Partial Coherent Light Research Articles

Introducing Corrections to the Reflectance of Graphene by Light Emission

Monolayer graphene absorbs 2.3 percent of the incident visible light. This “small” absorption has been used to emphasize the visual transparency of graphene, but it in fact means that multilayer graphene absorbs a sizable fraction of incident light, which causes non-negligible fluorescence. In this paper, we formulate the light emission properties of multilayer graphene composed of tens to hundreds of layers using a transfer matrix method and confirm the method’s validity experimentally. We quantitatively explain the measured contrasts of multilayer graphene on SiO2/Si substrates and find sizable corrections, which cannot be classified as incoherent light emissions, to the reflectance of visible light. The new component originates from coherent emission caused by absorption at each graphene layer. Multilayer graphene thus functions as a partial coherent light source of various wavelengths, and it may have surface-emitting laser applications.

A spatial carrier dynamic quantitative differential phase imaging method

Differential interference contrast (DIC) microscopy is an important method for quantitative phase imaging (QPI) due to its high compatibility regarding to partial coherent light illumination and excellent optical sectioning ability. However, limited by the on-axis interferometric configuration of Nomarski DIC microscopic imaging system, it is difficult to achieve single-shot phase retrieval. Here, we propose a simple and efficient method for dynamic quantitative differential phase imaging (QDPI) by introducing a spatial carrier device into DIC microscope. A Wollaston prism (WP) is placed on the imaging plane of DIC microscope and then projected by a 4f imaging system, so two orthogonally polarized imaging beams with a certain shearing amount will interfere on the conjugate plane of the 4f imaging system and form a spatial carrier DIC image, thus the QDPI can be conveniently realized. Importantly, the system not only possesses high temporal phase stability provided by the common-path geometries and low spatial phase noise due to partially coherent light illumination, but also the advantages of simple optical implementation, no additional phase distortion, high light energy utilization efficiency, and high signal-to-noise ratio. The experimental result demonstrates that using the proposed method, the phase measurement sensitivity reaches 0.003 rad, the corresponding applicability is verified by a polystyrene microsphere crown and biological cells.

Towards practical physical-optics rendering

Physical light transport (PLT) algorithms can represent the wave nature of light globally in a scene, and are consistent with Maxwell's theory of electromagnetism. As such, they are able to reproduce the wave-interference and diffraction effects of real physical optics. However, the recent works that have proposed PLT are too expensive to apply to real-world scenes with complex geometry and materials. To address this problem, we propose a novel framework for physical light transport based on several key ideas that actually makes PLT practical for complex scenes. First, we restrict the spatial coherence shape of light to an anisotropic Gaussian and justify this restriction with general arguments based on entropy. This restriction serves to simplify the rest of the derivations, without practical loss of generality. To describe partially-coherent light, we present new rendering primitives that generalize the radiometric radiance and irradiance, and are based on the well-known Stokes parameters. We are able to represent light of arbitrary spectral content and states of polarization, and with any coherence volume and anisotropy. We also present the wave BSDF to accurately render diffractions and wave-interference effects. Furthermore, we present an approach to importance sample this wave BSDF to facilitate bi-directional path tracing, which has been previously impossible. We show good agreement with state-of-the-art methods, but unlike them we are able to render complex scenes where all the materials are new, coherence-aware physical optics materials, and with performance approaching that of "classical" rendering methods.

Physical light-matter interaction in hermite-gauss space

Our purpose in this paper is two-fold: introduce a computationally-tractable decomposition of the coherence properties of light; and, present a general-purpose light-matter interaction framework for partially-coherent light. In a recent publication, Steinberg and Yan [2021] introduced a framework that generalises the classical radiometry-based light transport to physical optics. This facilitates a qualitative increase in the scope of optical phenomena that can be rendered, however with the additional expressibility comes greater analytic difficulty: This coherence of light, which is the core quantity of physical light transport, depends initially on the characteristics of the light source, and mutates on interaction with matter and propagation. Furthermore, current tools that aim to quantify the interaction of partially-coherent light with matter remain limited to specific materials and are computationally intensive. To practically represent a wide class of coherence functions, we decompose their modal content in Hermite-Gauss space and derive a set of light-matter interaction formulae, which quantify how matter scatters light and affects its coherence properties. Then, we model matter as a locally-stationary random process, generalizing the prevalent deterministic and stationary stochastic descriptions. This gives rise to a framework that is able to formulate the interaction of arbitrary partially-coherent light with a wide class of matter. Indeed, we will show that our presented formalism unifies a few of the state-of-the-art scatter and diffraction formulae into one cohesive theory. This formulae include the sourcing of partially-coherent light, scatter by rough surfaces and microgeometry, diffraction grating and interference by a layered structure.

Quantitative imaging for optical field via a single-pixel detector

Quantitative phase imaging (QPI) is important in many applications such as microscopy and crystallography. To quantitatively reveal phase information, people could either employ interferometric pictures for phase shift calculation, or utilize diffraction patterns for phase retrieval reconstruction. Traditionally, both of these two ways use pixelated detectors. In this work, a novel QPI scheme is designed inspired by single-pixel camera (SPC), which retrieves images using structured illumination and single-pixel signals. We use partial coherent light with phase modulation for illumination, and a point detector to detect the zero-order diffraction spectrum of the object. Based on the illumination structures and point signals, a complex value image is reconstructed using a truncated amplitude flow phase retrieval algorithm. This approach is universal for various wavelengths, and needs no a priori information of the targets. Both simulation and experiment show that our single-pixel QPI scheme exhibits great performance even with objects in an extremely rough phase distribution.

Influence of Partial Coherent Light on the Transmission Spectrum and Goos-Hänchen Shift in Rydberg Atomic Medium

A cold atomic medium (Rydberg medium) with cascade configuration under the blockade mechanism is considered. A partial coherent light (PCL) beam is incident on the medium, which makes an angle θ with z-axis. We study the influence of PCL field on the transmission spectrum and find high transmission of probe field for PCL field. Conversely, it is investigated that the transparency of probe field decrease for coherent light field. The transmission of probe field is also studied via beam width of PCL field and investigated high transmission of probe field for small beam width and vice versa. Interestingly, the Goos-Hänchen shift (GHS) in the transmitted light (TL) is studied for PCL field. Large negative and positive GHS in the TL are investigated for PCL field and small beam width of PCL field.

Coherence of cold atoms trapped by partially coherent light

Abstract The coherence of cold atom trapped and cooled by the partially coherent light (PCL) is investigated experimentally through Rabi oscillations. We control the degree of the spatial coherence of the laser beams by the modulation of electro-optic crystal. The experimental results show that the cold atoms captured by the different coherent degree of light have little different coherence properties and almost the same capacity of resisting disturbance, which indicates that the coherence of cold atom is affected weakly by the coherence of cooling field.

Measurements of slit-width effects in Young’s double-slit experiment for a partially-coherent source

We provide measurements of Young’s double-slit experiment using a partially-coherent light source consisting of a helium-neon laser incident on a rotating piece of white paper. The data allow a quantitative comparison with both the standard theory that does not account for the width of the slits, and a full, analytic model that does. The data agree much more favorably with the full calculation.

Numerical simulations of spectral shifts in the far-field spectrum of light due to source correlations

We discuss how to simulate numerically the far-field propagation of the spectrum of light by propagating the cross-spectral density for a planar light source with a given coherence model. To test our approach, we performed simulations for two source models: a Gaussian Schell-model source and a nonuniformly Gaussian-correlated source. We show that our algorithm correctly reproduces the theoretical solutions by Emil Wolf for planar Gaussian Schell-model source, namely, the spectral shifts of spectral lines due to source correlations. Our approach can be used for two-dimensional source models in which the spatial coherence components are frequency independent. It can also be used for nonhomogeneous extended sources of partial coherent light.

Diffraction of partially-coherent light beams by microlens arrays.

The synthesis method including wave-optics and ray-tracing for the acceleration of the simulation of micro-optical systems has been developed. The effects of the spatial coherence and randomization of microlens array (MLA) parameters have been considered. The method based on coherent states representation for the calculation of the optical efficiency of microlens arrays taking into account the light source polarization has been developed. Numerical simulations of the intensity distributions and spreading angle of a diffracted beam have been carried out.

Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials.

The Goos-Hänchen (GH) shifts in the reflected light are investigated both for p and s polarized partial coherent light beams incident on epsilon-near-zero (ENZ) metamaterials. In contrary to the coherent counterparts, the magnitude of GH shift becomes non-zero for p polarized partial coherent light beam; while GH shift can be relatively large with a small degree of spatial coherence for s polarized partial coherent beam. Dependence on the beam width and the permittivity of ENZ metamaterials is also revealed for partial coherent light fields. Our results on the GH shifts provide a direction on the applications for partial coherent light sources in ENZ metamaterials.

Goos–Hänchen shifts of partially coherent light beams from a cavity with a four-level Raman gain medium

We theoretically investigate spatial and angular Goos–Hänchen (GH) shifts (both negative and positive) in the reflected light for a partial coherent light incident on a cavity. A four-level Raman gain atomic medium is considered in a cavity. The effects of spatial coherence, beam width, and mode index of partial coherent light fields on spatial and angular GH shifts are studied. Our results reveal that a large magnitude of negative and positive GH shifts in the reflected light is achievable with the introduction of partial coherent light fields. Furthermore, the amplitude of spatial (negative and positive) GH shifts are sharply affected by the partial coherent light beam as compared to angular (negative and positive) GH shifts in the reflected light.

Study of birefringence influence on image quality of photolithography systems in view of partially-coherent light source

Subject of study. A vector model for conversion of electromagnetic radiation in optical systems is considered, taking into account the influence of birefringence, as well as partially coherent illumination. Model. The proposed model is based on the representation of the complex amplitude of the monochromatic field through thesuperposition of basic plane waves. Transmitted light image with partially coherent illumination is performed by the sourceintegration method. Main results. The results of simulation for the point spread function are demonstrating the level of the birefringence influence on the image quality. In the presence of the wave aberration about 0.098 of the wavelength, the wave energy loss in the center of the Airy disk with an average birefringence of 4 nm/cm was 8%, and at 16 nm/cm it reached 30%. The calculation of the point spread function for a real sample of fluorite is given. The central peak of the PSF without birefringence was 0.722, with regard to birefringence it was equal to 0.701. Practical significance. The findings can be used in the development of photolithographic lenses, as well as for the manufacturing of any other optical systems that require consideration of the polarization properties of the materials.

Negative and positive Goos-Hänchen shifts of partially coherent light fields

The negative and positive Goos-H\"anchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.

A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length

We propose a method for calculating the optical response to partially-coherent light based on the coherence length. Using a Fourier transform of a randomly-generated partially-coherent wave, we demonstrate that the reflectance, transmittance, and absorption with the incidence of partially-coherent light can be calculated from the Poynting vector of the incident coherent light. We also demonstrate that the statistical field distribution of partially-coherent light can be obtained from the proposed method using a rigorous coupled wave analysis. The optical characteristics of grating structures in photovoltaic devices are analyzed as a function of coherence length. The method is capable of providing a general procedure for analyzing the incoherent optical characteristics of thick layers or nano particles in photovoltaic devices with the incidence of partially-coherent light.

Giga-Pixel Lensfree Holographic Microscopy and Tomography Using Color Image Sensors

We report Giga-pixel lensfree holographic microscopy and tomography using color sensor-arrays such as CMOS imagers that exhibit Bayer color filter patterns. Without physically removing these color filters coated on the sensor chip, we synthesize pixel super-resolved lensfree holograms, which are then reconstructed to achieve ∼350 nm lateral resolution, corresponding to a numerical aperture of ∼0.8, across a field-of-view of ∼20.5 mm2. This constitutes a digital image with ∼0.7 Billion effective pixels in both amplitude and phase channels (i.e., ∼1.4 Giga-pixels total). Furthermore, by changing the illumination angle (e.g., ±50°) and scanning a partially-coherent light source across two orthogonal axes, super-resolved images of the same specimen from different viewing angles are created, which are then digitally combined to synthesize tomographic images of the object. Using this dual-axis lensfree tomographic imager running on a color sensor-chip, we achieve a 3D spatial resolution of ∼0.35 µm×0.35 µm×∼2 µm, in x, y and z, respectively, creating an effective voxel size of ∼0.03 µm3 across a sample volume of ∼5 mm3, which is equivalent to >150 Billion voxels. We demonstrate the proof-of-concept of this lensfree optical tomographic microscopy platform on a color CMOS image sensor by creating tomograms of micro-particles as well as a wild-type C. elegans nematode.

Two-dimensional performance of uniform irradiation with the use of a concentricity deviation lens array and partially coherent light

A method of employing a lens array (LA) and partially coherent light (PCL) is presented for uniform irradiation on targets in inertial confinement fusion. Quasi-near field spots with a profile of sharp edge and flat top can be obtained with an LA, while the spatial coherence of the incidence beam is reduced by PCL. An appropriate concentricity deviation (CD) of LA results in the superposition of beamlets at the focus dislocated by a small amount each other and the CD and PCL reduce the fringe separations, thus the interference fringes become denser and the small-scale intensity non-uniformity of intensity distribution is suppressed. Based on the generalized diffraction integral theory, the intensity distribution of a Gaussian Schell Beam (GSB), point focused by an LA and a spherical lens is investigated in detail by two-dimensional simulation. And irradiation uniformity effects are compared with coherent light and partially coherent light after the LA. Numerical results indicate that using an appropriate CD and moving the target slightly from the exact focal plane of the principal focusing, a well-irradiated laser spot and great energy efficiency can be obtained.

Application of partially coherent light in live cell imaging with digital holographic microscopy

The main drawbacks of laser-based digital holographic microscopy (DHM) are coherent noise and disturbances due to parasitic reflections in the experimental setup. To overcome some of these problems, investigations on the performance of partially coherent light in DHM-based live cell imaging were carried out. First, the impact of different partially coherent light sources on the formation and the reconstruction of digital off-axis holograms was analyzed. Therefore, the achieved lateral resolution and the accuracy for the detection of optical path length changes were compared to results obtained with laser light. In additional experiments, we investigated if partial coherent light can be utilized in DHM for quantitative phase contrast imaging of living cells in incident light configuration by using light from specifically selected reflective sample interfaces. The obtained results show the applicability of partially coherent light in off-axis DHM and its use to for the reduction of disturbances due to coherence effects. Furthermore, it is demonstrated that quantitative DHM phase contrast imaging of phase objects can be performed with experimental arrangements in which an illumination of the sample in transmission due to geometric conditions is not possible.

Dual Grating Interferometric Lithography for 22-nm Node

An extreme ultraviolet (EUV) interference lithography beamline using a single grating has been constructed at the BL3 beamline in the NewSUBARU synchrotron radiation facility. Using a single grating, a 400-nm line and space (L&S) resist pattern was replicated on a wafer by single grating interferometric lithography system combined with a bending magnet as a light source. In addition, a dual grating interferometric lithography which is suitable for a bending magnet as a light source has been designed and constructed at the BL3 beamline in NewSUBARU. Dual grating interferometric lithography has a capability to replicate of a 28 nm L&S pattern on the basis of the interference-fringes calculation under conditions of a partial coherent light source such as a bending magnet. In the dual grating interference optical system, two transparent gratings was employed. In addition, the dual grating interference lithographic exposure method can be combined with a stand alone EUV source, such as a laser produced plasma or a discharge produced plasma. Therefore, this exposure system is a compact system for the evaluation of resolution and line edge roughness (LER) in a EUV resist.

Theoretical Analysis and Pre-compensation Simulation of Pattern Distortion in Proximity UV-lithography

Improving graphics quality is one of the important factors for fabrication of high precision and high aspect ratio microstructure.For investigating the pattern transfer accuracy of proximity UV-lithography,a theoretical model is constructed based on partial coherent light theory.The intensity distribution on the photo resist surface is attained and the related lithography profile is simulated.A compensation method which employs the genetic algorithm(GA)is studied to optimize photo mask.The strategy of the method is to modulate the optic field distribution by adjusting the pattern of the photo-mask.The evaluation strategy is proposed based on the simulation profile.The profile character is classified and limited to reduce the searching space.With the GA method,an optimum mask pattern is achieved.The simulation results show that the graphics distortion of photoresist is reduced obviously and the study provides a new approach to improving the graphics quality in lithography.