The Binet equation in mechanics describes the orbital geometry of a moving particle under a central force field. In this paper, as its counterpart in optics, we show this formula can be similarly utilized in ray tracing of a gradient-index (GRIN) medium with a concentric field. As an inference of Fermat's principle, this generalization is called the optical Binet equation (OBE). A remarkable advantage of OBE is that it can not only determine the ray trace or concentric GRIN field once one of them is given, but also derive the propagation time inside the medium. As examples, we apply OBE to rays passing through a Maxwell fish-eye lens, Luneburg lens, Eaton lens, concentrator, and hyperbolic deflector, the time delay of which can be calculated once the GRIN field or ray trace equation is solved. The results are well matched with simulations, proving it to be an effective tool in solving problems of the concentric GRIN field.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1364/JOSAA.456203 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Ray tracing is a fundamental geometric-optics issue which gives a single ray path but seldom presents the collective behavior of light. The optical field distribution usually involves the calculation of an electromagnetic field and is rarely discussed from the perspective of geometric optics. However, in this paper, we show for a concentric medium with spherically symmetric refractive index, how the relative angular distribution of refractive beams can be obtained from the pure classical geometric optics method.
View Article and Find Full Text PDFDoes exposure to nature make children more intelligent? Analysis in Polish children with and without ADHD.
Int J Hyg Environ Health
August 2023
Institute of Psychology, Jagiellonian University, Krakow, Poland; Health and Quality of Life in a Green and Sustainable Environment, SRIPD, Medical University of Plovdiv, Plovdiv, Bulgaria.
Article Synopsis
- A study looked at whether spending time in nature (like parks and lakes) helps children aged 10-13 get smarter, especially those with and without ADHD.
- Researchers checked how much green (plants) and blue (water) space kids were around their homes and tested their intelligence with special IQ tests.
- They found that being around nature didn't really make a difference in intelligence, and physical activity didn't seem to help either.
Objective: This study aimed to specify whether family communication and satisfaction are predictors of a child's executive functions and whether attention deficit hyperactivity disorder (ADHD) severity lies in the pathway between these variables.
Method: Two hundred Polish children with ADHD, aged 10 to 13, were tested using Conners 3, the PU1 Battery of Cognitive Tests and Stanford-Binet Intelligence Scale, Fifth Edition (SB5). Parents filled out the FACES IV-SOR questionnaire.
Limits to Gauge Coupling in the Dark Sector Set by the Nonobservation of Instanton-Induced Decay of Super-Heavy Dark Matter in the Pierre Auger Observatory Data.
Phys Rev Lett
February 2023
Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia.
Instantons, which are nonperturbative solutions to Yang-Mills equations, provide a signal for the occurrence of quantum tunneling between distinct classes of vacua. They can give rise to decays of particles otherwise forbidden. Using data collected at the Pierre Auger Observatory, we search for signatures of such instanton-induced processes that would be suggestive of super-heavy particles decaying in the Galactic halo.
View Article and Find Full Text PDFRay tracing in concentric gradient-index media: optical Binet equation.
J Opt Soc Am A Opt Image Sci Vis
June 2022
The Binet equation in mechanics describes the orbital geometry of a moving particle under a central force field. In this paper, as its counterpart in optics, we show this formula can be similarly utilized in ray tracing of a gradient-index (GRIN) medium with a concentric field. As an inference of Fermat's principle, this generalization is called the optical Binet equation (OBE).
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!