Coupled-resonator-induced transparency

Smith, David D.; Chang, Hongrok; Fuller, Kirk A.; Rosenberger, A. T.; Boyd, Robert W.

doi:10.1103/physreva.69.063804

Cited by 477 publications

(259 citation statements)

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“…More recently, EIT has been discovered in meta materials [9][10][11][12] where resonant structures can be fabricated to correspond to dark and bright modes. Resonators provide certain advantages [13] because by design we can manipulate EIT to produce desired transmission properties of a structure. It would thus be especially interesting to study resonators coupled to other systems such as cavity optomechanical systems.…”

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confidence: 99%

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Electromagnetically induced transparency in mechanical effects of light

2010

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We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field at the probe frequency. Our calculations show explicitly the origin of EIT-like dips as well as the characteristic changes in dispersion from anomalous to normal in the range where EIT dips occur. Remarkably the pump-probe response for the optomechanical system shares all the features of the Λ system as discovered by Harris and collaborators.PACS numbers: 42.50. Gy,42.50.Wk Since its original discovery in the context of atomic vapors, electromagnetically induced transparency (EIT) [1][2][3] has been at the center of many important developments in optical physics [4] and has led to many different applications, most notably in the context of slow light [5][6][7] and the production of giant nonlinear effects. EIT is helping the progress towards studying nonlinear optics at the single-photon level. EIT has been reported in many other systems [8]. More recently, EIT has been discovered in meta materials [9][10][11][12] where resonant structures can be fabricated to correspond to dark and bright modes. Resonators provide certain advantages [13] because by design we can manipulate EIT to produce desired transmission properties of a structure. It would thus be especially interesting to study resonators coupled to other systems such as cavity optomechanical systems. Such nanomechanical systems have attracted considerable interest recently [14][15][16][17][18][19][20][21]. In this letter, we demonstrate the possibility of EIT in the context of cavity optomechanics. Before discussing our model and results, we set the stage for EIT in cavity optomechanics. As in typical EIT experiments [1][2][3][4], for example, in the context of atomic vapors, we need to examine the pump-probe response of a nanomechanical oscillator of frequency ω m coupled to a high-quality cavity via radiation pressure effects [22,23] as schematically shown in Fig. 1. Thus, the cavity oscillator of frequency ω 0 and the nano-oscillator interact nonlinearly with each other. The system is driven by a strong pump field of frequency ω c . This is the coupling field. The probe field has frequency ω p and is much weaker than the pump field. The mechanical oscillator's damping is much smaller than that of the cavity oscillator. This is very important for considerations of EIT. The decay rate of the mechanical oscillator plays the same role as the decay rate of the ground-state coherence in EIT experiments. The analog of the two-photon resonance condition where EIT occurs would be ω c + ω m = ω p . We show how the absorptive and dispersive responses of the probe change by the coupling field and how EIT emerges. We present a clear physical origin of EIT in such a system.Let us denote the cavity annihilation (creation) operator by c (c † ) with the commutation relation [c, c † ] = 1.The momentum and position o...

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“…The cavity oscillator is damped at the rate κ, whereas the mirror is damped at the rate γ m ≪ κ. This situation typically results [9][10][11][12][13] in line shapes such as (7).…”

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Electromagnetically induced transparency in mechanical effects of light

2010

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“…Specifically, we consider a nanosphere consisting of four concentric layers that alternate between a high-index dielectric ( = 12, can be silicon or gallium arsenide) and a low-index dielectric ( = 1, can be a transparent aerogel 65 ). For a particle of size [r 1 , r 2 , r 3 , r 4 ] = [40, 90, 150, 160] nm, Figure 5 shows the exact scattering cross section divided into individual channels as in Eq 2. Scattering dark states can be seen in the TE 1 , TE 2 , and TE 3 channels.…”

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Theoretical Criteria for Scattering Dark States in Nanostructured Particles

et al. 2014

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Nanostructures with multiple resonances can exhibit a suppressed or even completely eliminated scattering of light, called a scattering dark state. We describe this phenomenon with a general treatment of light scattering from a multi-resonant nanostructure that is spherical or non-spherical but subwavelength in size. With multiple resonances in the same channel (i.e. same angular momentum and polarization), coherent interference always leads to scattering dark states in the low-absorption limit, regardless of the system details. The coupling between resonances is inevitable and can be interpreted as arising from far-field or near-field. This is a realization of coupled- and interference effects. 5-9 A particularly interesting phenomenon is the suppressed scattering in nanostructures with multiple plasmonic resonances, [10][11][12][13][14][15][16][17][18][19][20][21][22][23] plasmonic and excitonic resonances, [24][25][26][27][28][29][30] or dielectric resonances, 31,32 referred to collectively as a "scattering dark state." A wealth of models has been employed to describe this suppressed scattering, ranging from perturbative models, 12 generalization of the Fano formula, 13-15 and electrostatic approximation, 22,23 to coupled-mechanical-oscillator models. 17-21 These models reveal valuable insights and facilitate the design of specific structures with desired line shapes. However, the general criteria for observing such scattering dark states remain unclear. Non-scattering states have been known in atomic physics since the early works of Fano 33 and have been discovered in a variety of nanoscale systems in recent years [5][6][7][8]34,35 . However, Fano resonances generally concern the interference between a narrow discrete resonance and a broad resonance or continuum. Meanwhile, many occurrences of the scattering dark state involve the interference between multiple narrow discrete resonances, and it seems necessary to treat the multiple resonances at equal footing. Thus, we seek a formalism analogous to the phenomenon of coupled-resonator-induced transparency 5 that has been established in certain other systems such as coupled mechanical oscillators 36,37 , coupled cavities 38,39 , coupled microring resonators [40][41][42][43][44] , and planar metamaterials [45][46][47][48] .Here, we derive the general equations governing the resonant light scattering from a spherical or a non-spherical but subwavelength obstacle, accounting for multiple resonances with low loss. Due to the spherical symmetry (or the small size) of the obstacle, different channels of the multipole fields are decoupled. We find that within each channel, n resonances always lead to n − 1 scattering dark states in the low-absorption limit. This universal result is independent of the radiative decay rates of the resonances, method of coupling (can be 3 near-field or far-field), nature of the resonances (can be plasmon, exciton, whispering-gallery, etc.), number of resonances, which of the multipole, TE or TM polarization, and other system det...

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“…Coherent processes leading to EIT and ATS have been studied in: atomic gases 7,13 , atomic and molecular systems 14 , solid-state systems 15 , superconductors 16,17 , plasmonics 18 , metamaterials 19 , optomechanics 20,21 , electronics 22 , photonic crystals 23 and whispering-gallery-mode microresonators (WGMRs) [24][25][26][27][28][29][30][31][32][33] . Systems in which EIT and ATS have been studied are listed in Fig.…”

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What is and what is not electromagnetically induced transparency in whispering-gallery microcavities

et al. 2014

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There has been an increasing interest in all-optical analogues of electromagnetically induced transparency and Autler-Townes splitting. Despite the differences in their underlying physics, both electromagnetically induced transparency and Autler-Townes splitting are quantified by a transparency window in the absorption or transmission spectrum, which often leads to a confusion about its origin. While the transparency window in electromagnetically induced transparency is a result of Fano interference among different transition pathways, in Autler-Townes splitting it is the result of strong field-driven interactions leading to the splitting of energy levels. Being able to tell objectively whether an observed transparency window is because of electromagnetically induced transparency or Autler-Townes splitting is crucial for applications and for clarifying the physics involved. Here we demonstrate the pathways leading to electromagnetically induced transparency, Fano resonances and AutlerTownes splitting in coupled whispering-gallery-mode resonators. Moreover, we report the application of the Akaike Information Criterion discerning between all-optical analogues of electromagnetically induced transparency and Autler-Townes splitting and clarifying the transition between them.

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Coupled-resonator-induced transparency

Cited by 477 publications

References 20 publications

Electromagnetically induced transparency in mechanical effects of light

Electromagnetically induced transparency in mechanical effects of light

Theoretical Criteria for Scattering Dark States in Nanostructured Particles

What is and what is not electromagnetically induced transparency in whispering-gallery microcavities

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