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NASA NTRS1993

FD-TD modeling of 2-D dielectric waveguides for propagation and scattering of femtosecond optical solitons

Experimentalists have produced all-optical switches capable of 100-fs responses. To adequately model such switches, nonlinear effects in optical materials (both instantaneous and dispersive) must be included. In principle, the behavior of electromagnetic fields in nonlinear dielectrics can be determined by solving Maxwell's equations subject to the assumption that the electric polarization has a nonlinear relation to the electric field. However, until our previous work, the resulting nonlinear Maxwell's equations have not been solved directly. Rather, approximations have been made that result in a class of generalized nonlinear Schrodinger equations (GNLSE) that solve only for the envelope of the optical pulses. In this paper, we present first-time calculations from the vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional systems of dielectric waveguides exhibiting the Kerr and Raman quantum effects. We use the finite-difference time-domain (FD-TD) method in an extension of our 1-D work. There, in a fundamental innovation, we treated the linear and nonlinear convolutions for the electric polarization as new dependent variables. By differentiating these convolutions in the time domain, we derived an equivalent system of coupled, nonlinear second-order ODE's. These equations together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in inhomogeneous nonlinear dispersive media. Backstorage in time is limited to only that needed by the time-integration algorithm for the ODE's, rather than that needed to store the time-history of the kernel functions of the convolutions (1000-10,000 time steps). Thus, a 2-D nonlinear optics model from Maxwell's equations is now feasible.

Joseph, Rose↗

NASA NTRS1972

Research in nonlinear optics

A theoretical investigation revealed that a steady state mode-locked solution appropriate to ultrashort pulses is induced by Kerr liquids. An experimental investigation using a Q-switched ruby laser passively mode-locked by the insertion of a Kerr liquid verified the theory. Pulses of about 10 to the -11th power sec were generated when the relaxation time of the liquid was temperature tuned to approximately 10 to the -11th power sec.

Yariv, A.↗

NASA NTRS1992

Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons

The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.

Goorjian, Peter M.↗

NASA NTRS1994

Numerical Simulations of Light Bullets, Using the Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗

NASA NTRS1994

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Goorjian, Peter M.↗

DOE OSTI2022

Enhanced stimulated Raman scattering during intense laser propagation

Stimulated Raman scattering is ubiquitous in many high-intensity laser environments. Parametric four-wave mixing between the pump and Raman sidebands can affect the Raman gain, but stringent phase matching requirements and strongly nonlinear dynamics obscure clear understanding of its effects at high laser powers. Here we investigate four-wave mixing in the presence of strong self-focusing and weak ionization at laser powers above the Kerr critical power. Theoretical analysis shows that the plasma generated at focus naturally leads to phase matching conditions suitable for enhanced Raman gain, almost without regard to the initial phase mismatch. Multidimensional nonlinear optical simulations with multiphoton and collisional ionization confirm the enhancement and suggest that it may lead to significantly higher Raman losses in some high-intensity laser environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗

DOE OSTI2026

Propagation of partially spatially coherent laser beams in instantaneous Kerr media

The propagation of intense, partially spatially coherent laser beams in a medium with instantaneous third-order susceptibility is studied analytically and numerically. For sufficiently high power relative to that required for nonlinear self-focusing, the propagation initially proceeds in two stages. In the first stage, spatial coherence builds up, and in the second stage, the number of speckles reduces. Once the degree of coherence is sufficiently high, whole-beam self-focusing occurs. The beam power is mostly confined within the initial spot radius. Two analytical approaches for describing the evolution of the beam are presented. The method of moments leads to an analytical solution for the rms spot radius that is in excellent agreement with simulations. This method does not require any knowledge of the field statistics beyond the initial conditions and provides no information about the evolution of the individual speckles. The other approach employs a self-similar solution for the second-order coherence function of the field and assumes that the fourth-order coherence function is factorizable and obeys complex circular Gaussian random statistics. The latter method also leads to an analytical expression for the spot radius, but its predictions for the qualitative evolution of the speckles disagree with wave-optics simulations.

lasers↗

DOE OSTI2023

Plasmon-enhanced optical nonlinearity in graphene nanomeshes

Using the density-matrix formalism, here we show that graphene nanomeshes (GNMs)—graphene sheets patterned with antidots—have large plasmon-enhanced nonlinear optical response. GNMs can be designed to behave as quasi-one-dimensional plasmonic crystals in which plasmons with large propagation lengths are efficiently excited. The associated third-order Kerr and third-harmonic-generation susceptibility can be as high as 10 –7 and 10 –9 m 2 V –2 , respectively, over the mid-to-near-infrared frequency range. Furthermore, carrier-density tuning in GNMs can flip the propagation direction of plasmonic waves and enables bidirectional switching of optical signals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Non-resonant Bragg scattering four-wave mixing at near-visible wavelengths in low-confinement silicon nitride waveguides

Quantum state coherent frequency conversion processes—such as Bragg-scattering four-wave mixing (BSFWM)—hold promise as a flexible technique for networking heterogeneous and distant quantum systems. In this Letter, we demonstrate BSFWM within an extended (1.2-m) low-confinement silicon nitride waveguide and show that this system has the potential for near-unity frequency conversion in visible and near-visible wavelength ranges. Using sensitive classical heterodyne laser spectroscopy at low optical powers, we characterize the Kerr coefficient (∼1.55 W −1 m −1 ) and linear propagation loss (∼0.0175 dB/cm) of this non-resonant waveguide system, revealing a record-high nonlinear figure of merit (NFM = γ / α ≈ 3.85 W −1 ) for BSFWM of near-visible light in non-resonant silicon nitride waveguides. We predict how, at high yet achievable on-chip optical powers, this NFM would yield a comparatively large frequency conversion efficiency, opening the door to near-unity flexible frequency conversion without cavity enhancement and resulting bandwidth constraints.

Jaber, Nicholas (ORCID:000900070106809X)↗

NASA NTRS1992

Computational modeling of femtosecond optical solitons from Maxwell's equations

An algorithm is developed that permits the direct time integration of full-vector nonlinear Maxwell's equations. This capability permits the modeling of both linear and nonlinear instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained. The fundamental innovation is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. A coupled system of nonlinear second-order ordinary differential equations can then be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations, are solved to determine the electromagnetic fields in nonlinear dispersive media. Results are presented of calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier, taking into account as the Kerr and Raman interactions.

Goorjian, Peter M.↗

NASA NTRS1982

Kerr Reservoir LANDSAT experiment analysis for March 1981

LANDSAT radiance data were used in an experiment conducted on the waters of Kerr Reservoir to determine if reliable algorithms could be developed that relate water quality parameters to remotely sensed data. A mix of different types of algorithms using the LANDSAT bands was generated to provide a thorough understanding of the relationships among the data involved. Except for secchi depth, the study demonstrated that for the ranges measured, the algorithms that satisfactorily represented the data encompass a mix of linear and nonlinear forms using only one LANDSAT band. Ratioing techniques did not improve the results since the initial design of the experiment minimized the errors against which this procedure is effective. Good correlations were found for total suspended solids, iron, turbidity, and secchi depth. Marginal correlations were discovered for nitrate and tannin + lignin. Quantification maps of Kerr Reservoir are presented for many of the water quality parameters using the developed algorithms.

Lecroy, S. R.↗

NASA NTRS1978

Conversion loss and noise of microwave and millimeter-wave mixers. I - Theory. II - Experiment

The conversion loss and noise of microwave and millimeter-wave mixers are analyzed. Nonlinear capacitance, arbitrary embedding impedances, as well as shot, thermal and scattering noise arising in the diode, figure in the analysis. The anomalous mixer noise noted in millimeter-wave mixers by Kerr (1975) is shown to be explainable in terms of the correlation of down-converted components of the time-varying shot noise. A digital computer analysis of the conversion loss, noise, and output impedance of an 80-120-GHz mixer is also conducted.

Held, D. N.↗

NASA NTRS1993

Femtosecond pulses generated from a synchronously pumped chromium-doped forsterite laser

Kerr lens mode-locking (KLM) has become a standard method to produce femtosecond pulses from tunable solid state lasers. High power inside the laser resonator propagating through the laser-medium with nonlinear index of refraction, coupled with the stability conditions of the laser modes in the resonator, result in a passive amplitude modulation which explains the mechanism for pulse shortening. Recently, chromium doped forsterite was shown to exhibit similar pulse behavior. A successful attempt to generate femtosecond pulses from a synchronously pumped chromium-doped forsterite laser with intracavity dispersion compensation is reported. Stable, transform limited pulses with duration of 105 fs were routinely generated, tunable between 1240 to 1270 nm.

Seas, A.↗

DOE OSTI2025

Linear Quantum Coupler for Clean Bosonic Control

Quantum computing with superconducting circuits relies on high-fidelity driven nonlinear processes. An ideal quantum nonlinearity would selectively activate desired coherent processes at high strength, without activating parasitic mixing products or introducing additional decoherence. The wide bandwidth of the Josephson nonlinearity makes this difficult, with undesired drive-induced transitions and decoherence limiting qubit readout, gates, couplers, and amplifiers. Significant strides have recently been made into building better “quantum mixers,” with promise being shown by Kerr-free three-wave mixers that suppress driven frequency shifts, and balanced quantum mixers that explicitly forbid a significant fraction of parasitic processes. We propose a novel mixer that combines both these strengths, with engineered selection rules that make it essentially linear (not just Kerr-free) when idle, and activate clean parametric processes even when driven at high strength. Furthermore, its ideal Hamiltonian is simple to analyze analytically, and we show that this ideal behavior is first-order insensitive to dominant experimental imperfections. We expect this mixer to allow significant advances in high-𝑄 control, readout, and amplification.

Quantum circuits↗

NASA NTRS1982

Laboratory upwelled radiance and reflectance spectra of Kerr reservoir sediment waters

Reflectance, chromaticity, and several other physical and chemical properties were measured for various water mixtures of bottom sediments taken from two sites at Kerr Reservoir, Virginia. Mixture concentrations ranged from 5 to 1000 ppm by weight of total suspended solids (TSS) in filtered deionized tap water. The two sets of radiance and reflectance spectra obtained were similar in shape and magnitude for comparable values of TSS. Upwelled reflectance was observed to be a nonlinear function of TSS with the degree of curvature a function of wavelength. Sediment from the downstream site contained a greater amount of particulate organic carbon than from the upstream site. No strong conclusions can be made regarding the effects of this difference on the radiance and reflectance spectra. Near-infrared wavelengths appear useful for measuring highly turbid water with concentrations up to 1000 ppm or more. Chromaticity characteristics do not appear useful for monitoring sediment loads above 150 ppm.

Witte, W. G.↗

DOE OSTI2023

Characterizing non-polarization-maintaining highly nonlinear fiber toward squeezed-light generation

Squeezed light, which is easily degraded by loss, could benefit from generation directly in optical fiber. Furthermore, highly nonlinear fiber could offer more efficient generation with lower pump power and shorter fiber lengths than standard single-mode fiber. We investigate non-polarization-maintaining highly nonlinear fiber (HNLF) for squeezed-light generation by characterizing possible sources of excess noise, including its zero-dispersion wavelength (ZDW) variation and polarization noise. We find significant ZDW variation and excess polarization noise. We believe the polarization noise is from non-linear polarization-mode dispersion. We model this polarization noise and find that it is likely to degrade Kerr squeezing but not squeezing from four-wave mixing.

47 OTHER INSTRUMENTATION↗

NASA NTRS1979

Shot-noise in resistive-diode mixers and the attenuator noise model

The representation of a pumped exponential diode, operating as a mixer, by an equivalent lossy network, is reexamined. It is shown that the model is correct provided the network has ports for all sideband frequencies at which (real) power flow can occur between the diode and its embedding. The temperature of the equivalent network is eta/2 times the physical temperature of the diode. The model is valid only if the series resistance and nonlinear capacitance of the diode are negligible. Expressions are derived for the input and output noise temperature and the noise-temperature ratio of ideal mixers. Some common beliefs concerning noise-figure and noise-temperature ratio are shown to be incorrect.

Kerr, A. R.↗