Abstract

The ultimate limits of performance for any classical optical system are set by sub-wavelength fluctuations within the host material, which may be frozen-in or even dynamically induced. The most common manifestation of such subwavelength disorder is Rayleigh light scattering, which is observed in nearly all waveguiding technologies today and can lead to both irreversible radiative losses as well as undesirable intermodal coupling. While it has been shown that backscattering from disorder can be suppressed by breaking the time-reversal symmetry in magneto-optic and topological insulator materials, common optical dielectrics possess neither of these properties. Here, we demonstrate an optomechanical approach for dynamically suppressing Rayleigh backscattering within dielectric resonators. We achieve this by locally breaking the time-reversal symmetry in a silica resonator through a Brillouin scattering interaction that is available in all materials. Near-complete suppression of Rayleigh backscattering is experimentally confirmed through two independent measurements—the elimination of a commonly seen normal-mode splitting or “doublet” effect and by measurement of the reduction in intrinsic optical loss. Additionally, a reduction of the back-reflections caused by disorder is also observed. Our results provide new evidence that it is possible to dynamically suppress Rayleigh backscattering within any optical dielectric medium using time-reversal symmetry breaking, for achieving robust light propagation in spite of scatterers or defects.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband Brillouin modulation,” Nat. Photonics 12, 613–619 (2018).
[Crossref]

L. D. Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Zhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the Kerr effect,” Optica 5, 279–282 (2018).
[Crossref]

2017 (3)

S. Kim and G. Bahl, “Role of optical density of states in Brillouin optomechanical cooling,” Opt. Express 25, 776–784 (2017).
[Crossref]

J. Kim, S. Kim, and G. Bahl, “Complete linear optical isolation at the microscale with ultralow loss,” Sci. Rep. 7, 1647 (2017).
[Crossref]

S. Kim, X. Xu, J. M. Taylor, and G. Bahl, “Dynamically induced robust phonon transport and chiral cooling in an optomechanical system,” Nat. Commun. 8, 205 (2017).
[Crossref]

2016 (4)

Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10, 657–661 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Ylmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113, 6845–6850 (2016).
[Crossref]

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]

A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, “Efficient microwave to optical photon conversion: an electro-optical realization,” Optica 3, 597–604 (2016).
[Crossref]

2015 (3)

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’Shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, “Nanophotonic optical isolator controlled by the internal state of cold atoms,” Phys. Rev. X 5, 041036 (2015).
[Crossref]

2014 (1)

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

2013 (2)

Q. Li, A. A. Eftekhar, Z. Xia, and A. Adibi, “Unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators,” Phys. Rev. A 88, 033816 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

2012 (2)

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

2011 (3)

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref]

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).
[Crossref]

2010 (3)

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

2009 (4)

S. Groblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[Crossref]

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-factor-enhanced scattering from Si nanocrystals in an optical microcavity,” Phys. Rev. Lett. 103, 027406 (2009).
[Crossref]

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref]

2008 (1)

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
[Crossref]

2007 (2)

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

2000 (3)

R. Lenke and G. Maret, “Magnetic field effects on coherent backscattering of light,” Eur. Phys. J. B 17, 171–185 (2000).
[Crossref]

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
[Crossref]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

1997 (1)

1995 (1)

1988 (2)

M. Büttiker, “Absence of backscattering in the quantum hall effect in multiprobe conductors,” Phys. Rev. B 38, 9375–9389 (1988).
[Crossref]

F. C. MacKintosh and S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[Crossref]

1984 (1)

A. A. Golubentsev, “The suppression of interference effects in multiple scattering of light,” Sov. Phys. JETP 59, 26–32 (1984).

1982 (1)

B. I. Halperin, “Quantized hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential,” Phys. Rev. B 25, 2185–2190 (1982).
[Crossref]

1973 (1)

D. Pinnow, T. Rich, F. Ostermayer, and M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” App. Phys. Lett. 22, 527–529 (1973).
[Crossref]

1969 (1)

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J 48, 3187–3215 (1969).
[Crossref]

Adibi, A.

Q. Li, A. A. Eftekhar, Z. Xia, and A. Adibi, “Unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators,” Phys. Rev. A 88, 033816 (2013).
[Crossref]

Albrecht, B.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’Shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, “Nanophotonic optical isolator controlled by the internal state of cold atoms,” Phys. Rev. X 5, 041036 (2015).
[Crossref]

Alegre, T. P. M.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

Aspelmeyer, M.

S. Groblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[Crossref]

Bahl, G.

S. Kim, X. Xu, J. M. Taylor, and G. Bahl, “Dynamically induced robust phonon transport and chiral cooling in an optomechanical system,” Nat. Commun. 8, 205 (2017).
[Crossref]

J. Kim, S. Kim, and G. Bahl, “Complete linear optical isolation at the microscale with ultralow loss,” Sci. Rep. 7, 1647 (2017).
[Crossref]

S. Kim and G. Bahl, “Role of optical density of states in Brillouin optomechanical cooling,” Opt. Express 25, 776–784 (2017).
[Crossref]

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012).
[Crossref]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Bender, C. M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Benson, O.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[Crossref]

Bino, L. D.

Butsch, A.

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).
[Crossref]

Büttiker, M.

M. Büttiker, “Absence of backscattering in the quantum hall effect in multiprobe conductors,” Phys. Rev. B 38, 9375–9389 (1988).
[Crossref]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref]

Cardenas, J.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

Carmon, T.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012).
[Crossref]

Chan, J.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref]

Chang, D. E.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref]

Chen, W.

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Ylmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U.S.A. 113, 6845–6850 (2016).
[Crossref]

Chen, Y.

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Figures (4)

Fig. 1.
Fig. 1. Rayleigh backscattering in a whispering-gallery resonator (WGR) and concept for optomechanical suppression. (a) Optical WGRs support degenerate modes (a±) that are time-reversed partners (cw/ccw) and can be individually accessed via directional probing. Rayleigh backscattering from disorder intrinsic to the WGR can couple these modes, leading to loss of their distinguishable directionality. (b) Experimentally, this results in normal-mode splitting or “doublet” (measured here in a silica WGR) when the disorder-induced backscattering rate is comparable to the intrinsic optical loss rate. Such doublets are routinely observed in high-Q resonator systems and impose a technological constraint. In this representative example, we observe a Rayleigh-backscattering-induced coupling rate of about V=0.33MHz. (c) We suppress Rayleigh backscattering by breaking time-reversal symmetry within the bandwidth of the a± optical modes. This is achieved through a Brillouin scattering process [21,25], in which a high-coherence cw mechanical mode, b+, is coupled to the cw a+ mode by a cw directional pump, c+. The interaction is subject to the phase-matching constraint illustrated by the grey triangle. The momentum-matching requirement implies that the cw pump does not directly induce any effect for the ccw optical mode, a. (d) Toy model for the WGR and waveguide system, in which we distinguish the two directional subsystems and indicate both Rayleigh (V) and optomechanical (G) couplings. All variables are defined in the main text. The directional Brillouin optomechanical coupling significantly reduces the susceptibility of the a+ mode only and “open-circuits” the backscattering channel, thereby suppressing Rayleigh scattering.
Fig. 2.
Fig. 2. Demonstration of dynamic optomechanical suppression of Rayleigh backscattering. (a) General configuration of optical pump, probe, and mechanical sidebands with respect to the c+ and a+ optical modes in the cw direction—used throughout this work. (b) This experiment uses a 116 MHz mechanical mode in a 90 μm radius silica WGR. The Rayleigh-scattering-induced doublet is readily observed in probing of the a± optical modes for an off-resonance pump. As the pump is brought on-resonance, the Brillouin-scattering-induced transparency is generated for the cw mode only (its on-resonance susceptibility is reduced), which breaks time-reversal symmetry within the bandwidth of the a± modes. These observations show two key predictions of the model—improved coupling of the a mode to the waveguide and the elimination of the doublet—both confirming the suppression of Rayleigh backscattering within the WGR. The reflection measurement at Port 1 represents a suppression of light coupling into the resonator due to the transparency. However, this Port 1 reflection should be identical to the reflection measured from Port 2 (Supplement 1, Section 1), which corresponds to a reduction in Rayleigh backscattering. Solid lines are simultaneous fits to the theoretical model. The reflection is very large due to resonant enhancement.
Fig. 3.
Fig. 3. Near-complete suppression of Rayleigh backscattering with Brillouin strong coupling. (a) This experiment was performed with the 229.5 MHz mechanical mode of a 101 μm radius silica WGR. By initially detuning the pump laser we observe the Rayleigh-backscattering-induced optical doublet. Fitting to the theoretical model (solid line) indicates intrinsic loss, κi, extrinsic loss, κex, and backscattering rate, V. (b) We now set the pump to zero detuning so that strong cw optomechanical coupling is achieved (with G=0.5MHz), resulting in a prominent change in susceptibility for the cw (a+) mode only. The time-reversed (a) mode, which we did not modify, simultaneously exhibits much narrower line width, and the backscattering-induced doublet is eliminated. (c) The avoided crossing due to Brillouin strong coupling is observed in both the optical transmission spectrum and the mechanical spectrum for various detunings of the pump. The data closely match the theoretical eigenfrequencies (see Section 1.F of Supplement 1). Mechanical spectra are measured from the beating between the pump and scattered light on a photodetector [31].
Fig. 4.
Fig. 4. Determination of intrinsic loss rate and suppression of Rayleigh-backscattering-induced loss. (a) By adjusting the extrinsic coupling between the resonator and waveguide, κex, we are able to explore the point of critical coupling for the ccw mode, a. Critical coupling is the point where on-resonance transmission reaches zero and occurs when the extrinsic coupling rate, κex, and the intrinsic loss rate, κi, are matched. (b) We use experimentally measured parameters in the theoretical model [Supplement 1, Eq. (S8)] to establish theoretical predictions for the on-resonance transmission as a function of extrinsic coupling rate. When optomechanical coupling is zero (i.e., Rayleigh backscattering is active) the predicted critical coupling point is at 0.75 MHz. Experimental data points (blue) are well matched to this predicted curve. On the other hand, with an optomechanical coupling of G=0.5MHz, we estimate a ccw effective intrinsic loss rate of 0.46 MHz, a very close match to the purely intrinsic loss rate of 0.45 MHz. The measured on-resonance transmission (red) from the experimental measurements in (a) are also very well matched to the theoretical predictions from the model. We additionally plot the theoretical case where Rayleigh scattering does not contribute (occurs when either V0 or G).

Equations (3)

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Hint=(Ga+b++G*a+b+)+V(a+a+aa+).
κeff+=κ(1+C)+4V2κ,
κeff=κ+4V2κ(1+C).