Intriguing insights into optical resonances determined by the fascinating topology of the Möbius strip — ScienceDaily

in the current issue Nature Photonics, prof. Dr. Oliver G. Schmidt, head of the Materials Systems Professorship for Nanoelectronics at Chemnitz University of Technology and Scientific Director of the Materials, Architectures and Integration of Nanomembranes (MAIN) Research Center, Leibniz’s Dr. Libo Ma Solid State and Materials Research Institute (IFW) Dresden and other collaborative partners present a strategy for observing and manipulating the optical Berry phase in Möbius ring microcavities. In their research paper, they discuss how an optical Berry phase can be produced and measured in dielectric Möbius rings. They also provide the first experimental evidence for the existence of a variable Berry phase for linear or elliptical polarized resonant light.

Fascinating Möbius strip

A Möbius strip is a fascinating object. By bending the two ends of a paper strip 180 degrees, you can easily create a Möbius strip and tie them together. On closer inspection, you’ll notice that this strip has only one surface. It cannot be steered and cannot be distinguished from inside or outside or up and down. Because of this particular “topological” property, the Möbius ribbon has become an object of numerous mathematical discourses, artistic representations, and practical applications, for example, in the paintings of MC Escher, as a wedding ring or as a drive belt for attaching both sides of it. belt equal.

Optical ring resonators

Closed bands or loops also play an important role in optics and optoelectronics. But until now they were not made of Möbius strips and were not made of paper, but of optical materials such as silicon and silicon dioxide or polymers. These “normal” rings are also micrometers in size, not centimeters. If light of a certain wavelength is emitted in a microring, constructive interference causes optical resonances to occur. This principle can be exemplified by a guitar string that produces different tones at different lengths – the shorter the string, the shorter the wavelength and the higher the tone. An optical resonance or constructive interference occurs exactly when the circumference of the ring is a multiple of the wavelength of light. In these cases the light resonates in the ring and is called the ring optical ring resonator. Conversely, when the circumference of the ring is only one-half the wavelength of the light, the light is strongly attenuated and destructive interference occurs. Thus, an optical ring resonator amplifies light of certain wavelengths and strongly attenuates light of other wavelengths that do not “fit” into the ring. In technological terms, the ring resonator acts as an optical filter integrated on a photonic chip, which can selectively “sequence” and process light. Optical ring resonators are central elements of optical signal processing in today’s data communication networks.

How does polarized light travel in the Möbius strip?

Besides wavelength, polarization is a fundamental property of light. Light can be polarized in various ways, for example linearly or circularly. If light is emitted in an optical ring resonator, the polarization of the light does not change and remains the same at every point of the ring.

The situation changes fundamentally if the optical ring resonator is replaced with a Möbius strip, or better still, a Möbius ring. To better understand this situation, it is helpful to consider the detail of the geometry of the Möbius ring. The cross-section of a Möbius ring is typically a thin rectangle with two sides much longer than two adjacent sides, as in a thin strip of paper.

Now suppose that linearly polarized light travels through the Möbius ring. Since the polarization prefers to align itself in the direction of the long cross-sectional edge of the Möbius ring, the polarization continuously rotates up to 180 degrees as it passes completely around the Möbius ring. This is a huge difference from a “normal” ring resonator, where the polarization of the light is always maintained. And that’s not all. The bending of the polarization causes a change in the phase of the light wave so that optical resonances no longer occur at multiples of full wavelength that fit the ring, but at odd multiples of half the wavelength. Some of the research group had predicted this effect theoretically in 2013. This prediction is based on the work of physicist Michael Berry in 1983, who described the change in the phase of light that is de-polarized, called the “Berry phase”. changes as it spreads.

First experimental evidence

in the current article Nature Photonics, the Berry phase of light circulating in a Möbius ring was revealed experimentally for the first time. For this purpose, two rings of the same diameter were made. The first is a “normal” ring and the second is a Möbius ring. And as predicted, optical resonances in the Möbius ring appear at different wavelengths compared to the “normal” ring. However, the experimental results go far beyond previous estimates. For example, linear polarization not only rotates, it also becomes increasingly elliptical. Resonances do not occur exactly in odd multiples of half the wavelength, but rather generally in non-integer multiples. To find the cause of this deviation, Möbius rings with decreasing band width were made. This study revealed that the degree of ellipticity in polarization and the deviation of the resonance wavelength compared with the “normal” ring gradually weakened as the Möbius strip narrowed and narrowed. This is easily understood because the special topological properties of the Möbius ring combine with those of a “normal” ring when the width of the band is reduced to its thickness. But this also means that the Berry phase in the Möbius rings can be easily controlled by changing the design of the band.

In addition to the fascinating new core features of optical Möbius rings, new technological applications are also opening up. The tunable optical Berry phase in Möbius rings can serve the purely optical data processing of qubits as well as classical bits and support quantum logic gates in quantum computing and simulation.

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materials provided by Chemnitz University of Technology. Original written by Matthias Fejes; Translated by Brent Benofsky. Note: Content can be edited for style and length.

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