Nadia Belabas

Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Using a solution of Maxwells equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).

Mid-infrared electric field characterization using a visible charge-coupled-device-based spectrometer

We characterize ultrashort mid-infrared pulses through upconversion by using the stretched pulses obtained from the uncompressed output of a chirped-pulse amplifier. The power spectrum thus translated into the visible region can be readily measured with a standard silicon CCD camera-based spectrometer. The spectral phase is also characterized by a variant of zero-added-phase spectral phase interferometry for direct electric field reconstruction. This is a general method that provides a multiplex advantage over conventional infrared detector array-based methods.

Visible-infrared two-dimensional Fourier-transform spectroscopy

We report on a new class of optical multidimensional Fourier-transform spectroscopy associated with a visible excitation-infrared emission configuration, in which the emitted field results from second-order optical nonlinearities. This configuration is demonstrated on a phase-matched sample of known nonlinear response by coherent measurement of the mid-infrared field emitted after a femtosecond visible double-pulse excitation.

Coherent broadband pulse shaping in the mid infrared

We demonstrate broadband infrared pulse shaping by difference-frequency mixing of two visible phase-locked linearly chirped pulses in GaAs. Control of the temporal profile of the emitted field is achieved through this direct tailoring of the exciting visible intensity. The results are in agreement with a simulation with no adjustable parameter.

Three-dimensional view of signal propagation in femtosecond-four-wave mixing with application to the boxcars geometry

Maxwells equations for the apparently complicated generation and propagation of femtosecond four-wave-mixing signals in optically thick samples can be solved by triple Fourier transformation into the three-dimensional (3D) frequency domain. Given the linear absorption and refractive-index spectra, the propagation problem can be solved in three dimensions under the assumption that nonlinear distortions of the excitation pulses can be neglected. A propagation function exactly incorporates the linear evolution of the excitation pulses, the nonlinear generation of the signal, and the linear propagation of the signal. A quantitative treatment of the directional filtering of the 3D susceptibility that arises from excitation with noncollinear pulses and selective interference detection of signal in one phase-matched direction is developed. This 3D treatment is used to examine the influence of phase-matching bandwidth, directional filtering, and sample absorption on femtosecond four-wave-mixing signals in the rectangular and square boxcars phase-matching geometries.

Discrete photonics in waveguide arrays

In homogeneous arrays of coupled waveguides, Floquet-Bloch waves are known to travel freely across the waveguides. We introduce a systematic discussion of the built-in patterning of the coupling constant between neighboring waveguides. Key patterns provide functions such as redirecting, guiding, and focusing these waves, up to nonlinear all-optical routing. This opens the way to light control in a functionalized discrete space, i.e., discrete photonics.

Confining light flow in weakly coupled waveguide arrays by structuring the coupling constant: towards discrete diffractive optics

Structuring the coupling constant in coupled waveguide arrays opens up a new route towards molding and controlling the flow of light in discrete structures. We show coupled mode theory is a reliable yet very simple and practical tool to design and explore new structures of patterned coupling constant. We validate our simulation and technological choices by successful fabrication of appropriate III-V semiconductor patterned waveguide arrays. We demonstrate confinement of light in designated areas of one-dimensional semi-conductor waveguide arrays.

Analytical first-order extension of coupled-mode theory for waveguide arrays.

Coupled mode theory for waveguide arrays is extended to next-nearest neighbor interactions using propagation equations. Both lateral diffraction and propagation of Floquet-Bloch waves are altered respectively by extra coupling and non-orthogonality between isolated waveguide modes. The analytical formula describing the distortions of the diffraction relation is validated by direct numerical simulation for weakly coupled InP and GaAs shallow ridge waveguides and for strongly coupled Si-SiO(2) buried strip waveguides. The impact of extended coupled mode theory on propagation and diffraction design in waveguide arrays is discussed with reference to available experimental work.

Fourier algorithm for four-wave-mixing signals from optically dense systems with memory

A triple Fourier-transform algorithm for generating and propagating femtosecond four-wave-mixing signals in optically thick samples is demonstrated. The algorithm has a dynamic range that is useful for tests of theory and simulations of experiments with an arbitrary nonlinear response. Although two-pulse echoes decay faster as optical density increases for a Bloch model, we find that systems with memory exhibit the opposite trend.

A dense array of small coupled waveguides in fiber technology: trefoil channels of microstructured optical fibers

We calculate the limit to which the density of two-dimensional arrays of diffraction limited fiber waveguides can be reduced while maintaining weakly-coupled characteristics. We demonstrate that this density can be experimentally reached in an array of trefoil channels formed by the air holes of a microstructured optical fiber specially designed to meet limiting size and density specifications at lambda=1.55 microm.