Nonlinear interaction of laser modes

Haken, Hermann; Sauermann, H.

doi:10.1007/bf01377828

Cited by 150 publications

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“…As in conventional laser theory [28,29], where one usually has a high-Q cavity, we require γ c ≪ ω. Since in the steady state we do not want to have too many atoms in the non-condensate part, we require γ c Γ, as suggested by Eq.…”

Section: Initial Conditions and Parametersmentioning

confidence: 99%

Generic model of an atom laser

et al. 1998

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We present a generic model of an atom laser by including a pump and loss term in the GrossPitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a non-vanishing value in steady-state. We study the transient regime of this atom laser and find oscillations around the stationary solution even in the presence of a loss term. These oscillations are damped away when we introduce a position dependent loss term. For this case we present a modified Thomas-Fermi solution that takes into account the pump and loss. Our generic model of an atom laser is analogous to the semi-classical theory of the laser. PACS number(s): 03.75 Fi, 05.30.Jp, 42.55.Ah

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Section: Initial Conditions and Parametersmentioning

confidence: 99%

Generic model of an atom laser

et al. 1998

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“…The nonlinear lasing behavior of these systems can, in principle, be modeled using the semi-classical Maxwell-Bloch (MB) equations [13][14][15][16]. Due to their time-dependent nature these equations are, however, usually difficult to solve for all but the most simple cases.…”

Section: Introductionmentioning

confidence: 99%

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

et al. 2015

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We investigate the range of validity of the recently developed steady-state ab-initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring fully or nearly degenerate pairs of resonator modes above the lasing threshold. Here we demonstrate how SALT can indeed be extended to describe such cases as well, with the effect that we significantly broaden the theory's scope. In particular, we show how to use SALT in conjunction with a linear stability analysis to obtain stable single-mode lasing solutions that involve a degenerate mode pair. Our flexible and efficient approach is tested on one-dimensional ring lasers as well as on two-dimensional microdisk lasers with broken symmetry.

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“…Note that biorthogonal modes have been used extensively in resonator theory [14] (notably for the case of unstable resonators) but have not previously been applied to multimode lasing theory. For multimode lasing the main difficulty is treating modal interactions and the related effects of spatial hole-burning [15]. We sketch below an efficient method for treating these effects exactly which can in principle be used in designing laser cavities to predict power output and tailor the mode spectrum of the laser.…”

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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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Nonlinear interaction of laser modes

Cited by 150 publications

References 0 publications

Generic model of an atom laser

Generic model of an atom laser

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

Theory of the spatial structure of nonlinear lasing modes

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