Talk:Gaussian beam

message: Jones, I don't see why you insist on showing the first step in the derivation of the peak intensity. It really doesn't seem all that important. In fact, I think that mentioning that the derivation is done using l'Hôpital's rule is already too much information. Notwithstanding the fact that some other articles show derivations, Wikipedia is not a textbook or an instruction manual. Derivations are really not appropriate content, especially when the derviation is not absolutely central to the subject of the article.--Srleffler 00:43, 23 October 2006 (UTC)
thread_title:  L'Hôpital's rule 

message: The value of characteristic impedance is wrong, and reflects a common mistake in both undergraduate and graduate texts where the characteristic impedance of free space is stated to be EXACTLY 120 pi and therefore approximately 377. It is only exactly 120 pi if you assert that the speed of light equals 3x10^8.
characteristic impedance (free space) = Sqrt[(mu_0/eps_0)] = mu_0*speed_of_light_in_vacuum
If we assume that c = 3x10^8, then this becomes:
4*pi*10^-7 3*10^-8 = 120 pi
But, since c = 299792458
4*pi*10^-7 299792458 != 120 pi ~ 120 pi ~ 377
65.202.227.181 (talk)mjd 2008-04-18-17:08EDT  —Preceding comment was added at 21:07, 17 April 2008 (UTC)
thread_title:  Characteristic Impedance 

message: I would like to raise a concern regarding the figure of the high order LG modes. I am sorry but it is wrong: LG modes are cylindrically symmetric, and those in the figure are clearly not. Pure LG modes have a number of dark rings given by the number p, while the orbital angular momentum number $\ell$ affects the phase, so its effect is more clearly visible if we plot the argument of the amplitude. The only difference in intensity is the radius of maximum intensity, which grows as $\sqrt{\ell}$. --ziofil 23.31 3 November 2012  —Preceding undated comment added 03:31, 4 November 2012 (UTC)
replies: text: The modes as plotted are superpositions of +\ell and -\ell modes; i.e., the phase factor \exp(i\ell\phi) is replaced by \cos(\ell\phi). This is done (I assume) because these are the intensity patterns you expect to see when working with linearly polarized light. I put a note in the figure caption, but in the longer term someone may wish to add a note in the text of the article, or else redo the diagram. Zueignung (talk) 06:49, 4 November 2012 (UTC)
replies: text:  Independently of what one sees while working with polarisers, the equations in the text are not vectorial equations, they are solutions of the scalar wave equation, i.e. polarisation is never considered. It doesn't make much sense in my opinion to show an equation and then show intensity plots of something different. I have produced a new version of the same graphics grid without superpositions of +\ell and -\ell. How can I share it for consideration as a replacement? User:ziofil 23:26, 10 November 2012 (UTC)
replies: text:  On the left-hand side of the page, under "toolbox" there is a link called "Upload file". This will walk you through uploading the image. Zueignung (talk) 02:01, 11 November 2012 (UTC)
replies: text:  Done, it's at the address LG modes. User:ziofil 04:06, 11 November 2012 (UTC)
replies: text: I like the new image, and have added it to the article. I notice, though, that the file is in "pdf" format. Would it be possible for you to export the image in a straight image format, and upload it again (with a new filename)? PNG format would be best, but JPEG would also be fine. These formats are more portable, and less dependent on browser plugins.--Srleffler (talk) 23:13, 11 November 2012 (UTC)

text: Here it is in jpg: LG modes jpg User:ziofil 06:07, 15 November 2012 (UTC)
replies: text: Thanks.--Srleffler (talk) 07:01, 16 November 2012 (UTC)
thread_title: Laguerre-Gaussian modes

message: Who was the first to calculate Gaussian Beams? Are there any papers on it? I assume it was done first in the 50th or early 60th when Lasers came up. --2001:4CA0:4FFF:1:0:0:0:7A (talk) 09:35, 26 June 2012 (UTC)
thread_title:  History 

message: I have a few concerns with today's edit by Zueignung, which I haven't yet decided how best to address. I thought it would be easier to summarize them here rather than in edit comments.
*There is some redundancy between the second paragraph of the introduction and the new section.
*There is a discrepancy in focus between the new section and the existing lead and "mathematical form" sections. The latter discuss a "Gaussian beam" as a physical thing, whose field amplitude is described by a mathematical equation. The new section talks about Gaussian beams as solutions to an equation, rather than as physical things.
*I don't object to showing a short summary of the mathematical derivation of Gaussian solutions to the wave equation as the new section does, however I'm not sure it belongs right after the introduction. This relates to the "focus" concern, above. I'm not sure yet whether the best fix is to move the section or edit it in place.
*I disagree with the last statement of the new section, "...yields an infinite set of functions known as the Gaussian beams." I would prefer to keep the existing terminology in this article: "Gaussian beam" by itself refers only to the TEM00 mode. Higher-order solutions have distinct family names: Hermite-Gaussian, Laguerre-Gaussian, Ince-Gaussian, etc. I will remove the statement as not supported by any citation, but my objection is as much about organizing material for this article as it is about whether the term is actually used that way somewhere in the literature.
*The section title "Mathematical form of Gaussian beams" violates WP:MOSHEAD.
I do like the treatment of the derivation: just the right level of detail for this article, I think.--Srleffler (talk) 19:01, 19 August 2012 (UTC)
replies: text: On looking at this further, I think that moving the derivation later in the article, just before the section on higher-order modes, makes more sense. The existing article introduction already mentions that Gaussian beams are derived by solving the paraxial wave equation. I think it makes the most sense for the article to go directly from the introduction to a description of Gaussian beams and their properties. Wikipedia is not a textbook. The derivation functions nicely as a lead-in to the discussion of higher-order modes, since it answers the question "higher-order modes of what?"--Srleffler (talk) 19:26, 19 August 2012 (UTC)

text: I thought about this some more, and I think it isn't so crucial to write down the derivation right away, as long as there are a few sentences at the beginning of the section for the reader to get oriented. As it currently stands, none of the relevant introductory information in the lead has made it into the body of the article. I'll add this. Zueignung (talk) 22:48, 19 August 2012 (UTC)

text: I like the changes you've made to the article.--Srleffler (talk) 05:16, 21 August 2012 (UTC)
thread_title:  Concerns with today's edit 

message: Index of refraction needs to be made consistent through these equations. Right now, I think some of the formulas assume n=1.--Srleffler (talk) 04:38, 29 July 2014 (UTC)
thread_title:  To-do 

message: Should the units of measurement of physical quantities be included underneath the given formulas? They is confusing without any units being mentioned. Are all units in SI?  — Preceding unsigned comment added by 212.117.13.53 (talk) 15:05, 4 October 2015 (UTC)
replies: text: No, because in many cases you can use any consistent system of units in a formula and it will work. Units should only be given when the formula is specific to one system of units. If you're going to use one of the formulas, I recommend using SI units, though.--Srleffler (talk) 00:51, 5 October 2015 (UTC)
thread_title:  Regarding units of measurement 

message: At the start of the document, w(z) is mentioned as the 1/e value. In the beam divergence section, to me, w(z) is implied to be the 1/e^2 value. I think that should be clarified. Pjfcarle (talk) 16:33, 8 May 2016 (UTC)
replies: text: Intensity is the square of amplitude, so 1/e in amplitude is 1/e2 in intensity.--Srleffler (talk) 18:44, 8 May 2016 (UTC)
thread_title:  1/e vs 1/e^2 

message: The figure for the discussion of Gouy phase shift compares the phase advance of a plane wave with that of a gaussian beam. It seems to me that the gaussian beam is slowing in the focal region and lagging the plane wave when it should be speeding up and overtaking the plane wave. If this is inddeed incorrect, this could be a sign error in code used to make the figure.  — Preceding unsigned comment added by 73.113.140.122 (talk) 15:15, 1 April 2020 (UTC)
replies: text: Yes, you are absolutely right. As far as sign, you also have to consider that if you use the understood time factor as e^jωt (common in EE) then a negative phase is a delay but if  e^-iωt (common in physics) then a negative phase is an advance. But in any case the figure is wrong. And moreover it is wrong geometrically, contradicting the very previous section regarding the curvature vs. z (unless, possibly, if you accept a great aspect ratio exagaration in the "picture". I'm removing it. Interferometrist (talk) 18:51, 3 April 2020 (UTC)
thread_title:  Gouy Phase Figure 

message: Researchers at King's College London have created some physically accurate renders of a focused Laguerre-Gaussian 1,0 beam. We would like to insert the following video into the Laguerre-Gaussian modes subsection, and would welcome any suggestions/comments from the community. The 3D animation helps the reader conceptualize the spiralling nature of the wavefronts, how they propagate with time, and highlights how the positive and negative regions of the Laguerre polynomial functions give rise to a double-helix structure.--J.Kingsley-Smith (talk) 12:30, 2 February 2022 (UTC)
replies: text: Wow, that is a nice video!Maria Gemmi (talk) 12:34, 2 February 2022 (UTC)
thread_title:  Animation of LG10 mode 

message: The paragraph beginning "Arbitrary solutions of the paraxial Helmholtz equation can be expressed as combinations of Hermite–Gaussian modes (whose amplitude profiles are separable in x and y..." is way to high level to be introductory paragraph of the content. This should be moved later.
Geoffrey.landis (talk) 23:15, 4 March 2024 (UTC)
thread_title:  Decomposition 

message: I moved that text into a new section futher down in the article. I'm also going to move the subsection "Gouy Phase" further down, it is not going to be of main interest to a person looking at an encyclopedia article to understand what a Gaussian beam is.
Geoffrey.landis (talk) 16:52, 5 March 2024 (UTC)
thread_title: Moved