Spherical Microlenses Research Articles

Influence of sphere-surface distance and exposure dose on resolution of sphere-lens-array lithography.

Sphere-surface distance and exposure dose effects on lithography resolution of microsphere lens array are studied. A transparent gap is introduced between photoresist film and polystyrene microspheres to adjust light distribution of photoresist surface. The pores size on the photoresist film varies when the gap thickness is changed. By optimization gap thickness and exposure dose, sub-100 nm surface patterning array is achieved for sphere of 2.06 µm diameter and optical wavelength λ of 400 nm theoretically and experimentally. Furthermore, when smaller polystyrene sphere (1.25 µm diameter) is chosen, spot width of 35 nm is realized by numerical calculation. This nano-fabrication method is simple, low-cost and high-efficiency, which can provide opportunities to make a variety of nano-devices, such as biosensors and nano-antennas.

Biconvex Polymer Microlenses with Tunable Imaging Properties Designed by Janus Droplet Microfluidics

This work presents a technique for fabricating biconvex polymer microlenses using microfluidics, and then evaluates their tunable optical properties. A glass microfluidic channel was employed to rapidly mass-produce nanoliter-sized biphasic Janus droplets, which consist of a biconvex segment of a photocurable monomer and a concave-convex segment of a non-curable silicone oil that contained a surfactant. Subsequent photopolymerization produces polymeric biconvex spherical microlenses with templated dual curvatures. By changing the flow-rate ratios of the photocurable and non-curable droplet phases in the microfluidic channel, the radii of curvature of the two lens surfaces and the thicknesses of the resultant microlenses can be varied. The resulting biconvex microlenses with different shapes were used in image projection experiments. Different magnification properties were observed, and were consistent with the properties estimated quantitatively from the geometrical parameters of the lenses.

Deep-UV microsphere projection lithography.

In this Letter, we present a single-exposure deep-UV projection lithography at 254-nm wavelength that produces nanopatterns in a scalable area with a feature size of 80 nm. In this method, a macroscopic lens projects a pixelated optical mask on a monolayer of hexagonally arranged microspheres that reside on the Fourier plane and image the mask's pattern into a photoresist film. Our macroscopic lens shrinks the size of the mask by providing an imaging magnification of ∼1.86×10(4), while enhancing the exposure power. On the other hand, microsphere lens produces a sub-diffraction limit focal point-a so-called photonic nanojet-based on the near-surface focusing effect, which ensures an excellent patterning accuracy against the presence of surface roughness. Ray-optics simulation is utilized to design the bulk optics part of the lithography system, while a wave-optics simulation is implemented to simulate the optical properties of the exposed regions beneath the microspheres. We characterize the lithography performance in terms of the proximity effect, lens aberration, and interference effect due to refractive index mismatch between photoresist and substrate.

Shape optimization of microlenses.

Microlenses are highly attractive for optical applications such as super resolution and photonic nanojets, but their design is more demanding than the one of larger lenses because resonance effects play an important role, which forces one to perform a full wave analysis. Although mostly spherical microlenses were studied in the past, they may have various shapes and their optimization is highly demanding, especially, when the shape is described with many parameters. We first outline a very powerful mathematical tool: shape optimization based on shape gradient computations. This procedure may be applied with much less numerical cost than traditional optimizers, especially when the number of parameters describing the shape goes to infinity. In order to demonstrate the concept, we optimize microlenses using shape optimization starting from more or less reasonable elliptical and semi-circular shapes. We show that strong increases of the performance of the lenses may be obtained for any reasonable value of the refraction index.

Liquid crystal microlens arrays recorded by polarization holography.

We report the characterization of diffractive microlens arrays (MAs) using a polarization holographic approach assisted by a spatial light modulator (SLM), in a nematic liquid crystal (NLC) cell. The MAs were recorded in the photoaligning substrates of the cell and then replicated in the NLC bulk, through the surface interactions. The transparency of the NLC on a wide range of wavelengths and the ability to tune its optical birefringence, through an external voltage, allowed us to create MAs with high efficiency. We have presented the results obtained for diverse MAs configurations, composed by spherical and cylindrical microlenses and characterized by different focal lengths. The efficiency reaches a value of 90%, at a wavelength of 633nm.

Glasses-Free Three-Dimensional Display Based on Microsphere-Lens Array

A 3D display based on a microsphere-lens (MSL) array is proposed. This 3D display uses the MSL array to project the parallax images on a 2D display panel into different spatial directions. Each MSL can work as a conventional micro-lens. However, the MSL has a much shorter focal length than the conventional micro-lens. The shorter focal length is helpful for increasing the viewing angle. A prototype of the 3D display is developed. Experiment result shows that the proposed display has a large viewing angle and the crosstalk is also limited in a low level.

Fabrication of long-focal-length plano-convex microlens array by combining the micro-milling and injection molding processes.

A uniform plano-convex spherical microlens array with a long focal length was fabricated by combining the micromilling and injection molding processes in this work. This paper presents a quantitative study of the injection molding process parameters on the uniformity of the height of the microlenses. The variation of the injection process parameters, i.e., barrel temperature, mold temperature, injection speed, and packing pressure, was found to have a significant effect on the uniformity of the height of the microlenses, especially the barrel temperature. The filling-to-packing switchover point is also critical to the uniformity of the height of the microlenses. The optimal uniformity was achieved when the polymer melts completely filled the mold cavity, or even a little excessively filled the cavity, during the filling stage. In addition, due to the filling resistance, the practical filling-to-packing switchover point can vary with the change of the filling processing conditions and lead to a non-negligible effect on the uniformity of the height of the microlenses. Furthermore, the effect of injection speed on the uniformity of the height of the microlenses was analyzed in detail. The results indicated that the effect of injection speed on the uniformity of the height of the microlenses is mainly attributed to the two functions of injection speed: transferring the filling-to-packing switchover point and affecting the distribution of residual flow stress in the polymer melt.

Role of the immersion medium in the microscale spherical lens imaging

The role of the immersion medium in the microscale speherical lens imaging is studied. We find that when a microsphere lens is semi-immersed in the SU-8 resist, both the microsphere and the SU-8 resist can work as a lens. The microsphere lens forms the images from the small-k Fourier components of an object, and this image formation does not depend on the immersion of the SU-8 resist. The SU-8 resist can work as a lens and form the images from the large-k Fourier components. When the distance d between the focal spot of the SU-8 lens and the object is close, the clear large-k Fourier components image can be observed even without the microsphere.

Fabrication of concave spherical microlenses on silicon by femtosecond laser irradiation and mixed acid etching.

All-silicon plano-concave microlens arrays with spherical profiles and good image performance were obtained using femtosecond laser direct irradiation and mixed acid etching. A femtosecond laser was employed to produce microhole arrays on silicon, and the microholes were expanded and smoothed by the mixed acid to form concave microlenses. The effects of the etching time, laser power, and pulse number on the microlens morphology were investigated. This method has potential applications in the fabrication of all-silicon plano-concave microlenses for use in infrared devices.

Fabricating Microlenses on Photodiodes to Increase the Light-Current Conversion Efficiency

This letter presents a microlenses (MLs) fabrication process for enhancing the photocurrent (PC) generation efficiency of photodiodes (PDs). The concept was demonstrated with a plano-convex spherical ML fabricated directly on top of a PD. The PDs are of type n+-p-substrate junction fabricated in a standard CMOS process. The base and sag height of the MLs measure 26 and 5 μm, respectively. The PC generation was measured inside a dark chamber under normally incident red light illuminance both with and without the ML on top of the PD. The illuminance was linearly incremented from 0 to 2000 lux. The ML forces more light to impinge into the PDs active area and, therefore, promotes more PC generation. The measurements show that the PD generates, at an approximately constant rate of 14%, more PC with the MLs than without the MLs.

Oil droplets of bird eyes: microlenses acting as spectral filters

An important component of the cone photoreceptors of bird eyes is the oil droplets located in front of the visual-pigment-containing outer segments. The droplets vary in colour and are transparent, clear, pale or rather intensely yellow or red owing to various concentrations of carotenoid pigments. Quantitative modelling of the filter characteristics using known carotenoid pigment spectra indicates that the pigments' absorption spectra are modified by the high concentrations that are present in the yellow and red droplets. The high carotenoid concentrations not only cause strong spectral filtering but also a distinctly increased refractive index at longer wavelengths. The oil droplets therefore act as powerful spherical microlenses, effectively channelling the spectrally filtered light into the photoreceptor's outer segment, possibly thereby compensating for the light loss caused by the spectral filtering. The spectral filtering causes narrow-band photoreceptor spectral sensitivities, which are well suited for spectral discrimination, especially in birds that have feathers coloured by carotenoid pigments.

Performance Optimization of InSb Infrared Focal-Plane Arrays with Diffractive Microlenses

In this paper, diffractive microlens arrays are studied to concentrate incident light onto the effective photosensitive area of InSb infrared focal-plane arrays and thus enhance the quantum efficiency and reduce the crosstalk. Four designs of diffractive microlenses are investigated by a phase-matched Fresnel-elements approach. The quantum efficiency and crosstalk of the devices are calculated by using a two-dimensional device simulation with unit cell of 50 μm. Light propagation through the diffractive microlenses is simulated by the finite-difference time-domain method based on a rigorous vector solution of Maxwell’s equations. The results show that the highest quantum efficiency of the device with a diffractive microlens array is about 51.6% and the corresponding crosstalk is 5.06%. The quantum efficiency is 2.1% higher than that of the device with a spherical refractive microlens array.

Cost-efficient and flexible fabrication of rectangular-shaped microlens arrays with controllable aspect ratio and spherical morphology

This paper presents a cost-efficient and flexible approach to the development of controllable-shape concave and convex microlens arrays by using femtosecond laser wet etch and replication techniques. Periodic concave rectangular-shaped microlens arrays with different length–width ratios were achieved by firstly introducing periodic microcraters on silica glass using an 800nm femtosecond laser, and subsequently enlarging the craters into microlens with smooth curved surfaces in hydrofluoric (HF) acid solution. The concave microlens can serve as molds of replication to obtain convex microlenses on polymers. Over 10,000 rectangular-shaped concave and convex microlens with controllable aspect ratio, high fill factor and spherical morphology can be fabricated in 5h. A simulation result and a projection experiment result verify the optical performance of these rectangular-shaped spherical microlens arrays (MLAs).

The fabrication of aspherical microlenses using focused ion-beam techniques

Aspheric lenses are the most common method for correcting for spherical aberrations but, in microlens production, highly-controlled lens profiles are hard to achieve. We demonstrate a technique for creating bespoke, highly-accurate aspheric or spherical profile silicon microlens moulds, of almost any footprint, using focused ion-beam milling. Along with this, we present a method of removing induced ion-beam damage in silicon, via a hydrofluoric acid etch, helping to recover the surface's optical and chemical properties.In this paper, we demonstrate that our milled and etched moulds have a roughness of 4.0–4.1nm, meaning they scatter less than 1% of light, down to wavelengths of 51nm, showing that the moulds are suitable to make lenses that are able to handle light from UV up to infra-red.Using empirical experiments and computer simulations, we show that increasing the ion-dose when milling increases the amount of gallium a hydrofluoric acid etch can remove, by increasing the degree of amorphisation within the surface. For doses above 3000μC/cm2 this restores previous surface properties, reducing adhesion to the mould, allowing for a cleaner release and enabling higher quality lenses to be made.Our technique is used to make aspheric microlenses of down to 3μm in size, but with a potential to make lenses smaller than 1μm.

Research on Fabricating of Square Aperture Spherical Micro-Lens Array through the Laser Lithography

Due to the practical problems nowadays that the duty cycle is small and the utility rate of solar energy is low of photoelectric sensor light sensitive array, and having analyzed the advantages on solar energy utilization of square aperture spherical micro-lens than traditional circular aperture micro-lens array, we conduct a research on the fabricating of square aperture spherical micro-lens and testing technology. With the help of light spread theory, we analyses the relationship between light amplitude distributing rules, exposure length and exposure energy, establish a mathematical model of light distributing rules and use computer software to emulate the model. The results indicate solar energy distributes regularly in adhesive film. If the energy is fixed, exposure length will gradually become saturated following time. At the same time, we fabricate infrared quartz micro-lens array with array 256×256, single element lens 40×40μm, spherical radius 60μm, single element spacing 1μm.The experiment data are the same as emulation results.

Experimental and theoretical study of the Gouy phase anomaly of light in the focus of microlenses

We report on the Gouy phase anomaly of light in the focus of cylindrical and spherical microlenses. The prime subject of our study concerns a discussion of how the very small size of microlenses affects the phase properties of light in their foci. We put emphasis on determining the amount of the Gouy phase shift for line and point foci within the limited axial space. Contrary to macroscopic lenses, the optical properties of microlenses are strongly governed by the effect of diffraction when their size tends to be comparable to the operation wavelength. In our study, we clearly show how such diffraction features affect the axial phase shift. For instance, phase singularities, which occur at discrete points on the optical axis where the total intensity vanishes for spherical microlenses, cause an additional axial phase shift when compared to the cylindrical microlens where those axial phase singularities are absent. The rotational symmetry of the Fresnel zones is the origin of such a difference between point and line foci.

Investigation of Radiation Collection by InSb Infrared Focal-Plane Arrays with Micro-optic Structures

Three designs of micro-optic structures have been analyzed by two-dimensional simulation. Compared with traditional spherical microlenses, the micro-optic structures have the same ability to collect radiation and do not have the disadvantages of traditional microlenses. In our analysis the micro-optic structures are simple grooved notches above the space between two adjacent mesas. We also investigate the characteristics of InSb focal-plane arrays with both spherical microlenses and micro-optic structures under oblique incident radiation. Empirical formulas were derived to describe the response and crosstalk as a function of incident radiation angle. Our results show that the micro-optic structures can be effectively used in radiation collection for InSb infrared focal-plane arrays.

Classical imaging theory of a microlens with super-resolution

Super-resolution in imaging through a transparent spherical microlens has attracted lots of attention because of recent promising experimental results with remarkable resolution improvement. To provide physical insight for this super-resolution phenomenon, previous studies adopted a phenomenological explanation mainly based on the super-focusing effect of a photonic nanojet, while a direct imaging calculation with classical imaging theory has rarely been studied. Here we theoretically model the imaging process through a microlens with vectorial electromagnetic analysis, and then exclude the previously plausible explanation of super-resolution based on the super-focusing effect. The results showed that, in the context of classical imaging theory subject to the two-point resolution criterion, a microlens with a perfect spherical shape cannot achieve the experimentally verified sub-100 nm resolution. Therefore, there must be some other physical mechanisms that contribute to the reported ultrahigh resolution but have not been revealed in theory.

Large Area IR Microlens Arrays of Chalcogenide Glass Photoresists by Grayscale Maskless Lithography

The ability to use chalcogenide glass thin films as photoresists for one-step maskless grayscale lithographic patterning is demonstrated. It is shown that the chalcogenide photoresists can be used to fabricate grayscale patterns with smooth and continuous profiles such as arrays of cylindrical and spherical microlenses, which are useful as optical structures for IR applications. The etching and exposure parameters are optimized to obtain smooth reproducible lens arrays of 150 μm periodicity and up to ∼170 nm height on large areas (∼1 cm(2)). The roughness is found to increase as a function of the exposure dose and is attributed to the selective dissolution of the As-Se, As-As, and Se-Se bonds present in the nanodistributed phases and the presence of the oxide phase. Thus, a minimum exposure dose produces optimally patterned lens arrays. The focal length calculated for the smooth microlens array is ∼9.3 mm, indicating the suitability of the lens arrays for focusing applications in the IR region.

Method to design two aspheric surfaces for imaging system

This paper proposes a method of designing two aspheric surfaces simultaneously for an imaging system. By coupling the three rays (two marginal rays and one chief ray from the exit pupil) of each field of view to their corresponding image point, microspherical lens corresponding to each field of view can be obtained by the refraction law. Profiles of the aspheric surfaces can be obtained by employing the position and normal vector of midpoint of the microsphere corresponding to each field of view. Theoretically, through this method, we can realize any mapping relationship between the object points and their image points in 2D. Combining an original projector with the aspheric lens designed in this paper, an example that realizes projection onto a spherical surface with both low distortion and high image quality is presented.