Annular Bragg resonators (ABR): the ideal tool for biochemical sensing, nonlinear optics, and cavity QED

Scheuer, Jacob; Green, William M. J.; Yariv, Amnon

doi:10.1117/12.640285

Cited by 4 publications

(2 citation statements)

References 20 publications

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“…In particular, the variations δω δn and δω δσ are formally computed. In [SGY06], transfer matrix methods were used to design low-loss 2D resonators with radial symmetry. In each of these papers, gradient-based optimization methods were used to solve the optimization problem.…”

Section: Related Workmentioning

confidence: 99%

Long-Lived Scattering Resonances and Bragg Structures

Osting¹,

Weinstein²

2013

SIAM J. Appl. Math.

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We consider a system governed by the wave equation with index of refraction n(x), taken to be variable within a bounded region Ω ⊂ R d , and constant in R d \ Ω. The solution of the time-dependent wave equation with initial data, which is localized in Ω, spreads and decays with advancing time. This rate of decay can be measured (for d = 1, 3, and more generally, d odd) in terms of the eigenvalues of the scattering resonance problem, a non-selfadjoint eigenvalue problem governing the time-harmonic solutions of the wave (Helmholtz) equation which are outgoing at ∞. Specifically, the rate of energy escape from Ω is governed by the complex scattering eigenfrequency, which is closest to the real axis. We study the structural design problem: Find a refractive index profile n (x) within an admissible class which has a scattering frequency with minimal imaginary part. The admissible class is defined in terms of the compact support of n(x) − 1 and pointwise upper and lower (material) bounds on n(x) for x ∈ Ω, i.e., 0 < n − ≤ n(x) ≤ n + < ∞. We formulate this problem as a constrained optimization problem and prove that an optimal structure, n (x) exists. Furthermore, n (x) is piecewise constant and achieves the material bounds, i.e., n (x) ∈ {n − , n + }. In one dimension, we establish a connection between n (x) and the well-known class of Bragg structures, where n(x) is constant on intervals whose length is one-quarter of the effective wavelength.

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Section: Related Workmentioning

confidence: 99%

Long-Lived Scattering Resonances and Bragg Structures

Osting¹,

Weinstein²

2013

SIAM J. Appl. Math.

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“…Circularly symmetric structures are generally preferred because they eliminate the need for alignment to the dipole orientation of the emitter. Circular gratings have previously been considered for cavity-defect mode enhancement [36], high-Q resonators [37], and emission out-coupling of quantum dots [38,39]. Experiments with circular gratings on a diamond membrane have shown measured single NV photon count rates of ∼ 3 Mcps [40].…”

Section: Introductionmentioning

confidence: 99%

Chirped circular dielectric gratings for near-unity collection efficiency from quantum emitters in bulk diamond

Zheng¹,

Liapis²,

Chen³

et al. 2017

Opt. Express

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Efficient collection of fluorescence from nitrogen vacancy (NV) centers in diamond underlies the spin-dependent optical read-out that is necessary for quantum information processing and enhanced sensing applications. The optical collection efficiency from NVs within diamond substrates is limited primarily due to the high refractive index of diamond and the non-directional dipole emission. Here we introduce a light collection strategy based on chirped, circular dielectric gratings that can be fabricated on a bulk diamond substrate to modify an emitter's far-field radiation pattern. Using a genetic optimization algorithm, these grating designs achieve 98.9% collection efficiency for the NV zero-phonon emission line, collected from the back surface of the diamond with an objective of aperture 0.9. Across the broadband emission spectrum of the NV (600-800 nm), the chirped grating achieves 82.2% collection efficiency into a numerical aperture of 1.42, corresponding to an oil immersion objective again on the back side of the diamond. Our proposed bulk-dielectric grating structures are applicable to other optically active solid state quantum emitters in high index host materials.

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Optofluidic Ring Resonators

Suter¹,

Fan²

2010

Handbook of Optofluidics

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Annular Bragg resonators (ABR): the ideal tool for biochemical sensing, nonlinear optics, and cavity QED

Cited by 4 publications

References 20 publications

Long-Lived Scattering Resonances and Bragg Structures

Long-Lived Scattering Resonances and Bragg Structures

Chirped circular dielectric gratings for near-unity collection efficiency from quantum emitters in bulk diamond

Optofluidic Ring Resonators

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