arXiv subjects
Publications and source records attributed to David W. Ward.
We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for classical fields to photons, generalize to non-zero rest mass particles, and simplify using approximations consistent with non-relativistic particles.
Are we smarter now than Socrates was in his time? Society as a whole certainly enjoys a higher degree of education, but humans as a species probably don't get intrinsically smarter with time. Our knowledge base, however, continues to grow at an unprecedented rate, so how then do we keep up? The printing press was one of the earliest technological advances that expanded our memory and made possible our present intellectual capacity. We are now faced with a new technological advance of the same magnitude--the internet--but how do we use it effectively? A new tool is available on Google (http://www.google.com) that allows a user not only to numerically evaluate equations, but to automatically perform unit analysis and conversion as well, with most of the fundamental physical constants built in.
Using femtosecond laser machining, we have fabricated photonic bandgap materials that influence propagation of phonon-polaritons in ferroelectric crystals. Broadband polaritons were generated with impulsive stimulated Raman scattering (ISRS) using an ultrashort laser pulse, and the spatial and temporal evolution of the polaritons were imaged as they propagated through the fabricated structures with polariton real-space imaging. These techniques offer a new approach to optical materials design.
We report on the design, fabrication, and testing of ferroelectric patterned materials in the guided-wave and polaritonic regime. We demonstrate their functionality and exploit polariton confinement for amplification and coherent control using temporal pulse shaping.
The physical origins of negative refractive index are derived from a dilute microscopic model, producing a result that is generalized to the dense condensed phase limit. In particular, scattering from a thin sheet of electric and magnetic dipoles driven above resonance is used to form a fundamental description for negative refraction. Of practical significance, loss and dispersion are implicit in the microscopic model. While naturally occurring negative index materials are unavailable, ferromagnetic and ferroelectric materials provide device design opportunities.
We describe a simple and intuitive implementation of the method of finite difference time domain simulations for propagating electromagnetic waves using the simplest possible tools available in Microsoft Excel. The method overcomes the usual obstacles of familiarity with programming languages as it relies on little more than the cut and paste features that are standard in Excel. Avenues of exploration by students are proposed and sample graphs are included. The pedagogical effectiveness of the implementation was tested during an Independent Activities Period class, composed of 80% freshmen, at MIT, and yielded positive results.
We simulate propagation of phonon-polaritons (admixtures of polar lattice vibrations and electromagnetic waves) in ferroelectric LiNbO3 with a model that consists of a spatially periodic array of harmonic oscillators coupled to THz electromagnetic waves through an electric dipole moment. We show that when this model is combined with the auxiliary differential equation method of finite difference time domain (FDTD) simulations, the salient features of phonon-polaritons may be illustrated. Further, we introduce second order nonlinear coupling to an optical field to demonstrate phonon-polariton generation by impulsive stimulated Raman scattering (ISRS). The phonon-polariton dispersion relation in bulk ferroelectric LiNbO3 is determined from simulation.
We explore the possibility of realizing intrinsic far infrared negative index materials (NIM) in multiferroic crystals (crystals simultaneously possessing a ferroelectric and ferromagnetic phase) possessing electric and magnetic dipole resonances with nearby resonance frequencies, or overlapping regions of negative permittivity and permeability. We demonstrate the functionality of such a material using finite difference time domain simulations. In order to motivate the connection between multiferroics and negative index materials, we discuss the negative index of refraction in the polariton picture.
Using time resolved ultrafast spectroscopy, we have demonstrated that the far infrared (FIR) excitations in ferroelectric crystals may be modified through an arsenal of control techniques from the fields of guided waves, geometrical and Fourier optics, and optical pulse shaping. We show that LiNbO3 and LiTaO3 crystals of 10-250 micron thickness behave as slab waveguides for phonon-polaritons, which are admixtures of electromagnetic waves and lattice vibrations, when the polariton wavelength is on the order of or greater than the crystal thickness. Furthermore, we show that ferroelectric crystals are amenable to processing by ultrafast laser ablation, allowing for milling of user-defined patterns designed for guidance and control of phonon-polariton propagation. We have fabricated several functional structures including THz rectangular waveguides, resonators, splitters/couplers, interferometers, focusing reflectors, and diffractive elements. Electric field enhancement has been obtained with the reflective structures, through spatial shaping, of the optical excitation beam used for phonon-polariton generation, and through temporal pulse shaping to permit repetitive excitation of a phonon-polariton resonant cavity.