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Author Topic: Direction of Radiation Emitted from Atoms  (Read 22460 times)

Offline Mr Andrew

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« on: 10/12/2007 16:38:32 »
Light is a directional wave...it is a linear wave which propagates in a specific direction.  What in the atom determines which direction it emits radiation in?  Is it dipole moment or something to do with the nucleus?  I can't seem to find anything on the internet.  Anyone have an idea?


 

Offline Soul Surfer

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« Reply #1 on: 11/12/2007 09:05:48 »
In general for atoms in a gas there is no particular direction in which light is emitted but for example in a gas laser when there is already radiation of the same wavelength going in a particular direction atoms that are on the verge of emitting radiation will do it in the same (or possibly the opposite) direction ie along a single line.  That is how lasers work.  In solids the situation may be more complex and molecular structure can affect the propagation of light but this is usually seen in absorption because solids don't emit light unless there is an unusually high level of excitation as in solid state lasers  which are very structured and have mirrored reflectors like gas lasers
 

lyner

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« Reply #2 on: 11/12/2007 17:51:11 »
Quote
Light is a directional wave...it is a linear wave which propagates in a specific direction.
Not strictly true. It is, essentially, a spherical wave. It travels in the same speed in all directions. All 'rays' cover a range of angles, however small. The wavefront is spherical because each part of it has traveled the same distance after a given time.
As Soul  Surfer says, atoms don't have a directional light pattern. You can use many sources, radiating in phase, as do the atoms in a laser, or a number of radiating dipoles with the same radio frequency signal to produce a directional beam. Alternatively you can use a pinhole, lens or tube to select or direct the energy to go in a particular  direction. The wavefront is still spherical but its energy is restricted to a narrow range of directions.
 

Offline JP

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« Reply #3 on: 11/12/2007 20:42:34 »
Quote
Light is a directional wave...it is a linear wave which propagates in a specific direction.
Not strictly true. It is, essentially, a spherical wave. It travels in the same speed in all directions. All 'rays' cover a range of angles, however small. The wavefront is spherical because each part of it has traveled the same distance after a given time.

Both are true.  A light field can be written in terms of summing a bunch of plane waves (directional waves) or it can be written as the sum of a bunch of spherical waves emanating from each source point.
 

Offline Mr Andrew

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« Reply #4 on: 11/12/2007 22:09:19 »
Here's my problem with the spherical wave model:  when a wave (which has a photon of energy) is detected it loses energy.  Since it can only have integer multiples of hf in energy, it loses all of its energy.  Therefore, if I put a detector one meter from a light source, none of that light would ever reach me if I stand on the other side of the light source but 1.1 m away.  However, two people can see the same light bulb from different distances...how does that work?

-I know you can model light like a spherical waves but are they really like that or are they directional and it is only when there are many of them that you can treat light like a spherical wave?
 

Offline JP

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« Reply #5 on: 11/12/2007 23:03:34 »
Classically light is a wave.  If you put a detector in the way, it will catch all the energy from the wave that would pass through the space it occupies.  Two people can see the light bulb from different distances because they are both absorbing different parts of the wave.  If I stood right behind someone else, they would absorb all the light coming to me, and I wouldn't see the light bulb.

If you go to quantum mechanics, the light comes in packets which move about according to probability waves.  for each photon that gets emitted, each detector has a probability of seeing it that's proportional to the amount of probability wave it intercepts.  If we both look at source that emits a single photon, only one of us will see it.  However, as lots of photons are emitted, we'll each see some in proportion to the probability we expect to see. 
 

lyner

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« Reply #6 on: 11/12/2007 23:36:49 »
Quote
Light is a directional wave...it is a linear wave which propagates in a specific direction.
Not strictly true. It is, essentially, a spherical wave. It travels in the same speed in all directions. All 'rays' cover a range of angles, however small. The wavefront is spherical because each part of it has traveled the same distance after a given time.

Both are true.  A light field can be written in terms of summing a bunch of plane waves (directional waves) or it can be written as the sum of a bunch of spherical waves emanating from each source point.
I don't know where the plane wave analysis is used - I only know of Huygens (secondary wavelet) construction, which is, effectively, standard diffraction treatment. In standard diffraction methods, the intergrals used assume that a wavefront consists of a line of sources and these are summed at a subsequent point or surface. Where does the plane wave analysis take its origin for the plane waves? It would have to be from infinitely wide sources and it would be difficult to describe what happens at an aperture / object. It would be interesting to see how it's done.
When you are far enough away to treat the source  as a point then parts of the wave which are in  phase (i.e. wavefronts) must be equal distances from the source - that makes the wavefront spherical. However you choose to analyse it (Huygens or other), the spherical nature of the resulting wavefront must exist unless you say the speed is different in different directions.
'Rays' as such, don't  / can't really exist - they are just constructional tools - like magnetic lines of force.
 

Offline Soul Surfer

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« Reply #7 on: 11/12/2007 23:52:12 »
All electromagnetic radiation behaves in the same way.  if you want to see the statistical and classical wave behaviour it id best to look at radio and reasonable intensities of light where the many photons emitted randomly in all directions from the source produce spherical wavefronts with limited coherency.  to appreciate what is really going on in the quantum world look at much higher energy gamma ray emission from an excited nucleus.  Here to the radiation can be emitted in any direction but in doing so the nucleus also reacts because of the momentum of the emitted energy.
 

Offline JP

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« Reply #8 on: 12/12/2007 01:38:56 »
@ sophiecentaur:  The thesis work I'm doing right now uses a lot of plane wave analysis of fields.  The way it works is that you look at any field satisfying the Helmholtz equation.  If you solve the equation in Cartesian coordinates, you get plane-waves as a basic solution.  If you don't care about evanescent components of the field (i.e. the exponentially decaying components that decay by a few wavelengths from the source), you can write any field as a sum of weighted plane waves traveling in all different directions.  If you're mathematically inclined, the plane waves form a "complete basis" for describing fields.  The mathematics is also analogous to working in "spatial frequency" (i.e. the Fourier spatial transform of the field).

You're right that an aperture/object gets somewhat difficult.  You end up having to take a Fourier transform of the object in order to see how it influences the plane waves.  However, for propagation in free space, it's often quite a bit easier to deal with plane waves instead of diffraction integrals.  And it provides a nice framework for defining "rays." 
 

Offline lightarrow

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« Reply #9 on: 12/12/2007 13:15:54 »
Quote
Light is a directional wave...it is a linear wave which propagates in a specific direction.
Not strictly true. It is, essentially, a spherical wave. It travels in the same speed in all directions. All 'rays' cover a range of angles, however small. The wavefront is spherical because each part of it has traveled the same distance after a given time.

Both are true.  A light field can be written in terms of summing a bunch of plane waves (directional waves) or it can be written as the sum of a bunch of spherical waves emanating from each source point.
Ok, however, quantum mechanically, light is made of photons and if there are only a few photons (per unit time ecc.) in the region of space considered, you can't use that description anylonger and the directionality of light is lost (in the absence of specific apparatus/equipments).
 

lyner

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« Reply #10 on: 12/12/2007 20:14:37 »
1. Lightarrow: don't you just need to replace 'intensity' with 'probability' when you are dealing with small numbers? The same pattern will apply at a distance.

2. jpetruccelli: what is the application for your work? It sounds interesting.
 

Offline JP

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« Reply #11 on: 12/12/2007 21:04:59 »
2. jpetruccelli: what is the application for your work? It sounds interesting.

My particular area of research involves a creature called a "Wigner function:" http://en.wikipedia.org/wiki/Wigner_function.  It basically allows you to take any optical field that satisfies the Helmholtz equation, and map it onto a set of rays by specifying the weight assigned to each ray.  It has some funny properties (such as some rays having negative weight), but these properties are required in order to describe interference and diffraction. 

The purpose of this is to take an optical field, do one (relatively simple) computation to assign weight to a bunch of rays, and then use ray-tracing (which is much more efficient than diffraction integrals) to propagate the field through whatever optical system we want.  It's also a nice way of deriving an exact ray-optical picture of field propagation by starting from Maxwell's equations.
 

Offline Mr Andrew

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« Reply #12 on: 13/12/2007 02:13:49 »
Ok, so light is a spherical probability wave (it has no direction but outwards)...it is spread out over a spherical surface and any detector on that surface has a probability of detecting that photon inversely proportional to the size of the surface.  That is all well and good and easy to picture but what is it about light that makes it behave that way?  What mechanism decides where the light should be absorbed?  Probabilities only come into play when we don't know enough about the initial conditions to predict what outcome will prevail.  If I have two cups on a table and I put a coin under one while you are not looking, there is a 50% chance that the coin will be under the cup you choose.  However, if you peak over your shoulder you know with absolute certainty where the coin is even though there are still two cups and only one coin.  Therefore, can we really rule out light having a directionality?  The only systems we ever deal with are systems with a lot of photons emitted in all directions.  Dividing our chances of absorbing x amount of photons at position P by the number of photons there are gives a probability of absorbing an individual photon at that position...but isn't that just like the coin and the cup?-I don't know in what direction (under what cup) the photon (coin) is but I know the probability that I am going to absorb it.
 

Offline JP

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« Reply #13 on: 13/12/2007 03:46:13 »
Probabilities only come into play when we don't know enough about the initial conditions to predict what outcome will prevail.  If I have two cups on a table and I put a coin under one while you are not looking, there is a 50% chance that the coin will be under the cup you choose.  However, if you peak over your shoulder you know with absolute certainty where the coin is even though there are still two cups and only one coin.

In quantum mechanics, even if you know as much as possible about the initial conditions, you can't predict the outcome exactly.  In other words, a quantum mechanical coin is under both cups at the same time, with probability of 50% until you peek.  No matter how early you try to peek into the system, it's got a 50% chance of showing up in either cup.

If there is a directionality, it shows up in the probability being higher that photons will be detected in a certain direction.  This would be like if your coin was loaded to land head up more often.  You couldn't tell this from one flip alone, but if you take a bunch of flips, you'd notice the pattern.  Similarly, you need to measure a bunch of photons in order to determine if your atom is emitting a field in a given direction.

But all this is confusing the question.  You want to look at the classical field direction emitted by the atom, which is an averaging over a lot of photons.  In that case, if you assume the atom is a small dipole, you probably could direct the light by somehow forcing the atom's dipole moment to align in a particular direction.  You would almost certainly get a pretty wide beam of light, since there's quantum fluctuations if you're dealing with a single atom, but you could probably end up relating the direction of the light to the polarization of the atom.
 

Offline lightarrow

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« Reply #14 on: 13/12/2007 08:42:58 »
1. Lightarrow: don't you just need to replace 'intensity' with 'probability' when you are dealing with small numbers? The same pattern will apply at a distance.
I think it's the same. Intensity is the power of electromagnetic radiation going through a unit area; you can measure this power counting the number of photons hitting that area in the unit time.
 

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« Reply #15 on: 13/12/2007 10:22:30 »
Whichever way you look at this, there are some difficult concepts. You can't get away with a simple, overall classical approach (of course) so you need to introduce, either some 'super-directivity' of the atom as an emitter of waves or the concept of quantum entanglement, so that only one of the possible target systems gets the photon energy.
My background of classical em treatment of antennae makes me very conscious of needing to treat the atom as a well behaved antenna, where possible. This implies a very broad beam with, perhaps, a few nulls in its pattern. I am then, as a consequence,  stuck with the other problem about what happens at the reveiving end of the event and there you have to bring in some quantum oddities. But  entanglement is already a factor which is acknowledged to apply in other quantum circumstances, so  I am not really rocking the boat by introducing it here.
If people insist on photons as little bullets then they have to suggest why a radiator would not be subjected to classical wave considerations which apply to a 'small' (or even 'not incredibly huge') system.
 

lyner

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« Reply #16 on: 13/12/2007 10:33:30 »

But all this is confusing the question.  You want to look at the classical field direction emitted by the atom, which is an averaging over a lot of photons.  In that case, if you assume the atom is a small dipole, you probably could direct the light by somehow forcing the atom's dipole moment to align in a particular direction.  You would almost certainly get a pretty wide beam of light, since there's quantum fluctuations if you're dealing with a single atom, but you could probably end up relating the direction of the light to the polarization of the atom.
Yes, a very broad directivity and the direction of the (dipole axis)  nulls would be the only control that you would have. No narrowly directed beams available here.
 

lyner

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« Reply #17 on: 13/12/2007 10:41:29 »
Ok, so light is a spherical probability wave (it has no direction but outwards)...it is spread out over a spherical surface and any detector on that surface has a probability of detecting that photon inversely proportional to the size of the surface.  That is all well and good and easy to picture but what is it about light that makes it behave that way?  What mechanism decides where the light should be absorbed? 
My argument is that, until  the uncertainty of which target system gets the photon energy is resolved, all you can discuss is the probablity (as in all quantum problems). Once there is an outcome (i.e. one system gets the energy) , that is communicated to all of space and no other outcome is possible (i.e. no one else gets the energy). This idea is ok, I think, because it applies in many  situations.
 

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« Reply #18 on: 13/12/2007 10:46:34 »
Not strictly true. It is, essentially, a spherical wave. It travels in the same speed in all directions. All 'rays' cover a range of angles, however small. The wavefront is spherical because each part of it has traveled the same distance after a given time.
As Soul  Surfer says, atoms don't have a directional light pattern. You can use many sources, radiating in phase, as do the atoms in a laser, or a number of radiating dipoles with the same radio frequency signal to produce a directional beam. Alternatively you can use a pinhole, lens or tube to select or direct the energy to go in a particular  direction. The wavefront is still spherical but its energy is restricted to a narrow range of directions.

OK, so this works from a quantum perspective.

Forgetting for the moment about the particulate perspective, how does the work from the relativistic perspective?  According to relativity, an EM wave is nothing but a manifestation of a contraction of space happening perpendicular to the direction of motion of a charge - so in which direction is the charge moving?  To have a spherical wavefront, would not the charge must somehow be moving in 3 dimensions at once?  Is this feasible?
 

Offline lightarrow

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« Reply #19 on: 13/12/2007 12:33:23 »
Forgetting for the moment about the particulate perspective, how does the work from the relativistic perspective?  According to relativity, an EM wave is nothing but a manifestation of a contraction of space happening perpendicular to the direction of motion of a charge - so in which direction is the charge moving?  To have a spherical wavefront, would not the charge must somehow be moving in 3 dimensions at once?  Is this feasible?
Can you explain this? (It's new to me!)
 

Offline lightarrow

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« Reply #20 on: 13/12/2007 12:39:20 »
Ok, so light is a spherical probability wave (it has no direction but outwards)...it is spread out over a spherical surface and any detector on that surface has a probability of detecting that photon inversely proportional to the size of the surface.  That is all well and good and easy to picture but what is it about light that makes it behave that way?  What mechanism decides where the light should be absorbed?
Good question. They are debating about it from ~ 80 years ago, but the answer is still "you can't know". As sophiecentaur wrote, you can only know the probability of detecting, not where the photon will be detected. If the wave optics computation tells you that in every point of a 1 m2 screen there is (e.g.) the same value of light intensity and you send one photon at a time, after many detections you will see a uniform pattern of light, but it's completely impossible (according to the present QM description) to predict which detector will "click" first, which second ecc.
« Last Edit: 13/12/2007 12:51:11 by lightarrow »
 

Offline lightarrow

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« Reply #21 on: 13/12/2007 12:53:06 »
My argument is that, until  the uncertainty of which target system gets the photon energy is resolved, all you can discuss is the probablity (as in all quantum problems). Once there is an outcome (i.e. one system gets the energy) , that is communicated to all of space and no other outcome is possible (i.e. no one else gets the energy). This idea is ok, I think, because it applies in many  situations.
Faster than light's speed? Doesn't it seem "quite strange"? :)
« Last Edit: 13/12/2007 12:54:37 by lightarrow »
 

Offline lightarrow

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« Reply #22 on: 13/12/2007 12:59:14 »
Whichever way you look at this, there are some difficult concepts. You can't get away with a simple, overall classical approach (of course) so you need to introduce, either some 'super-directivity' of the atom as an emitter of waves or the concept of quantum entanglement, so that only one of the possible target systems gets the photon energy.
I haven't understood this concept. Can you explain better?
 

lyner

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« Reply #23 on: 14/12/2007 15:30:58 »
What I mean by a 'super directive' radiator is ok, I assume, so you have a problem with the other idea(?)
Quantum entanglement is an idea which deals with two (or more) quantum systems, which are in unknown states but where the states are mutually connected - for instance, the spin of two electrons with, otherwise, identical quantum numbers. You don't know the spin of either electron - so it could be either value. If you measure / force the spin of one electron, you have immediately determined its state and that instantly determines the state of the other one. You can take two such systems miles apart and, once you have revealed/ resolved/measured the state of one, the other's condition is, instantly, determined and it will behave according to its newly determined state. The information about this is, magically, you might say, communicated through space. It's like a pair of Schroedinger cats in two boxes; when one is found alive, the other is, suddently dead and vice versa.
The principle is used in quantum computers - and they actually work - so I think we need to accept it as a valid idea.
http://en.wikipedia.org/wiki/Quantum_entanglement
Once you accept the principle, it allows you to accept my choice of ways of looking at the photon thing. If you can't go along with that, the bullet theory is preferable - despite the anti - classical behaviour it implies.
 

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« Reply #24 on: 14/12/2007 15:43:23 »
  To have a spherical wavefront, would not the charge must somehow be moving in 3 dimensions at once?  Is this feasible?
the radius of this sphere is equal to the distance from the source; the further you get from the source, the more nearly equal are the distances from each part of the source (it can be regarded as  a point source, eventually) and, as the wave spreads out in all directions at c, the wavefront will be a sphere - same radius in all directions. For a large radius, of course, this is more or less a plane in the region of the detector.
The above only refers to the phase - it does not imply omnidirectionality of amplitude. In fact, your  (valid, at first sight) objection is dealt with by allowing / insisting that there must be nulls in some directions in the radiation pattern. There is a throrem, somewhere, which deals with just that point - can't remember where I read it, tho.

 

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