An experimental and theoretical investigation of laser beam shaping using a simple binary diffractive optic is presented. Beam tailoring has been characterized by the experimental determination of two relevant parameters: beam propagation factor
M2 and the beam-shaping longitudinal range, which represents the propagating distance for which the tailored beam remains nearly unchanged.

Beam-shaping longitudinal range of a binary diffractive optical element

A four-stage unidirectional ring free-space optical interconnect system was designed, analyzed, implemented, and characterized. The optical system was used within a complementary metal-oxide semiconductor-self-electro-optic-effect-device-based optical backplane demonstrator that was designed to fit into a standard VME chassis. This optical interconnect was a hybrid microlens-macrolens system, in which the microlens relays were arranged in a maximum lens-to-waist configuration to route the optical beams from the optical power supply to the transceiver arrays, while the macrolens optical relays were arranged in a telecentric configuration to route optical signal beams from stage to stage. The following aspects of the optical system design are discussed: the optical parameters for the hybrid optical system, the image mapping of the two-dimensional array of optical beams from stage to stage, the alignment tolerance of the hybrid relay system, and the power budget of the overall optical interconnect. The implementation of the optical system, including the characterization of optical components, subsystem prealignment, and final system assembly, is presented. The two-dimensional array of beams for the stage-to-stage interconnect was adjusted with a rotational error of <0.05 degrees and a lateral offset error of <3.5 mum. The measured throughput is in good agreement with the lower-bound predictions obtained in the theoretical results, with an optical power throughput of -20.2 dB from the fiber input of the optical power supply to the modulator array and -25.5 dB from the fiber input to the detector plane.

Design, Implementation, and Characterization of a Hybrid Optical Interconnect for a Four-Stage Free-Space Optical Backplane Demonstrator

We propose a new scheme to generate a focusing hollow beam (FHB) by use of an azimuthally distributed 2pi-phase plate and a convergent thin lens. From the Fresnel diffraction theory, we calculate the intensity distributions of the FHB in free propagation space and study the relationship between the waist w_0 of the incident Gaussian beam (or the focal length f of the lens) and the dark spot size (or the beam radius) at the focal point and the relationship between the maximum radial intensity of the FHB and the dark spot size (or the beam radius) at the focal point, respectively. Our study shows that the FHB can be used to cool and trap neutral atoms by intensity-gradient-induced Sisyphus cooling due to an extremely high intensity gradient of the FHB itself near the focal point, or to guide and focus a cold molecular beam. We also calculate the optical potential of the blue-detuned FHB for ^85Rb atoms and find that in the focal plane, the smaller the dark spot size of the FHB is, the higher the optical potential is, and the greater the corresponding optimal detuning delta is; these qualities are beneficial to an atomic lens not only because it is profitable to obtain an atomic lens with a higher resolution, but also because it is helpful to reduce the spontaneous photon-scattering effect of atoms in the FHB.

Generation of a focused hollow beam by an 2pi-phase plate and its application in atom or molecule optics

A comparison of numerical analyses with experimental measurements suggests that both the ray-tracing and the Gaussian beam-propagation models overestimate the misalignment tolerances for on-axis beams and fail to predict the large longitudinal focal shift that occurs for off-axis beams propagating in free-space optical interconnects.

Experimental and numerical analyses of misalignment tolerances in free-space optical interconnects.

The purpose of this work was to develop formulas and accurate numerical techniques for computation of the optical transfer function (OTF) in the general case of unrestricted aberration and with the following different forms of nonuniform real amplitude: (1) when the real amplitude is described by a polynomial, (2) a Gaussian distribution of real amplitude, and (3) a pupil with a central obstruction. The resulting computer program has been carefully tested and used to study the influence of nonuniform amplitude on the OTF in typical cases, for which detailed numerical results are given.

Influence of nonuniform amplitude on the optical transfer function.

The position of the most focused point of a diffracted Gaussian beam through a finite aperture lens is investigated experimentally and numerically. It depends on the definition of the point, but it will be of most practical interest to define the point as the position where the maximum energy is received by a finite aperture detector. In considering the problem, we also discuss the effect of the curvature of the equiphase surface of the incident beam on the diffraction field.

Focus of a diffracted Gaussian beam through a finite aperture lens: experimental and numerical investigations.

Resultats concernant la position correspondant a l'energie maximum recue pour plusieurs dimensions du recepteur

Osamu Kanzaki

Papers

Focus of a diffracted Gaussian beam through a finite aperture lens: experimental and numerical investigations.

Effect of lens and receiver apertures on the encircled energy of a diffracted Gaussian beam.