Structured light engineering using a photonic nanojet.

In this Letter, we present the photonic nanojet as a phenomenon in a structured light generator system that is implemented to modify the source focal spot size and emission angle. The optical system comprises a microlens array that is illuminated by a focused Gaussian beam to generate a structured pattern in the far field. By introducing a spheroid with different aspect ratios in the focus of the Gaussian beam, the source optical characteristics change, and a photonic nanojet is generated, which will engineer the far-field distribution. To probe the light fields, we implement a high-resolution interferometry setup to extract both the phase and intensity at different planes. We both numerically and experimentally demonstrate that the pattern distribution in the far field can be engineered by a photonic nanojet. As an example, we examine prolate, sphere, and oblate geometries. An interesting finding is that depending on the spheroid geometry, a smaller transverse FWHM of a photonic nanojet with a higher divergence angle produces an increased pattern field of view at the same physical size of the optical system.

Inverse design and demonstration of high-performance wide-angle diffractive optical elements.

Diffractive optical elements are ultra-thin optical components required for constructing very compact optical 3D sensors. However, the required wide-angle diffractive 2D fan-out gratings have been elusive due to design challenges. Here, we introduce a new strategy for optimizing such high-performance and wide-angle diffractive optical elements, offering unprecedented control over the power distribution among the desired diffraction orders with only low requirements with respect to computational power. The microstructure surfaces were designed by an iterative gradient optimization procedure based on an adjoint-state method, capable to account for application-dependent target functions while ensuring compatibility with existing fabrication processes. The results of the experimental characterization confirm the simulated tailored power distributions and optical efficiencies of the fabricated elements.

Full field dependence of primary aberrations in perturbed double-plane symmetric systems with a circular pupil.

This paper deals with the theory of primary aberrations for perturbed double-plane symmetric optical systems consisting of a combination of tilted and decentered surfaces and a circular pupil. First, the analytical expressions describing the full field behavior of Zernike polynomials are derived from the fourth-order wavefront aberration function for this class of optical systems. Then, such expressions are combined to retrieve the full field dependence of primary coma, primary astigmatism, and field curvature. They are described by an elliptical conic-shaped surface with a variable apex location over the field of view, by a binodal surface with two nodes over the field of view, and by a general elliptical surface with one node. The proposed analytical expressions provide a better understanding of the primary aberration behavior for these systems and can be of great use in their optical design and aberration correction. An optical system constituted by a pair of tilted and decentered biconic lenses is studied to validate the proposed expressions.

Optical characterization of high numerical aperture microlenses for quality assessment and fabrication process optimization.

Accurate characterization of high numerical aperture aspheric microlenses currently is a nonstandard procedure that remains an open challenge. Here, we present and discuss a characterization method based on interferometric and point spread function measurements performed in transmission by a high-resolution interferometric microscope. In particular, we show that a single phase measurement performed under fixed testing conditions can be processed in a simple way that yields wavefront aberration as well as surface topography for plano-convex microlenses with arbitrary asphericity. This approach simultaneously allows both fabrication process optimization and optical quality testing for microlenses with different optical functions without heavy modification of the testing setup. For illustration, we present the case of a microlens with a numerical aperture of ${\sim}0.4 $∼0.4.

Tolerancing the surface form of aspheric microlenses manufactured by wafer-level optics techniques.

Tolerancing is an important step toward the fabrication of high-quality and cost-effective lens surfaces. It is critical for wafer-level optics, when up to tens of thousands microlenses are fabricated in parallel and whose surfaces cannot be formed individually. However, approaches developed for macro-optics cannot be directly transposed for microlenses because of differences in fabrication and testing techniques. In particular, microlens surfaces are usually limited to conical surfaces. Here, we study the connection between the microlens optical performance and the form of its surface, suggesting surface form representations suited for tolerancing purposes. Then, we compare them with common representations for tolerancing real optical systems. Measured surface forms of microlenses are also provided to make the tolerancing procedure realistic. In addition, we propose term definitions for micro-optics, complements to typical terms for macro-optics, to ease the communication between optical designers and manufacturers. Based on the results presented in this paper, guidelines are proposed for tolerancing microlenses. We suggest applying them as a first step toward a more effective and comprehensive tolerancing procedure.

Improvements on the uniformity of large-area microlens arrays in Fused Silica.

The uniformity of large microlens arrays in Fused Silica is governed by the production process. It comprises photolithographic patterning of a spin-coated layer of photoresist on a 200mm wafer with a molten resist reflow process and subsequent dry etching. By investigating systematic influences throughout the production process we show how to steer the lens production process with a single degree of freedom to improve the uniformity of the final microlens array. To enable this we describe the optical performance of microlenses with only one parameter: the principal aberration component. It is the result of principal component analysis of the chosen optical merit function. We present the case of manufactured microlens arrays with element sizes >100 mm × 100 mm where uniformity was improved by a factor of 2.

Computational rule-based approach for corner correction of non-Manhattan geometries in mask aligner photolithography.

In proximity mask aligner photolithography, diffraction of light at the mask pattern is the predominant source for image shape distortions such as line end shortening and corner rounding. One established method to mitigate the impact of diffraction is optical proximity correction. This method relies on a deliberate sub-resolution modification of photomask features to counteract such shape distortions, with the goal to improve pattern fidelity and uniformity of printed features. While previously considered for masks featuring only rectangular shapes in horizontal or vertical orientation, called Manhatten geometries, we demonstrate here the capabilities of computational mask aligner lithography by extending optical proximity correction to non-Manhattan geometries. We combine a rigorous simulation method for light propagation with a particle-swarm optimization to identify suitable mask patterns adapt to each occurring feature in the mask. The improvement in pattern quality is demonstrated in experimental prints. Our method extends the use of proximity lithography in optical manufacturing, as required in a multitude of micro-optical devices.

High-quality single crystal diamond diffraction gratings fabricated by crystallographic etching.

We demonstrate a novel method for fabricating single crystal diamond diffraction gratings based on crystallographic etching that yields high-quality diffraction gratings from commercially available <100> diamond plates. Both V-groove and rectangular gratings were fabricated and characterised using scanning electron microscopy and atomic force microscopy, revealing angles of 57° and 87° depending on the crystal orientation, with mean roughness below Ra = 5 nm on the sidewalls. The gratings were also optically characterised, showing good agreement with simulated results. The fabrication method demonstrated in this contribution shows the way for manufacturing high-quality diamond diffractive components that surpass existing devices both in quality and manufacturability.

High-resolution interference microscopy with spectral resolution for the characterization of individual particles and self-assembled meta-atoms.

We apply a high-resolution interference microscope with spectral resolution to investigate the scattering response of isolated meta-atoms in real space. The final meta-atoms consist of core-shell clusters that are fabricated using a bottom-up approach. The meta-atoms are investigated with an increasing complexity. We start by studying silica and gold spheres and conclude with the investigation of the meta-atom, which consists of a silica core sphere onto which gold nanospheres are attached. Numerical simulations entirely verify the measured data. The measuring process involves recording the intensity and phase of the total field emerging from the scattering process of an incident light at the particle in the transmitted half-space with spectral and high spatial resolution. We show that spectrally resolved high-resolution interference microscopy can be used to differentiate between nanoparticles and characterize single meta-atoms, something that is rarely accomplished.

High-power modular LED-based illumination systems for mask-aligner lithography.

Mask-aligner lithography is traditionally performed using mercury arc lamps with wavelengths ranging from 250 nm to 600 nm with intensity peaks at the i, g and h lines. Since mercury arc lamps present several disadvantages, it is of interest to replace them with high power light emitting diodes (LEDs), which recently appeared on the market at those wavelengths. In this contribution, we present a prototype of an LED-based mask-aligner illumination. An optical characterization is made and the prototype is tested in a mask-aligner. Very good performances are demonstrated. The measured uniformity in the mask plane is 2.59 ± 0.24 % which is within the uniformity of the standard lamp. Print tests show resolution of 1 micron in contact printing and of 3 microns in proximity printing with a proximity gap of 30 microns.

Printing sub-micron structures using Talbot mask-aligner lithography with a 193 nm CW laser light source.

A continuous improvement of resolution in mask-aligner lithography is sought after to meet the requirements of an ever decreasing minimum feature size in back-end processes. For periodic structures, utilizing the Talbot effect for lithography has emerged as a viable path. Here, by combining the Talbot effect with a continuous wave laser source emitting at 193 nm, we demonstrate successfully the fabrication of periodic arrays in silicon substrates with sub-micron feature sizes. The excellent coherence and the superior brilliance of this light source, compared to more traditional mercury lamps and excimer lasers as light source, enables the efficient beam shaping and a reduced minimum feature size at a fixed gap of 20 µm. We present a comprehensive study of proximity printing with this system, including simulations and selected experimental results of prints in up to the fourth Talbot plane. This printing technology can be used to manufacture optical metasurfaces, bio-sensor arrays, membranes, or microchannel plates.

Mask-aligner lithography using a continuous-wave diode laser frequency-quadrupled to 193 nm.

We present a mask-aligner lithographic system operated with a frequency-quadrupled continuous-wave diode laser emitting at 193 nm. For this purpose, a 772 nm diode laser is amplified by a tapered amplifier in the master-oscillator power-amplifier configuration. The emission wavelength is upconverted twice, using LBO and KBBF nonlinear crystals in second-harmonic generation enhancement cavities. An optical output power of 10 mW is achieved. As uniform exposure field illumination is crucial in mask-aligner lithography, beam shaping is realized with optical elements made from fused silica and CaF2 featuring a diffractive non-imaging homogenizer. A tandem setup of shaped random diffusers, one static and one rotating, is used to control speckle formation. We demonstrate first experimental soft contact and proximity prints for a field size of 1 cm2 with a standard binary photomask and proximity prints with a two-level phase mask, both printed into 120 nm layers of photoresist on unstructured silicon substrates.

Experimental demonstration of ray-rotation sheets.

We have built microstructured sheets that rotate, on transmission, the direction of light rays by an arbitrary, but fixed, angle around the sheet normal. These ray-rotation sheets comprise two pairs of confocal lenticular arrays. In addition to rotating the direction of transmitted light rays, our sheets also offset ray position sideways on the scale of the diameter of the lenticules. If this ray offset is sufficiently small so that it cannot be resolved, our ray-rotation sheets appear to perform generalized refraction.

Refraction limit of miniaturized optical systems: a ball-lens example.

We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between the refraction and diffraction regime. The former regime is dominated by observables for which it is sufficient to use a ray-optical picture for an explanation, e.g., a cusp catastrophe and caustics. A wave-optical picture, i.e. Mie theory, is required to explain the features, e.g., photonic nanojets, in the latter regime. The vanishing of the cusp catastrophe and the emergence of the photonic nanojet is here understood as the refraction limit. Three different criteria are used to identify the limit: focal length, spot size, and amount of cross-polarization generated in the scattering process. We identify at a wavelength of 642 nm and while considering ordinary glass as the ball-lens material, a diameter of approximately 10 µm as the refraction limit. With our study, we shed new light on the means necessary to describe micro-optical system. This is useful when designing optical devices for imaging or illumination.

Phase anomalies in Talbot light carpets of self-images.

An interesting feature of light fields is a phase anomaly, which occurs on the optical axis when light is converging as in a focal spot. Since in Talbot images the light is periodically confined in both transverse and axial directions, it remains an open question whether at all and to which extent the phase in the Talbot images sustains an analogous phase anomaly. Here, we investigate experimentally and theoretically the anomalous phase behavior of Talbot images that emerge from a 1D amplitude grating with a period only slightly larger than the illumination wavelength. Talbot light carpets are observed close to the grating. We concisely show that the phase in each of the Talbot images possesses an anomalous axial shift. We show that this phase shift is analogous to a Gouy phase of a converging wave and occurs due to the periodic light confinement caused by the interference of various diffraction orders. Longitudinal-differential interferometry is used to directly demonstrate the axial phase shifts by comparing Talbot images phase maps to a plane wave. Supporting simulations based on rigorous diffraction theory are used to explore the effect numerically. Numerical and experimental results are in excellent agreement. We discover that the phase anomaly, i.e., the difference of the phase of the field behind the grating to the phase of a referential plane wave, is an increasing function with respect to the propagation distance. We also observe within one Talbot length an irregular wavefront spacing that causes a deviation from the linear slope of the phase anomaly. We complement our work by providing an analytical model that explains these features of the axial phase shift.

Talbot images of wavelength-scale amplitude gratings.

By means of experiment and simulation, we achieve unprecedented insights into the formation of Talbot images to be observed in transmission for light diffracted at wavelength-scale amplitude gratings. Emphasis is put on disclosing the impact and the interplay of various diffraction orders to the formation of Talbot images. They can be manipulated by selective filtering in the Fourier plane. Experiments are performed with a high-resolution interference microscope that measures the amplitude and phase of fields in real-space. Simulations have been performed using rigorous diffraction theory. Specific phase features, such as singularities found in the Talbot images, are discussed. This detailed analysis helps to understand the response of fine gratings. It provides moreover new insights into the fundamental properties of gratings that often find use in applications such as, e.g., lithography, sensing, and imaging.

Phase anomalies in Bessel-Gauss beams.

Bessel-Gauss beams are known as non-diffracting beams. They can be obtained by focusing an annularly shaped collimated laser beam. Here, we report for the first time on the direct measurement of the phase evolution of such beams by relying on longitudinal-differential interferometry. We found that the characteristics of Bessel-Gauss beams cause a continuously increasing phase anomaly in the spatial domain where such beams do not diverge, i.e. there is a larger phase advance of the beam when compared to a referential plane wave. Simulations are in excellent agreement with measurements. We also provide an analytical treatment of the problem that matches both experimental and numerical results and provides an intuitive explanation.

Longitudinal-differential interferometry: direct imaging of axial superluminal phase propagation.

We introduce and demonstrate a new interferometric method called longitudinal-differential (LD) interferometry, which measures the spatially resolved phase difference of the scattered field by an object relative to the illumination. This method is combined with a high-resolution interference microscope that allows recording three-dimensional field distributions in amplitude and phase. The method is applied to study the axial phase behavior of Arago spots, an effect observable in low-Fresnel-number systems behind objects with a size comparable to the wavelength. We directly observe the initial phase delay in the Arago spot and prove that the local phase velocity exceeds the speed of light in air. Such LD phase studies are applicable not only to the Arago spot but also to other kinds of light interactions with wavelength-scale objects, e.g., photonic nanojets.

Engineering photonic nanojets.

Photonic Nanojets are highly localized wave fields emerging directly behind dielectric microspheres; if suitably illuminated. In this contribution we reveal how different illumination conditions can be used to engineer the photonic Nanojets by measuring them in amplitude and phase with a high resolution interference microscope. We investigate how the wavelength, the amplitude distribution of the illumination, its polarization, or a break in symmetry of the axial-symmetric structure and the illumination affect the position, the localization and the shape of the photonic Nanojets. Various fascinating properties are systematically revealed and their implications for possible applications are discussed.

Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings.

Despite the progress in the engineering of structures to enhance photocurrent in thin film solar cells, there are few comprehensive studies which provide general and intuitive insight into the problem of light trapping. Also, lack of theoretical propositions which are consistent with fabrication is an issue to be improved. We investigate a real thin film solar cell with almost conformal layers grown on a 1D grating metallic back-reflector both experimentally and theoretically. Photocurrent increase is observed as an outcome of guided mode excitation in both theory and experiment by obtaining the external quantum efficiency of the cell for different angles of incidence and in both polarization directions. Finally, the effect of geometrical parameters on the short circuit current density of the device is investigated by considering different substrate shapes that are compatible with solar cell fabrication. Based on our simulations, among the investigated shapes, triangular gratings with a very sharp slope in one side, so called sawtooth gratings, are the most promising 1D gratings for optimal light trapping.