I derive unidirectional wave equations for fields propagating in materials with both electric and magnetic dispersion and nonlinearity. The derivation imposes no conditions on the pulse profile except that the material modulates the propagation slowly, that is, that loss, dispersion, and nonlinearity have only a small effect over the scale of a wavelength. It also allows a direct term-to-term comparison of the exact bidirectional theory with its approximate unidirectional counterpart.
I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the uni-directional approximation used in many pulse propagation models. Results from numerical simulations support the theoretical predictions, and reveal the nature of the coupling between forward and backward waves.
I derive directional wave equations useful for pulses propagating in beam, rod, pipe, and disk geometries by using a cylindrical coordinate system; the scheme works equally well for either long multi-cycle or single-cycle ultrashort pulses. This is achieved by means of a factorization procedure that conveniently generates exact bi-directional and first order wave equations after the selection of propagation direction - either axial, radial, or even angular. I then discuss how to reduce these to a uni-directional form, and discuss the necessary approximation, which is essentially a paraxial app…
I calculate the limitations on the widely-used forward-only (uni-directional) propagation assumption by considering the effects of transverse effects (e.g. diffraction). The starting point is the scalar second order wave equation, and simple predictions are made which aim to clarify the forward-backward coupling limits on diffraction strength. The result is unsurprising, being based on the ratio of transverse and total wave vectors, but the intent is to present a derivation directly comparable to a recently published \emph{nonlinearity} constrained limits on the uni-directional approximation […
I construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. The emphasis is on detailed calculations, with a more general overview being published in Phys. Rev. A72 and arXiv. These directional variables enable us to not only judge the effect and significance of backward-travelling field components, but also to discard them when appropriate. They thereby have the potential to simplify numerical simulations, leading to potential speed gains of up to 1…
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward "factorization" mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a single uni-directional first order wave equation by means of a simple "slow evolution" approximation, where …
I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact coupled bi-directional equations that this approach generates can be efficiently approximated down to a uni-directional form in cases where an optical pulse changes little over one optical cycle. They also permit a direct term-to-term comparison of the exact bi-directional theory with its corresponding approximate uni-directional theory. Notably, temporal p…
We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not only judge the effect and significance of backward-travelling field components, but also to discard them when appropriate. They thereby have the potential to simplify numerical simulations, leading to potential speed gains of up to 100% over standard FDTD or PSSD simulations. We present results for various illustrative situations, including an example applic…
We present an analysis of two experimental approaches to controlling the directionality of molecular rotation with ultrashort laser pulses. The two methods are based on the molecular interaction with either a pair of pulses (a "double kick" scheme) or a longer pulse sequence (a "chiral pulse train" scheme). In both cases, rotational control is achieved by varying the polarization of and the time delay between the consecutive laser pulses. Using the technique of polarization sensitive resonance-enhanced multi-photon ionization, we show that both methods produce significant rotational directiona…
I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a) Maxwell's equations, (b) directional fields, and (c) the second order wave equation. While Maxwell's equations simulators are the most general, directional field methods can give significant computational and conceptual advantages. Factorizations of the second order wave equation complete the set by being the simplest to understand. One important conclusion…
In this paper we numerically study supercontinuum generation by pumping a silicon nitride waveguide, with two zero-dispersion wavelengths, with femtosecond pulses. The waveguide dispersion is designed so that the pump pulse is in the normal-dispersion regime. We show that because of self-phase modulation, the initial pulse broadens into the anomalous-dispersion regime, which is sandwiched between the two normal-dispersion regimes, and here a soliton is formed. The interaction of the soliton and the broadened pulse in the normal-dispersion regime causes additional spectral broadening through fo…
Transient structural changes of Al$_2$O$_3$ on subatomic length scales following irradiation with an intense x-ray laser pulse (photon energy: 8.70 keV; pulse duration: 6 fs; fluence: 8$\times$10$^2$ J/cm$^{2}$) have been investigated by using an x-ray pump x-ray probe technique. The measurement reveals that aluminum and oxygen atoms remain in their original positions by $\sim$20 fs after the intensity maximum of the pump pulse, followed by directional atomic displacements at the fixed unit cell parameters. By comparing the experimental results and theoretical simulations, we interpret that el…
A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter accounts for this duality with the onset of a mode locked regime in which increasing the number of activated modes results in an increased inter mode correlation and a pulse shortening ascribed to a synchronization phenomenon. An extended discussion of our experimental approach together with an original study of the spatial properties of the RL is reported h…
We demonstrate a novel approach to producing coherent, directional supercontinuum via cascaded dispersive wave generation. By pumping in the normal group-velocity dispersion regime, pulse compression of the first dispersive wave results in the generation of a second dispersive wave, resulting in an octave-spanning supercontinuum generated primarily to one side of the pump spectrum. We theoretically investigate the dynamics and show that the generated spectrum is highly coherent. We experimentally confirm this dynamical behavior and the coherence properties in silicon nitride waveguides by perf…
We design a high dynamic range electric field sensor based on domain inverted electro-optic (E-O) polymer Y-fed directional coupler for electromagnetic wave detection. This electrode-less, all optical, wideband electrical field sensor is fabricated using standard processing for E-O polymer photonic devices. Experimental results demonstrate effective detection of electric field from 16.7V/m to 750KV/m at a frequency of 1GHz, and spurious free measurement range of 70dB.
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully utilized for almost a decade. Unfortunately, they are restricted to applications in bulk media or, with additional approximations, to simple waveguide geometries in which only a few guided modes can approximate the propagating waveform. The purpose of this work is to generalize the directional pulse propagation equations to structures characterized by strong ref…
We report an asymmetric behavior of optical pulses during their propagation through a time-varying linear optical medium. The refractive index of the medium is considered to be varying with time and complex such that a sufficient amount of gain and loss is present to realize their effect on pulse propagation. We have exploited the universal formula for optical fields in time-varying media. Numerically simulated results reveal that pulses undergo opposite temporal shifts around their initial center position during their bi-directional propagation through the medium along with corresponding spec…
Polymer based electro-optic modulators have shown great potentials in high frequency analog optical links. Existing commercial LiNibO3 Mach-Zehnder modulators have intrinsic drawbacks in linearity to provide high fidelity communication. In this paper, we present the design, fabrication and characterization of a traveling wave directional coupler modulator based on electro-optic polymer, which is able to provide high linearity, high speed, and low optical insertion loss. A silver ground electrode is used to reduce waveguide sidewall roughness due to the scattering of UV light in photolithograph…
Platforms for all-optical computing possess photonic circuits made of silicon-based channels, metal wires or optical fibers, etc. However, such solid waveguides suffer from the lack of reversibility and reconfigurability if facing the next generation of light-guiding-light (LGL) computing scheme, which envisions circuitry-free and rapidly reconfigurable systems powered by dynamic interactions between light beams. Here, we proposed the ubiquitous air as a restorable LGL signal manipulation medium with transient air-plasma waveguide circuits. Briefly, by focusing femtosecond laser beams in the f…
Optical microcavities have received much attention over the last decade from different research fields ranging from fundamental issues of cavity QED to specific applications such as microlasers and bio-sensors. A major issue in the latter applications is the difficulty to obtain directional emission of light in the far-field while keeping high energy densities inside the cavity (i.e. high quality factor). To improve our understanding of these systems, we have studied the annular cavity (a dielectric disk with a circular hole), where the distance cavity-hole centers, d, is used as a parameter t…
We discuss the optical forces exerted on parity-time (PT) symmetric heterostructures under normal incidence of a single and two counter-propagating plane waves. The underlying strategy is through generalized parametric space, stemming from consideration of PT-symmetry condition and Lorentz reciprocity theorem. In such a generalized parametric space, we are able to not only exhaustively indicate various PT phases and extraordinary wave phenomena, but also deduce the directionality and magnitudes of optical forces. We find that when the system is illuminated by a normally incident wave, it can e…
The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity (refractive index less than unity) and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the refractive index. This transformation preserves the ray trajectories, but leads to a uniform phase delay. We show how to take advantage…
Here, we demonstrate a new type of 3-dB coupler that has an ultra-broadband operational range starting from 1300 nm to 1600 nm with low fabrication sensitivity. Overall device size is 800 micron including in/out S-bend waveguides. The coupler is an asymmetric non-uniform directional coupler that consists of two tapered waveguides. One of the coupler arms is shifted by 130 micron in the propagation direction, which reduces the phase mismatch between the odd and even mode of the coupled system resulting in a better wavelength-flattened response compared to a not shifted coupler. Moreover, compar…
We study experimentally and theoretically the interactions among ultrashort optical pulses in the soliton rain multiple-pulse dynamics of a fiber laser. The laser is mode-locked by a graphene saturable absorber fabricated using the mechanical transfer technique. Dissipative optical solitons aggregate into pulse bunches that exhibit complex behavior, which includes acceleration and bi-directional motion in the moving reference frame. The drift speed and direction depend on the bunch size and relative location in the cavity, punctuated by abrupt changes under bunch collisions. We model the main …
On-chip ultraviolet to infrared (UV-IR) spectrum frequency metrology is of crucial importance as a characterization tool for fundamental studies on quantum physics, chemistry, and biology. Due to the strong material dispersion, traditional techniques fail to demonstrate the device that can be applied to generate coherent broadband spectrum that covers the full UV-IR wavelengths. In this work, we explore several novel techniques for supercontinuum generation covering near-UV to near-IR spectrum using AlN micro-photonic waveguides, which is essential for frequency metrology applications: First, …
Manipulating the nanostructure of materials is critical for numerous applications in electronics, magnetics, and photonics. However, conventional methods such as lithography and laser-writing require cleanroom facilities or leave residue. Here, we describe a new approach to create atomically sharp line defects in hexagonal boron nitride (hBN) at room temperature by direct optical phonon excitation in the mid-infrared (mid-IR). We term this phenomenon "unzipping" to describe the rapid formation and growth of a <30-nm-wide crack from a point within the laser-driven region. The formation of these…
In this manuscript, we demonstrate the design and experimental proof of an optical cloaking structure which multi-directionally conceals a perfectly electric conductor (PEC) object from an incident plane wave. The dielectric modulation around the highly reflective scattering PEC object is determined by an optimization process for multi-directional cloaking purposes. And to obtain the multi-directional effect of the cloaking structure, an optimized slice is mirror symmetrized through a radial perimeter. Three-dimensional (3D) finite-difference time-domain method is integrated with genetic optim…
