Toufic G. Jabbour

Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates

Vector diffraction theory was applied to study the effect of two- and three-zone annular multi-phase plates (AMPs) on the three-dimensional point-spread-function (PSF) that results when linearly polarized light is focused using a high numerical aperture refractory lens. Conditions are identified for which a three-zone AMP generates a PSF that is axially superresolved by 19% with minimal change in the transverse profile and sufficiently small side lobes that the intensity pattern could be used for advanced photolithographic techniques, such as multi-photon 3D microfabrication, as well as multi-photon imaging. Conditions are also found in which a three-zone AMP generates a PSF that is axially elongated by 510% with only 1% change along the transverse direction. This intensity distribution could be used for sub-micron-scale laser drilling and machining.

Vectorial beam shaping

An algorithm is reported for the design of a phase-only diffractive optical element (DOE) that reshapes a beam focused using a high numerical aperture (NA) lens. The vector diffraction integrals are used to relate the field distributions in the DOE plane and focal plane. The integrals are evaluated using the chirp-z transform and computed iteratively within the Method of Generalized Projections (MGP) to identify a solution that simultaneously satisfies the beam shaping and DOE constraints. The algorithm is applied to design a DOE that transforms a circularly apodized flat-top beam of wavelength lambda to a square irradiance pattern when focused using a 1.4-NA objective. A DOE profile is identified that generates a 50 lambda x 50 lambda square irradiance pattern having 7% uniformity error and 74.5% diffraction efficiency (fraction of focused power). The diffraction efficiency and uniformity decrease as the size of the focused profile is reduced toward the diffraction limited spot size. These observations can be understood as a manifestation of the uncertainty principle.

Axial field shaping under high-numerical-aperture focusing

Kant reported [J. Mod. Optics 47, 905 (2000)] a formulation for solving the inverse problem of vector diffraction, which accurately models high-NA focusing. Here, Kants formulation is adapted to the method of generalized projections to obtain an algorithm for designing diffractive optical elements (DOEs) that reshape the axial point-spread function (PSF). The algorithm is applied to design a binary phase-only DOE that superresolves the axial PSF with controlled increase in axial sidelobes. An 11-zone DOE is identified that axially narrows the PSF central lobe by 29% while maintaining the sidelobe intensity at or below 52% of the peak intensity. This DOE could improve the resolution achievable in several applications without significantly complicating the optical system.

Particle-swarm optimization of axially superresolving binary-phase diffractive optical elements

A particle-swarm optimization (PSO) algorithm was developed for designing binary-phase-only diffractive optical elements (DOEs) that superresolve the axially focused point-spread function. The method is based on vector diffraction theory to ensure solutions are valid under high-NA conditions. A DOE is identified that superresolves the focal spot by 34% and maintains the sidelobes below 50% of the peak intensity. The algorithm was used to obtain the Pareto front of the fitness-value space, which describes the achievable superresolution versus an allowed upper bound in sidelobe intensity. The results suggest that the algorithm yields solutions that are global in terms of the co-optimized fitness values G and M.

CAD-integrated system for automated multi-photon three-dimensional micro- and nano-fabrication

Multi-photon three-dimensional micro-/nano-fabrication (3DM) is a powerful technique for creating complex 3D micro-scale structures of the type needed for micro-electromechanical systems (MEMS), micro-optics, and microfluidics. In 3DM high peak-power laser pulses are tightly focused into a medium which undergoes a physical or chemical change following multi-photon excitation at the focal point. Complex structures are generated by serial 3D-patterned exposure within the material volume. To further the application of 3DM to micro-component engineering, we are developing a fully automated and integrated 3DM system capable of creating complex cross-linked polymer structures based on patterns designed in a CAD environment. The system consists of four major components: (1) a femtosecond laser and opto-mechanical system; (2) 3-axis micro-positioner; (3) a computer-controlled fabrication interface; and (4) software for fabrication-path planning. The path-planning software generates a 3DM command sequence based on an object-design input file created using standard commercial CAD software. The 3DM system can be used for start-to-finish design and fabrication of waveguides, 3D photonic crystals, and other complex micro-structures. These results demonstrate a technological path for implementing 3DM as a tool for micro- and nano-optical component manufacture.

Transverse and axial beam shaping in the non-paraxial domain

The design of beam-shaping pupil filters most commonly employs the scalar theory of diffraction, which does not accurately describe the focal field distribution under high numerical aperture focusing. To account for the full vector character of the field, we have developed computational algorithms for designing phase-only pupil filters that incorporate the electromagnetic theory of diffraction. These algorithms use the method of generalized projects or particle swarm optimization to generate phase-filter solutions based on a targeted focal field irradiance distribution. Computational results are presented that demonstrate how these procedures can be used to design phase filters that reshape the transverse beam, or achieve axial super-resolution for a single focused spot. The methods can be applied in the design of beam-shaping and superresolving optics used for imaging, direct laser writing, and lithography.

Axial field engineering in the nonparaxial domain

The design of axially super-resolving phase pupil filters based on the scalar theory of diffraction is limited to low numerical aperture (NA) focusing. To account for the non-paraxiality encountered in high-NA optical systems, we propose a design procedure based on the method of generalized projections that incorporates the electromagnetic theory of diffraction. A solution is identified that narrows the axial intensity of the central lobe by 29% while maintaining the side lobe intensity below 52% of the peak intensity. It is found that solutions obtained with this method depend strongly on the applied constraints and the starting pupil filter.

Design of axially super-resolving phase pupil filter for high-numerical aperture applications

The method of generalized projection was used to design a phase pupil filter that super-resolves the axial point-spread-function (PSF) by 29% while holding the side-lobe intensities at below 52% of the peak intensity in the non-paraxial regime. The resulting phase filter has a binary 0/π eleven-zone rotationally symmetric profile. Although the filters performance is theoretically satisfactory, it can be greatly compromised by imperfections introduced during experimental implementation. Such imperfections include fabrication errors, surface quality variation, and optical misalignment. A model based on vectorial diffraction was used to simulate and analyze quantitatively the effect of these imperfections on the superresolved PSF.

Effect of two- and three-zone phase masks on the axial and transverse intensity distribution under high numerical aperture focusing

Vector diffraction theory was applied to study computationally the effect of two and three-zone annular multi-phase plates (AMPs) on the three-dimensional point-spread-function (PSF). The two- and four-dimensional solutions spaces associated with a two- and three-zone AMP, respectively, were discretized and the PSF was calculated using the Wolf diffraction integrals for each unique combination of zone radius and relative phase. Conditions are identified in which a three-zone AMP generates an intensity distribution that is super-resolved by 19% in the axial direction with minimal change in the transverse distribution and sufficiently small axial side-lobes that this intensity pattern could be used for advanced photolithographic techniques, such as multi-photon three-dimensional microfabrication.