Absolute Instruments Research Articles

540-degree deflecting lens and its general version.

We demonstrate an isotropic device called 540-degree deflecting lens, which has symmetric refractive index and can deflect parallel beam by 540 degrees. The expression of its gradient refractive index is obtained and generalized. We discover it's an optical absolute instrument with self-imaging characteristic. Using conformal mapping, we deduce its general version in one-dimensional space. We also introduce a combined lens called the generalized inside-out 540-degree deflecting lens similar to the inside-out Eaton lens. Ray tracing and wave simulations are used to demonstrate their characteristics. Our study expands the family of absolute instruments and provides new ideas to design optical systems.

Role played by port drains in a Maxwell fish-eye lens

The Maxwell fish-eye lens was proposed to reach super-resolution with the addition of a wave drain, and the interaction of multiple drains is theoretically predicted to improve subwavelength resolution further. In this paper, we discuss the role played by port drains in optical absolute instruments and verify by wave simulation that the coupling nature for the wave source and drain applies correctly in the picture of scanning imaging for an absolute instrument. This work has prospects for scanning near fields shaped from far-field wave propagation.

Anisotropic Fermat’s principle for controlling hyperbolic van der Waals polaritons

Transformation optics (TO) facilitates flexible designs of spatial modulation of optical materials via coordinate transformations, thus, enabling on-demand manipulations of electromagnetic waves. However, the application of TO theory in control of hyperbolic waves remains elusive due to the spatial metric signature transition from ( + , + ) to ( − , + ) of a two-dimensional hyperbolic geometry. Here, we proposed a distinct Pythagorean theorem, which leads to establishing an anisotropic Fermat’s principle. It helps to construct anisotropic geometries and is a powerful tool for manipulating hyperbolic waves at the nanoscale and polaritons. Making use of absolute instruments, the excellent collimating and focusing behaviors of naturally in-plane hyperbolic polaritons in van der Waals α – MoO 3 layers are demonstrated, which opens up a new way for polaritons manipulation.

A Procedure to Correct the Historical Atmospheric Longwave Irradiance Data When the World Reference Is Established with Respect to the International System of Units

Historical atmospheric longwave irradiance data sets with traceability to the International System of Units (SI) are essential for renewable energy and atmospheric science research and applications. To date, all pyrgeometers used to measure the irradiance are traceable to the interim World Infrared Standard Group (WISG), not to SI units. In 2013, the Absolute Cavity Pyrgeometer (ACP) (Reda et al. 2012) was developed at the National Renewable Energy Laboratory (NREL) to measure the atmospheric longwave irradiance. The ACP has been compared against the InfraRed Integrating Sphere (IRIS), developed by the Physikalisch-Meteorologisches Observatorium Davos/World Radiation Center (PMOD/WRC) (Gröbner 2012). The ACP and the IRIS are absolute instruments traceable to SI units through the International Temperature Scale of 1990. Results of six comparisons between the ACP and the IRIS at different locations have shown that the irradiance measured by WISG pyrgeometers underestimates clear-sky atmospheric longwave irradiance by 2 W/m2 to 6 W/m2 (Gröbner et al. 2014); therefore, once the world reference is established with traceability to SI units, the WISG would be corrected, then used to calibrate field pyrgeometers with traceability to SI units. The following described method is used to correct the historical atmospheric longwave irradiance data sets in anticipation of the WISG scale change.

Solid Immersion Maxwell's Fish-Eye Lens Without Drain

Maxwell's fish-eye lens (MFEL) with positive refraction has been shown to achieve perfect imaging, but with the cost of drain assistance. This has led to ongoing heated debates about the rigor of the physics of super-resolution phenomena in MFEL. In this work, we report that a MFEL embedded in an exterior coating, inspired by the solid immersion concept, can realize super-resolution imaging without a drain. Such a solution mitigates and bypasses the corresponding criticisms and debates of the past decades. We find that the total reflection at the outer solid-immersion interface and the native perfect focusing of MFEL synthetically contribute to a super-resolution image formed in the air. Moreover, this intuitive yet simple recipe can be robustly applied to other absolute instruments, such as the general Luneburg lens and more versatile superimaging systems are anticipated. We demonstrate the imaging performance in a solid immersion general Luneburg lens both numerically and experimentally, which indirectly verifies the imaging validity of the solid immersion MFEL without a drain.

Mimicking the gravitational effect with gradient index lenses in geometrical optics

General relativity establishes the equality between matter-energy density and the Riemann curvature of spacetime. Therefore, light or matter will be bent or trapped when passing near the massive celestial objects, and Newton’s second law fails to explain it. The gravitational effect is not only extensively studied in astronomy but also attracts a great deal of interest in the field of optics. People have mimicked black holes, Einstein’s ring, and other fascinating effects in diverse optical systems. Here, with a gradient index lens, in the geometrical optics regime, we mimic the Schwarzschild precession in the orbit of the star S2 near the Galactic Center massive black hole, which was recently first detected by European Southern Observatory. We also find other series of gradient index lenses that can be used to mimic the possible Reissner–Nordström metric of Einstein’s field equation and dark matter particle motion. Light rays in such gradient lenses will be closed in some cases, while in other cases it would be trapped by the center or keep dancing around the center. Our work presents an efficient toy model to help investigate some complex celestial behaviors, which may require long period detection by using high-precision astronomical tools. The induced gradient lenses enlightened by the gravitational effect also enrich the family of absolute optical instruments for their selective closed trajectories.

Multi-Core Conformal Lenses**Supported by the National Natural Science Foundation of China (Grant No. 11874311).

We propose multi-core conformal lenses by combining conformal transformation optics with absolute instruments. Depending on the cores and incident angles, the conformal lenses have tunable functionalities like focusing, reflection, and transparency, thereby providing a feasible general method for designing multi-functional devices.

Observation of light rays on absolute geodesic lenses.

Absolute optical instruments with rotation symmetry and corresponding absolute geodesic lenses have drawn considerable attention for their property of perfect imaging of light rays. In this paper, we systematically explore a series of absolute geodesic lenses which is mapped from generalized Maxwell's fish-eye lenses with a rational number index {p}. Moreover, we construct new types of duplex absolute geodesic lenses by splicing two different half absolute geodesic lenses, which is inspired by the work [Huiyan Peng, et al Phys. Rev. Applied13, 034050 (2020)]. Also, we fabricate some samples of absolute geodesic lenses based on the 3D printing technique and observe light rays on them. Our findings enlarge the family of absolute geodesic lenses and might find an application on classical imaging systems.

Duplex Mikaelian and Duplex Maxwell’s Fish-Eye Lenses

In this paper, we report two new kinds of absolute optical instruments that can make stigmatically images for geometric optics in two dimensional space. One is called the duplex Mikaelian lens, which is made by splicing two half Mikaelian lenses with different periods. The other is exponential conformal transformer of duplex Mikaelian lens with the ratio of different periods of its two half Mikaelian lenses a rational number, which we call duplex Maxwell's fish eye lens. Duplex Mikaelian lenses have continuous translation symmetry with arbitrary real number, while duplex Maxwell's fish eye lenses have continuous rotational symmetry from 0 to 2*Pi. Hence each duplex Maxwell's fish eye lens corresponds to a duplex Mikaelian lens. We further demonstrate the caustic effect of geometric optics in duplex Mikaelian lenses and duplex Maxwell's fish eye lenses. In addition, we investigate the Talbot effect of wave optics in the duplex Mikaelian lens based on numeric calculations. Our findings based on splicing and exponential conformal mapping enlarge the family of absolute optical instruments.

The Luneburg-Lissajous lens

We design a new absolute optical instrument by composing Luneburg lens and Lissajous lens, and analyze its imaging mechanism from the perspective of simple harmonic oscillations. The imaging positions are determined by the periods of motions in the x and y directions. Besides, instruments composed with multiparts are also devised, which can form imaging or self-imaging as long as the motion periods of the x and y directions are satisfied to similar conditions. We further investigate the imaging performance of such Luneburg-Lissajous lens in wave optics. Our work provides a new way to analyze the imaging of different lens by simply dissociating the equations of motions, and reveal the internal mechanism of some absolute optical instruments.

Light rays and waves on geodesic lenses

Starting from well-known absolute instruments for perfect imaging, we introduce a type of rotational-symmetrical compact closed manifolds, namely geodesic lenses. We demonstrate that light rays confined on geodesic lenses are closed trajectories. While for optical waves, the spectrum of geodesic lens is (at least approximately) degenerate and equidistant with numerical methods. Based on this property, we show a periodical evolution of optical waves and quantum waves on geodesic lenses. Moreover, we fabricate two geodesic lenses in sub-micrometer scale, where curved light rays are observed with high accurate precision. Our results may offer a new platform to investigate light propagation on curved surfaces.

Analysis of Several Years of DI Magnetometer Comparison Results by the Geomagnetic Network of China and IAGA

The comparison of absolute geomagnetic instruments is an important component of geomagnetic observation. To promote high quality standards in geomagnetic data acquisition, the International Association of Geomagnetism and Aeronomy (IAGA) organizes an international comparison every two years. In China, this comparison is part of quality control process for geomagnetic observation data, and is organized by the Geomagnetic Network of China (GNC). In this paper, the comparison results from several years are analysed in detail, and some useful information is presented that will help to guide the observatory’s future observation work and improve data quality. In addition, the quality of the absolute observation data of GNC and IAGA is evaluated using a statistical method. This should aid scientists who use these data to understand their research results.

Photonic crystal waveguide crossing based on transformation optics

The absolute instruments like the Maxwell’s fisheye (MFE) lens with aberration-free imaging properties have found interesting applications such as waveguide crossing. The flat wavefront of an optical wave in the waveguide does not match with the circular wavefront of the circular MFE lens at its edge, hence, we design and study the performance of a square MFE lens as photonic crystal waveguide crossing medium. We also have truncated the square MFE lens to a cross-shaped lens to squeeze it inside the crossing waveguides, therefore, practically no extra footprint is consumed by the truncated MFE lens. The numerical simulations show that graded photonic crystal-based implementation of the truncated MFE lens provides a bandwidth of 186 nm covering the entire S- and C-bands and partially covering the E- and L-bands of optical communication. The crosstalk levels are lower than −18 dB while the average insertion loss is 0.32 dB in the C-band.

Imaging along conformal curves

In this article, we prove that conformal transformation optics could be used to construct absolute instruments. The Mikaelian lens, whose refractive index profile is $1/cosh(\mathrm{x})$ [A. Mikaelian and A. Prokhorov, Progress in Optics 17, 279 (1980)], are of imaging functionalities along lines and will be used as a generic lens. Under a conformal mapping, it can be transformed to another lens, where imaging or self-imaging happens along predesigned curves. Ray tracing simulations are performed to confirm the imaging functionalities.

Absolute optical instruments, classical superintegrability, and separability of the Hamilton-Jacobi equation

An absolute optical instrument is a region of space, typically defined by a spatially varying index of refraction, in which bound ray trajectories are closed. Traditional examples of such devices include Maxwell's fisheye and the Eaton and Luneburg lenses. In this paper we employ the close analogy between classical mechanics and geometrical optics to develop a general theory of absolute instruments based on the Hamilton-Jacobi equation. Based on this theory, we derive many general properties of absolute instruments, and design a number of previously unknown examples. We also show how absolute optical instruments are related to superintegrable systems in mechanics and that the optical case is much less restrictive, which leads to an immense design space of absolute optical instruments.

On the possibility of producing definitive magnetic observatory data within less than one year

Geomagnetic observatory data are fundamental in geomagnetic field studies and are widely used in other applications. Often they are combined with satellite and ground survey data. Unfortunately, the observatory definitive data are only available with a time lag ranging from several months up to more than a year. The reason for this lag is the annual production of the final calibration values, i.e. baselines that are used to correct preliminary data from continuously recording magnetometers. In this paper, we will show that the preparation of definitive geomagnetic data is possible within a calendar year and presents an original method for prompt and automatic estimation of the observatory baselines. The new baselines, obtained in a mostly automatic manner, are compared with the baselines reported on INTERMAGNET DVDs for the 2009–2011 period. The high quality of the baselines obtained by the proposed method indicates its suitability for data processing in fully automatic observatories when automated absolute instruments will be deployed at remote sites.

Long term drifts in baselines of ground magnetic observatories

Abstract The stability of baseline is the most important criterion for evaluating the data quality of a ground magnetic observatory. Theoretically, a baseline should be a straight line, provided, there are no error factors affecting the absolute instruments, the variometer and the observational procedure. But in practice, we observe that the baselines are affected by some errors in the form of random errors and long term baseline drifts. It is known that temperature, pier tilts, aging of electronic components, etc. can affect the long term stability of baselines, but in this paper we discuss a new type of error which affects the baseline in the form of long term drifts due to the variation in the gradient field between the absolute room and the variometer room. Even though, a site is selected with the least magnetic gradient for the establishment of an observatory, in many cases, it is found that the magnetic gradient patterns are not permanent and changes over the time. This slow gradient changes can distort the actual temporal magnetic variations and thus affecting the purity of data recorded at a geomagnetic observatory. We have analytically shown that an ideal baseline has to be a horizontal straight line and the RHS of the fundamental equation of an observatory should be a constant. We have further shown that baseline instabilities are caused by variation in gradient field between the absolute and variometer pillars in addition to the measurement errors from absolute observations and variometer recording. This variation in the gradient field causes long term drifts in baselines. We have derived the correction factor which can filter out the signals arising out of variation in the gradient field. Finally we present how far the data quality can be improved by applying this correction.

Photonic crystals composed of Eaton lenses and invisible lenses

A densely arranged grid of absolute optical instruments, namely Eaton and invisible lenses, provides a photonic crystal with properties that are the opposite of its tiny constituents. The band structure of the photonic crystal dictates the wavelengths that are reflected or transmitted.

Theory of Maxwell's fish eye with mutually interacting sources and drains

Maxwell's fish eye is predicted to image with a resolution not limited by the wavelength of light. However, interactions between sources and drains may ruin the subwavelength imaging capabilities of this and similar absolute optical instruments. Nevertheless, as we show in this paper, at resonance frequencies of the device, an array of drains may resolve a single source, or alternatively, a single drain may scan an array of sources, no matter how narrowly spaced they are. It seems that near-field information can be obtained from far-field distances.

Absolute optical instruments without spherical symmetry

Until now, the known set of absolute optical instruments has been limited to those containing high levels of symmetry. Here, we demonstrate a method of mathematically constructing refractive index profiles that result in asymmetric absolute optical instruments. The method is based on the analogy between geometrical optics and classical mechanics and employs Lagrangians that separate in Cartesian coordinates. In addition, our method can be used to construct the index profiles of most previously known absolute optical instruments, as well as infinitely many different ones.