The Strehl ratio as a phase histogram.

It is shown that the Strehl ratio can always be written as an integral over an apodization-weighted phase histogram. The corresponding mathematical formalism, based on Federer's co-area formula, is enumerated, and a practical numerical method to quickly and accurately calculate apodization-weighted phase histograms is detailed and compared with similar methods. Conditions for expressing the Strehl ratio as a product S=S 1 S 2 are investigated.

Zernike-like Laguerre-Gaussian orthonormal polynomials for optical field reconstruction.

Analytic closed form expressions for orthonormal polynomials exhibiting both rotational and Gaussian symmetries are derived for both circular and elliptical geometries. They exhibit a close correspondence to the Zernike polynomials but are of Gaussian shape and orthogonal over the (x,y) plane. Consequently, they may be expressed in terms of Laguerre polynomials. Formulas for calculating the centroid of a real function are also presented and, along with the analytic expressions for the polynomials, may prove to be of especial use in reconstruction of the intensity distribution incident on a Shack-Hartmann wavefront sensor.

Time-ordering in Heisenberg's equation of motion as related to spontaneous radiation.

Despite many years of research into Raman phenomena, the problem of how to include both spontaneous and stimulated Raman scattering into a unified set of partial differential equations persists. The issue is solved by formulating the quantum dynamics in the Heisenberg picture with a rigorous accounting for both time- and normal-ordering of the operators. It is shown how this can be done in a simple, straightforward way. Firstly, the technique is applied to a two-level Raman system, and comparison of analytical and numerical results verifies the approach. A connection to a fully time-dependent Langevin operator method is made for the spontaneous initiation of stimulated Raman scattering. Secondly, the technique is demonstrated for the much-studied two-level atom both in vacuum and in a lossy dielectric medium. It is shown to be fully consistent with accepted theories: using the rotating wave approximation, the Einstein A coefficient for the rate of spontaneous emission from a two-level atom can be derived in a manner parallel to the Weisskopf-Wigner approximation. The Lamb frequency shift is also calculated. It is shown throughout that field operators corresponding to spontaneous radiative terms do not commute with atomic/molecular operators. The approach may prove useful in many areas, including modeling the propagation of next-generation high-energy, high-intensity ultrafast laser pulses as well as spontaneous radiative processes in lossy media.

Raman Characterization of Fungal DHN and DOPA Melanin Biosynthesis Pathways.

Fungal melanins represent a resource for important breakthroughs in industry and medicine, but the characterization of their composition, synthesis, and structure is not well understood. Raman spectroscopy is a powerful tool for the elucidation of molecular composition and structure. In this work, we characterize the Raman spectra of wild-type Aspergillus fumigatus and Cryptococcus neoformans and their melanin biosynthetic mutants and provide a rough "map" of the DHN (A. fumigatus) and DOPA (C. neoformans) melanin biosynthetic pathways. We compare this map to the Raman spectral data of Aspergillus nidulans wild-type and melanin biosynthetic mutants obtained from a previous study. We find that the fully polymerized A. nidulans melanin cannot be classified according to the DOPA pathway; nor can it be solely classified according to the DHN pathway, consistent with mutational analysis and chemical inhibition studies. Our approach points the way forward for an increased understanding of, and methodology for, investigating fungal melanins.

Identification of toxic mold species through Raman spectroscopy of fungal conidia.

We use a 785 nm shifted excitation Raman difference (SERDS) technique to measure the Raman spectra of the conidia of 10 mold species of especial toxicological, medical, and industrial importance, including Stachybotrys chartarum, Penicillium chrysogenum, Aspergillus fumigatus, Aspergillus flavus, Aspergillus oryzae, Aspergillus niger, and others. We find that both the pure Raman and fluorescence signals support the hypothesis that for an excitation wavelength of 785 nm the Raman signal originates from the melanin pigments bound within the cell wall of the conidium. In addition, the major features of the pure Raman spectra group into profiles that we hypothesize may be due to differences in the complex melanin biosynthesis pathways. We then combine the Raman spectral data with neural network models to predict species classification with an accuracy above 99%. Finally, the Raman spectral data of all species investigated is made freely available for download and use.

Molecular origin of the Raman signal from Aspergillus nidulans conidia and observation of fluorescence vibrational structure at room temperature.

Successful approaches to identification and/or biological characterization of fungal specimens through Raman spectroscopy may require the determination of the molecular origin of the Raman response as well as its separation from the background fluorescence. The presence of fluorescence can interfere with Raman detection and is virtually impossible to avoid. Fluorescence leads to a multiplicity of problems: one is noise, while another is "fake" spectral structure that can easily be confused for spontaneous Raman peaks. One solution for these problems is Shifted Excitation Raman Difference Spectroscopy (SERDS), in which a tunable light source generates two spectra with different excitation frequencies in order to eliminate fluorescence from the measured signal. We combine a SERDS technique with genetic breeding of mutant populations and demonstrate that the Raman signal from Aspergillus nidulans conidia originates in pigment molecules within the cell wall. In addition, we observe unambiguous vibrational fine-structure in the fluorescence response at room temperature. We hypothesize that the vibrational fine-structure in the fluorescence results from the formation of flexible, long-lived molecular cages in the bio-polymer matrix of the cell wall that partially shield target molecules from the immediate environment and also constrain their degrees of freedom.

Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing.

Probing remote matter with laser light is a ubiquitous technique used in circumstances as diverse as laser-induced breakdown spectroscopy and barcode scanners. In classical optics, the intensity that can be brought to bear on a remote target is limited by the spot size of the laser at the distance of the target. This spot size has a lower bound determined by the diffraction limit of classical optics. However, amplified femtosecond laser pulses generate intensity sufficient to modify the refractive index of the ambient air and undergo self-focusing. This self-focusing effect leads to the generation of highly intense laser filaments which maintain their intensity and small sub-millimeter diameter size at distances well beyond the classical Rayleigh length. Such intensity provides the capability of remote scanning, imaging, sensing, and spectroscopy with enhanced spatial resolution. We describe a technique for generating filaments with a femtosecond regenerative chirped-pulse amplifier, and for using the resulting filament to conduct imaging and spectroscopic measurements at remote distances of at least several meters.

Remote sub-diffraction imaging with femtosecond laser filaments.

Achieving super-resolution has become a scientific imperative for remote imaging of objects and scenes needing increased detail and has motivated the development of various laser-based techniques. We demonstrate a scheme which achieves subdiffraction imaging of remote objects by using femtosecond laser filaments. The use of laser filaments for imaging is destined to have applications in many environments.

Shaper-assisted phase optimization of a broad "holey" spectrum.

We develop a technique for optimizing the phase of broad spectrally-separated frequency sidebands-a "holey" spectrum. We use a source of multiple-order coherent Raman sidebands, obtained by crossing femtosecond pump and Stokes beams in synthetic single-crystal diamond. We combine the sidebands into a single beam and show the phase coherence among the sidebands by investigating the interference between them in groups of three while varying one sideband phase by an acousto-optics pulse shaper. We then show how we optimize the broad "holey" spectrum by overcoming the limited temporal shaping window of the pulse shaper. We also explore how the resultant second harmonic/sum frequency generation of the full combined broadband spectrum varies as we vary different sideband phases. This step-by-step phase optimization of the "holey" spectrum can be applied to sidebands with similar structure to synthesize arbitrary optical waveforms.

Equivalent path lengths in an integrating cavity: comment.

The equivalent absorption path length in an integrating cavity is examined. In an otherwise excellent paper, Tranchart et al. [Appl. Opt. 35, 7070 (1996)] made an important error in obtaining the expressions for the equivalent path length in an integrating cavity. This error has been propagated through several other publications in the literature. Since the equivalent path length is the sine qua non for obtaining an accurate absorption coefficient when using an integrating cavity, it is our intent here to give the correct formulas to prevent further errors when extracting absorption coefficients.

Propagation of ultrashort laser pulses in water: linear absorption and onset of nonlinear spectral transformation.

We study propagation of short laser pulses through water and use a spectral hole filling technique to essentially perform a sensitive balanced comparison of absorption coefficients for pulses of different duration. This study is motivated by an alleged violation of the Bouguer-Lambert-Beer law at low light intensities, where the pulse propagation is expected to be linear, and by a possible observation of femtosecond optical precursors in water. We find that at low intensities, absorption of laser light is determined solely by its spectrum and does not directly depend on the pulse duration, in agreement with our earlier work and in contradiction to some work of others. However, as the laser fluence is increased, interaction of light with water becomes nonlinear, causing energy exchange among the pulse's spectral components and resulting in peak-intensity dependent (and therefore pulse-duration dependent) transmission. For 30 fs pulses at 800 nm center wavelength, we determine the onset of nonlinear propagation effects to occur at a peak value of about 0.12 mJ/cm(2) of input laser energy fluence.

Propagation of femtosecond laser pulses through water in the linear absorption regime.

We investigate the controversy regarding violations of the Bouguer-Lambert-Beer (BLB) law for ultrashort laser pulses propagating through water. By working at sufficiently low incident laser intensities, we make sure that any nonlinear component in the response of the medium is negligible. We measure the transmitted power and spectrum as functions of water cell length in an effort to confirm or disprove alleged deviations from the BLB law. We perform experiments at two different laser pulse repetition rates and explore the dependence of transmission on pulse duration. Specifically, we vary the laser pulse duration either by cutting its spectrum while keeping the pulse shape near transform-limited or by adjusting the pulses chirp while keeping the spectral intensities fixed. Over a wide range of parameters, we find no deviations from the BLB law and conclude that recent claims of BLB law violations are inconsistent with our experimental data. We present a simple linear theory (based on the BLB law) for propagation of ultrashort laser pulses through an absorbing medium and find our experimental results to be in excellent agreement with this theory.