Ideal Thin Lens Research Articles

Lens stars and Platonic lenses

Lens stars comprise identical ideal thin lenses arranged in a regular star shape centred on the common principal point. They satisfy the edge-imaging condition of transformation optics (TO) and are thus suitable as building blocks of ideal-lens TO devices [J. Opt. Soc. Am. A 37, 305 (2020)10.1364/JOSAA.37.000305]. Here we show that the ray trajectories in lens stars are piecewise straight approximations of conic sections. We also generalise lens stars to Platonic lenses, highly symmetric combinations of lens stars based on Platonic solids, and find that ray trajectories in Platonic lenses are closed and planar; we design a more general ideal-lens cloak; and we clarify the process of designing ideal-lens TO devices. Throughout, we illustrate our results with ray-tracing simulations. Our results add to the knowledge of TO with ideal lenses.

Propagation characteristics of Gaussian-Schell model beams through optical systems in Kerr media.

For the beam spreading case, the propagation formulae of Gaussian-Schell model (GSM) beams through general optical systems in Kerr media are derived, and the propagation characteristics of GSM beams through an ideal thin lens in Kerr media are studied in detail. It is shown that the size and position of the beam waist can be controlled by the Kerr effect. Furthermore, the formula of the focal shift of the GSM beams focused by an ideal thin lens in Kerr media is also derived. It is found that in self-focusing media the focal shift decreases as the beam power or the beam coherence degree increases. In addition, there exists a maximum of the focal shift, and the formula of the focal shift maximum is derived. On the other hand, for the beam self-focusing case, the focusing characteristics of GSM beams focused by an ideal thin lens in Kerr media are also investigated.

Interference rings induced by ultrafast laser pulse in GaAs crystal

Gallium arsenide (GaAs) is an important semiconductor material with direct bandgap and clear-cut absorption edge. High-quality crystal is available, which has excellent performances in the field of high power transmission and luminescence because of high laser damage threshold and high thermal conductivity. Nonlinear optics is of great significance for developing the laser technology, spectroscopy, and optoelectronic devices. The Z-scan technology is a nonlinear measurement method based on the analysis of single beam transmittance. Previous studies mainly focused on the measurement of the nonlinear absorption coefficient of the sample by open-aperture configuration of Z-scan and the nonlinear refractive index of the sample by shut-aperture configuration of Z-scan. We build a dual-channel Z-scan system with variable optical path difference, equipped together with a high speed camera, to observe the spatial distribution of transmitted light. Besides, we find the interference rings induced by nonlinear absorption in semiconductor GaAs crystals. Using three kinds of lasers (continuous-wave laser, 80 MHz femtosecond pulsed laser, 1 kHz femtosecond pulsed laser) to illuminate the GaAs crystal separately, multi-level interference rings come out only when a GaAs crystal wafer is illuminated by a femtosecond pulsed laser. In the single-channel Z-scan experiment, we observe that the interference rings contract or expand regularly when changing pulsed laser intensity incident on the surface of GaAs crystal. The higher the intensity of pulse, the more interference rings appear, and the maximum exiting angle becomes larger. Nonlinear effect of high intensity femtosecond pulsed laser locally changes the refractive index of GaAs crystals, resulting in optical path difference (Kerr lens effect). However, the Kerr lens generated by ultrafast light pulse in GaAs crystal cannot focus a beam as done by an ideal thin lens, leading the transmitted light to form interference rings instead. By analyzing the variation of the interference rings, the nonlinear absorption coefficient and refractive index of GaAs crystal can be obtained. In the dual-channel Z-scan experiment, different interference rings are induced in the GaAs crystal as the path difference between the two pulses changes, as done by the nonlinear transmission power. Thus we obtain the formation time of the interference rings and ascribe it to the ultrafast relaxation process of GaAs carriers.

Spatial resolution improvement for an optical transition radiation monitor by asymmetric light collection.

The applicability of optical transition radiation (OTR) for measurements of micron sized transverse electron beam profiles is limited not only by the optical system resolution which has a fundamental limit imposed by the uncertainty principle. In the case of OTR generation, a single electron crossing the boundary between vacuum and screen cannot be considered as a single emitting point with isotropic angular distribution. On the contrary, the radiation is emitted from an area with a transverse range that is defined by the radial extension of the electron's Lorentz contracted Coulomb field and is typically estimated as γλ (with γ the Lorentz factor and λ the wavelength of observation). The OTR angular distribution has a characteristic "funnel" shape. As a result the one-dimensional image of a single electron measured with an ideal thin lens has a double lobe shape, and the resolution of any OTR based imaging system is determined by this double lobe function which is also known as OTR Point Spread Function (PSF). As a consequence, the reconstruction of micron sized electron beam profiles is hampered not only due to the fundamental diffraction limit, but also due to the PSF lobe shape. In this paper we present two approaches to improve the spatial resolution of an OTR monitor based on asymmetric light collection using a traditional optical system which allows blocking of one of the lobes. With such a scheme, an OTR PSF can be achieved that is comparable to the one of an ideal point source (Airy distribution).

Ray-optical transformation optics with ideal thin lenses makes omnidirectional lenses.

We present the theory of ray-optical transformation optics (RTO) with ideal thin lenses and show that ideal-thin-lens RTO devices are omnidirectional lenses. Key to designing such devices are two theorems, the loop-imaging theorem, and the edge-imaging theorem, which ensure that the interior physical space is distorted in the same way for all viewing directions. We discuss the possibility of realising such devices using lens holograms or Fresnel lenses, as both are in principle capable of changing the directions of rays incident from a specific point precisely like an ideal thin lens, thereby enabling macroscopic and broad-band RTO devices that work for at least one viewing position. Even when restricted in this way, our work opens up new possibilities in ray optics. Our devices have the potential to form the basis of new microscope objectives, virtual-reality headsets, and medical spectacles.

Large area metalenses: design, characterization, and mass manufacturing.

Optical components, such as lenses, have traditionally been made in the bulk form by shaping glass or other transparent materials. Recent advances in metasurfaces provide a new basis for recasting optical components into thin, planar elements, having similar or better performance using arrays of subwavelength-spaced optical phase-shifters. The technology required to mass produce them dates back to the mid-1990s, when the feature sizes of semiconductor manufacturing became considerably denser than the wavelength of light, advancing in stride with Moore's law. This provides the possibility of unifying two industries: semiconductor manufacturing and lens-making, whereby the same technology used to make computer chips is used to make optical components, such as lenses, based on metasurfaces. Using a scalable metasurface layout compression algorithm that exponentially reduces design file sizes (by 3 orders of magnitude for a centimeter diameter lens) and stepper photolithography, we show the design and fabrication of metasurface lenses (metalenses) with extremely large areas, up to centimeters in diameter and beyond. Using a single two-centimeter diameter near-infrared metalens less than a micron thick fabricated in this way, we experimentally implement the ideal thin lens equation, while demonstrating high-quality imaging and diffraction-limited focusing.

Ray optics of generalized lenses.

We study the ray optics of generalized lenses (glenses), which are ideal thin lenses generalized to have different object- and image-sided focal lengths, and the most general light-ray-direction-changing surfaces that stigmatically image any point in object space to a corresponding point in image space. Gabor superlenses [UK patent541,753 (1940); J. Opt. A1, 94 (1999)JOAOF81464-425810.1088/1464-4258/1/1/013] can be seen as pixelated realizations of glenses. Our analysis is centered on the nodal point. Whereas the nodal point of a thin lens always resides in the lens plane, that of a glens can reside anywhere on the optical axis. Utilizing the nodal point, we derive simple equations that describe the mapping between object and image space and the light-ray-direction change. We demonstrate our findings with the help of ray-tracing simulations. Glenses allow novel optical instruments to be realized, at least theoretically, and our results facilitate the design and analysis of such devices.

Electrically tunable lens based on a dual-frequency nematic liquid crystal

We report on an electrically controlled liquid-crystal-based variable optical lens filled with a dual-frequency nematic material. The lens design employs a hole-patterned electrode structure in a flat nematic cell. In order to decrease the lens switching time we maximize the dielectric torque by using a dual-frequency nematic material that is aligned at an angle approximately 45 degrees with respect to the bounding plates by obliquely deposited SiO(x), and by using an overdrive scheme of electrical switching. Depending on the frequency of the applied field, the director realigns either toward the homeotropic state (perpendicular to the substrates) or toward the planar state (parallel to the substrates), which allows one to control not only the absolute value of the focal length but also its sign. Optical performance of the liquid-crystal lens is close to that of an ideal thin lens.

Radiometry in line-shape modeling of Fourier-transform spectrometers.

A radiometric model of the instrument line shape (ILS) of Fourier-transform spectrometers is presented. We show first that common line-shape models are based on distribution of the radiant intensity in the interferometer. The complete steps between the source and the ILS are exposed as the core of the model. Relationships between the ILS, the spectrum as measured by the instrument, and the spectrum as emitted by the scene are demonstrated from the ILS model. Then the formal radiometric modeling of the ILS is derived, including the contribution of the aperture of the optical system. The particular case of a centered circular aperture with a uniform Lambertian radiance in the field of view is discussed. Conditions are deduced to ensure that the only spectral variation of the ILS is a scaling with wave number, as is usually assumed in current line-shape models. The ILS dependence on the scene is also discussed, and the effect of taking into account the radiometry on the ILS is estimated for the case of an ideal thin lens used as a collimator.

Scattering losses from dielectric apertures in vertical-cavity lasers

In vertical-cavity lasers (VCLs) employing oxide or airgap apertures, the lasing mode typically travels unguided throughout most of the structure. For the aperture to exactly compensate for the diffraction of the mode in these regions, it would need to have a parabolic lateral index profile (i.e. that of an ideal thin lens). Although nonparabolic aperture shapes will partially compensate diffraction losses, some light will be scattered out of the mode. These scattering losses increase as the aperture size is reduced and will limit the performance of the smallest devices. We analyze these losses first using a semianalytic approach which allows us to frame the problem in terms of two parameters of the structure: the Fresnel number and the effective optical path length across the aperture. We compare the estimate with experimental results and with an iterative numerical calculation of the actual mode and losses. Lastly, we compare the loss reduction with different amounts of tapering that provide a better approximation to the ideal parabolic lens.

Resolving power of laser electron-beam tubes (quantoscopes)

An analysis is made of the conditions of focusing of non-Gaussian beams by an ideal thin lens which transfers light from a laser projection tube (quantoscope) to a large screen. It is shown that, under certain conditions, the resolving power of an image on a distant screen can be several times higher than the electron-optical resolving power of such tubes.

Cosinusoidal transforms in white light

Theory and techniques of white light interferometry have been studied to devise an optoelectronic hybrid for diffraction pattern sampling. For an incoherently illuminated input scene, we obtain an output intensity that is the 2-D spatial cosine transform of the input plus a bias term. The bias can be subtracted electronically to within shot noise fluctuation limitations. The optical system consists of a double-imaging interferometer with a beam-splitter cube and crossed right-angle-prism reflectors followed by an achromatic-optical-transform lens pair. A photodiode array is placed in the optical transform plane, and this is coupled to a digital computer for further signal processing. Theoretical results are presented for the synthesis of the cosinusoidal transform configuration. From Fresnel-zone theory, a general form is derived for the impulse response of a cascade of ideal thin lenses, and this is used to design Fourier transform achromats that are well suited to this application. Experiments are presented showing cosine transforms for rough objects and for objects in reflection using illumination of negligible spatial coherence at the object. Excellent sensitivity is obtained with the bias subtraction, and a high space–bandwidth product is attained for the system.

Empfangsleistung in Abhängigkeit von der Zielentfernung bei optischen Kurzstrecken–Radargeräten

The dependence of the received optical power on the range in optical short-distance radar range finders is calculated by means of the methods of geometrical optics. The calculations are based on a constant intensity of the transmitter-beam cross section and on an ideal thin lens for the receiver optics. The results are confirmed by measurements. Even measurements using a nonideal thick lens system for the receiver optics are in reasonable agreement with the calculations.