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Publication - Journal Article

Photonics Research, 8, 1333 (2020)
DOI: 10.1364/PRJ.393070
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Unidirectional reflection from an integrated “Taiji” microresonator

A. Calabrese, F. Ramiro-Manzano, H. M. Price, S. Biasi, M. Bernard, M. Ghulinyan, I. Carusotto, L. Pavesi


We study light transmission and reflection from an integrated microresonator device, formed by a circular microresonator coupled to a bus waveguide, with an embedded S-shaped additional crossover waveguide element that selectively couples counter-propagating modes in a propagation-direction-dependent way. The overall shape of the device resembles a “taiji” symbol, hence its name. While Lorentz reciprocity is preserved in transmission, the peculiar geometry allows us to exploit the non-Hermitian nature of the system to obtain high-contrast uni- directional reflection with negligible reflection for light incident in one direction and a significant reflection in the opposite direction.


The development of unidirectional optical circuits, which exhibit different behaviors depending on the direction of incident light, has been a major focus in the optical community. However, in linear systems, it is not possible to violate the reciprocity theorem of Lorentz without using non-reciprocal, such as magnetic elements, which makes the realization of a miniaturized optical isolator a challenging task. Non-Hermitian dynamics can be used to engineer direction-dependent features in non-magnetic materials that can be easily integrated on a standard silicon photonics platform. A promising device for achieving this is the taiji resonator, which is a ring cavity with an S-shaped crossover branch that selectively couples the counter-propagating cavity modes. A bus waveguide laterally coupled to the resonator is used to inject light into it.

The taiji resonator has been successfully used in unidirectional lasers, topological systems, and to control light velocity in monolithic microfibers, but a detailed study of its transmission and reflection properties in a waveguide/microresonator system is still lacking. In this study, we present a joint theoretical and experimental investigation of the linear optical transmission and reflection properties of a taiji microresonator excited via a bus waveguide. The device is fabricated on an integrated silicon photonics platform and probed through a bus waveguide. The transmission and reflection properties are investigated analytically, numerically, and experimentally, and the expected reciprocity of the transmission is accurately confirmed by the experiment. A direction-dependent reflection is found, and the reflection asymmetry is shown to be robust against the Fabry-Perot fringes due to spurious reflections at the ends of the bus waveguide.

The results confirm the promise of taiji resonator elements to obtain unidirectional reflection in an optical integrated circuit. This study provides a fundamental step towards the full exploitation of a family of devices that holds great promise in view of obtaining new behaviors when endowed with optical gain and/or optical nonlinearities.


Sketch of the taiji microresonator with coupling coefficients
Fig. 1. Sketch of the taiji microresonator
Taiji microresonator, spectra of transmitted and reflected intensities (Left excitation and Right excitation)
Fig. 2. Panels (a) and (b): numerical results for the field intensity in the taiji microresonator with light incident from the left and right, respectively. The geometrical dimensions are in μm. The frequency is resonant with the ring and the bus waveguide is critically coupled. The color plot shows the electric field amplitude in V/m. It is note- worthy that only light incident from the right excites the S waveguide. This highlights the non-symmetrical behavior of light reflection. Panels (c) and (d): transmitted (blue dots) and reflected intensity as a function of the incident wavelength for light incident from the left (black dots) and from the right (green dots). The red lines display the fitting results employing the analytical model.
SEM images, optical images and optical setup, Taiji microresonator
Fig. 3. Panels (a) and (b) show the optical micrograph and the SEM image of the top and the cross-section view of a taiji microresonator, respectively. Panel (c): sketch of the experimental setup.
Taji microresonator. Unidirectional reflectance. Experimental spectra transmitted reflected intensities.
Fig 4. Experimental spectra of the (a) transmitted and (b), (c) reflected intensities as a function of the incident wavelength. The blue lines show the experimental measurements while the red lines display the fitting results employing the analytical model. The bottom panels show the zoom of the transmitted (Zoom 1) and reflected (Zoom 2, 3) intensities for the resonance highlighted by the vertical dashed lines
Coupling calculations, Comsol FEM, ring-waveguide, Taiji microresonator.
Fig. 6. Results of the simulation of the ring-bus waveguide coupling region of the taiji. Plotted curves represent the power transmission to either the bus waveguide or the ring, as a function of their mutual separation. The inset shows the distribution of electric field amplitude in the system in V/m, for a chosen distance of 335 nm. Geometrical dimensions are in μm.


Open access article
Fernando Ramiro Manzano, PhD 
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