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I would like to know how the physics(and possibly mathematics) for how quarter-wave stacks could be utilized to make an ideal rejection filter that rejects all visible coherent green or blue or red laser light, not at the same time, in a given narrow spectral wavelength range (10 nanometers to 20 nanometers wide) and transmits everything else within the visible light band.

I have read some optics books on the analysis of quarter wave plates for normal incidence. I analyzed how the Boeing 757 aircraft's nose geometry forces incoming laser rays aimed from the ground on approach to hit the cockpit window at large angles of incidence and high orders of interference. If you would like to see this analysis , I will post it as an image. So, I would be interested in how to analyze the blocking and transmission properties of quarter-wave stacks at large angles of incidence.

Also, I would like to know the relationship between coherence length of visible light laser pointer beams and the distance between quarter wave plates so we could discriminate between coherent and incoherent light over a very narrow wavelength range.

The reason I ask this question is because I read Fred Goldstein's chapter, Optical Filters , in the book "Geometrical and Instrumental Optics" edited by Daniel Malacara and published by Academic Press in 1988. In Section 6.3.4 , page 294 , Fred Goldstein wrote that, "There is interest in filters which reject in an extremely narrow spectral regions. These could be superior to current filters utilized for eye protection near lasers. In theory, such filters can be constructed from a great number of quarter-wave layers of materials with nearly identical indices.[EDIT June 8 2016 Why?] Inhomogenous films with periodic index variations represent another possiblity. [EDIT June 8 2016 Why?]"

I believe that matrix and Fourier transform formalism may be necessary here. Please correct me if I am wrong.

Any help is greatly appreciated.

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closed as off-topic by CuriousOne, John Rennie, honeste_vivere, ACuriousMind, Gert Jun 9 '16 at 2:43

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    $\begingroup$ I thought you have your "technology" under control? You said you were going to present your "whiteboard formulas" to the FAA... and, yet, here you are, again, asking about trivial stuff that you can't seem to figure out on your own. :-) Remember what I told you about invalidating any possibility to patent if you keep talking about in public? $\endgroup$ – CuriousOne Jun 8 '16 at 5:30
  • $\begingroup$ @Curious One, Thank you for your comment. I can show you whiteboard formulas I derived last week. The real patent the FAA would be interested in is an advanced semiconductor fabrication of a photonics circuit which could calculate a solution to an original system of equations. May I ask why you think I am asking about trivial stuff here? $\endgroup$ – Frank Jun 8 '16 at 6:02
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    $\begingroup$ The FAA isn't interested in any patents, but that's something you can much better "discuss" over at the aviation SE. $\endgroup$ – CuriousOne Jun 8 '16 at 6:03
  • $\begingroup$ There are already great optical coatings used for laser safety glasses (lg7, here thorlabs.de/newgrouppage9.cfm?objectgroup_id=762) which are having the needed characteristics. Dolby 3D is also based on dichroic filteres. Dielectric laser filters are also state of the art since decades. Much work was put into dielectric coatings since 1988... $\endgroup$ – user_na Jun 8 '16 at 6:58
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    $\begingroup$ Do you have a source where you can buy a big enough block of single-crystal quartz (or some other birefringent crystal) to carve a cockpit window out of? $\endgroup$ – The Photon Jun 9 '16 at 1:52
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As for "I would like to know how the physics": that question is too broad to answer; I'd suggest that you get a book on Fourier optics and work through it by solving the exercise problems - you can ask for hints to solve the exercises here on Physics SE.

I'll answer the more specific questions and address some misconceptions.

As for "coherent light": coherence of light and laser beams is often misunderstood, partially because there are different definitions of coherence, depending on what aspect of the light you're interested in. A laser beam has transversal coherence, which means that the light propagates as a beam. A laser typically also has longitudinal coherence, which is a measure for its wavelength bandwidth (or rather, the inverse of of its wavelength bandwidth).

Any filtering optics will not distinguish between a ray of light from a green laser or a ray of light from a green lightbulb. All you can do is trying to select for direction of the ray and wavelength of the ray.

For a quarter-wave stack: it's not a series of quarter-wave plates that you can arrange by hand. It's a series of layers, each of them with a thickness $\lambda/(4n)$, where $n$ is the refractive index of the layer and without air gaps in between (unless you count the air gap as a layer by itself). The layers must alternate between high and low refractive indices. For example, if a layer refractive index is 1.5 and the wavelength to reflect is 532 nm, you need a layer of 89 nm thickness. For more on the topic: Wikipedia: dielectric mirror; how to calculate: Wikipedia: transfer-matrix method. You can also calculate it for non-normal incidence, but for that you'll have to get an advanced optics book.

I suppose that you would want the mirror/filter to be automatically adjustable in case of an incident laser beam. Such a variable dielectric mirror would need to adapt itself to a specific wavelength and specific angle of incidence. If you want to keep the mirror fixed in orientation, you will need to adjust the refractive index and/or the thickness of the layers by a substantial amount (a factor 2 or so). I don't think that this is possible in practice.

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  • $\begingroup$ And even then, that quarter-wave stack is optimized for a certain fixed angle of incidence, while pilots generally need to see all around them. $\endgroup$ – Jon Custer Jun 8 '16 at 13:17
  • $\begingroup$ @JonCuster I suppose that the idea is that you have a sensor that detects a laser beam and then adjusts the filter within milliseconds, before the pilot is dazzled. $\endgroup$ – Han-Kwang Nienhuys Jun 8 '16 at 13:31
  • $\begingroup$ @Han-Kwang Nienhuys, Thank you for your excellent answer which I enjoyed reading. This evening I will post several comments on your answer. I hope you can respond to these comments. $\endgroup$ – Frank Jun 8 '16 at 15:17
  • $\begingroup$ @Jon Custer, Thank you for your great comment. If the quarter-wave stack needs to be optimized for a certain fixed angle of incidence, how much the transmissivity deteriorate once a ray deviates from the fixed angle of incidence.?Are there alternate optical structures for implementing rejection filters? $\endgroup$ – Frank Jun 8 '16 at 15:22
  • $\begingroup$ @Frank - that is a pretty basic optics question, with an intro in the Wikipedia article reference above on the transfer-matrix method. You seem very excited about your idea. I would suggest stepping back and looking at what is already out there frpm a business point of view (multi-wavelength anti-dazzle products are a reality), and dig deeper in to understanding more about optical physics (both active and passive devices). $\endgroup$ – Jon Custer Jun 8 '16 at 15:29

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