Effects of boundary roughness on a Q factor of whispering-gallery-mode lasing microdisk cavities

Rahachou, Aliaksandr; Zozoulenko, Igor

doi:10.1063/1.1625781

Cited by 37 publications

(31 citation statements)

References 22 publications

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“…These internal losses in the material can be alternatively taken into account by the mode equation using a complex-valued refractive indexñ = n + iλα/4π. Also the surface roughness Q surf can be directly modeled by the mode equation provided that fluctuations in the boundary function ρ = ρ(ϕ) are taken explicitly into account; see, e.g., (Rahachou and Zozoulenko, 2003).…”

Section: B Optical Losses and Quality Factorsmentioning

confidence: 99%

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

2015

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Section: B Optical Losses and Quality Factorsmentioning

confidence: 99%

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

2015

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“…The Q-factor is so huge that our numerics is pushed to the limit; as a conservative lower bound we estimate Q ≈ 10 8 . In practise, this theoretical bound for the Q-factor is unreachable nowadays due to absorption [2] and surfaces roughness [27], i.e. the introduction of the hole does not affect the experimental Q-factor.…”

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Unidirectional light emission from high-Qmodes in optical microcavities

2006

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We introduce a new scheme to design optical microcavities supporting high-Q modes with unidirectional light emission. This is achieved by coupling a low-Q mode with unidirectional emission to a high-Q mode. The coupling is due to enhanced dynamical tunneling near an avoided resonance crossing. Numerical results for a microdisk with a suitably positioned air hole demonstrate the feasibility and the potential of this concept. PACS numbers: 42.55.Sa, 42.60.Da, 05.45.Mt Confinement and manipulation of light in microcavities is important for a wide range of research areas and applications, e.g., cavity quantum electrodynamics or novel light sources [1]. A key quantity characterizing a cavity mode is its quality factor Q = ω/∆ω, where ω is the mode frequency and ∆ω is the linewidth. A large Q-factor is a basic requirement for low threshold lasing, high sensor sensitivity, narrow wavelength-selective filtering, and strong light-matter interaction. Whispering-gallery modes (WGMs) in microdisks [2], microspheres [3], and microtori [4] have ultra-high Q-factors. For state-of-the-art semiconductor microdisks, the record Qfactor is > 3.5 × 10 5 [5,6]. The applicability of those cavities as microlasers and single-photon sources is, however, limited by isotropic light emission. The best directionality so far is provided by VCSEL-micropillars; see, e.g., Ref. [7]. The emission is unidirectional at the cost of a reduced Q-factor, typically well below 10 4 . With present technology, there is a trade-off between Q-factor and directionality.This dilemma remains when breaking the rotational symmetry of a microdisk. Shape deformation [8,9] allows improved directionality of emission due to refractive escape, but the Q-factors are significantly spoiled. Unidirectional emission has been reported for rounded triangles [10] with Q ≈ 35 and for spiral-shaped disks [11]. In the latter case, a strong degradation of the cavity Q allows lasing operation only for spirals of the size of conventional edge emitting lasers.Another approach is to break the symmetry by modifying the evanescent leakage (the optical analogue of tunneling) from WGMs, thereby keeping the high Q-factor. Ref.[12] reported unidirectional lasing from a vertical double-disk structure. Unfortunately, the study was restricted to the nearfield pattern. Another suggestion has been to introduce a linear defect into the evanescent inner region of WGMs [13]. Nearly spherical, high-Q fused-silica cavities showed emission into four directions explained by dynamical tunneling from a WGM to the exterior of the cavity [14]. Dynamical tunneling is a generalization of conventional tunneling which allows to pass not only through an energy barrier but also through other kinds of dynamical barriers in phase space [15].In this Letter, we overcome the trade-off between Q-factor and directionality by combining dynamical tunneling and refractive escape. We couple a uniform high-Q mode (HQM) and a directional low-Q mode (LQM) using enhanced dynamical tunneling near avoided resonance crossings ...

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“…We introduce the scattering matrix S in a standard fashion 11,12 , B = SA, where A, B are column vectors composed of the expansion coefficients A q , B q for incoming and outgoing states in Eq. (2).…”

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Elastic scattering of surface electron waves in quantum corrals: Importance of the shape of the adatom potential

Rahachou

Zozoulenko

2004

Phys. Rev. B

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We report elastic scattering theory for surface electron waves in quantum corrals defined by adatoms on the surface of noble metals. We develop a scattering-matrix technique that allows us to account for a realistic smooth potential profile of the scattering centers. Our calculations reproduce quantitatively all the experimental observations, which is in contrast to previous theories (treating the adatoms as point scatterers) that require additional inelastic channels of scattering into the bulk in order to achieve the agreement with the experiment. Our findings thus indicate that surface states are not coupled to the bulk electrons.PACS numbers: 72.10. Fk, 73.20.At, 68.73.Ef, 03.65.Nk Advances in modern nanotechnology made it possible to manipulate adatoms on the surface of a metal, arranging them into ordered structures coined as "quantum corrals". Using the scanning tunneling microscopy (STM), Crommie et al.1,2,3 studied the scattering of the surface electron waves residing at (111) faces of Cu. These surface states interact strongly with Fe adatoms, and the spatial variation of the STM differential conductance revealed beautiful images of the standing wave patterns in the quantum corrals. In addition, the experiment showed a series of pronounced peaks in the energy spectrum of the differential conductance dI/dV at the center of the corrals.In order to describe the experimental observation 1,2 , Heller et al.4 have developed the multiple-scattering theory for surface electron waves in quantum corrals. In their theory each adatom was modelled as a point-like δ-function potential supporting isotropic s-wave scattering. The quantitative agreement with the experiment was achieved by assuming an additional (inelastic) channel of scattering (presumably into the bulk metallic states). The authors concluded that absorption is the dominant mechanism for the broadening of the energy levels seen in the experiment, and estimated that ∼ 25% of the incident amplitude is reflected, ∼ 25% is transmitted, and ∼ 50% is absorbed. The importance of the electron scattering to the bulk states for the level width broadening in the quantum corrals was also asserted by Crampin et al.5 and Cramplin and Bryant 6 .An alternative purely elastic scattering theory for the same quantum corral structures was reported by Harbury and Porod 7 . They modelled the adatoms by finite-height potential barriers, as opposed to "black dot" δ-point absorbing scattering potential adopted in the above cited works 4,5,6 . The elastic theory accounts well for the spatial variation of the wave function in the quantum corrals, but overestimates the broadening of the resonant levels, especially for higher energies. The findings of Harbury and Porod therefore suggest that the features of the spectrum can be sensitive to the detailed shape of the scattering potential.It is important to stress that accounting for a detailed shape of a scattering potential was crucial for quantitative description of many phenomena in quantum nanostructures. This for example inc...

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Effects of boundary roughness on a Q factor of whispering-gallery-mode lasing microdisk cavities

Cited by 37 publications

References 22 publications

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Unidirectional light emission from high-Qmodes in optical microcavities

Elastic scattering of surface electron waves in quantum corrals: Importance of the shape of the adatom potential

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