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

doi:10.1364/PRJ.393070

Research · Publication & note

Unidirectional Reflection from an Integrated “Taiji” Microresonator

Journal article

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

Photonics Research Volume 8 Issue 8 1333–1341 2020

Abstract

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 unidirectional reflection with negligible reflection for light incident in one direction and a significant reflection in the opposite direction.

How to cite

Initials first

A. Calabrese, F. Ramiro-Manzano, H. M. Price, S. Biasi, M. Bernard, M. Ghulinyan, I. Carusotto and L. Pavesi. Unidirectional reflection from an integrated “taiji” microresonator. Photonics Research 8(8), 1333–1341 (2020). DOI: 10.1364/PRJ.393070.

Family name first

Calabrese, A., Ramiro-Manzano, F., Price, H. M., Biasi, S., Bernard, M., Ghulinyan, M., Carusotto, I., & Pavesi, L. (2020). Unidirectional reflection from an integrated “taiji” microresonator. Photonics Research, 8(8), 1333–1341. https://doi.org/10.1364/PRJ.393070

Article access and reuse

The Version of Record is openly available from the journal. The Photonics Research copyright transfer agreement permits authors to reuse all or part of the work, including the publisher-formatted version, on their personal web homepage when the Chinese Laser Press copyright notice is retained. The figures below are the complete original compositions extracted from the article PDF and are reproduced with that notice.

Figures

Figure 1 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 1.** Sketch of the taiji microresonator: E^L_in and E^R_in (E^L_out and E^R_out) are input (output) field amplitudes at the left and right facet, respectively, while E_e1 and E_e2 are the amplitudes of fields emitted as radiative dissipation; κ_i and t_i, with i = 1, 2, 3, are the coupling and transmission amplitudes at the different beamsplitting regions indicated by the gray squares. The gray dashed lines define the spatial size of the different segments.

Figure 2 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 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 noteworthy 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.

Figure 3 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 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.

Complete transmitted and reflected intensity spectra with three detailed zoom panels — **Figure 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.

Figure 5: complete resonant intensity plot with axes and legend — **Figure 5.** Intensity as a function of the wavelength computed with Eqs. (7) and (8) using the parameters of Table 1 (Appendix B) at the resonant wavelengths (λ_i). Precisely, the red squares are the transmitted intensity, the upward light blue triangles are the reflected intensity for light incident from right and the downward blue triangles are the reflected intensity for light incident from left. The light blue and blue dashed lines denote the average of the resonant values for |r_R(λ_i)|² and |r_L(λ_i)|², respectively.

Figure 6 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 6.** Map of the fields within the device, used to calculate the scattering matrix elements when light enters from the left. Labels E_m, with m = 1,…,6, represent complex amplitudes of the guided fields propagating in the device. Labels E_e1 and E_e2 indicate the modes that are radiated into the cladding. t_i and κ_i, where i = 1, 2, 3, are the transmission and coupling amplitudes at the different beamsplitting regions.

Figure 7 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 7.** Map of the fields within the device, used to calculate the scattering matrix elements when light enters from the right. Again E_m, with m integers, are complex amplitudes of guided-mode fields, while E_e1 and E_e2 indicate the amplitudes of the modes that are radiated into the cladding. t_i and κ_i, where i = 1, 2, 3, are the transmission and coupling amplitudes at the different beamsplitting regions.

Figure 8 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 8.** 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.

Figure 9 from Unidirectional Reflection from an Integrated Taiji Microresonator — **Figure 9.** Results of the simulation of the ring-S-shaped waveguide coupling region of the taiji. Plotted curves represent the power transmission to either the ring or the S-shaped branch, 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 289 nm. Geometrical dimensions are in μm.