Intriguing insights into optical resonances governed by the intriguing topology of the Möbius strip – Zoo House News
In the current issue of Nature Photonics, Prof. Dr. Oliver G. Schmidt, Head of the Professorship of Material Systems for Nanoelectronics and Scientific Director of the Research Center for Materials, Architectures and Integration of Nanomembranes (MAIN) at Chemnitz University of Technology, Dr. Libo Ma from the Leibniz Institute for Solid State and Materials Research (IFW) Dresden and other cooperation partners present a strategy for observing and manipulating the optical Berry phase in Möbius ring microcavities. In their research they discuss how an optical Berry phase can be generated and measured in dielectric Möbius rings. Furthermore, they present the first experimental evidence for the existence of a variable Berry phase for linearly or elliptically polarized resonant light.
Fascinating Möbius strip
A Möbius strip is a fascinating object. You can easily create a Mobius strip by twisting the two ends of a piece of paper 180 degrees and connecting them together. A closer look reveals that this band has only one surface. It cannot be oriented and one cannot distinguish between inside and outside or below and above. Due to this special “topological” property, the Möbius strip has become the subject of countless mathematical discourses, artistic representations and practical applications, for example in paintings by MC Escher, as a wedding ring or as a belt to be worn on both sides.
Optical ring resonators
Closed bands or rings also play an important role in optics and optoelectronics. So far, however, they are not made of Möbius strips and they are not made of paper but of optical materials such as silicon and silicon dioxide or polymers. Even these “normal” rings are not centimeters in size, but micrometers. When light with a certain wavelength propagates in a micro ring, optical resonances arise through constructive interference. This principle can be illustrated by a guitar string producing different tones at different lengths – the shorter the string, the shorter the wavelength and the higher the pitch. Optical resonance, or constructive interference, occurs precisely when the circumference of the ring is a multiple of the wavelength of the light. In these cases the light resonates in the ring and the ring is called an optical ring resonator. In contrast, when the circumference of the ring is an odd multiple of half the wavelength of the light, the light is severely attenuated and destructive interference occurs. Thus, an optical ring resonator amplifies light of certain wavelengths and severely attenuates light of other wavelengths that do not “fit” in the ring. From a technical point of view, the ring resonator functions as an optical filter which, integrated on a photonic chip, can “sort” and process light in a targeted manner. Optical ring resonators are central elements of optical signal processing in today’s data communication networks.
How polarized light circulates in the Möbius strip
In addition to wavelength, polarization is an essential property of light. Light can be polarized in different ways, such as linear or circular. When light propagates in an optical ring resonator, the polarization of the light does not change and remains the same at any point in the ring.
The situation changes fundamentally when the optical ring resonator is replaced by a Möbius strip, or rather a Möbius ring. To better understand this case, it helps to look at the geometry of the Möbius ring in detail. The cross-section of a Möbius ring is typically a slender rectangle with two edges much longer than their two adjacent edges, such as B. with a thin strip of paper.
Let us now assume that linearly polarized light circulates in the Möbius ring. Since the polarization preferentially aligns towards the long cross-sectional side of the Möbius ring, the polarization continuously rotates by up to 180 degrees while completely encircling the Möbius ring. This is a huge difference to a “normal” ring resonator, where the polarization of the light is always preserved. And that’s not all. The twisting of the polarization causes a phase change in the light wave, so that the optical resonances no longer occur at full multiples of the wavelength that fit into the ring, but at odd multiples of half the wavelength. Part of the research group had already theoretically predicted this effect in 2013. This prediction, in turn, is based on the work of the physicist Michael Berry, who introduced the eponymous “Berry phase” in 1983 and thus described the change in the phase of light, whose polarization changes during propagation.
First experimental evidence
In the current article, published in Nature Photonics, the Berry phase of light circulating in a Möbius ring is experimentally demonstrated for the first time. Two rings with the same diameter were produced for this purpose. The first is a “normal” ring and the second is a Moebius ring. And as predicted, the optical resonances in the Möbius ring occur at different wavelengths compared to the “normal” ring. However, the experimental results go far beyond previous predictions. For example, linear polarization not only rotates but also becomes increasingly elliptical. The resonances do not occur exactly at odd multiples of half the wavelength, but quite generally at non-integer multiples. To find out the reason for this discrepancy, Möbius rings were made with decreasing bandwidths. This investigation revealed that the degree of ellipticity in the polarization and the deviation of the resonance wavelength compared to the “normal” ring became weaker as the Möbius band became narrower. This is easy to understand since the peculiar topological properties of the Möbius ring merge into the properties of a “normal” ring as the band’s width decreases to its thickness. However, this also means that the berry phase in Möbius rings can be easily controlled by simply changing the band design.
In addition to the fascinating new fundamental properties of optical Möbius rings, new technological applications are also opening up. The tunable optical Berry phase in Möbius rings could be used for all-optical data processing of classical bits as well as qubits and support quantum logic gates in quantum computation and simulation.
Materials provided by TU Chemnitz. Originally written by Matthias Fejes; translated by Brent Benofsky. Note: Content can be edited for style and length.