Skip to main content

Research · Publication & note

July 17, 2020 September 9, 2026

Unidirectional Reflection from an Integrated “Taiji” Microresonator - Notes

Research publication featured image

Published 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.

Figures

The diagram defines the taiji resonator as a bus-coupled microring containing an asymmetric S-shaped branch. Three coupling regions connect the bus, ring and branch, while separate ports identify the guided input and output fields and the radiation emitted from the branch ends. The geometry preserves reciprocal transmission but couples the counterpropagating cavity modes asymmetrically, which permits different reflection for illumination from opposite directions.
Figure 1. Summary. The diagram defines the taiji resonator as a bus-coupled microring containing an asymmetric S-shaped branch. Three coupling regions connect the bus, ring and branch, while separate ports identify the guided input and output fields and the radiation emitted from the branch ends. The geometry preserves reciprocal transmission but couples the counterpropagating cavity modes asymmetrically, which permits different reflection for illumination from opposite directions.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 2 from Unidirectional Reflection from an Integrated Taiji Microresonator
Figure 2. Summary. 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.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 3 from Unidirectional Reflection from an Integrated Taiji Microresonator
Figure 3. Summary. 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.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Complete transmitted and reflected intensity spectra with three detailed zoom panels
Figure 4. Summary. 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.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 5: complete resonant intensity plot with axes and legend
Figure 5. Summary. 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 (λi).

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

This field map follows excitation from the left through the three coupling regions of the taiji device. The numbered amplitudes identify the guided fields in the bus, ring and S-shaped branch, while the two external amplitudes represent radiation into the cladding. Their interference cancels the field returning to the left input port in the ideal model, providing the scattering-matrix basis for vanishing left-side reflection.
Figure 6. Summary. This field map follows excitation from the left through the three coupling regions of the taiji device. The numbered amplitudes identify the guided fields in the bus, ring and S-shaped branch, while the two external amplitudes represent radiation into the cladding. Their interference cancels the field returning to the left input port in the ideal model, providing the scattering-matrix basis for vanishing left-side reflection.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

This complementary field map follows excitation from the right using the same bus, ring, branch and radiation channels. Right-side illumination opens additional circulation and branch-coupling paths, so the amplitudes returning through the bus do not undergo the cancellation obtained for left-side excitation. Comparing Figures 6 and 7 therefore makes the origin of direction-dependent reflection explicit while transmission remains reciprocal.
Figure 7. Summary. This complementary field map follows excitation from the right using the same bus, ring, branch and radiation channels. Right-side illumination opens additional circulation and branch-coupling paths, so the amplitudes returning through the bus do not undergo the cancellation obtained for left-side excitation. Comparing Figures 6 and 7 therefore makes the origin of direction-dependent reflection explicit while transmission remains reciprocal.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 8 from Unidirectional Reflection from an Integrated Taiji Microresonator
Figure 8. Summary. 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.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 9 from Unidirectional Reflection from an Integrated Taiji Microresonator
Figure 9. Summary. 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.

© 2020 Chinese Laser Press. Source: A. Calabrese et al., Photonics Research 8(8), 1333-1341 (2020), DOI 10.1364/PRJ.393070. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

How to cite

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.

Related publications

Connections within F. Ramiro-Manzano's publication record, selected from shared research topics and evidence reviewed in the source papers.

IEEE Photonics Journal identification graphic
Article
IEEE Photon. J. 11(2), 6101114 (2019)
Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator
S. Biasi, F. Ramiro-Manzano, F. Turri, P.-É. Larré, M. Ghulinyan, I. Carusotto and L. Pavesi

What the related paper adds

This earlier paper establishes a scientific basis for Unidirectional Reflection from an Integrated “Taiji” Microresonator. This paper explains asymmetric resonance doublets by combining phase-sensitive transmission, finite-element simulation and coupled-mode theory. It shows that stochastic surface roughness produces both conservative and dissipative coupling between counter-propagating modes, so a purely Hermitian description cannot reproduce the measured imbalance.

What this paper adds to the related work

Building on the earlier contribution Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator, this paper advances the research line. This work engineers the non-Hermitian coupling deliberately in a taiji microresonator. Its internal S-shaped branch couples counter-propagating modes in a direction-dependent way, preserving reciprocal transmission while producing high-contrast reflection in one direction and almost none in the other.

Figure 6: pump and probe experiment
Journal article
Photonics Research 5(3), 168-175 (2017)
Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning
M. Bernard, F. Ramiro-Manzano, L. Pavesi, G. Pucker, I. Carusotto and M. Ghulinyan

What the related paper adds

This earlier paper establishes a scientific basis for Unidirectional Reflection from an Integrated “Taiji” Microresonator. This study uses local thermo-optical tuning to drive two interacting Fano resonances through a complete crossing. The experiment continuously changes their spectral separation and asymmetry and reaches the critical condition where one modal feature disappears, offering a controlled probe of intermode coupling inside one integrated cavity.

What this paper adds to the related work

Building on the earlier contribution Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning, this paper advances the research line. This work engineers the non-Hermitian coupling deliberately in a taiji microresonator. Its internal S-shaped branch couples counter-propagating modes in a direction-dependent way, preserving reciprocal transmission while producing high-contrast reflection in one direction and almost none in the other.

Featured image for Microring Resonators and Silicon Photonics
Journal article
MRS Advances 1(48), 3281-3293 (2016)
Microring Resonators and Silicon Photonics
F. Ramiro-Manzano, S. Biasi, M. Bernard, M. Mancinelli, T. Chalyan, F. Turri, M. Ghulinyan, M. Borghi, A. Samusenko, D. Gandolfi, R. Guider, A. Trenti, P.-É. Larré, L. Pasquardini, N. Prtljaga, S. Manna, I. Carusotto, G. Pucker and L. Pavesi

What the related paper adds

This earlier paper establishes a scientific basis for Unidirectional Reflection from an Integrated “Taiji” Microresonator. This review explains microring resonators as reusable building blocks of silicon photonics. It brings together coupling, filtering, sensing, nonlinear response and integration choices, providing a compact technical map for understanding why changes in geometry and access waveguide produce very different device functions.

What this paper adds to the related work

Building on the earlier contribution Microring Resonators and Silicon Photonics, this paper advances the research line. This work engineers the non-Hermitian coupling deliberately in a taiji microresonator. Its internal S-shaped branch couples counter-propagating modes in a direction-dependent way, preserving reciprocal transmission while producing high-contrast reflection in one direction and almost none in the other.

Silicon Microresonators
Book chapter
New Horizons in Nanoscience and Engineering · Chapter 2 · pp. 37-86 (2015)
Silicon Microresonators: How to Give a New Twist to Silicon Photonics
M. Borghi, D. Gandolfi, M. Ghulinyan, R. Guider, M. Mancinelli, G. Pucker, F. Ramiro-Manzano, F. Turri and L. Pavesi

What the related paper adds

This earlier paper establishes a scientific basis for Unidirectional Reflection from an Integrated “Taiji” Microresonator. This chapter follows silicon microresonators from individual components to complex photonic functions. It connects interferometric switching, coupled-resonator chaos, vertical coupling, nonlinear bistability, biosensing and optomechanics, showing how one device family can support both fundamental experiments and scalable circuits.

What this paper adds to the related work

Building on the earlier contribution Silicon Microresonators: How to Give a New Twist to Silicon Photonics, this paper advances the research line. This work engineers the non-Hermitian coupling deliberately in a taiji microresonator. Its internal S-shaped branch couples counter-propagating modes in a direction-dependent way, preserving reciprocal transmission while producing high-contrast reflection in one direction and almost none in the other.

Featured image for Intermode reactive coupling induced by waveguide-resonator interaction
Journal article
Phys. Rev. A 90, 053811 (2014)
Intermode reactive coupling induced by waveguide-resonator interaction
M. Ghulinyan, F. Ramiro-Manzano, N. Prtljaga, M. Bernard, L. Pavesi, G. Pucker and I. Carusotto

What the related paper adds

This earlier paper establishes a scientific basis for Unidirectional Reflection from an Integrated “Taiji” Microresonator. This work identifies a waveguide-induced reactive coupling between different radial mode families of a microdisk, analogous to an off-diagonal Lamb shift. The resulting Fano line shapes connect open-system theory, full-vector simulations and measured transmission, showing that the access waveguide actively reshapes the cavity spectrum.

What this paper adds to the related work

Building on the earlier contribution Intermode reactive coupling induced by waveguide-resonator interaction, this paper advances the research line. This work engineers the non-Hermitian coupling deliberately in a taiji microresonator. Its internal S-shaped branch couples counter-propagating modes in a direction-dependent way, preserving reciprocal transmission while producing high-contrast reflection in one direction and almost none in the other.

Research fields

Top-down

The Taiji resonator is fabricated as an integrated microring with an embedded S-shaped branch and a side-coupled bus waveguide. This patterned geometry selects the conversion between clockwise and counter-clockwise cavity modes while remaining compatible with an on-chip circuit.

Simulations & fits

A transfer-matrix scattering model is validated against finite-element field simulations. Together they identify how the internal branch redistributes the circulating field and predicts direction-dependent reflection without violating reciprocal transmission.

Characterization

Optical transmission and reflection are recorded from both ends of the bus waveguide and compared with micrographs and cross-sectional SEM images. Measuring both launch directions distinguishes the resonator asymmetry from residual Fabry-Pérot fringes at the chip facets.

RESEARCH TOPICS

CouplingThe taiji device combines a racetrack resonator, a side bus waveguide and an S-shaped branch inside the ring. As Figures 6 and 7 make explicit, the structure can be decomposed into three evanescent beam splitters: one couples bus and ring, while two couple the ring to the ends of the S branch.InterferenceThe measured reflection contains more than the taiji resonance. Weak reflections at the two chip facets create a Fabry-Pérot background, and Figure 4(b) shows beating between those fringes and the field reflected by the resonator.MultimodeHere the relevant pair of modes is not a set of unrelated transverse profiles but the two counter-propagating waves of the same ring resonance. The device thus uses controlled mode conversion to obtain direction-dependent output without claiming a linear optical isolator.ResonatorsExperiments, finite-element simulations and an analytical transfer-matrix description all show high-contrast unidirectional reflection: one incidence direction has a significant reflected resonance and the opposite direction nearly none. It establishes the taiji geometry as an integrated building block for directional reflection and for later nonlinear or laser implementations.
F. Ramiro-Manzano website
Home Publications News Gallery Misc About
Site designed by F. Ramiro-Manzano. You are welcome to share, adapt and use my original content, including commercially, under CC BY 4.0, with citation to F. Ramiro-Manzano. Publisher and third-party materials remain subject to their own policies.