Negative refraction in active and passive media: a discussion of various criteria

There are three widely-used conditions for characterizing negative refraction in isotropic dielectric-magnetic materials. Here we demonstrate that whilst all the different conditions are equivalent for purely passive media, they are distinct if active media are considered. Further, these criteria can also be applied to negative refraction in acoustic materials, where we might replace the dielectric permittivity $epsilon$ with a bulk modulus $kappa$, and the magnetic permeability $mu$ with the mass density $rho$.

Carrier-wave steepened pulses and gradient-gated high-order harmonic generation using linear ramp waveforms

We show how to optimize the process of high-harmonic generation (HHG) by gating the interaction using the field gradient of a driving pulse with a linear ramp waveform. Since maximized field gradients are efficiently generated by self-steepening processes, we first present a generalized theory of optical carrier-wave self-steepened (CSS) pulses. This goes beyond existing treatments, which only consider third-order nonlinearity, and has the advantage of describing pulses whose wave forms have a range of symmetry properties. Although a fertile field for theoretical work, CSS pulses are difficult to realize experimentally because of the deleterious effect of dispersion. We therefore consider synthesizing CSS-like profiles using a suitably phased sub-set of the harmonics present in a true CSS wave form. Using standard theoretical models of HHG, we show that the presence of gradient-maximized regions on the wave forms can raise the spectral cut-off and so yield shorter attosecond pulses. We study how the quality of the attosecond bursts created by spectral filtering depends on the number of harmonics included in the driving pulse.

Transverse limits on the uni-directional pulse propagation approximation

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 [Kinsler, J. Opt. Soc. Am. B (2007)].

Phase coherence and extreme self phase modulation

I study how pulse to pulse phase coherence in a pulse train can survive super-broadening by extreme self phase modulation (SPM). Such pulse trains have been used in phase self-stabilizing schemes as an alternative to using a feedback process. However, such super-broadened pulses have undergone considerable distortion, and it is far from obvious that they necessarily retain any useful phase information. I propose measures of phase coherence (i.e. supercontinuum coherence) applicable to such pulse trains, and use them to analyze numerical simulations comparable to self-stabilization experiments.

Pulse propagation methods in nonlinear optics

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) Maxwells equations, (b) directional fields, and (c) the second order wave equation. While Maxwells 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 is that that envelope methods based on forward-only directional field propagation has made the traditional envelope methods (such as the SVEA, and extensions) based on the second order wave equation utterly redundant.

Proposal for absolute CEP measurement using 0-to-f self-referencing

We show how to adapt a 0-f self-referencing technique to provide a single shot absolute Carrier Envelope Phase (CEP) measurement by using the CEP reference provided by difference frequency generation (DFG) between the spectral wings of the fundamental pulse. Usually, the beat between the input pulse and the DFG signal then provides feedback with which to stabilize the CEP slip in a pulse train. However, with a simple extension we can get a single shot absolute CEP measurement. Success relies on having well characterized input pulses, and the use of accurate propagation models through the nonlinear crystal -- these enable us to construct a mapping between the experimental measurement and the CEP of the optical pulse.

Causality-based criteria for a negative refractive index must be used with care

Using the principle of causality as expressed in the Kramers-Kronig relations, we derive a generalized criterion for a negative refractive index that admits imperfect transparency at an observation frequency $omega$. It also allows us to relate the global properties of the loss (i.e. its frequency response) to its local behaviour at $omega$. However, causality-based criteria rely the on the group velocity, not the Poynting vector. Since the two are not equivalent, we provide some simple examples to compare the two criteria.

Limits of the uni-directional pulse propagation approximation

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.

Optical carrier wave shocking: detection and dispersion

Carrier wave shocking is studied using the Pseudo-Spectral Spatial Domain (PSSD) technique. We describe the shock detection diagnostics necessary for this numerical study, and verify them against theoretical shocking predictions for the dispersionless case. These predictions show Carrier Envelope Phase (CEP) and pulse bandwidth sensitivity in the single-cycle regime. The flexible dispersion management offered by PSSD enables us to independently control the linear and nonlinear dispersion. Customized dispersion profiles allow us to analyze the development of both carrier self-steepening and shocks. The results exhibit a marked asymmetry between normal and anomalous dispersion, both in the limits of the shocking regime and in the (near) shocked pulse waveforms. Combining these insights, we offer some suggestions on how carrier shocking (or at least extreme self-steepening) might be realised experimentally.