Abstract

Artificial structures that exhibit narrow resonance features are key to a myriad of scientific advances and technologies. In particular, exploration of the terahertz (THz) spectrum—the final frontier of the electromagnetic spectrum—would greatly benefit from high-quality resonant structures. Here we present a new paradigm of terahertz silicon disc microresonators with subwavelength thickness. Experimental results utilizing continuous-wave THz spectroscopy establish quality factors in excess of 120,000 at 0.6 THz. Reduction of the disc thickness to a fraction of the wavelength reduces the losses from the silicon substrate and paves the way to unparalleled possibilities for light–matter interaction in the THz frequency range.

© 2020 Chinese Laser Press

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2019 (7)

A. L. Gaeta, M. Lipson, and T. J. Kippenberg, “Photonic-chip-based frequency combs,” Nat. Photonics 13, 158–169 (2019).
[Crossref]

A. Rueda, F. Sedlmeir, M. Kumari, G. Leuchs, and H. G. Schwefel, “Resonant electro-optic frequency comb,” Nature 568, 378–381 (2019).
[Crossref]

N. L. B. Sayson, T. Bi, V. Ng, H. Pham, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Octave-spanning tunable parametric oscillation in crystalline Kerr microresonators,” Nat. Photonics 13, 701–706 (2019).
[Crossref]

D. W. Vogt, A. H. Jones, H. G. Schwefel, and R. Leonhardt, “Anomalous blue-shift of terahertz whispering-gallery modes via dielectric and metallic tuning,” Opt. Lett. 44, 1319–1322 (2019).
[Crossref]

D. W. Vogt, A. H. Jones, and R. Leonhardt, “Free-space coupling to symmetric high-Q terahertz whispering-gallery mode resonators,” Opt. Lett. 44, 2220–2223 (2019).
[Crossref]

Z. Wang, S. Yuan, G. Dong, R. Wang, L. Chen, X. Wu, and X. Zhang, “On-chip single-mode high-Q terahertz whispering gallery mode resonator,” Opt. Lett. 44, 2835–2838 (2019).
[Crossref]

D. W. Vogt, M. Erkintalo, and R. Leonhardt, “Coherent continuous wave terahertz spectroscopy using Hilbert transform,” J. Infrared Millimeter Terahertz Waves 40, 524–534 (2019).
[Crossref]

2018 (4)

D. W. Vogt and R. Leonhardt, “Ultra-high Q terahertz whispering-gallery modes in a silicon resonator,” APL Photon. 3, 051702 (2018).
[Crossref]

C. Mathai, R. Jain, V. Achanta, S. Duttagupta, D. Ghindani, N. Joshi, R. Pinto, and S. Prabhu, “Sensing at terahertz frequency domain using a sapphire whispering gallery mode resonator,” Opt. Lett. 43, 5383–5386 (2018).
[Crossref]

D. W. Vogt, A. H. Jones, and R. Leonhardt, “Thermal tuning of silicon terahertz whispering-gallery mode resonators,” Appl. Phys. Lett. 113, 011101 (2018).
[Crossref]

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361, eaan8083 (2018).
[Crossref]

2017 (3)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

D. W. Vogt and R. Leonhardt, “Fano resonances in a high-Q terahertz whispering-gallery mode resonator coupled to a multi-mode waveguide,” Opt. Lett. 42, 4359–4362 (2017).
[Crossref]

D. W. Vogt and R. Leonhardt, “High resolution terahertz spectroscopy of a whispering gallery mode bubble resonator using Hilbert analysis,” Opt. Express 25, 16860–16866 (2017).
[Crossref]

2016 (2)

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

2015 (2)

A. J. Deninger, A. Roggenbuck, S. Schindler, and S. Preu, “2.75 THz tuning with a triple-DFB laser system at 1550  nm and InGaAs photomixers,” J. Infrared Millimeter Terahertz Waves 36, 269–277 (2015).
[Crossref]

S. Tsuzuki, N. Kuzuu, H. Horikoshi, K. Saito, K. Yamamoto, and M. Tani, “Influence of OH-group concentration on optical properties of silica glass in terahertz frequency region,” Appl. Phys. Express 8, 072402 (2015).
[Crossref]

2014 (2)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

2013 (1)

2012 (2)

W. Cao, R. Singh, I. A. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37, 3366–3368 (2012).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

2009 (2)

S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94, 091118 (2009).
[Crossref]

C. M. Yee and M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

2008 (3)

2007 (2)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

2006 (1)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering gallery modes I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3–14 (2006).
[Crossref]

2005 (1)

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

2003 (3)

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

J. Zhang and D. Grischkowsky, “Whispering-gallery-mode cavity for terahertz pulses,” J. Opt. Soc. Am. B 20, 1894–1904 (2003).
[Crossref]

1999 (1)

1997 (1)

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microw. Theory Tech. 45, 2025–2034 (1997).
[Crossref]

1989 (1)

Achanta, V.

Al-Naib, I. A.

Anderson, M. H.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Annino, G.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microw. Theory Tech. 45, 2025–2034 (1997).
[Crossref]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Armani, D.

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Bi, T.

N. L. B. Sayson, T. Bi, V. Ng, H. Pham, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Octave-spanning tunable parametric oscillation in crystalline Kerr microresonators,” Nat. Photonics 13, 701–706 (2019).
[Crossref]

Brasch, V.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Cao, W.

Cassettari, M.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microw. Theory Tech. 45, 2025–2034 (1997).
[Crossref]

Chen, L.

Coen, S.

N. L. B. Sayson, T. Bi, V. Ng, H. Pham, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Octave-spanning tunable parametric oscillation in crystalline Kerr microresonators,” Nat. Photonics 13, 701–706 (2019).
[Crossref]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Deninger, A. J.

A. J. Deninger, A. Roggenbuck, S. Schindler, and S. Preu, “2.75 THz tuning with a triple-DFB laser system at 1550  nm and InGaAs photomixers,” J. Infrared Millimeter Terahertz Waves 36, 269–277 (2015).
[Crossref]

Döhler, G.

Dong, G.

Duttagupta, S.

Erkintalo, M.

D. W. Vogt, M. Erkintalo, and R. Leonhardt, “Coherent continuous wave terahertz spectroscopy using Hilbert transform,” J. Infrared Millimeter Terahertz Waves 40, 524–534 (2019).
[Crossref]

N. L. B. Sayson, T. Bi, V. Ng, H. Pham, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Octave-spanning tunable parametric oscillation in crystalline Kerr microresonators,” Nat. Photonics 13, 701–706 (2019).
[Crossref]

Evers, J.

Fattinger, C.

Freude, W.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Gaeta, A. L.

A. L. Gaeta, M. Lipson, and T. J. Kippenberg, “Photonic-chip-based frequency combs,” Nat. Photonics 13, 158–169 (2019).
[Crossref]

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361, eaan8083 (2018).
[Crossref]

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Ghindani, D.

Goh, K.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Gorodetsky, M.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Gorodetsky, M. L.

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361, eaan8083 (2018).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[Crossref]

Gossard, A.

Grischkowsky, D.

Hanson, M.

Harsha, S. S.

S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94, 091118 (2009).
[Crossref]

Hartinger, K.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

He, M.

Herr, T.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic illustration of a THz disc resonator with subwavelength thickness. The insert depicts 2 orders of magnitude of the normalized electric field distribution of the fundamental TM mode of a disc resonator with 12 mm diameter and 66.5 μm thickness at 0.6 THz on a logarithmic scale. The HRFZ-Si disc is indicated with the grey solid line. (b) Simulated intrinsic Q factor Q0 for two discs with 6 mm diameter and 72 μm thickness (blue dots) and 12 mm diameter and 66.5 μm thickness (orange dots). The green-shaded area indicates the Q0 of a solid sphere with 6 mm diameter. For simplicity, a constant permittivity corresponding to a material absorption of α=0.006  cm1 is assumed. (c) Optimal disc thickness (black) and maximal intrinsic Q factor (brown) for diameters from 6 to 60 mm at a design frequency of about 560 GHz. The green-shaded area shows the intrinsic Q factors for solid sphere resonators. (d) FSRs of the disc resonators for diameters from 6 to 60 mm with optimal thicknesses (blue) and solid spheres (green). The solid lines are interpolations of the simulated data points to guide the eye.
Fig. 2.
Fig. 2. Microscope images of (a) the top and (b) the rim of the 12 mm diameter disc with (66±1) μm thickness. The thin disc resonator is mounted on a 1 mm diameter metallic rod. The different colors in the photograph are due to reflections from various light sources.
Fig. 3.
Fig. 3. Schematic of the experimental setup. The disc resonators are mounted on a 3D computer-controlled translation stage with 0.2 μm precision to accurately control the distance between the waveguide and the resonator. The position of the resonator is monitored using two USB microscopes. The typical resonator–waveguide position for strong coupling is about 200 μm inside the edge of the disc at a height of about 100–200 μm above the disc. The entire setup is placed inside a closed environment with less than 0.02% relative humidity to minimize distortions from water vapor [32].
Fig. 4.
Fig. 4. Normalized transmission of the waveguide coupled to (a) the 6 mm disc resonator and (b) the 12 mm disc resonator. Measured (c) normalized transmission and (d) phase profiles (blue) of the resonance at 556 GHz of the 12 mm diameter disc. The corresponding resonance in (b) is highlighted in red. The fit of the analytical model is shown in orange. The frequency step size in subfigures (c) and (d) is 1 MHz.
Fig. 5.
Fig. 5. Measured intrinsic Q factors of the 6 mm diameter (blue dots) and 12 mm diameter (orange dots) disc resonators in the frequency range from 535 to 600 GHz. The green-shaded area indicates the measured (green dots) material-loss-limited Q0 of a 4 mm diameter HRFZ-Si spherical resonator. The smaller error bars around the water absorption line at 557 GHz are results of more averaged measurements to minimize effects on the Q factor from potential variations in the residual water vapor content in the resonator’s environment. The blue and orange dashed curves indicate the simulated intrinsic Q factors for discs with 6 mm diameter and 70.2 μm thickness and a 12 mm diameter disc with 66.5 μm thickness, respectively. The uncertainty at the absolute resonance frequencies is typically less than 0.5 GHz as indicated with the error bars.