Turning losses into a bargain with parity-time symmetry
The development of nanofabrication technologies in the wake of micro- and nanoelectronics has triggered the emergence of many artificial structures with exciting electromagnetic behaviors, such as photonic crystals, metamaterials, and plasmonic resonators. Recently, the intriguing class of PT-symmetric devices, where PT refers to parity-time symmetry,1 has attracted much attention. The characteristic feature of PT symmetry is that describing the changes in refractive index throughout the structure requires complex numbers. This is due to the presence of alternating, or staggered, gain and loss regions in the system. To provide new features, these regions must be combined in such a way that they are more than just a succession of gains and losses. This is done by coupling two or more optical elements such as resonators, waveguides, or optical modes.
Apart from fundamental research motivations, interest in these artificial systems is strongly driven by the functionalities that can be achieved by modulating gain and loss in such structures. A disruptive aspect of the PT-symmetry paradigm is that the combination and modulation of gain and loss can lead to unconventional switching and memory behaviors, progressing well beyond the basic idea of loss compensation. One simple example of these concepts, detailed below, is a pair of coupled waveguides, one with gain and the other with loss, as illustrated in Figure 1.
In such a PT-symmetric system, the effective detuning (i.e., the propagation eigenvalue difference among supermodes, and thus their beat length) of the propagation constants between the two familiar odd and even supermodes is gradually reduced upon increasing the level of combined gain and loss in the system, until the imaginary part of these constants is above a critical point. Variation of the effective detuning can be exploited through variation of the gain-loss level below the critical point. This could be used to implement switches and modulators, as well as to mitigate the problems caused by lack of electro-optical tunability in fiber optics, metamaterials, and plasmonic devices. Our theoretical findings also predict a remarkable feature, deeply connected to PT symmetry. The gain level required for switching can be reduced by increasing the loss contribution, with a penalty that turns out to be quite affordable on the transmission level.2–4
Another striking functionality related to PT symmetry is a peculiar flavor of non-reciprocity, distinctly different from that based on the Faraday magneto-optical effect. In the case of a system of PT-symmetric coupled waveguides, the transmission differs depending on whether light injection is performed into the gain or loss waveguide. This kind of asymmetric operation can be used for the implementation of a novel optical buffer memory function.5 This is a highly valuable function for holding information at nodes in optical fiber networks, addressing issues such as contention.
Another example of unidirectional behavior is shown in Figure 2: the case of a PT-symmetric Bragg mirror, for which reflectivity can be extremely low for light incident from one side, and extremely high when light is incident from the opposite side. This property can even be obtained without any gain, using a fully passive approach, provided that an appropriate amount of loss is incorporated in the system.6–9 This can further extend the range of application for the passive-type PT-symmetry approach from the optical to terahertz and microwave domains, where the realization of gain media is still a pending issue.
PT symmetry can also provide innovative solutions in the field of integrated optics around 1.5μm wavelength. One major bottleneck of the hybrid integration approach, where semiconductors made from group III-V elements are combined with silicon, is that each type of active device (lasers, modulators, and so on) requires a specific composition of semiconductor compounds. The PT-symmetry principle provides an alternative way to realize active devices that could enable a new platform for integrated optics. By using PT-symmetric coupled waveguides and Bragg reflectors as fundamental building blocks, it is possible to build a wide variety of functional optical devices, such as unidirectional distributed feedback lasers, switches, and reconfigurable modal demultiplexers.10
The advantage of a PT-symmetry-based solution is that the fabrication of all these devices could be done with the same composition of III-V semiconductor compound. This greatly simplifies the manufacturing process. This paradigm could thus provide a major boost to integrated optics, metamaterials, and plasmonics, and is expected to foster a new generation of tunable, reconfigurable, and profoundly asymmetric devices.
Université Paris Sud
Anatole Lupu is a CNRS research scientist with more than 25 years of research experience in optoelectronics, both in academic and industrial labs. His current interests address theoretical and experimental studies in the areas of metamaterials, plasmonics, slow light, and PT-symmetric devices.
Aloyse Degiron is a tenured CNRS researcher at the IEF. His studies focus on theoretical and experimental investigations in the areas of nano-optics, plasmonic metamaterials, and PT-symmetric devices.
Institut d'Optique Graduate School
Henri Benisty has investigated microcavities and photonic crystals since the mid-1990s, studying both their basic properties and their applications in systems, covering LEDs, miniature photonic integrated circuits, and biophotonics. More recent topics of interest relate to plasmonics and PT symmetry, such as hybrid dielectric-metal waveguides, thermal emitters, and PT-symmetric systems.