Excess Quantum Noise due to Nonorthogonal Polarization Modes

Lee, A. M. van der; Druten, N. J. van; Mieremet, Arnout; Eijkelenborg, Martijn A. van; Lindberg, A.; Exter, M. P. van; Woerdman, J. P.

doi:10.1103/physrevlett.79.4357

Cited by 61 publications

(41 citation statements)

References 14 publications

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“…(9) and (10)] establishes that the enhancement generally consists of two terms, one that scales linearly and one that scales quadratically with the quality factor. In Secs.…”

Section: Discussionmentioning

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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“…(9) and (10)] establishes that the enhancement generally consists of two terms, one that scales linearly and one that scales quadratically with the quality factor. In Secs.…”

Section: Discussionmentioning

confidence: 99%

“…2.C, we present a condensed derivation of our key analytical result-a formula for the LDOS at an EP [Eqs. (9) and (10)]. …”

Section: Local Density Of States and Green's Function Expansionsmentioning

confidence: 99%

General theory of spontaneous emission near exceptional points

Pick¹,

Zhen²,

et al. 2017

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“…Apart from notation these results agree with earlier works. 3,6 We conclude that our model correctly accounts for non-orthogonal polarization modes.…”

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confidence: 53%

“…The restriction to the polarization case does not limit the validity of our conclusions: in earlier works it has been shown experimentally and theoretically that the polarization K factor shows all the features of a generic K factor. 3,6 The main message of our Letter is that there is no spontaneous emission enhancement in parametric down conversion.…”

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confidence: 83%

“…[2][3][4][5][6][7][8][9] This excess noise may occur when the laser cavity has nonorthogonal eigenmodes; it is then as if there are K noise photons in the laser mode. There is no doubt regarding the physical reality of excess quantum noise; it has been verified in many experiments on lasers with nonorthogonal longitudinal, 4 transverse 5 and polarization 3,6 modes. However, there is a continuing debate whether the noise enhancement arises from an amplification of spontaneously emitted photons by the gain medium 7 or from a cavity-enhanced single-atom decay rate.…”

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Does excess quantum noise exist in spontaneous processes?

Aiello

Exter

Nienhuis

et al. 2002

Optics Communications

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We investigate the role of excess quantum noise in type-II degenerate parametric down conversion in a cavity with non-orthogonal polarization eigenmodes. Since only two modes are involved we are able to derive an analytical expression for the twin-photon generation rate measured outside the cavity as a function of the degree of mode nonorthogonality. Contrary to recent claims we conclude that there is no evidence of excess quantum noise for a parametric amplifier working so far below threshold that spontaneous processes dominate.PACS numbers: 42.50.Lc, 42.60.Da, 42.65.YjThe ultimate noise limit of optical devices is set by the quantum noise. A textbook example is formed by the laser, where phase and intensity fluctuations have a quantum origin. These fluctuations can be seen as the consequence of having "one noise photon in the laser mode" [Ref. 1, p. 72]. For small lasers, in particular semiconductor lasers, this quantum noise limit is easily reached in practical cases. More recently, there has been a large body of work pointing at the fact that the quantum noise may be enhanced by the so called excess noise factor or Petermann K factor.2-9 This excess noise may occur when the laser cavity has nonorthogonal eigenmodes; it is then as if there are K noise photons in the laser mode. There is no doubt regarding the physical reality of excess quantum noise; it has been verified in many experiments on lasers with nonorthogonal longitudinal, 4 transverse 5 and polarization 3, 6 modes. However, there is a continuing debate whether the noise enhancement arises from an amplification of spontaneously emitted photons by the gain medium 7 or from a cavity-enhanced single-atom decay rate.10 If the latter interpretation applied, excess noise would also be a valid concept (far) below the oscillation threshold of the device under consideration. In this case excess noise could be very useful; for instance it has been claimed that it could lead to an enhanced generation of twin photons in Spontaneous Parametric Down Conversion (SPDC), by placing the nonlinear crystal in an unstable cavity (which has nonorthogonal transverse eigenmodes). 11The reason that there is room for uncertainty is that all theoretical approaches of this problem are (necessarily) model dependent. The most common experimental realization of mode nonorthogonality concerns the transverse modes of an unstable cavity. However, this case is intrinsically difficult to treat: one deals with an infinite manifold of transverse modes which cannot be truncated since there is no sharp distinction between system modes (= cavity modes) and reservoir modes (= free space modes).12 This has motivated us to study the effect of excess noise on cavity-enhanced SPDC, for a case where one can construct an exactly solvable quantum theory of mode nonorthogonality. In fact, we use a cavity with nonorthogonal polarization modes (instead of transverse modes). Our model comprises (and reduces to those as particular subcases) two theoretical models both of which have been experim...

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Theory of Excess Noise

Ujihara¹

2010

Output Coupling in Optical Cavities and Lasers

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Excess Quantum Noise due to Nonorthogonal Polarization Modes

Abstract: Excess quantum noise due to nonorthogonal polarization modes van der Lee, A.M.; van Druten, N.J.; Mieremet, A.L.; van Eijkelenborg, M.A.; Lindberg, Å.M.; van Exter, M.P.; Woerdman, J.P.

Cited by 61 publications

References 14 publications

General theory of spontaneous emission near exceptional points

General theory of spontaneous emission near exceptional points

Does excess quantum noise exist in spontaneous processes?

Theory of Excess Noise

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