are most often considered in terms of plasmons, the coupled states of light and quasi-free electrons. Here we predict that confinement of electrons inside the nanostructure leads to another, very different, type of resonance, which determines the optical properties in the frequency range significantly below the plasmonic resonance. We demonstrate that closely placed confinement-induces resonances typically join into a single composite "super-resonance" which produces giant nonlinearity at low frequencies. Our simulations show how such nonlinearities…
Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystal like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal pumped in the mid-IR gives multiple-octave spanning supercontinua. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source…
Experimental data of femtosecond thick-crystal second-harmonic generation shows that when tuning away from phase matching, a dominating narrow spectral peak appears in the second harmonic that can be tuned over 100's of nm by changing the phase-mismatch parameter. Traditional theory explains this as phase matching between a sideband in the broadband pump to its second-harmonic. However, our experiment is conducted under high input intensities and instead shows excellent quantitative agreement with a nonlocal theory describing cascaded quadratic nonlinearities. This theory explains the detuned …
In the last three decades or so, we have witnessed an extraordinary progress in the research and technology of carbon-based nanomaterials. Among the peculiar highlights are the discoveries of fullerene, the carbon nanotubes and the magnificent simple scotch tape exfoliated graphene. The unique photophysical properties of these different allotropic forms of the nanocarbon have opened up vast application possibilities in many fields of science and technology, with particular emphasis on optoelectronics and photonics. A prerequisite for many of these applications is a thorough understanding of th…
Metasurfaces control optical wavefronts via arrays of nanoscale resonators laid out across a surface. When combined with III-V semiconductors with strong optical nonlinearities, a variety of nonlinear effects such as harmonic generation and all optical modulation can be enabled and enhanced at the nanoscale. This review presents our research on engineering and boosting nonlinear effects in ultrafast and nonlinear semiconductor metasurfaces fabricated at the Center for Integrated Nanotechnologies (CINT). We cover our recent works on parametric generation of harmonic light via direct and cascade…
Second-order optical nonlinearities can be greatly enhanced by orders of magnitude in resonantly excited nanostructures, theoretically predicted and experimentally investigated in a variety of semiconductor systems. These resonant nonlinearities continually attract attention, particularly in newly discovered materials, but tend not to be as efficient as currently predicted. This limits their exploitation in frequency conversion. Here, we present a clear-cut theoretical and experimental demonstration that the second-order nonlinear susceptibility can vary by orders of magnitude as a result of g…
Terahertz (THz) generation by optical rectification (OR) using tilted-pulse-fronts is studied. One-dimensional (1-D) and 2-D spatial models, which simultaneously account for (i) the nonlinear coupled interaction of the THz and optical radiation, (ii) angular and material dispersion, (iii) absorption, iv) self-phase modulation and (v) stimulated Raman scattering are presented. We numerically show that the large experimentally observed cascaded frequency down-shift and spectral broadening (cascading effects) of the optical pump pulse is a direct consequence of THz generation. In the presence of …
