Influence of transverse resonator symmetry on excess noise

Eijkelenborg, Martijn A. van; Lindberg, A.; Thijssen, Michiel; Woerdman, J. P.

doi:10.1016/s0030-4018(97)00005-9

Cited by 20 publications

(7 citation statements)

References 14 publications

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“…This is seen in both the theoretical and experimental curves. Again, this agrees with theory: it can be shown in a simple geometrical model that for half-integer values of N eq the K factor increases linearly with N eq [22]. The experimental peak in Fig.…”

Section: Resonance Of Quantum Noise In An Unstable Cavity Lasersupporting

confidence: 87%

Resonance of Quantum Noise in an Unstable Cavity Laser

et al. 1996

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We have measured the quantum-limited lpinewidth of a hard-edged unstable cavity gas laser. Our results confirm the predicted resonant behavior of the quantum-noise strength as a function of equivalent Fresnel number. This behavior is due to the nonorthogonality of the transverse eigenmodes. [S0031-9007(96) PACS numbers: 42.50.Lc Unavoidable quantum noise sets a limit to the coherence of a laser. The phase of the laser field diffuses under the influence of spontaneous emission, leading to the so-called Schawlow-Townes laser linewidth. This has been the subject of many theoretical and experimental investigations and is well understood for lasers with stable cavities and small losses per cavity transit [1,2]. The eigenmodes of such a laser form a set of orthogonal modes. For stable cavity lasers which have large mirror transmission and for lasers which operate on an unstable cavity the eigenmodes are nonorthogonal; as a consequence the Schawlow-Townes linewidth is enhanced by the so-called K factor or excess-noise factor [3][4][5][6][7][8][9][10][11][12]. Strong enhancement of the quantum-limited linewidth of unstable cavity lasers has been predicted and observed for a solid-state laser with a variable reflectivity mirror (VRM) [10,11] and most recently also in a hard-edged-mirror solid-state laser [12]. It has been predicted [4-6], but not yet verified, that this enhancement shows resonant behavior as a function of the equivalent Fresnel number. This resonance will occur only in hard-edged resonators, since it is essential that the shape of the transverse mode profile is determined by the precise cavity dimensions. In our experiments on a hard-edged unstable cavity gas laser we have been able to confirm this most intriguing aspect of unstable-resonator quantum-noise theory: the resonance of the quantum noise with equivalent Fresnel number.In a hard-edged unstable resonator a fraction of the reproducing mode spills, each round-trip, over a small feedback mirror. We call this mode the matched mode. It is biorthogonal to the so-called adjoint mode, which is a direction-reversed version of the matched mode [5,10,13]. It has been shown that the K factor is identical to the injected wave excitation factor, which is the factor by which the power of the mode, when excited by the adjoint mode, exceeds that when using matched-mode excitation [3,5]. This factor, and thus the K factor, depends strongly on the precise shape of the transverse mode profile. We emphasize that there exists no fundamental relation between large losses (or gain) and excess noise factors; two different transverse mode profiles that have identical diffraction losses may have K factors that differ by orders of magnitude if their nonorthogonality differs appreciably.Note that the quantum-noise properties of a hard-edged unstable-resonator laser are described by two parameters only: the round-trip linear magnification M and the equivalent Fresnel number N eq ͑M 2 2 1͒a 2 ͞2MlB where l is the wavelength, a is the radius of the small feedback mirror, and B...

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Section: Resonance Of Quantum Noise In An Unstable Cavity Lasersupporting

confidence: 87%

Resonance of Quantum Noise in an Unstable Cavity Laser

et al. 1996

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“…Further applications may, for example, be possible in the area of understanding excess quantum noise, 34,35 where the transverse symmetry of a resonator is known to have a significant effect. [14][15][16]…”

Section: Discussionmentioning

confidence: 99%

“…The explicit mathematical form of our results may also lend physical insight into other diffraction-related phenomena in physics; for example, the origins of excess quantum noise in lasers, where the transverse symmetry of the aperturing element has been shown to play a central role in the observed phenomena. [14][15][16][17] In Fraunhofer theory, the far-field approximation allows diffraction patterns and derivative concepts (for example, holography, filtering, convolution, and coherence) to be expressed in terms of simple Fourier integrals and transform theorems, respectively. Our main results describe the physical and mathematical character of near-field diffraction patterns in terms of their elemental spatial structures (edge waves).…”

Section: Introductionmentioning

confidence: 99%

Fresnel diffraction and fractal patterns from polygonal apertures

2006

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Two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures under uniform illumination are detailed. In particular, a simple expression for the diffracted field from constituent edges is derived. These results have fundamental importance as well as specific applications, and they promise new physical insights into diffraction-related phenomena. The usefulness of the formulations is illuminated in the context of a virtual source theory that accounts for two transverse dimensions. This application permits calculation of fractal unstable-resonator modes of arbitrary order and unprecedented accuracy.

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“…Several research groups have experimentally confirmed this excess noise factor in various laser systems [5][6][7][8][9][10][11]. Further theoretical progresses have also been made [12 -21].…”

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confidence: 90%

Spontaneous Emission of an Atom in a Cavity with Nonorthogonal Eigenmodes

Cheng

2006

Phys. Rev. Lett.

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The spontaneous emission of an excited atom in a lossy cavity with nonorthogonal eigenmodes is analyzed. The quantum Langevin formalism is used to describe the dynamics of the spontaneous decay. The analysis shows that the spontaneous decay is modified by the Q value and the effective mode volume factor of each cavity eigenmode. The effective mode volume is generalized for cavities with nonorthogonal modes, which can be a very significant modification in the microcavity regime. It is shown that the spontaneous decay is not enhanced by the excess noise factor as claimed by other analyses.

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Influence of transverse resonator symmetry on excess noise

Cited by 20 publications

References 14 publications

Resonance of Quantum Noise in an Unstable Cavity Laser

Resonance of Quantum Noise in an Unstable Cavity Laser

Fresnel diffraction and fractal patterns from polygonal apertures

Spontaneous Emission of an Atom in a Cavity with Nonorthogonal Eigenmodes

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