Wave-optical Effects Research Articles

Effects of Photon Recycling and Luminescent Coupling in All‐Perovskite Tandem Solar Cells Assessed by Full Opto‐electronic Simulation

The impact of photon recycling (PR) and of luminescent coupling (LC) on the photovoltaic performance of all‐perovskite tandem solar cells is analyzed by the means of optical and full opto‐electronic device simulation. Optical processes are assessed using a comprehensive Green function formalism that considers wave optical effects also in emission. Starting from a consistent fit of experimental sub‐cell and tandem characteristics, the effects of re‐absorption are propagated from the optical limit to a situation with consideration of realistic charge transport across the entire tandem device. This also provides insight into the origin of performance losses due to sub‐cell and interconnection quality.

Optical characteristics of thin film-based InGaN micro-LED arrays: a study on size effect and far field behavior

Micro-light emitting diodes (µ-LEDs) are considered the key enabler for various high-resolution micro-display applications such as augmented reality, smartphones or head-up displays. Within this study we fabricated nitride-based µ-LED arrays in a thin film chip architecture with lateral pixel sizes down to 1 µm. A metal mirror on the p-side enhances the light outcoupling via the n-side after removal of the epitaxial growth substrate. Mounted devices with pixel sizes ranging from 1×1 to 8×8 µm2 were electro-optically characterized within an integrating sphere and in a goniometer system. We measure increased external quantum efficiencies on smaller devices due to a higher light extraction efficiency (LEE) as predicted by wave optical simulations. Besides this size dependence of the LEE, also the far field properties show a substantial change with pixel size. In addition, we compared µ-LEDs with 40 nm and 80 nm thick aluminium oxide around the pixel mesa. Considerably different far field patterns were observed which indicate the sensitivity of optical properties to any design changes for tiny µ-LEDs. The experimentally obtained radiation behavior could be reasonably predicted by finite-difference time-domain simulations. This clearly reveals the importance of understanding and modeling wave optical effects inside µ-LED devices and the resulting impact on their optical performance.

Wave effects in double-plane lensing

We discuss the wave optical effects in gravitational lens systems with two point mass lenses in two different lens planes. We identify and vary parameters (i.e., lens masses, related distances, and their alignments) related to the lens system to investigate their effects on the amplification factor. We find that due to a large number of parameters, it is not possible to make generalized statements regarding the amplification factor. We conclude by noting that the best approach to study two-plane and multi-plane lensing is to study various possible lens systems case by case in order to explore the possibilities in the parameter space instead of hoping to generalize the results of a few test cases. We present a preliminary analysis of the parameter space for a two-lens system here.

Wave-optical Effects in the Microlensing of Continuous Gravitational Waves by Star Clusters

Rapidly rotating neutron stars are promising sources for existing and upcoming gravitational-wave interferometers. While relatively dim, these systems are expected to emit continuously, allowing for signal to be accumulated through persistent monitoring over year-long timescales. If, at some point during the observational window, the source comes to lie behind a dense collection of stars, transient gravitational lensing may occur. Such events, though rare, would modulate the waveform, induce phase drifts, and ultimately affect parameter inferences concerning the nuclear equation of state and/or magnetic field structure of the neutron star. Importantly, the radiation wavelength will typically exceed the Schwarzschild radius of the individual perturbers in this scenario, implying that (micro)lensing occurs in the diffractive regime, where geometric optics does not apply. In this paper, we make use of numerical tools that borrow from Picard–Lefschetz theory to efficiently evaluate the relevant Fresnel–Kirchhoff integrals for n ≳ 102 microlenses. Modulated strain profiles are constructed both in general and for particular neutron star trajectories relative to some simulated macrolenses.

Rigorous approach for unifying wave optics and state of the art rendering techniques.

With the capabilities of diffractive optics there is a rising demand for determining the light interaction of diffractive elements with arbitrary illumination and scenery. Since the structured surfaces' scale lies within the visible wavelengths and below, the light's interaction cannot be simulated with state of the art geometric optic rendering approaches. This paper presents a new model for the inclusion of wave-optical effects into Monte Carlo path rendering concepts. The derived method allows the coupling of a rigorous full-field approach with the concept of backward ray propagation through complex scenes. Therefore, the rendering of arbitrarily structured periodic optical components is now possible for complex sceneries for design, verification and testing purposes. The method's performance is demonstrated by comparing rendering results of complex sceneries including CDs with corresponding photographs.

Spectral x-ray imaging: Conditions under which propagation-based phase-contrast is beneficial

Energy-resolved attenuation data in spectral x-ray imaging enables material decomposition, in which the different materials inside an object can be identified and separated virtually. Material decomposition has the drawback of increased noise in the resulting material images relative to the measured images. Recently, spectral x-ray imaging was combined with propagation-based x-ray phase-contrast imaging, an x-ray technique that has the potential to greatly reduce image noise by utilizing wave-optical effects. The net combined effects on image noise of performing spectral material decomposition with phase-contrast are not yet well understood, and we provide a detailed theoretical investigation of this topic here. In particular, we investigate how the addition of phase-contrast in spectral imaging affects material decomposition compared to using conventional spectral attenuation data. We show how the underlying equations can be rearranged into parts that resemble low- and high-pass filters on the input images, from which we are able to identify different energy-dependent cases where phase-contrast is or is not advantageous. Our results suggest that the benefits of phase-contrast in the context of material decomposition are primarily restricted to x-ray energies under a certain threshold, where that threshold depends on the given material combination, and sits in a region where photoelectric absorption dominates x-ray attenuation. Additionally, we show that decomposition of the electron density using an image basis spanned by functions of the Alvarez-Macovski model benefits from phase-contrast, regardless of the x-ray energies. All our findings are based purely on theoretical considerations, and can, therefore, be used to determine the feasibility and utility of propagation-based phase-contrast in spectral x-ray imaging ahead of any data collection.

Towards fully self-consistent optoelectronic simulation of planar devices

Photon recycling plays an important role in various optoelectronic devices, such as thin-film solar cells and intracavity double-diode structures presently studied for electroluminescent cooling. However, a complete description of photon recycling requires developing fully self-consistent simulation tools of photon and electronic charge transport in realistic device structures. In this paper, we describe a possible route towards such simulation tools in planar devices by combining the radiative transfer (RT) equation of photon transport with the drift-diffusion (DD) equations of electron and hole dynamics. We investigate the feasibility of the approach by selected proof-of-principle device studies. The results indicate that combining the RT and DD models not only yields the expected device characteristics, but also produces new insight into the pertinent local emission and absorption properties within the device structures. In particular, the model allows to accurately investigate how emission directivity and saturation affect the coupling coefficient in the double diode structures, showing that the main contribution to the coupling coefficient arises from the reflectivity of the top contact. For completeness, we also discuss how interference affects photon transport in resonant devices by an example calculation using the quantized fluctuational electrodynamics framework, paving way for self-consistent modeling tools that also account for wave-optical effects.

Rigorous wave-optical treatment of photon recycling in thermodynamics of photovoltaics: Perovskite thin-film solar cells

The establishment of a rigorous theory on thermodynamics of light management in photovoltaics that accommodates various loss mechanisms as well as wave-optical effects in the absorption and reemission of light is at stake in this contribution. To this end, we propose a theoretical framework to calculate the open-circuit voltage enhancement resulting from photon recycling ($\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$) with rigorous wave-optical treatment. It can be applied to both planar thin-film and nanostructured single-junction solar cells. We derive an explicit expression for $\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$, which reveals its dependence on internal quantum luminescence efficiency, parasitic reabsorption, and on photon escape probabilities of reemmited photons. While the internal quantum luminescence efficiency is an intrinsic material property, both latter quantities can be determined rigorously for an arbitrary solar cell architecture by three-dimensional electrodynamic dipole emission calculations. We demonstrate the strengths and validity of our framework by determining the impact of photon recycling on the $V_{\mathrm{oc}}$ of a conventional planar organo-metal halide perovskite thin-film solar cell and compare it to established reference cases with perfect antireflection and Lambertian light scattering. Our calculations reveal $\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$ values of up to 80 mV for the considered device stack in the absence of angular restriction and up to 240 mV when the escape cone above the cell is restricted to $\theta_{\mathrm{out}}=2.5^\circ$ around the cell normal. These improvements impose severe constraints on the parasitic absorption as a parasitic reabsorption probability of only 2\% reduces the $\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$ to 100 mV for the same angular restriction. Our work here can be used to provide design guidelines.

Ray tracing the Wigner distribution function for optical simulations

We study a simulation method that uses the Wigner distribution function to incorporate wave optical effects in an established framework based on geometrical optics, i.e., a ray tracing engine. We use the method to calculate point spread functions and show that it is accurate for paraxial systems but produces unphysical results in the presence of aberrations. The cause of these anomalies is explained using an analytical model.

Optical Beam Propagation and Ray Tracing Simulation of Interruption-Free Asymmetric Multimode Bus Couplers

In this article, we present a coupling concept for an interruption-free asymmetric bidirectional optical bus coupler for board and module level. With this approach, it is possible to connect several electro-optical devices to a single waveguide. A core-to-core connection principle is used, where the cores get into physical contact at their side faces. The coupling ratio can be tuned by adjusting the overlap area of the two cores with different contact pressures. Because of a bending in one of the waveguides, it is possible to achieve a specific asymmetric coupler design, where the coupling ratio depends on the coupling direction (bent waveguide to rigid one or vice versa). To derive design rules for prototyping, a simulation is performed using two different independent approaches for cross-checking. With a ray tracing simulation, coupling ratios and energy distribution within the bent core are analyzed. In addition, a simulation with the beam propagation method is used to take wave optical effects into account as well as to establish a holistic view on the coupling concept.

Experimental realization of the Ehrenberg-Siday thought experiment

In 1949, at the end of a paper dedicated to the concept of the refractive index in electron optics, Ehrenberg and Siday noted that wave-optical effects will arise from an isolated magnetic field even when the rays themselves travel in magnetic-field-free space. They proposed a two-slit experiment, in which a magnetic flux is enclosed between interfering electron beams. Now, through access to modern nanotechnology tools, we used a focused ion beam to open two nanosized slits in a gold-coated silicon nitride membrane and focused electron beam induced deposition to fabricate a thin magnetic bar between the two slits. We then performed Fraunhofer experiments in a transmission electron microscope equipped with a field emission gun and a Lorentz lens. By tilting the specimen in the objective lens field of the electron microscope, the magnetization of the bar could be reversed and the corresponding change in the phase of the electron wave observed directly in the form of a shift in the interference fringe pattern.

A fluctuational electrodynamics model for the optimization of light-extraction efficiency in thin-film light-emitting diodes

The rapid development of thin film light-emitting diodes (LEDs) has enabled the enhancement of the light extraction beyond geometrical limits but more quantitative understanding of the underlying optical processes is required to fully optimize the extraction. We present first-principle calculations of the light extraction efficiency and optical energy flow in thin-film LEDs. The presented model generalizes the methods of fluctuational electrodynamics to excited semiconductors and simultaneously accounts for wave optical effects, e.g., interference and near-field coupling as well as the internal absorption of the light-emitting material in determining the rate of light emission and internal dissipation in the optical cavity formed by a planar LED. The calculations show that in structures with a metallic mirror, the emissivity of the active region can approach unity at selected wavelengths, even when the nominal emissivity of the active region is only moderate. However, the results also show that near-field coupling of emission from the active region to the mirror can provide a substantial non-radiative loss channel reducing the maximum light extraction efficiency to 0.67 in our example setup. These losses can be partly compensated by the efficient photon recycling enabled by thick active regions that quench emission to confined modes and thereby reduce parasitic absorption.

Local Chirality of Optical Resonances in Ultrasmall Resonators

In wavelength-scale cavities with chiral-symmetric geometry, wave optical effects can introduce local chirality, that is, a spatial separation of the clockwise and counterclockwise propagating resonant modes. We show that this local chirality results in unidirectional lasing emission in the far field. In the presence of a waveguide, the local chirality also allows for directional evanescent coupling of the lasing modes, and the output direction can be varied by selecting the coupling position along the cavity boundary. Our results demonstrate that the local chirality of optical resonances can be utilized to control the output directionality and enhance the collection efficiency of emission from ultrasmall resonators.

Ray optical light trapping in silicon microwires: exceeding the 2n2 intensity limit

We develop a ray optics model of a silicon wire array geometry in an attempt to understand the very strong absorption previously observed experimentally in these arrays. Our model successfully reproduces the n2 ergodic limit for wire arrays in free space. Applying this model to a wire array on a Lambertian back reflector, we find an asymptotic increase in light trapping for low filling fractions. In this case, the Lambertian back reflector is acting as a wide acceptance angle concentrator, allowing the array to exceed the ergodic limit in the ray optics regime. While this leads to increased power per volume of silicon, it gives reduced power per unit area of wire array, owing to reduced silicon volume at low filling fractions. Upon comparison with silicon microwire experimental data, our ray optics model gives reasonable agreement with large wire arrays (4 μm radius), but poor agreement with small wire arrays (1 μm radius). This suggests that the very strong absorption observed in small wire arrays, which is not observed in large wire arrays, may be significantly due to wave optical effects.

Projection lithography below lambda/7 through deep-ultraviolet evanescent optical imaging

An approach is presented to allow for imaging down to 26 nm using 193 nm projection reduction lithography together with evanescent wave optical effects at the imaging plane. The physical limitations of imaging imposed by the refractive indices of the materials were surpassed through the interference of evanescent waves at near fields. This has allowed for the imaging into photoresist of half-pitch resolution below lambda/7. A special situation where imaging at a system numerical aperture above the resist refractive index is discussed. Lithography results are shown using image media including air, water, and a high refractive index fluid together with a systematic gauge control to determine gap requirements and tolerances to achieve adequate image contrast into the resist. Gauging methods include both optical and mechanical approaches to achieve nanometer level gap control. It is found that gap depths as large as 50 nm can be tolerated using this approach, well beyond the levels associated with alternative high resolution approaches such as those using surface plasmons.

Electro – optical simulation of diffraction in solar cells

A simulation method is presented and evaluated for simulating two- and three dimensional wave optical effects in crystalline silicon solar cells. Due to a thickness in the 100 µm range, optical properties of these solar cells typically are simulated, primarily through the use of ray-tracing. Recently, diffractive elements such as gratings or photonic crystals have been investigated for their application in crystalline silicon solar cells, making it necessary to consider two- and three dimensional wave optical effects. The presented approach couples a rigorous wave optical simulation to a semiconductor device simulation. In a first step, characteristic parameters, simulated for a reference setup using the electro-optical method and the standard procedure are compared. Occurring differences provide a measure to quantify the errors of the electro-optical method. These errors are below 0.4% relative. In a second step the electro-optical method is used to simulate a crystalline silicon solar cell with a back side diffractive grating. It is found that the grating enhances to short circuit current density jSC of the solar cell by more than 1 mA/cm².

Geometrical and wave-optical effects on the performance of a bent-crystal dispersive X-ray spectrometer

The X-ray focusing properties of a bent single crystal diffracting in Bragg geometry are discussed. First, it is assumed that a polychromatic point source is focused to a point image. The elliptical arc that the crystal must trace and the aberrations caused by bending the crystal cylindrically are derived from the ray paths. For a source of finite size, the magnification is found to vary over the crystal's length, so that rays of different wavelength produce images of different size. More realistic treatments of penetration and diffraction are performed with spherical monochromatic incident waves, using Takagi–Taupin calculations to create the diffracted wave and the Fresnel integral to trace the diffracted wave's evolution. Such “wave-optical” calculations on a symmetric Si (111) crystal with 7keV X-rays predict beam sizes different from those found in ray traces. Optimal sample and detector placement therefore requires wave effects to be considered.

Resolution enhanced proximity printing by phase andamplitude modulating masks

Photolithography based on proximity printing offers a highthroughput and cost effective patterning technology for production of, forinstance, large area liquid crystal displays. The resolution of thistechnique is limited due to wave-optical effects in the proximity gapbetween the binary amplitude mask and the substrate. We can improve theresolution drastically by replacing the conventional photomask with a maskcausing both amplitude and phase modulation of the illumination wave. Wedescribe a wave-optical design procedure for such masks. The feasibilityof the method is demonstrated by results from computer simulations andpractical experiments. We show that, for a 50 µm gap, a 3 µmline/space pattern is resolved clearly for visible light illumination,whereas under conventional conditions the image is completely degraded.The proximity mask used in our experiments was fabricated by e-beamlithography with four height levels and two amplitude transmissionvalues.

Thermal diffusivity determination by the photodeflection method. The influence of wave optical effects

Possible approaches to thermal wave based measurement of thermal diffusivity are considered. The calculation of the transverse photodeflection signal in the framework of wave optics prove to be a more accurate approach compared to that of geometrical optics. The influence of the account of wave optical effects on the accuracy of the thermal diffusivity determination is theoretically analyzed under various conditions.

Wave-optical effects in semiconductor laser amplifiers

A wave-optical model is used to investigate the power scaling of semiconductor laser amplifiers. The configurations investigated are single-pass amplifiers, double-pass amplifiers, phase-conjugate double-pass amplifiers, regenerative amplifiers, and injection-locked lasers. We are interested in a comparison of conventional double-heterostructure and quantum-well gain media, the factors affecting optical power extraction, and conditions leading to filamentation in the laser beam.