- #1
zrek
- 115
- 0
Please help me to understand the difference/connection between the coherence length, packet length, wavelength and their effect on the interference. I'd like to understand these terms in case of one photon.
"The degree of coherence is measured by the interference visibility..."
http://en.wikipedia.org/wiki/Coherence_(physics)
"Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length"
http://en.wikipedia.org/wiki/Coherence_length
I also found that the different kinds of light sources can produce different quality of coherence, even with the same frequency. Here is a strong statement about the lengths:
"Interference is only visible if the coherence length of the light is at least as long as the path-length difference that creates the interference."
http://wiki.answers.com/Q/What_are_the_coherence_lengths_of_the_different_types_of_lasers
Until this point this is very clear for me.
Now let's switch to a photon representation, first I'll try to imagine the photon as a (probability) wave packet.
http://en.wikipedia.org/wiki/Wave_packet
The wave packet is just like the wave group, the speed of it is an "envelope" speed, not completely independent of the phase speed.
http://en.wikipedia.org/wiki/Group_velocity
(The speed of a particle is the superponated phase velocity of he waves that builds up the group http://doboandor.freeweb.hu/pdfs/fazis_es_csoportsebesseg.pdf )
Now let's take a single photon, which is a wave packet. I can see no more possibility than assume that the coherence length is the same as the group length (if there is a group velocity, then we have a group length too)
Now let's imagine a "normal" light source, emitting a single photon (with a specific energy that determines the wave length "L"), that going through a double slit and acting as expected and hitting the screen on the position that (in case of lots of similar photons later on) finally will produce an interference pattern.
I assume that the group length is depending only on the energy of the photon, which depends on the wavelength (L). The interference visibility depends on the coherence length, by this there will be far places on the screen (over the point X) that will not display interference pattern.
Now let's change our light source to a "high-quality" laser and repeat the experiment with the same wavelength (L). The article above said that the coherence length can be "greater than 100 km"! The point X will be changed...
What is the difference between the photon emitted by the "normal" light source or the "high-quality" laser?
How it is possible that the coherence length is independent from the wavelength in case of single photons? Maybe the photon have a "hidden, local" quantum number that is about the coherence length?
Thank you for your help.
"The degree of coherence is measured by the interference visibility..."
http://en.wikipedia.org/wiki/Coherence_(physics)
"Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length"
http://en.wikipedia.org/wiki/Coherence_length
I also found that the different kinds of light sources can produce different quality of coherence, even with the same frequency. Here is a strong statement about the lengths:
"Interference is only visible if the coherence length of the light is at least as long as the path-length difference that creates the interference."
http://wiki.answers.com/Q/What_are_the_coherence_lengths_of_the_different_types_of_lasers
Until this point this is very clear for me.
Now let's switch to a photon representation, first I'll try to imagine the photon as a (probability) wave packet.
http://en.wikipedia.org/wiki/Wave_packet
The wave packet is just like the wave group, the speed of it is an "envelope" speed, not completely independent of the phase speed.
http://en.wikipedia.org/wiki/Group_velocity
(The speed of a particle is the superponated phase velocity of he waves that builds up the group http://doboandor.freeweb.hu/pdfs/fazis_es_csoportsebesseg.pdf )
Now let's take a single photon, which is a wave packet. I can see no more possibility than assume that the coherence length is the same as the group length (if there is a group velocity, then we have a group length too)
Now let's imagine a "normal" light source, emitting a single photon (with a specific energy that determines the wave length "L"), that going through a double slit and acting as expected and hitting the screen on the position that (in case of lots of similar photons later on) finally will produce an interference pattern.
I assume that the group length is depending only on the energy of the photon, which depends on the wavelength (L). The interference visibility depends on the coherence length, by this there will be far places on the screen (over the point X) that will not display interference pattern.
Now let's change our light source to a "high-quality" laser and repeat the experiment with the same wavelength (L). The article above said that the coherence length can be "greater than 100 km"! The point X will be changed...
What is the difference between the photon emitted by the "normal" light source or the "high-quality" laser?
How it is possible that the coherence length is independent from the wavelength in case of single photons? Maybe the photon have a "hidden, local" quantum number that is about the coherence length?
Thank you for your help.
Last edited by a moderator: