Nonlinear Optical Propagation Research Articles

Light-Induced Self-Oscillations and Spoiling of the Bragg Resonance Due to Nonlinear Optical Propagation in Heliconical Cholesteric Liquid Crystals

In a recent paper, we have reported the results of a study of the nonlinear light propagation of a beam traveling along the helix direction of a heliconical cholesteric liquid crystal, showing that optical reorientation leads to instabilities in the optical transmission when the light wavelength is close to the Bragg resonance. Here we report a detailed study of this phenomenon, using Ambartsumian’s layer addition modified method to take into account the continuous modification of the wave field during propagation. We show that the whole transmission spectrum is modified by increasing the light intensity and point out that self-induced oscillations take place at lower intensities on the red side edge of the Bragg resonance while stable values of transmittivity are still observed on the blue side edge. A further increase in the intensity leads to oscillations of lower amplitude on the blue side while an irregular behavior of the transmission is achieved on the red side. At higher intensities, the Bragg resonance disappears and transmission becomes unstable for any light wavelength. A simple phenomenological model is proposed to account for the onset of the oscillations and the asymmetry of the behavior at the opposite side of the Bragg resonance. We also point out that the static electric field is a driving parameter to switch from stable to oscillatory to irregular behavior in the transmittivity at a given light wavelength.

Design and analysis of recurrent neural networks for ultrafast optical pulse nonlinear propagation.

In this work, we analyze different types of recurrent neural networks (RNNs) working under several different parameters to best model the nonlinear optical dynamics of pulse propagation. Here we studied the propagation of picosecond and femtosecond pulses under distinct initial conditions going through 13 m of a highly nonlinear fiber and demonstrated the application of two RNNs returning error metrics such as normalized root mean squared error (NRMSE) as low as 9%. Those results were further extended for a dataset outside the initial pulse conditions used on the RNN training, and the best-proposed network was still able to achieve a NRMSE below 14%. We believe that this study can contribute to a better understanding of building RNNs employed for modeling nonlinear optical pulse propagation and of how the peak power and nonlinearity affect the prediction error.

Solving nonlinear Schrodinger equation using stable implicit finite difference method in single‐mode optical fibers

The different nonlinear Schrodinger equation (NLSE) types describe a lot of interesting physical phenomena. The NLSE which models the light in single‐mode nonlinear optical fibers propagation when the wave packet drift and attenuation are neglected has been studied. A stable implicit scheme is developed to solve this equation. The accuracy of this method is second order over both the space and time. By using von‐Neumann stability analysis, we have proven that our scheme is unconditionally stable. Numerically, many tests have been proceeded to present the scheme robustness. It is proven that the mass, momentum, and energy are conserved. The interaction between solitons with different directions has been studied. The effects of the factors of chromatic dispersion and self‐phase modulation on the solitons movement and conserved quantities as well as the relation between the factors have been discussed. It has been found that the physical parameters of self‐phase modulation and chromatic dispersion impacts are beneficial especially for fiber optical investigations.

Linear and nonlinear optical propagation in 2D materials

Recently, a lot of effort has been dedicated to developing next-generation optoelectronic devices based on two-dimensional materials, thanks to their unique optical properties that are significantly different from those of their bulk counterparts. In order to implement high-performance nanoscale optical devices, an in-depth study of how linear and nonlinear propagation occurs in two-dimensional materials is required. We focus here on the theory behind the propagation of electromagnetic waves in two-dimensional materials, as well as emerging applications in the fields of electronics, optics, and sensors that are summarized and discussed in the paper.

Excitation of nonlinear beams: from the linear Talbot effect through modulation instability to Akhmediev breathers.

The smooth transition between stable, Talbot-effect-dominated and modulationally unstable nonlinear optical beam propagation is described as the superposition of oscillating, growing and decaying eigenmodes of the common linearized theory of modulation instability. The saturation of the instability in form of breather maxima is embedded between eigenmode growth and decay. This explains well the changes of beam characteristics when the input intensity increases in experiments on modulation instability and breather excitation in spatial-spatial experimental platforms. An increased accuracy of instability gain measurements, a variety of interesting nonlinear beam scenarios and a more selective and well-directed breather excitation are demonstrated experimentally.

Comparative study of neural network architectures for modelling nonlinear optical pulse propagation

Ultrashort pulses have a crucial role in the evolution of different areas of science such as ultra fast imaging, femtochemistry and high harmonic spectroscopy and therefore, diagnosing and reconstructing ultrashort pulses is important. The interplay of dispersion and nonlinear effects gives rise to a wide variety of pulse dynamics. On the other hand, dispersion, linear and nonlinear effects have proven to be a fundamental bottleneck for high speed communications. Conventionally, time consuming and computationally inefficient algorithms are used to solve these problems. Since machine learning (ML) has proved to be more powerful than other analytical methods we show a comprehensive comparison of different neural network (NN) architectures to learn the mapping of the nonlinear schrödinger equation (NLSE). We have used a ML based approach to construct the distorted output pulse resulting from nonlinear propagation through the fiber. Additionally, the trained network can also predict the dispersion and nonlinear parameters. We have also reconstructed the temporal and spectral profile of transmitted pulse from the pulse distorted due to propagation through a highly nonlinear fiber (HNLF). These techniques can work without the knowledge of fiber parameters. A detailed comparison of six different NN based techniques namely fully connected NN (FCNN), cascade NN (CaNN), convolutional NN (CNN), long short term memory networks (LSTM), bidirectional LSTM (BiLSTM) and gated recurrent unit (GRU) is presented. Results show that a FCNN regressor outperforms the all other architectures.

Thermal and non-thermal intensity dependent optical nonlinearities in ethanol at 800 nm, 1480 nm, and 1560 nm

Intensity dependent self-action of a continuous wave (CW) or pulsed optical beam can lead to spatial or spectral effects upon propagation through a nonlinear medium, which can be described as an intensity dependence of the refractive index, known as self-phase modulation (SPM). In this work, we revisit the nonlinear optical propagation of a CW and a CW mode-locked (CW-ML) high repetition rate [ ∼ megahertz (MHz)] laser propagating through pure ethanol in regions of very low optical absorption (800 nm) or very high absorption (1480 nm, 1560 nm). Spatial and spectral SPM and Z -scan experiments were performed to clarify the origin of the third-order nonlinear optical response in the different optical excitation regimes. From spatial SPM and Z -scan at either CW or CW-ML MHz regime, a thermal nonlinear response was determined to be the origin of the nonlinearity at 800 nm or 1480 nm, 1560 nm region, with the nonlinear refractive index response of the order of 10 − 4 − 10 − 9 c m 2 / W . From the spectral SPM, the non-thermal origin of the nonlinearity, arising from electronic or nuclear processes in the ethanol, was determined, and values of the order of 10 − 13 − 10 − 16 c m 2 / W were obtained, depending upon the spectral region. The results were supported by theoretical calculations using the nonlinear Schrödinger equation for the spectral behavior or Fresnel–Kirchhoff integral for the spatial results and clarify some of the misinterpreted results reported in the literature, besides complementing other nonlinear refraction data available at different wavelengths from 355 nm to 1560 nm.

Nonlinear optical propagation near the Bragg resonance in heliconical cholesteric liquid crystals.

We show here that the light-induced tuning of the Bragg reflection recently demonstrated in heliconical cholesterics opens new perspectives to nonlinear optical propagation in liquid crystals. We highlight that, by properly adjusting the static electric field that stabilizes the heliconical structure, a dramatic change of the refractive index of the circularly polarized resonant mode can be achieved. Additionally, a stop band for a definite range of light intensity is obtained that can be tuned in order to get the conditions of self-induced transparency.

Dramatic Acceleration of Wave Condensation Mediated by Disorder in Multimode Fibers.

Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization, in analogy with the quantum Bose-Einstein condensation. Wave condensation originates in the divergence of the thermodynamic equilibrium Rayleigh-Jeans distribution, which is responsible for the macroscopic population of the fundamental mode of the system. However, achieving complete thermalization and condensation of incoherent waves through nonlinear optical propagation is known to require prohibitive large interaction lengths. Here, we derive a discrete kinetic equation describing the nonequilibrium evolution of the random wave in the presence of a structural disorder of the medium. Our theory reveals that a weak disorder accelerates the rate of thermalization and condensation by several order of magnitudes. Such a counterintuitive dramatic acceleration of condensation can provide a natural explanation for the recently discovered phenomenon of optical beam self-cleaning. Our experiments in multimode optical fibers report the observation of the transition from an incoherent thermal distribution to wave condensation, with a condensate fraction of up to 60% in the fundamental mode of the waveguide trapping potential.

Soliton self-mode conversion: revisiting Raman scattering of ultrashort pulses

Nonlinear optical wave propagation manifests in a multitude of frequencies generated from quantum-noise, and selecting desired nonlinear products usually requires seeding the medium with extraneous waves, employing spatial or spectral filters, or operation in resonant cavities. This is especially true for multimode systems because of their high density of states. Here we report the discovery of a self-action effect, originating from quantum noise, leading to complete nonlinear optical conversion of an ultrashort soliton pulse between two distinct, spatially coherent eigenmodes that are frequency-separated by one Raman Stokes shift. That systematic nonlinear spatial reconfiguration occurs in fibers with mode counts exceeding 10,000, which are often deemed to be chaotic, points to the fundamental role of intermodal group velocity dispersion in the selection rules for multimode nonlinear optics. We demonstrate wideband spectral translations of ~70% of the carrier frequency, and the generation of record, Megawatt peak-power pulses in the biologically crucial 1300-nm spectral window, directly out of a flexible optical fiber. More generally, this novel nonlinear coupling mechanism may be applied to fibers or on-chip waveguides, and facilitate, power-scalable spatially coherent, ultrashort pulse generation from the visible to the mid-IR.

Synthesis and characterization of electro-optic waveguide material polyurethane-imides

The electro-optic (EO) polymers of Y-type polyurethane-imides (PUI-1 and PUI-2) were synthesized by reaction of monomer azo-based chromophores, phenyl diisocyanate and aromatic dianhydride, based on polycondensation mechanism. Molecular structure characteristics for the polymers were evidenced by 1HNMR, FTIR, elemental analysis and gel permeation chromatography. The polymers exhibited a glass transition temperature (Tg) of 185 °C and 192 °C and a temperature of 5% weight loss at 256 °C and 325 °C and showed EO coefficient, γ33, of 43 pm/V and 51 pm/V at 1550 nm wavelength. A type of single-mode embedded PUI polymeric inverted rib waveguide Mach-Zehnder (MZ) interferometer electro-optic modulators was fabricated and measured, and exhibiting favorable electro-optical modulation response and the average propagation loss of the waveguide was less than 2.0 dB/cm at 1550 nm. The experimental results indicated that the PUI were promising candidates for the preparation of comprehensive performance excellent EO polymer waveguide materials, due to their large nonlinear optic effects, thermal stability, good processability and low optical propagation loss.

Squeezing in a nonlocal photon fluid

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information and simulation. However the implications of the quantum nature of light in the nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in highly nonlocal regime. These results open a new scenario in quantum photon fluids and may lead to novel applications in fields like metrology and analogues of quantum gravity.

Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects.

We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.

Strong Correlation Between Experiment and Simulation for Two-Photon Absorption Induced Carrier Generation

This correspondence comments on the correlation between measured and simulated charge collection in two diode structures presented in [1] . In [1] , results from pulsed-laser-induced charge deposition via two-photon absorption revealed reasonable correlation between experimental data and simulations in some aspects but showed lack of correlation in terms of the measured and predicted magnitudes of the collected charge. The source of this poor agreement has recently been determined, and is attributed to an incorrect pulse energy calibration used for those experiments. With the proper energy calibration applied, the agreement between simulation and experiment is nearly quantitative for all observables in both devices. These results significantly strengthen the validity of the nonlinear optical beam propagation method numerical approach for accurately predicting pulsed-laser-induced charge deposition.

Ultraviolet laser filaments for underwater acoustic generation using shaped plasmas

NRL is developing underwater laser acoustic generation techniques using nonlinear optics to form shaped plasmas. One or more laser pulses are focused to ionization intensity in water, where enhanced absorption causes plasma generation and intense localized heating. The size and shape of the resulting super-heated steam “shaped charge” determines the acoustic waveform, energy spectral density (ESD), and directivity. Using a single laser pulse we have demonstrated the ability to vary the ESD centroid frequency from 15 kHz to a few MHz, with lower frequencies generated by more elongated plasmas. Recent research has focused on a proposed “igniter-heater” technique utilizing two laser pulses to generate meter-scale elongated plasma (T.G. Jones, et al., “Two Laser Generation of Extended Underwater Plasma,” U.S. patent 9,088,123), with ESD centered near 1 kHz, which is useful for long-range sonar and communications. Key to this technique is generation of an underwater plasma filament serving as an ionized “igniter” target for a subsequent “heater” laser beam. Experiments use ultraviolet picosecond pulses, which can exploit weakly-bound “hydrated” free-electron states with high stored energy. Computational modeling includes nonlinear optical propagation and ionization. We will discuss recent experimental and modeling results. [This work was supported by NRL Base Funds.]

Hyperbolic Carbon Nanoforest for Phase Matching of Ordinary and Backward Electromagnetic Waves: Second Harmonic Generation

We show that a deliberately engineered dispersive metamaterial slab can enable the coexistence and phase matching of ordinary fundamental and contra-propagating backward second harmonic electromagnetic waves. Energy flux and phase velocity are contra-directed in the backward waves, which is the extraordinary phenomenon that gives rise to unique nonlinear optical propagation processes. We demonstrate that frequencies, phase, and group velocities, as well as the losses inherent to the guided electromagnetic modes supported by such metamaterial, can be tailored to maximize the conversion of frequencies and to reverse the propagation direction of the generated second harmonic wave. Such a possibility, which is of paramount importance for nonlinear photonics, is proven using a numerical model describing the hyperbolic metamaterial made of carbon nanotubes standing on the metal surface. Extraordinary properties of the backward-wave second harmonic generation in the reflection direction and of the corresponding frequency doubling metareflector in the THz are investigated with a focus on the pulsed regime.

Polarization Shaping for Control of Nonlinear Propagation.

We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization-radially symmetric vector beams and Poincaré beams with lemon and star topologies-in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.

Dependence of the shape of fiber tapers on the nonlinear pulse propagation

Using a model for the shape of tapered fiber optics, we numerically study the effect of the taper shape profile on nonlinear optical pulse propagation. We show that super-Gaussian pulses can be generated and controlled and that they are independent of higher-order nonlinearities, which makes them a good candidate for optical communications. We see that it is possible to compensate for the [Formula: see text] variation of the dispersion with the nonlinear parameter and obtain the solutions of the homogeneous nonlinear Schrödinger equation. In addition, pulse collisions can be produced using chirped pump pulses. Finally, using a variational method, we study the chirp and time evolution for the generated super-Gaussian pulses as a function of the taper elongation profile.

Comparison of pulse propagation and gain saturation characteristics among different input pulse shapes in semiconductor optical amplifiers

This paper presents the pulse propagation and gain saturation characteristics for different input optical pulse shapes with different energy levels in semiconductor optical amplifiers (SOAs). A finite-difference beam propagation method (FD-BPM) is used to solve the modified nonlinear Schrödinger equation (MNLSE) for the simulation of nonlinear optical pulse propagation and gain saturation characteristics in the SOAs. In this MNLSE, the gain spectrum dynamics, gain saturation are taken into account those are depend on the carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. From this simulation, we obtained the output waveforms and spectra for different input pulse shapes considering different input energy levels. It has shown that the output pulse shape has changed due to the variation of input parameters, such as input pulse shape, input pulse width, and input pulse energy levels. It also shown clearly that the peak position of the output waveforms are shifted toward the leading edge which is due to the gain saturation of the SOA. We also compared the gain saturation characteristics in the SOA for different input pulse shapes.

Near-infrared spectroscopic photoacoustic microscopy using a multi-color fiber laser source.

We demonstrate a simple multi-wavelength optical source suitable for spectroscopic optical resolution photoacoustic microscopy (OR-PAM) of lipid-rich tissue. 1064 nm laser pulses are converted to multiple wavelengths beyond 1300 nm via nonlinear optical propagation in a birefringent optical fiber. OR-PAM experiments with lipid phantoms clearly show the expected absorption peak near 1210 nm. We believe this simple multi-color technique is a promising cost-effective approach to spectroscopic OR-PAM of lipid-rich tissue.