How to calculate shadows in nanophotonics

[qnach]

Could anyone tell me how to calculate the shadow of an object in nanophotonics.
Is there any book discussed such issue?
I emphasize nanophotinics becuase at that scale there might have diffraction etc.

 

[hutchphd]

Are you looking for the scattering from an object much smaller than the wavelength of the incident EM radiation? It is not clear what you mean from your question.

 

[qnach]

Are you looking for the scattering from an object much smaller than the wavelength of the incident EM radiation? It is not clear what you mean from your question.

It might be interpreted as scattering. But I think of shadows...is there such theory in some books? or only scattering theory?

 

[hutchphd]

What you choose to call it does not change the physics. The solutions are older than the term "nano" prepended to everything.
Specifically what wavelength light are you scattering from what sizes of what kind particle?

 

[qnach]

What you choose to call it does not change the physics. The solutions are older than the term "nano" prepended to everything.
Specifically what wavelength light are you scattering from what sizes of what kind particle?

It should not matter. Actually, I have no idea. Could you please tell me any textbook discussing such issue?

 

[Paul Colby]

It should not matter. Actually, I have no idea. Could you please tell me any textbook discussing such issue?

Yes it matters. Which books/methods depend on it. Also what is the issue? For example, the shadow cast by the Earth depends on the geometry of the sun/earth system and where one puts the screen. what are your light sources?

 

[hutchphd]

What specifically prompts your inquiry? "Tell me about shadows" is not really a question...

 

[qnach]

Yes it matters. Which books/methods depend on it. Also what is the issue? For example, the shadow cast by the Earth depends on the geometry of the sun/earth system and where one puts the screen. what are your light sources?

Whatever that is you never told me anything.

http://aven.amritalearning.com/index.php?sub=99&brch=290&sim=1452&cnt=3307

I want to calculate such a shadow.

 

[DaveE]

Whatever that is you never told me anything.

http://aven.amritalearning.com/index.php?sub=99&brch=290&sim=1452&cnt=3307

I want to calculate such a shadow.

Is that the right link? I didn't see anything "nano" in it. It looks to me like all of that stuff can be described by simple ray-tracing geometry.

However, when the radiation wavelength is comparable to the objects, then ray tracing doesn't work as well. As you said, diffraction can be an issue. Diffraction of light is a common topic taught in university physics classes, so there are lots of different references. To really understand it you do need a bit of math first, IMO. Things like calculus and Fourier transforms.

Since you asked for a book, but haven't told us your level of math & physics understanding, I'll just toss out my favorite "Introduction to Fourier Optics" by Joseph Goodman. BUT... don't go out and buy it if you don't already know about Fourier Transforms.

Really a better approach might be to look on the web (Google, YouTube, etc.) for explanations of diffraction, then you can find one that fits your level and interest best.

Finally, the diffraction around any complex shape (like a bird outline) will require numerical solutions on a computer for anything but the roughest estimates of the effect.

 

[Paul Colby]

Whatever that is you never told me anything.

I've actually written ray tracers. It's pretty simple, actually. Work out the intersection between a line (aka ray) and a triangle. Represent the object as a simplex of triangles. You can use a Monte Carlo methods or simply populate a grid of rays.

Or if you're just interested in cheap and sleazy results try the PovRay code and extract the shadow from the png produced. There are likely other ray tracers for designing optics which would be more suitable but they can be kinda pricy.

One text that comes to mind is

"Geometrical Theory of Diffraction for Electromagnetic Waves" by Graeme L. James, IEE Electromagnetic Waves Series

Not so much for ray tracing as for physical optics and some better approximations like the physical theory of diffraction. I suspect that for what ever it is you're asking, this text is more appropriate but then you haven't shared dick about your actual problem so it's nearly impossible to tell.

 

[qnach]

I've actually written ray tracers. It's pretty simple, actually. Work out the intersection between a line (aka ray) and a triangle. Represent the object as a simplex of triangles. You can use a Monte Carlo methods or simply populate a grid of rays.

Or if you're just interested in cheap and sleazy results try the PovRay code and extract the shadow from the png produced. There are likely other ray tracers for designing optics which would be more suitable but they can be kinda pricy.

One text that comes to mind is

"Geometrical Theory of Diffraction for Electromagnetic Waves" by Graeme L. James, IEE Electromagnetic Waves Series

Not so much for ray tracing as for physical optics and some better approximations like the physical theory of diffraction. I suspect that for what ever it is you're asking, this text is more appropriate but then you haven't shared dick about your actual problem so it's nearly impossible to tell.

Could you show me your work?

 

[Paul Colby]

Could you show me your work?

No, I don't own it.

 

[Paul Colby]

https://en.wikipedia.org/wiki/Nanophotonics

@qnach I think ray tracing would be of little value for most applications in nanophotonics since many of the structures are sub wavelength in size. There are a great number of EM analysis techniques and methods out there. If you think calculating shadows is the appropriate approach you’re likely mistaken.

 

[qnach]

https://en.wikipedia.org/wiki/Nanophotonics

@qnach I think ray tracing would be of little value for most applications in nanophotonics since many of the structures are sub wavelength in size. There are a great number of EM analysis techniques and methods out there. If you think calculating shadows is the appropriate approach you’re likely mistaken.

So...what are the other techniques?

 

[Paul Colby]

So...what are the other techniques?

Well, this depends very strongly on the dimensions of the system being modeled in wavelengths and the desired accuracy. For electrically large systems ray tracing can be useful. Also of note are the physical theory of diffraction which utilizes piecewise canonical solutions. For small to medium large 1 to 100 wavelengths in dimension the Method of Moments based on the electric field or magnetic field integral equations. FEM methods can be quite general useful for inhomogeneous materials but the have some issues with propagation errors that don't diminish with mesh refinement. The finite difference time domain can also be useful if the geometry is simple. Another technique I've found useful when the system is close to an ideal solvable system, such as a waveguide, is to use perturbation techniques. The number of techniques are quite broad and I have in no way exhausted ones options. Which ones really really depend on the details which you seem reticent to share. This is fine. Good luck.

 

[Paul Colby]

Actually, I do have a recommendation. I would look at FEM methods. In particular I'd look at FreeFEM++ which is an open source FEM code of considerable generality. Slight propagation errors are like not going to prevent you from obtaining useful information along this route.

 

[qnach]

Well, this depends very strongly on the dimensions of the system being modeled in wavelengths and the desired accuracy. For electrically large systems ray tracing can be useful. Also of note are the physical theory of diffraction which utilizes piecewise canonical solutions. For small to medium large 1 to 100 wavelengths in dimension the Method of Moments based on the electric field or magnetic field integral equations. FEM methods can be quite general useful for inhomogeneous materials but the have some issues with propagation errors that don't diminish with mesh refinement. The finite difference time domain can also be useful if the geometry is simple. Another technique I've found useful when the system is close to an ideal solvable system, such as a waveguide, is to use perturbation techniques. The number of techniques are quite broad and I have in no way exhausted ones options. Which ones really really depend on the details which you seem reticent to share. This is fine. Good luck.

Is there any book discuss these methods?

 

[sophiecentaur]

Is there any book discuss these methods?

First, I think the term "shadows" is not helpful or meaningful for anything other than large objects and apertures.

You have already been given loads of information. PF isn't in the business of spoon feeding. It seems that your field of interest happens to sit somewhere between simple Ray Optics and the region where diffraction becomes significant. There is little hope of coming across a book with a title that's the same as the title of this thread. There is not much chance, either, of PF doing your searches for you.

If you haven't already done so then I suggest you try a Google search using the terms in the title. Then go to a textbook on optics to get the basics of diffraction theory. Start with the simple, broad cases. Apply the wavelengths and dimension that correspond to your situation and that will give you a better than ballpark figure of the scattering patterns involved. As mentioned higher up the thread, you will need some ability to handle transforms if your shadowing object is two dimensional but there is lots of information about simple slits (or, indeed, discs and round holes). All this theory goes back several centuries.

Come back later with some more specific questions that can indicate that you have done some work on this and you will surely get a better response from PF.