The fundamental limits set by diffraction in optics have motivated the investigation of ‘diffraction-free’ beams. Examples of monochromatic diffraction-free beams include those whose profiles conform to Bessel, Mathieu, Weber, and Airy functions. For pulsed beams (wave packets or optical bullets), different functional forms of the field in space and time have been found to be propagation-invariant. Here we describe experiments on the synthesis and characterization of a unique class of pulsed optical beams called ‘space-time’ (ST) wave packets that are diffraction-free and dispersion-free in free space. The most salient features of such wave packets that determines their characteristics is the tight spatio-temporal spectral correlations underlying their construction. We identify 10 unique classes of ST wave packets according to the magnitude and sign of the group velocity, and whether the ST wave packet is ‘baseband’ or ‘sideband’; that is, whether low spatial frequencies are allowed in the wave-packet construction or are forbidden. Such wave packets can be propagation invariant even for extended distances. Furthermore, sculpting the spatio-temporal spectrum of the wave packet allows control over its propagation characteristics in optical materials, namely over the group velocity and group velocity dispersion, whether the material itself is dispersive or non-dispersive.
Diffractive spreading is a fundamental property of light and inversely proportional to the beam waist of a propagating beam. For instance, a Gaussian beam at a wavelength of 800 nm focused into 7 micrometers full-width at half maximum (FWHM) at its beam waist would only have 137 micrometers Rayleigh range—the propagation distance from the waist for a beam to double its cross section. Here, we demonstrate a diffraction-free space-time light sheet (one-dimensional pulsed beam) with 7 micrometers FWHM propagating in free space for 25 mm while preserving its spatial features. By introducing a highly correlated spatio-temporal spectrum via a two-dimensional pulse shaper (consisting of a phase-only reflective spatial light modulator, a grating and a few cylindrical lenses), we generate various light sheets with arbitrary beam profiles at the pulse center and diffraction-free propagation distance of approximately 200 Rayleigh range that corresponds to its beam waist size at the pulse center. Arbitrary light-sheet profiles also include hollow sheets (bottle beams) and even Airy light sheets that are only transversely accelerating in the local time frame of the pulse and acceleration-free as a function of propagation distance. Moreover, we obtain the spatio-temporal beam profiles of the light sheets by experimentally measuring the complex spectra and performing computational two-dimensional Fourier transformations. Light sheets with arbitrary beam profiles and controllable spectrum properties may be instrumental in super-resolution light-sheet microscopy for 3D bio-imaging, nonlinear and multimodality spectroscopy, standoff detection of chemicals, and one-dimensional plasma and filamentation generation.
Coherent light traversing disordered media usually attains a random field both in amplitude and phase with independent Gaussian statistics and results in thermal light (associated with Bose-Einstein photon-number statistics) upon ensemble averaging. This is expected according to the central limit theorem, which dictates the addition of a large number of independent random variables leads to a normal (Gaussian) distribution. Here, we show that certain network topologies that light travels within preclude the central limit theorem and result in non-Gaussian statistics. We realize such networks in the form of evanescently-coupled waveguide arrays (photonic lattices) and obtain the photon statistics at the output by time gating and averaging over multiple realizations of disordered photonic lattices. The effect of lattice topology, however, only exists when the photonic lattice is endowed with chiral-symmetric eigenmode pairs a disorder-immune symmetry where the eigenmodes appear in pairs with oppositely signed eigenvalues and the coherent input field satisfies certain conditions. We specifically examine one-dimensional arrays of randomly coupled identical waveguides (off-diagonal disorder) arranged on linear and ring topologies. The emerging field exhibits super-thermal statistics (associated with modified Bose-Einstein photon-number statistics) only for ring lattices with even parity and linear lattices (independent of its parity), whereas input coherent fields traversing ring lattices with odd parity attain sub-thermal statistics. By controlling the relative phase of a coherent input field exciting two neighboring lattice sites, we also demonstrate a deterministic tuning of photon-number statistics, namely photon bunching, while maintaining the mean photon number fixed.
We present the design, fabrication, characterization of spatially variable infrared filter and a demonstration
of the filter as a simple infrared spectrometer. A varying photonic band gap filter which consists of thermally
evaporated, high refractive index contrast amorphous chalcogenide glass multilayers, makes the structure suitable
to be used as spectrometer. Due to graded thickness structure, the filter exhibits a position dependent stop band
and a cavity mode ranging from 2 to 8 μm wavelengths. It is demonstrated that the filter can be used to detect
absorption peaks of common gases in the cavity mode range of the filter.
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