Resonance of Quantum Noise in an Unstable Cavity Laser

Abstract

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...

Resonant excess quantum noise in focused-gain lasers

“…This is very similar to the case of the hard-edged unstable resonator, in which each resonance in K is also accompanied by a near degeneracy of eigenvalues. 5 The example illustrated in Fig. 1 is readily achievable experimentally; in fact, the situation is quite close to that of some of our own experimental work.…”

“…The interest in the excess-noise factor K has surged in recent years, sparked by the demonstration 4,5 that large K values ͑$100͒ can be reached experimentally in hard-edged unstable resonators, in which the transverse modes are nonorthogonal. Although excess quantum noise has also been demonstrated for nonorthogonal longitudinal and polarization modes, and for stable-cavity lasers with a small aperture (see Ref.…”

“…This system has so far been of special interest not only because of the size of the K factors but also because of the intriguing resonances that occur in K for relatively small changes in the resonator parameters. 5 In contrast, for unstable resonator lasers with a Gaussian variable-ref lectivity mirror (acting as a soft aperture), the eigenmodes can be readily calculated, and no such resonances are found. 2 Hard-edged unstable resonators have complicated transverse-mode prof iles whose calculation requires significant numerical effort; the prof iles can even exhibit fractal behavior.…”

General theory of spontaneous emission near exceptional points

“…While it is well known that resonances can enhance spontaneous emission rates via the celebrated Purcell effect [1][2][3] by confining light to small volumes for long times, recent work [4][5][6] suggests that giant enhancements can occur via the less familiar Petermann effect [7][8][9][10][11]. The Petermann enhancement factor is a measure of non-orthogonality of the modes in non-Hermitian systems and it appears to diverge when two modes coalesce at an exceptional point (EP)-an exotic degeneracy in which two modes share the same frequency and mode profile [12,13].…”

Quantum theory of multimode fields: applications to optical resonators

“…The field quantization in the presence of mode overlap has generated a substantial literature in recent years [6,7,8]. The motivation for our work came from recent studies of unstable optical cavities [9,10,11] and from experiments on strongly disordered amplifying media [12,13,14,15], so-called random lasers. The losses in such lasers are typically much larger than in traditional lasers as the light is not confined by mirrors Open optical cavities studied in this paper: (a) A one-dimensional dielectric slab of length l with (positive) refractive index n bounded on one side (x = −l) by a perfectly reflecting mirror.…”