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From: AES on 2 Dec 2009 12:49 In article <rf0iu6-ga4.ln1(a)ph-kinsle.qols.ph.ic.ac.uk>, p.kinsler(a)ic.ac.uk wrote: > Here's how the theory can be described (simplified, obviously): > > (a) solve Maxwell's equations for a suitable system, and get a set > of normalizable basis functions allowing you to describe any field > configuration. > > (b) these basis functions usually have both electric and magnetic > field contributions; they are usually called "mode functions", and > tend to oscillate in space and time (although not all will). > > (c) quantize the field inside each mode; this gives you a countable > series of possible mode excitations. > > (d) to describe some chosen field configuration, you combine a > suitable set of modes containing appropriate quantum excitations. > You may need to account for non-trivial correlations between the > modes, and between the quantum states in the same and different > modes. > > > There is no "particle of light". Instead there are countable > excitations of the wave-like field modes. These modes usually > combine both electric and magnetic contributions. > > It's not a particle, it's a wave. But you _can_ count the > excitations. Agreed. That's absolutely the classic (not classical!) approach to quantum analysis of e-m problems. But any thoughts on how to extend this approach (or connect it) to the whole class of "open systems" (all the systems like unstable resonators/gain-guided waveguides, etc) where the actual operating or oscillating or amplifying modes of the system (the "real modes", not just some set of basis functions) are non-orthogonal, non-Hermitian, non-self-adjoint, biorthogonal, so that you run into the Petermann excess noise factor and "adjoint coupling" concepts and so on. Obviously you can choose any more or less arbitrary set of Hermitian basis functions to use in analyzing these systems; but since these basis functions will _not_ be the actual "modes" that the system actually operates in, your superposition will in general, and more or less unavoidably, be a very inefficient way of describing the system. I believe (and I think Han Woerdman does) that the nonhermitian biorothogonal modes + Petermann excess noise factor approach predicts the correct quantum results for these systems (or at least some of the important quantum results?), and futhermore does so in an efficient and simple fashion. But, I've never really understood how this approach ties into, or can be connected to, the classic approach you describe.
From: BURT on 2 Dec 2009 15:16 On Dec 2, 3:43 am, p.kins...(a)ic.ac.uk wrote: > BURT <macromi...(a)yahoo.com> wrote: > > What wave is the particle of light in? the electric opr > > magnetic wave? > > Here's how the theory can be described (simplified, obviously): > > (a) solve Maxwell's equations for a suitable system, and get a set > of normalizable basis functions allowing you to describe any field > configuration. > > (b) these basis functions usually have both electric and magnetic > field contributions; they are usually called "mode functions", and > tend to oscillate in space and time (although not all will). > > (c) quantize the field inside each mode; this gives you a countable > series of possible mode excitations. > > (d) to describe some chosen field configuration, you combine a > suitable set of modes containing appropriate quantum excitations. > You may need to account for non-trivial correlations between the > modes, and between the quantum states in the same and different > modes. > > There is no "particle of light". Instead there are countable > excitations of the wave-like field modes. These modes usually > combine both electric and magnetic contributions. > > It's not a particle, it's a wave. But you _can_ count the > excitations. > > -- > ---------------------------------+--------------------------------- > Dr. Paul Kinsler > Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714 > Imperial College London, Dr.Paul.Kins...(a)physics.org > SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/ There are only a very few quantizations in light energy quantities of the atom. Certainly not enough for white light we see. This does not correspond to the reality of the full spectrum produced by the white light. A light bulb passed through a prism produces a full spectrum of energy levels but does not have enough quantized states in its atom to do so. Mitch Raemsch
From: George Herold on 2 Dec 2009 16:04 On Dec 2, 3:16 pm, BURT <macromi...(a)yahoo.com> wrote: > On Dec 2, 3:43 am, p.kins...(a)ic.ac.uk wrote: > > > > > > > BURT <macromi...(a)yahoo.com> wrote: > > > What wave is the particle of light in? the electric opr > > > magnetic wave? > > > Here's how the theory can be described (simplified, obviously): > > > (a) solve Maxwell's equations for a suitable system, and get a set > > of normalizable basis functions allowing you to describe any field > > configuration. > > > (b) these basis functions usually have both electric and magnetic > > field contributions; they are usually called "mode functions", and > > tend to oscillate in space and time (although not all will). > > > (c) quantize the field inside each mode; this gives you a countable > > series of possible mode excitations. > > > (d) to describe some chosen field configuration, you combine a > > suitable set of modes containing appropriate quantum excitations. > > You may need to account for non-trivial correlations between the > > modes, and between the quantum states in the same and different > > modes. > > > There is no "particle of light". Instead there are countable > > excitations of the wave-like field modes. These modes usually > > combine both electric and magnetic contributions. > > > It's not a particle, it's a wave. But you _can_ count the > > excitations. > > > -- > > ---------------------------------+--------------------------------- > > Dr. Paul Kinsler > > Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714 > > Imperial College London, Dr.Paul.Kins...(a)physics.org > > SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/ > > There are only a very few quantizations in light energy quantities of > the atom. Certainly not enough for white light we see. This does not > correspond to the reality of the full spectrum produced by the white > light. A light bulb passed through a prism produces a full spectrum of > energy levels but does not have enough quantized states in its atom to > do so. > > Mitch Raemsch- Hide quoted text - > > - Show quoted text - Mitch, The light bulb can be thought of as a black body radiator. It doesn't matter what kind of atoms the black body is made of. All that is important is the temperature. http://en.wikipedia.org/wiki/Blackbody_radiation George H.
From: p.kinsler on 2 Dec 2009 16:12 AES <siegman(a)stanford.edu> wrote: >> > There is no "particle of light". Instead there are countable > > excitations of the wave-like field modes. These modes usually > > combine both electric and magnetic contributions. > But any thoughts on how to extend this approach (or connect it) to the > whole class of "open systems" (all the systems like unstable > resonators/gain-guided waveguides, etc) where the actual operating or > oscillating or amplifying modes of the system (the "real modes", not > just some set of basis functions) are non-orthogonal, non-Hermitian, > non-self-adjoint, biorthogonal, so that you run into the Petermann > excess noise factor and "adjoint coupling" concepts and so on. Oh, maybe (I never had cause to use this for anything though) Brown S.A.; Dalton B.J. http://arxiv.org/abs/quant-ph/0107039 ... also in JMO 49, 1009 (2002) http://dx.doi.org/10.1080/09500340110095625 -- ---------------------------------+--------------------------------- Dr. Paul Kinsler Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714 Imperial College London, Dr.Paul.Kinsler(a)physics.org SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/
From: p.kinsler on 2 Dec 2009 16:03
George Herold <ggherold(a)gmail.com> wrote: > > It's not a particle, it's a wave. But you _can_ count the > > excitations. > Paul, I feel I'm in way over my head, but is there something wrong > with calling the excited quantized mode a photon? Calling a single (extra) excitation of a mode a "photon" is pretty much exactly what you should do. Just don't call it a particle as well. -- ---------------------------------+--------------------------------- Dr. Paul Kinsler Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714 Imperial College London, Dr.Paul.Kinsler(a)physics.org SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/ |