Nonlinear Wave-mixing Processes Research Articles

Localized Alfvén wave current drive in axisymmetric toroidal geometry

We develop the theory of the production of a steady state current in the Alfvén resonance region for an incompressible resistive plasma in axisymmetric toroidal geometry. We discover the existence of a net total current associated with externally excited Alfvén waves. The physics of the current generation lies within a dynamo mechanism, which assumes the form of a nonlinear wave mixing process caused by the plasma medium nonlinearities. The efficiency of the current drive is high and comparable to ohmic and the position of the current can be controlled externally. Therefore, Alfvén waves can be successfully used to modify existing current profiles in order to improve confinement in nuclear fusion reactors. In the process of deriving the current drive theory, we analytically solve the linearized equations of resistive MHD in a boundary layer about the Alfvén resonance surface.

Infrared upconversion imaging in nonlinear metasurfaces

Infrared imaging is a crucial technique in a multitude of applications, including night vision, autonomous vehicles navigation, optical tomography, and food quality control. Conventional infrared imaging technologies, however, require the use of materials like narrow-band gap semiconductors which are sensitive to thermal noise and often require cryogenic cooling. Here, we demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas, using a nonlinear wave-mixing process. We experimentally show the up-conversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation. In this process, an infrared image of a target is mixed inside the metasurface with a strong pump beam, translating the image from infrared to the visible in a nanoscale ultra-thin imaging device. Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences.

Hybridization of circular and rectangular transverse profiles of nanophotonic modes for nonlinear optics.

Nanophotonic modes within rectangular cross sections are typically considered to have transverse rectangular field profiles. In this work, we show that, despite the rectangular cross section of most integrated waveguides and microring resonators, there exists considerable hybridization of transverse rectangular modes and transverse circular modes. These hybridized modes can be advantageous in nonlinear wave mixing processes. We use third-harmonic generation as an example to confirm that such a hybridized mode is advantageous in combining reasonable mode overlap and waveguide coupling to a fundamental mode in a silicon nitride microring. Our work illuminates the potential of using transverse circular modes in nanophotonic applications.

Second harmonic generation in gallium phosphide nano-waveguides.

We designed, fabricated and tested gallium phosphide (GaP) nano-waveguides for second harmonic generation (SHG). We demonstrate SHG in the visible range around 655 nm using modal phase matching. We observe phase matched SHG for different combinations of interacting modes by varying the widths of the waveguides and tuning the wavelength of the pump. We achieved a normalized internal SHG conversion efficiency of 0.4% W-1cm-2 for a continuous-wave pump at wavelength of 1283.5 nm, the highest reported in the literature for a GaP waveguide. We also demonstrated temperature tuning of the SHG wavelength with a slope of 0.17 nm/°C. The presented results contribute to the development of integrated photonic platforms with efficient nonlinear wave-mixing processes for classical and quantum applications.

Higher radial orders of Laguerre–Gaussian beams in nonlinear wave mixing processes

We generalize the study of Laguerre–Gaussian beams in nonlinear wave mixing processes, considering optical beams with both integer azimuthal and non-null radial mode index as input modes combined in the nonlinear crystal. Here, we present a deeper discussion of the generation of higher radial orders through a nonlinear wave mixing process leading to a more complete understanding of the nonlinear process considered.

Phase-matched nonlinear wave-mixing processes in XUV region with multicolor lasers.

We report here experimental results of perturbative nonlinear optical wave-mixing processes in the extreme ultraviolet region by using two-color and three-color laser fields. Besides the usual odd-harmonic spectrum of high harmonic generation, new spectral components are observed when multiple incommensurate lasers (one driving plus one or two control field) interact with neutral krypton gas. To demonstrate the wave-mixing process underlying such an observation, we first couple the driving field with either the signal or the idler field of an optical parametric amplifier in the gaseous ensemble to generate certain mixing frequencies. The two control fields are then simultaneously combined with the driving field to produce broad and distinguishable mixing peaks that clearly reveal the contribution of each control laser. Finally, the variation of the intensity of the mixing waves with the intensity of each control field, the gas density, and the relative focus position is examined for signatures of phase-matched generation of the mixing fields in this spectral region.

Invited Article: Distributed analysis of nonlinear wave mixing in fiber due to forward Brillouin scattering and Kerr effects

Forward stimulated Brillouin scattering (F-SBS) is a third-order nonlinear-optical mechanism that couples between two co-propagating optical fields and a guided acoustic mode in a common medium. F-SBS gives rise to nonlinear wave mixing along optical fibers, which adds up with four-wave mixing induced by the Kerr effect. In this work, we report the distributed mapping of nonlinear wave mixing processes involving both mechanisms along standard single-mode fiber, in analysis, simulation, and experiment. Measurements are based on a multi-tone, optical time-domain reflectometry setup, which is highly frequency-selective. The results show that F-SBS leads to nonlinear wave mixing processes that are more complex than those that are driven by the Kerr effect alone. The dynamics are strongly dependent on the exact frequency detuning between optical field components. When the detuning is chosen near an F-SBS resonance, the process becomes asymmetric. Power is coupled from an upper-frequency input pump wave to a lower-frequency one, and the amplification of Stokes-wave sidebands is more pronounced than that of anti-Stokes-wave sidebands. The results are applicable to a new class of distributed fiber-optic sensors, based on F-SBS.

Nonlinearity-induced PT-symmetry without material gain

Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.

Dispersionless gaps and cavity modes in photonic crystals containing hyperbolic metamaterials

We theoretically study dispersionless gaps and cavity modes in one-dimensional photonic crystals composed of hyperbolic metamaterials and dielectric. Bragg gaps in conventional all-dielectric photonic crystals are always dispersive because propagating phases in two kinds of dielectrics decrease with incident angle. Here, based on phase variation compensation between a hyperbolic metamaterial layer and an isotropic dielectric layer, the dispersion of the gap can be offset and thus a dispersionless gap can be realized. Moreover, the dispersionless property of such gap has a wide parameter space. The dispersionless gap can be used to realize a dispersionless cavity mode. The dispersionless gaps and cavity modes will possess significant applications for all-angle reflectors, high-$Q$ filters excited with finite-sized sources, and nonlinear wave mixing processes.

Plasmon-Enhanced Nonlinear Wave Mixing in Nanostructured Graphene

Localized plasmons in metallic nanostructures have been widely used to enhance nonlinear optical effects due to their ability to concentrate and enhance light down to extreme-subwavelength scales. As alternatives to noble metal nanoparticles, graphene nanostructures can host long-lived plasmons that efficiently couple to light and are actively tunable via electrical doping. Here we show that doped graphene nanoislands present unique opportunities for enhancing nonlinear optical wave-mixing processes between two externally applied optical fields at the nanoscale. These small islands can support pronounced plasmons at multiple frequencies, resulting in extraordinarily high wave-mixing susceptibilities when one or more of the input or output frequencies coincide with a plasmon resonance. By varying the doping charge density in a nanoisland with a fixed geometry, enhanced wave mixing can be realized over a wide spectral range in the visible and near infrared. We concentrate in particular on second- and third-order processes, including sum and difference frequency generation, as well as on four-wave mixing. Our calculations for armchair graphene triangles composed of up to several hundred carbon atoms display large wave mixing polarizabilities compared with metal nanoparticles of similar lateral size, thus supporting nanographene as an excellent material for tunable nonlinear optical nanodevices.

Optical switching of optomechanically induced transparency and normal mode splitting in a double-cavity system

We study a double-cavity optomechanical system where an in-between membrane oscillator is shared by two identical cavities. Two relevant cavity modes experience the optomechanical coupling of same amplitudes but opposite signs when the membrane deviates from its equilibrium position due to radiation pressure. We demonstrate in theory efficient manipulations of optomechanically induced transparency in the weak coupling regime and normal mode splitting in the strong coupling regime via nonlinear wave-mixing processes. It is found that both absorptive and dispersive behaviors of the output probe field can be well controlled to switch between two different steady states by applying a coupling field and a driving field in separate cavities. This optomechanical switching scheme works in both coupling regimes and may be extended to develop new devices of light routing, conversion, delay, and isolation.

Third-harmonic generation in resonant-metamaterial-based photonic-band-gap materials

We present large enhancement of the nonlinear wave mixing process (third-harmonic generation) in photonic-band-gap materials made of negative and positive index media, at the band edge of the zero-$\overline{n}$ band gap. Incorporating metamaterial-based, electromagnetically induced transparency (EIT)--like resonance in the nonlinear layer leads to unprecedented line narrowing of the generated third harmonic. This scheme permits the mapping of the narrow EIT resonance at the fundamental frequency to the generated third-harmonic frequency with even narrower line shape.

Bichromatic field generation from double-four-wave mixing in a double-electromagnetically induced transparency system

We demonstrate double electromagnetically induced transparency (double-EIT) and double four-wave mixing (double-FWM) based on a new scheme of non-degenerate four-wave mixing (FWM) involving five levels of a cold 85Rb atomic ensemble, in which the double-EIT windows are used to transmit the probe field and enhance the third-order nonlinear susceptibility. The phase-matching conditions for both four-wave mixings can be satisfied simultaneously. The frequency of one component of the generated bichromatic field is less than the other by ground-state hyperfine splitting (3 GHz). This specially designed experimental scheme for simultaneously generating different nonlinear wave-mixing processes is expected to find applications in quantum information processing and cross-phase modulation. Our results agree well with the theoretical simulation.

Slow and fast light: basic concepts and recent advancements based on nonlinear wave‐mixing processes

AbstractAfter a review of the basic concepts of slow and fast light, recent advancements based on nonlinear wave‐mixing processes are described. As a nonlinear medium, the authors focus on a liquid crystal light valve showing that it allows obtaining a large control of the group delay, with a maximum fractional delay of 1, and a deceleration of light pulses down to group velocities as small as 0.2 mm/s. A theoretical model accompanies the observations and accounts for them in the general framework of two‐wave mixing in the light valve. At the end, a high‐sensitivity interferometer is presented as an example of slow light applications.

Broad angle phase matching in subdiffractive photonic crystals

We show that photonic crystals made of materials with normal dispersion allow broad angular range phase matching in nonlinear wave mixing processes if tuned to the subdiffractive (or equivalently self-collimated) beam propagation regimes for the frequencies of both interacting waves. This allows efficient parametric mixing of narrow beams. We demonstrate this idea by numerical simulation of the second harmonic generation in two-dimensional photonic crystal in particular nonlinear material (AlGaAs) in planar waveguide geometry.

Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals

We present experimentally the control of free space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process in an asymmetrically poled nonlinear photonic crystal. Changing the quasi-phase matching conditions, e.g., the crystal temperature or pump wavelength, alters the location of the Airy beam peak intensity along the same curved trajectory. We explain that the variation in the beam shape is caused by noncollinear interactions. Owing to the highly asymmetric shape of nonlinear crystal in the Fourier space, these noncollinear interactions are still relatively efficient for positive (nonzero) phase mismatch.

SLOW AND FAST LIGHTS WITH MOVING AND STATIONARY REFRACTIVE INDEX GRATINGS IN SOLIDS AT ROOM TEMPERATURE

We reviewed the recent progress on slow and fast lights in solids at room temperature based on moving and stationary refractive index gratings. A dispersive photorefractive phase coupling associated with moving gratings results in slow and fast lights. In principle, such phase-coupling-induced slow and fast lights can be observed in any nonlinear wave mixing process with a dispersive phase coupling effect. The slow and fast lights in the stationary gratings are also discussed. One advantage of the stationary gratings is the possibility to engineer the dispersion slope of the grating through designing the grating structure and parameters. As an example, we show that the dispersion slope of the gratings is enhanced significantly by stratifying a series of identical volume index gratings with homogeneous optical buffer layers sandwiched between every two neighboring grating layers. The slow and fast lights, therefore, can be controlled more effectively in such specifically designed grating structures than in the homogeneous gratings. Another advantage is the high transparency of the slow and fast lights with appropriate grating structure and parameters. Issues such as the pulse broadening effect and the pulse distortion are addressed. The slow and fast light techniques have many important potential applications such as optical delay lines and optical buffers.

Causal versus noncausal description of nonlinear wave mixing: Resolving the damping-sign controversy

Frequency-domain nonlinear wave mixing processes may be described either using response functions, whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are treated symmetrically with no specific time ordering. Closed Green's function expressions derived for the two types of signals have different analytical properties. The recent controversy regarding the sign of radiative damping in the linear (Kramers-Heisenberg) formula is put in a broader context.

Nonlinear wave-mixing processes in the extreme ultraviolet

We present data from two-color high-order harmonic generation in a hollow waveguide, that suggest the presence of a nonlinear-optical frequency conversion process driven by extreme ultraviolet light. By combining the fundamental and second harmonic of an $800\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ laser in a hollow-core fiber, with varying relative polarizations, and by observing the pressure and power scaling of the various harmonic orders, we show that the data are consistent with a picture where we drive the process of high-harmonic generation, which in turn drives four-wave frequency mixing processes in the extreme EUV. This work promises a method for extending nonlinear optics into the extreme ultraviolet region of the spectrum using an approach that has not previously been considered, and has compelling implications for generating tunable light at short wavelengths.

Phase-Coupling-Induced Ultraslow Light Propagation in Solids at Room Temperature

We show that the group velocities of light pulses can be decelerated dramatically by the use of a dispersive phase-coupling effect through a wave mixing process. We have observed experimentally such a phase-coupling-induced ultraslow light propagation with a group velocity as low as 0.05 m/s in a photorefractive Bi12SiO20 crystal at room temperature. Moreover, the ultraslow light is amplified in the Bi12SiO20 crystal because of the unidirectional energy transfer from a coupling beam to the ultraslow light. This technique to produce ultraslow light propagation is valid for all nonlinear wave mixing processes with a dispersive phase-coupling effect.