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The article currently (2006-02-14) suggests that semiconductor lasers have longer coherence lengths (100 m) than helium-neon lasers (20 cm). I don't think that's generally correct. Perhaps the article should say 100 microns, rather than 100 m. Opinions?
^I also think these statements are incorrect. Typical coherence lengths of monomode HeNe lasers are 100m to several km, while even a monomode semiconductor laser with a linewidth of about 10pm has a coherence length of about 10cm.
^This statement is technically correct, but is deceptive. A HeNe laser without frequency stabilization typically has a 20-30 cm coherence length. A frequency stabilized (monomode, as the previous comment states) HeNe can have a coherence length greater 1 km. A semiconductor laser can have a coherence length less than 1 mm or greater than 100 m. Again, the longest coherence lengths are achieved via frequency stabilization.
"The expression above is a frequently used approximation. Due to ambiguities in the definition of spectral width of a source, however, the following definition of coherence length has been suggested[citation needed]"
Does anybody have a citation related with the expression of linewidth vs. coherence length? Some sources refer to a pi factor added in the denominator of the expression while some others do not (this article does not). I did some simple numerical simulations with a sum of planar waves with a lorentzian distribution of the amplitude this gave a visibility of 50% for a path difference around ~3x times smaller than given by the expression in this article. This seems to confirm that pi is needed for a lorentzian linewidth. WB.
There is a merger template on this article and the article coherence time. I didn't put it there and the person who did has not discussed it. I will remove it in one day unless there is actually a discussion to be had. JHobbs103 ( talk) 17:24, 13 June 2010 (UTC)
The article indicates that coherence length is the distance from the source. Now, if that is the way it is used then I suppose, but as I understand it is the distance along the beam, not necessarily from the source. For holography, it needs to be more than, more or less, the distance between the plate (film) and object, which might be a long way from the laser source. Gah4 ( talk) 11:46, 2 February 2013 (UTC)
From the formula is seems that the coherence length of a single photon is infinite, because the spectral width is zero. But interference only shows with multiple photons, so in practice the visible coherence length depends on the spectral width of all photons together (the same for coherence time). Is that a right? DParlevliet ( talk) 09:26, 14 January 2014 (UTC)
I moved the statement about an Hg line. (I suspect 546nm, but didn't check the reference.) It seems that the way to make it longer is to use isotopic pure 198
80Hg
. We could also add some other sources and their coherence length.
Gah4 (
talk)
07:58, 5 April 2018 (UTC)
I copied the discussion below from my talk page. -- Srleffler ( talk) 03:59, 10 April 2022 (UTC)
Hi Srleffler, I see that on the Coherence Length wiki page, you revert changes to the coherence length equation for a Gaussian source that remove the square root. I looked at the paper you referenced, and I believe the paper is incorrect. In the paper, they say that the coherence length is the FWHM of the modulus of the complex temporal coherence function (Eq. 2 in the paper), but actually the coherence length should be the HWHM (half width half maximum), which is the FWHM/2. The coherence length being the HWHM agrees with the explanation that the coherence length can be thought of as the path offset at which the fringe visibility drops to 50% (when measured with a Michelson interferometer), and is also why the path offset is +-L. This is why Equation 8 in the paper is off by a factor of 2 from the "correct" answer, i.e., they report the FWHM number incorrectly as the coherence length, when the coherence length should actually be the HWHM. As for why Equation 12 looks "correct" in the paper but actually refers to a Lorentzian source, again they are off by a factor of 2 and Equation 12 should also be divided by 2. Thus, the conclusion should be that given some bandwidth, the coherence length of a Lorentzian source would be half the coherence length of a Gaussian source.
We can derive the correct answer (which again is Equation 8 in the paper divided by 2) using the fact that the fringe visibility is related to the Fourier transform of the source spectrum (in frequency). Starting with a Gaussian source that has a FWHM of Δν and some center frequency ν0, we first find the standard deviation of the Gaussian, σ, using the fact that FWHM = 2*sqrt{2 ln(2)}*σ, then we can write the full description of the Gaussian in frequency space. If we compute the Fourier transform of the Gaussian in frequency space using a Fourier kernel of e^{-i2*pi*ντ), where τ = l/c (τ is time, which corresponds to length divided by the speed of light), we get another Gaussian in length space with some standard deviation σ', which we can find in terms of σ. The coherence length is the HWHM of the Gaussian in length space, and when you plug in for σ' in terms of σ, and σ in terms of Δν, then use the fact that c/Δv = λ^2/Δλ, you find that there is no square root. We can sort of see this now, since the FWHM and the HWHM equations both have sqrt{2 ln(2)}, and when you do the math the two square roots are multiplied together and thus gets rid of the square root. — Preceding unsigned comment added by 2603:7080:6E01:72AE:9922:7A36:ACAC:8CC0 ( talk) 19:07, 8 April 2022 (UTC)
![]() | This article is rated Stub-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
The article currently (2006-02-14) suggests that semiconductor lasers have longer coherence lengths (100 m) than helium-neon lasers (20 cm). I don't think that's generally correct. Perhaps the article should say 100 microns, rather than 100 m. Opinions?
^I also think these statements are incorrect. Typical coherence lengths of monomode HeNe lasers are 100m to several km, while even a monomode semiconductor laser with a linewidth of about 10pm has a coherence length of about 10cm.
^This statement is technically correct, but is deceptive. A HeNe laser without frequency stabilization typically has a 20-30 cm coherence length. A frequency stabilized (monomode, as the previous comment states) HeNe can have a coherence length greater 1 km. A semiconductor laser can have a coherence length less than 1 mm or greater than 100 m. Again, the longest coherence lengths are achieved via frequency stabilization.
"The expression above is a frequently used approximation. Due to ambiguities in the definition of spectral width of a source, however, the following definition of coherence length has been suggested[citation needed]"
Does anybody have a citation related with the expression of linewidth vs. coherence length? Some sources refer to a pi factor added in the denominator of the expression while some others do not (this article does not). I did some simple numerical simulations with a sum of planar waves with a lorentzian distribution of the amplitude this gave a visibility of 50% for a path difference around ~3x times smaller than given by the expression in this article. This seems to confirm that pi is needed for a lorentzian linewidth. WB.
There is a merger template on this article and the article coherence time. I didn't put it there and the person who did has not discussed it. I will remove it in one day unless there is actually a discussion to be had. JHobbs103 ( talk) 17:24, 13 June 2010 (UTC)
The article indicates that coherence length is the distance from the source. Now, if that is the way it is used then I suppose, but as I understand it is the distance along the beam, not necessarily from the source. For holography, it needs to be more than, more or less, the distance between the plate (film) and object, which might be a long way from the laser source. Gah4 ( talk) 11:46, 2 February 2013 (UTC)
From the formula is seems that the coherence length of a single photon is infinite, because the spectral width is zero. But interference only shows with multiple photons, so in practice the visible coherence length depends on the spectral width of all photons together (the same for coherence time). Is that a right? DParlevliet ( talk) 09:26, 14 January 2014 (UTC)
I moved the statement about an Hg line. (I suspect 546nm, but didn't check the reference.) It seems that the way to make it longer is to use isotopic pure 198
80Hg
. We could also add some other sources and their coherence length.
Gah4 (
talk)
07:58, 5 April 2018 (UTC)
I copied the discussion below from my talk page. -- Srleffler ( talk) 03:59, 10 April 2022 (UTC)
Hi Srleffler, I see that on the Coherence Length wiki page, you revert changes to the coherence length equation for a Gaussian source that remove the square root. I looked at the paper you referenced, and I believe the paper is incorrect. In the paper, they say that the coherence length is the FWHM of the modulus of the complex temporal coherence function (Eq. 2 in the paper), but actually the coherence length should be the HWHM (half width half maximum), which is the FWHM/2. The coherence length being the HWHM agrees with the explanation that the coherence length can be thought of as the path offset at which the fringe visibility drops to 50% (when measured with a Michelson interferometer), and is also why the path offset is +-L. This is why Equation 8 in the paper is off by a factor of 2 from the "correct" answer, i.e., they report the FWHM number incorrectly as the coherence length, when the coherence length should actually be the HWHM. As for why Equation 12 looks "correct" in the paper but actually refers to a Lorentzian source, again they are off by a factor of 2 and Equation 12 should also be divided by 2. Thus, the conclusion should be that given some bandwidth, the coherence length of a Lorentzian source would be half the coherence length of a Gaussian source.
We can derive the correct answer (which again is Equation 8 in the paper divided by 2) using the fact that the fringe visibility is related to the Fourier transform of the source spectrum (in frequency). Starting with a Gaussian source that has a FWHM of Δν and some center frequency ν0, we first find the standard deviation of the Gaussian, σ, using the fact that FWHM = 2*sqrt{2 ln(2)}*σ, then we can write the full description of the Gaussian in frequency space. If we compute the Fourier transform of the Gaussian in frequency space using a Fourier kernel of e^{-i2*pi*ντ), where τ = l/c (τ is time, which corresponds to length divided by the speed of light), we get another Gaussian in length space with some standard deviation σ', which we can find in terms of σ. The coherence length is the HWHM of the Gaussian in length space, and when you plug in for σ' in terms of σ, and σ in terms of Δν, then use the fact that c/Δv = λ^2/Δλ, you find that there is no square root. We can sort of see this now, since the FWHM and the HWHM equations both have sqrt{2 ln(2)}, and when you do the math the two square roots are multiplied together and thus gets rid of the square root. — Preceding unsigned comment added by 2603:7080:6E01:72AE:9922:7A36:ACAC:8CC0 ( talk) 19:07, 8 April 2022 (UTC)