Giant Excess Noise and Transient Gain in Misaligned Laser Cavities

Firth, W. J.; Yao, Alison M.

doi:10.1103/physrevlett.95.073903

Cited by 21 publications

(14 citation statements)

References 19 publications

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“…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].…”

Section: Introductionmentioning

confidence: 99%

“…Then, in Sec. 4, we derive bounds on the maximal enhancement at an EP, and we explore these bounds using a periodic system, which allows us to tune gain, loss, and degeneracy independently. Our theory provides a quantitative prescription for achieving large enhancements in practical optical systems, which is applicable to arbitrary geometries and materials and can be implemented with the recent experimental realizations of EPs [16-18, 20-22, 37, 38].…”

Section: Introductionmentioning

confidence: 99%

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General theory of spontaneous emission near exceptional points

Pick¹,

Zhen²,

et al. 2017

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Abstract:We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes. References and links1. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681--681 (1946). (CRC Press, 1995, vol. X). 3. S. V. Gaponenko, Introduction to Nanophotonics (Cambridge University, 2010 H. Yokoyama and K. Ujihara, Spontaneous Emission and Laser Oscillation in Microcavities

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General theory of spontaneous emission near exceptional points

Pick¹,

Zhen²,

et al. 2017

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“…Therefore, the total energy cannot be written as the sum of the energies of the individual modes since one must include the mode-mode correlation terms too. Usually, the "modes" referred to in the explanation of this phenomenon have been interpreted as modes of the optical cavity, either open [4] or unstable [5] or with misaligned elements [6]. However, the "modes" in question are far more general: they are the modes of the dynamics of the system [7].…”

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confidence: 99%

State Dependent Pseudoresonances and Excess Noise

2008

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We show that strong response to non-resonant modulations and excess noise are state dependent in generic nonlinear systems, i.e. they affect some output states, but are absent from others. This is demonstrated in complex Swift-Hohenberg models relevant to optics, where it is caused by the non-normality of the linearized stability operators around selected output states, even though the cavity modes are orthogonal. In particular, we find the effective parameters that control excess noise and the response to modulations and show cases where these phenomena are enhanced by an order of magnitude.PACS numbers: 42.65. Sf,42.60.Mi,42.55.Ah Excess noise [1] is a term used in optical device physics to highlight the fact that the sum of the energy in the individual modes is greater than the total energy available. This phenomenon was first predicted by Petermann in [2] and its paradoxical result was explained in [3]: the modes of excess noise systems are correlated (non-orthogonal). Therefore, the total energy cannot be written as the sum of the energies of the individual modes since one must include the mode-mode correlation terms too. Usually, the "modes" referred to in the explanation of this phenomenon have been interpreted as modes of the optical cavity, either open [4] or unstable [5] or with misaligned elements [6]. However, the "modes" in question are far more general: they are the modes of the dynamics of the system [7]. In this respect excess noise is just one aspect of the enhanced response to modulation and transient growth typical of non-normal operators, i.e. operators that do not commute with their adjoint [8,9]. The main feature of non-normal operators is that their eigenvectors are not orthogonal. This can have dramatic consequences in terms of the dynamics of the system: perturbations of stable states can be substantially amplified before they eventually decay (transient growth) [8]; the response to an external modulation can be very large even far from resonance (pseudo-resonance) [10]. An essential point often overlooked is that when the system under investigation is nonlinear, then the operator responsible for these effects is the linear stability operator and this is state, not just model, dependent. This is particularly important when studying systems that are both timeand space-dependent and have a rich bifurcation structure. Enhanced response to external modulations critically affects, for example, the implementation of chaos synchronization in secure laser communications [11].In this letter we analyze three aspects of generic nonlinear systems. First of all primary bifurcation of a given state may be normal, while its secondary bifurcations, in general, are not. Secondly, the effects of non-normality on the nonlinear dynamics and response can vary from state to state and need to be quantified. Thirdly, the system response depends on the spatial and temporal frequency of the modulation. This opens the possibility of fine tuning the output of the system by carefully choosing the modulation wave ...

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“…Therefore, large surface fields in nanoparticles and large transient gain and excess noise in macroscopic unstable cavities and dissipative systems [10][11][12][13]h a v et h e same geometrical origin.…”

Section: Theorymentioning

confidence: 99%

The geometrical nature of optical resonances: from a sphere to fused dimer nanoparticles

Hourahine¹,

Papoff²

2012

Meas. Sci. Technol.

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This version is available at https://strathprints.strath.ac.uk/42181/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the AbstractWe study the electromagnetic response of smooth gold nanoparticles with shapes varying from a single sphere to two ellipsoids joined smoothly at their vertices. We show that the plasmonic resonance visible in the extinction and absorption cross sections shifts to longer wavelengths and eventually disappears as the mid-plane waist of the composite particle becomes narrower. This process corresponds to an increase of the numbers of internal and scattering modes that are mainly confined to the surface and coupled to the incident field. These modes strongly affect the near field, and therefore are of great importance in surface spectroscopy, but are almost undetectable in the far field.

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Giant Excess Noise and Transient Gain in Misaligned Laser Cavities

Cited by 21 publications

References 19 publications

General theory of spontaneous emission near exceptional points

General theory of spontaneous emission near exceptional points

State Dependent Pseudoresonances and Excess Noise

The geometrical nature of optical resonances: from a sphere to fused dimer nanoparticles

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