Propagation of Bessel-correlated specular and antispecular beams.

We address the specular properties of Bessel-correlated fields, generated by illuminating a tilted rotating plane-parallel glass plate with a coherent Gaussian beam and passing the output beam though a mirror-based wavefront folding interferometer. This device allows us to produce beams whose specular properties are preserved in propagation. In the far zone, the specular nature of these partially coherent fields is shown to produce intensity-profile oscillations in the sub-diffraction-limit scale. The analytical results at various propagation distances are verified experimentally by using another wavefront-folding interferometer for coherence measurements.

Mirror-based scanning wavefront-folding interferometer for coherence measurements.

We demonstrate a modification to the traditional prism-based wavefront-folding interferometer that allows the measurement of spatial and temporal coherence, free of distortions and diffraction caused by the prism corners. In our modified system, the two prisms of the conventional system are replaced with six mirrors. The whole system is mounted on a linear XY-translation stage, with an additional linear stage in the horizontal arm. This system enables rapid and exact measurement of the full four-dimensional degree of coherence, even for relatively weak signals. The capabilities of our system are demonstrated by measuring the spatial coherence of two inhomogeneous and non-Schell model light sources with distinct characteristics.

Large-angle beaming from asymmetric nanoslit-corrugation structures.

The beaming effect in single apertures surrounded by periodic corrugations and the manipulation of beaming directions from such structures has gained considerable attention since discovery. Different materials and structural profiles have been studied in this context but directional beaming at angles larger than 45° has not been achieved. We design and demonstrate nanoslits in a gold film flanked by corrugations, which give rise to beaming angles ranging from 45° to 60°. While the previous designs are based on achieving constructive interference at the aimed beaming angle, our approach complements such constructive interference with destructive interference at 0° and, as a result, enhances the directional beaming effect at angles larger than 45°. The structures are fabricated by electron beam lithography with two consecutive lift-off processes. The experimental far-field intensity distributions agree well with the designs.

Imaging-quality 3D-printed centimeter-scale lens.

Three-dimensional (3D) printing of imaging-quality optics has been challenging due to the tight tolerances on surface shape and roughness. We report on manufacturing such optics with Print optical Technology, which is based on modified ink-jet printing. We demonstrate for the first time a 3D-printed singlet lens with a surface profile deviation of ±500 nm within a 12-mm aperture diameter. Its RMS surface roughness is below 1 nm without surface polishing. The printed lens exhibits an imaging resolution of some 140 lp mm -1 at 100-mm focal length in the visible region.

Scanning wavefront folding interferometers.

We present modified scanning-type wavefront folding interferometers (WFIs), which allow spatial coherence measurements of non-uniformly correlated fields, where the degree of coherence is a function of two absolute spatial coordinates instead of coordinate separation only (Schell model). As an alternative to conventional prism-based WFI implementations, we introduce a scheme based on reflections by three mirrors. This setup allows us to avoid obstructions due to prism corners, and it is remarkably robust to polarization effects. Experimental results on measurement of fields that do not obey the Schell model are provided with the three-mirror WFI, and the results are compared to those obtained with a Young's interferometer realized using a digital micromirror device.

Young's interference experiment with electromagnetic narrowband light.

We consider electromagnetic spectral spatial coherence of random stationary light beams of arbitrary spectral width. We demonstrate that the normalized spectral coherence (or two-point) Stokes parameters and the electromagnetic spectral degree of coherence can be measured by narrowband filtering the light and detecting the spectral density and the polarization-state fringes around the optical axis of Young's interferometer. It is also shown that the normalized spectral polarization (or one-point) and coherence Stokes parameters are unaffected by filtering, and that the filtered light is strictly cross-spectrally pure. We further prove theoretically and confirm experimentally that the (time-domain) electromagnetic degree of spatial coherence of the filtered light at the pinholes does not increase when the passband of the filter is reduced.

Non-paraxial idealized polarizer model.

An idealized polarizer model that works without the structural and material information is derived in the spatial frequency domain. The non-paraxial property is fully included and the result takes a simple analytical form, which provides a straight-forward explanation for the crosstalk between field components in non-paraxial cases. The polarizer model, in a 2 × 2-matrix form, can be conveniently used in cooperation with other computational optics methods. Two examples in correspondence with related works are presented to verify our polarizer model.

Paraxial propagation of a class of Bessel-correlated fields.

The propagation of a novel class of paraxial spatially partially coherent beams exhibiting Bessel-type correlations is studied in free space and in paraxial optical systems. We show that, under certain conditions, such beams can have functionally identical forms of the absolute value of the complex degree of spatial coherence not only at the source plane and in the far zone, but also at all finite propagation distances. Under these conditions the degree of spatial coherence properties of the field is a shape-invariant quantity, but the spatial intensity distribution is only approximately shape-invariant. The main properties of this class of model beams are demonstrated experimentally by passing a coherent Gaussian beam through a rotating wedge and measuring the coherence of the ensuing beams with a Young-type interferometer realized with a digital micromirror device.

Grating interferometer for light-efficient spatial coherence measurement of arbitrary sources.

We present a theoretical analysis and experimental verification of a z-scanning double-grating interferometer for spatial coherence measurements in space-frequency and space-time domains. This interferometer permits the measurement of spatial coherence between an arbitrary pair of points along a one-dimensional line, and in favorable conditions, it has a high light efficiency compared to the classical Young's two-pinhole experiment. The scheme is applicable to both quasi-monochromatic and broadband sources that need not obey the Schell model. We first provide experimental results with several narrowband primary and secondary sources, and then apply the technique to broadband sources with discrete and continuous spectra. In the latter case, the complex degree of (time-domain) spatial coherence is retrieved from spectrally resolved measurements using the Friberg-Wolf theorem [Opt. Lett.20, 623 (1995)OPLEDP0146-959210.1364/OL.20.000623]. We compare all results to those obtained with Young's interferometer realized using a digital micromirror device.

Bessel-correlated supercontinuum fields.

We examine the spatial coherence properties of supercontinuum fields generated by illuminating rotating bulk media with intense pulsed beams. Theoretical models are presented, which indicate the possibility of generating a class of Bessel-correlated fields (in time-averaged sense) using tilted plane-parallel glass plates and wedges as media for generation of supercontinuum radiation. In special cases, the ensuing fields have a strictly identical functional form in the spatial and angular domains. Some of the main results are verified experimentally by measuring the spatial coherence properties of bulk-generated supercontinuum fields using a wavefront-folding interferometer.

Specular and antispecular light beams.

We consider a class of spatially partially coherent light beams, which are generated by passing a Gaussian Schell-model beam though a wavefront-folding interferometer. In certain cases these beams are shape-invariant on propagation and can exhibit sharp internal structure with a central peak (specular beam) or a central dip (antispecular beam) whose dimensions depend on the spatial coherence area. Such beams are demonstrated experimentally and their cross-like distributions of the complex degree of spatial coherence are measured with a digital micromirror device.

Coupling of spatially partially coherent beams into planar waveguides.

The second-order coherence theory of partially spatially coherent light and the overlap integral method are applied to study the end-coupling of stationary multimode light beams into planar waveguides. A method is presented for the determination of the cross-spectral density function of the guided field. Examples are given on the effects of spatial coherence, lateral shift, angular tilt, and defocusing of the incident beam on the coupling efficiency, spatial coherence, and propagation characteristics of the guided field.

Coherence measurement with digital micromirror device.

We measure the complex-valued spatial coherence function of a multimode broad-area laser diode using Young's classical double slit experiment realized with a digital micromirror device. We use this data to construct the coherent modes of the beam and to simulate its propagation before and after the measurement plane. When comparing the results to directly measured intensity profiles, we find excellent correspondence to the extent that even small details of the beam can be predicted. We also consider the number of measurement points required to model the beam with sufficient accuracy.

Spatial coherence of broad-area laser diodes.

We model the spatial coherence of broad-area laser diodes (BALDs) by representing the mutual intensity as superpositions of individually fully coherent but mutually uncorrelated fields. Consideration of spectroscopic modal structure measurements and intensity-based mode recovery shows that the standard Mercer-type coherent-mode expansion can lead to unsatisfactory results for real BALDs. However, we show that a so-called shifted elementary-field method provides a sufficiently accurate tool for spatial coherence and propagation modeling even if the modal structure of the BALD is severely distorted.