Theory of two-dimensional microcavity lasers

Harayama, Takahisa; Sunada, Satoshi; Ikeda, Kensuke S.

doi:10.1103/physreva.72.013803

Cited by 55 publications

(60 citation statements)

References 26 publications

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“…Besides, the lasing medium has played the most important role of nonlinearity that has offered a unique stage of the research on two-dimensional microcavity lasers different from quantum chaos in the sense that resonance modes interact with each other [20,[72][73][74][75][76][77][78][79][80].…”

Section: Laser and Photonics Reviewsmentioning

confidence: 99%

Two‐dimensional microcavity lasers

Harayama¹,

Shinohara

2011

Laser & Photonics Reviews

126

107

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Advances in processing technology, such as quantum-well structures and dry-etching techniques, have made it possible to create new types of two-dimensional (2D) microcavity lasers which have 2D emission patterns of output laser light although conventional one-dimensional (1D) edge-emitting-type lasers have 1D emission. Two-dimensional microcavity lasers have given nice experimental stages for fundamental researches on wave chaos closely related to quantum chaos. New types of 2D microcavity lasers also can offer the important lasing characteristics of directionality and high-power output light, and they may well find applications in optical communications, integrated optical circuits, and optical sensors. Fundamental physics of 2D microcavity lasers has been reviewed from the viewpoint of classical and quantum chaos, and recently developed theoretical approaches have been introduced. In addition, nonlinear dynamics due to the interaction among wave-chaotic modes through the active lasing medium is explained. Applications of 2D microcavity lasers for directional emission with strong light confinement are introduced, as well as high-precision rotation sensors designed by using wave-chaotic properties.A resonant mode of a stadium-shaped cavity showing wave chaos.

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Section: Laser and Photonics Reviewsmentioning

confidence: 99%

Two‐dimensional microcavity lasers

Harayama¹,

Shinohara

2011

Laser & Photonics Reviews

126

107

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“…In fact the intuitive picture of a lasing mode is that it arises when one of the resonances of the passive cavity is "pulled" up to the real axis by adding gain to the resonator. Often comparison of the numerically generated lasing modes with calculated linear resonances do show strong similarities in spatial structure, providing useful interpretation of lasing modes [5,6], although not a predictive theory. However with the current interest in complex laser cavities based on wave-chaotic shapes [7,8], photonic bandgap media [9,10] or random media [11,12] it is important to have a quantitative and predictive theory of the lasing states, as the numerical simulations required to solve the timedependent Maxwell-Bloch equations are time-consuming and not easy to interpret.…”

mentioning

confidence: 99%

Theory of the spatial structure of nonlinear lasing modes

Türeci

Stone

2007

Phys. Rev. A

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A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have non-trivial spatial structure even in the single-mode limit. In the multi-mode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic and random laser media.The steady-state electric field within and outside of a single or multi-mode laser arises as a solution of the non-linear coupled matter-field equations, the simplest of which are the two-level Maxwell-Bloch equations treated below. While the basic equations involved have been known for many years, and many aspects of their temporal dynamics have been studied [1], relatively little progress has been made in understanding the spatial structure of the non-linear electric field, particularly in the case of multi-mode solutions for which spatial holeburning and other non-linear effects are critical. It is natural to attempt to understand the non-linear solutions in terms of solutions of a linear wave equation. The two standard choices are either the hermitian solutions of a perfectly reflecting (closed) passive laser cavity [2], or the non-hermitian non-orthogonal resonances of the open passive cavity [3,4]). In fact the intuitive picture of a lasing mode is that it arises when one of the resonances of the passive cavity is "pulled" up to the real axis by adding gain to the resonator. Often comparison of the numerically generated lasing modes with calculated linear resonances do show strong similarities in spatial structure, providing useful interpretation of lasing modes [5,6], although not a predictive theory. However with the current interest in complex laser cavities based on wave-chaotic shapes [7,8], photonic bandgap media [9,10] or random media [11,12] it is important to have a quantitative and predictive theory of the lasing states, as the numerical simulations required to solve the timedependent Maxwell-Bloch equations are time-consuming and not easy to interpret.In recent work we have formulated a theory of steadystate multi-mode lasing which addresses these concerns [13]. The theory implies that the natural linear basis for decomposing lasing solutions is the dual set of biorthogonal states corresponding to constant outgoing and incoming Poynting vector at infinity at the lasing frequencies (referred to as "constant flux" (CF) states). Our theory shows that even in conventional lasers it is incorrect to regard the lasing modes as corresponding to a single resonance of the passive cavity and that multiple spatial frequencies occur even when there is a single lasing frequency close to the frequency of a single passive cavity resonance. These multiple spatial frequencies arise because several CF states contribu...

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“…This is possible within the Schrödinger-Bloch model (Harayama et al 2005), the state-of-the-art instrument to describe active microcavities (Kwon et al 2006). The results are shown in Fig.…”

Section: Towards Directional Emission From Spiral Microlasersmentioning

confidence: 93%

Optical Microcavities of Spiral Shape: From Quantum Chaos to Directed Laser Emission

Hentschel

Kwon

2009

NATO Science for Peace and Security Series B: Physics and Biophysics

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Abstract.Optical microcavities are open billiards for light in which electromagnetic waves can, however, be confined by total internal reflection at dielectric boundaries. These resonators enrich the class of model systems in the field of quantum chaos and are an ideal testing ground for the correspondence of ray and wave dynamics that, typically, is taken for granted. Using phase-space methods we show that this assumption has to be corrected towards the longwavelength limit. We also discuss the issue of achieving directional emission from optical microcavity lasers, highly desired concerning applications in photonic devices, with a focus on cavities of spiral shape.

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Theory of two-dimensional microcavity lasers

Abstract: We present theoretical models of two-dimensional ͑2D͒ microcavity lasers. The relation between stationary lasing modes and resonances or metastable states is elucidated for arbitrary shapes of 2D resonant microcavities.

Cited by 55 publications

References 26 publications

Two‐dimensional microcavity lasers

Two‐dimensional microcavity lasers

Theory of the spatial structure of nonlinear lasing modes

Optical Microcavities of Spiral Shape: From Quantum Chaos to Directed Laser Emission

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