Well looking at your figure, it seems that you have designed three structural parameters and accordingly, your modal parameters will be dependent on them. Regarding your first question, lattice structure plays an important role in the modal dynamics for a waveguide. So if you use hexagonal pack in lieu of square pack, modal dynamics will change. I mean to say that effective refractive index will vary. For these two structures, ERI is different which will eventually influence confinement loss, beam direction etc.

In order to develop model, I would suggest you to adopt Effective Index Method. You can also try the beam propagation method too. Best wishes,

Without pattern you draw main part of LED light will spread along dielectric slab. Introducing of the pattern will destroy TIR conditions and light will go out of slab. Sizes of the pattern gives you rights to apply geometrical optics relations, but diffraction is still take place and you can calculate its efficiency for near grazing incidence.

Dear Mr. Biswas,

thanks for your time and response. If you don't mind, I have some questions regarding your answer:

(1) Can you maybe tell me, how the lattice structure influences the modal dynamics?

(2) Do you know how exactly the effective refractive index (ERI) varies with varying structure?

(3) Do you have any good resources, so that I can read more about the two methods you have proposed?

Thanks in advance.

Best regards

Giuseppe

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Dear Mr. Sterligov,

thank you too for your answer. You have written that the size of the pattern allows me to apply relations from geometrical optics. Can you maybe tell me what relations you are exactly talking about?

Best regards

Giuseppe

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For me, the time you take to read and maybe give some answer is not a natural thing to do. So I appreciate that a lot :), thanks to everybody.

Modeling your system with an optical design program such as Zemax or CodeV (there are others, these two are the most used in optical engineering) will allow you to easily change parameters and analyze the results. I am sure one could come up with a mathematical solution, however, this kind of illumination designs are what design software are developed for.

Dear Mr. Ghorbani,

thanks for your response. Unfortunately, I do not have the license to use one of your mentioned programs. Browsing for Zemax, I read about LensMechanix and OpticStudio. With which of those is it possible to model the described problem? Can I simulate with Zemax also things like >Heat development< of LEDs and surrounding components?

Friendly regards

Giuseppe

Zemax OpticStudio is the program that will allow you to simulate your design. Unfortunately, For thermal analysis (heating issues) you would have to use other programs such as Ansys.

>Can you maybe tell me what relations you are exactly talking about?

I suppose that main part of LED light energy spread along slab bulk, along its axis.

If you neglect by corrugation pattern, you can calculate distribution of the light transmitted by plane interface.

Additional part of scattered light can be estimated by geometrical refraction and reflection by left edge of each groove, if you will present it as part of prism. Effect of the right edge will be weaker due to the shadowing effect. Yes, such calculations are approximate, but they can give you idea about main components of scattered light.

Next scattering component can be estimated from diffraction calculations by such pattern as grating.

Of course, more exact values can be obtained by calculations with help of Zemax, for example. Yes, such packages are expensive, but Zemax has 30 days free trial period, which you can successfully use for such calculations. Additionally, from my experience I know that during this trial period Zemax team is very user-friendly and they helps very efficiently not only with software features, but with formulation and solving optical problems. So, ask them for help. Good luck!

Dear Mr. Sterligov,

thanks for your answer.

Do you have any good resource (papers, books, etc.), where I can read more about the actual equations governing the scattering of the LED light mentioned by you?.

Furthermore I have never heard about "shadowing effect" before - do you mind giving me some more details about that?

As always, thanks in advance for your effort.

Best regards

Giuseppe

>Do you have any good resource (papers, books, etc.), where I can read more about the actual equations governing the scattering of the LED light mentioned by you?.

I'm not sure that such resources are exist because such distribution significantly depends on direct realization of your LED and its connection to your waveguide structure. You know, I suppose, what is LED structure, construction and you should start from this point.

>Furthermore I have never heard about "shadowing effect" before - do you mind giving me some more details about that?

It is known from theory of diffraction grating. Surprisingly some of geometrical optics ideas can work correctly in such area. So, if grating is metal one, part of the groove, which is not illuminated from geometrical point of view, has weaker influence on diffraction light distribution.

In similar way, if groove has flat part, in direction of geometrical reflection by such flat surface we will have significant increasing of diffraction efficiency, so called "blazing" effect, or "blazing" gratings.

Such effects are illustrating wave/particles light nature duality.

Dear Mr. Sterligov,

thanks a lot for your response - the information provided is amazing, never heard about that before. Currently, I am looking for a method with which I can tackle the problem stated at the beginning. It was mentioned above the effective index method and the beam propagation method. Do you have any experience in one of these? Or could you tell me the "right" method I should focus on?

Maybe you know any resources which trade the stuff mentioned by you (such as "blazing" and "shadowing" effect) in general? Would be really interesting for me to read and learn more about that.

If it is okay for you I would write you a private message regarding some more questions I have.

Best regards

Giuseppe

If I would be facing your task, I'll start from beginning: what is the LED indicatrice? Than I'll found its light distribution inside your waveguide. Next step is calculations of output light distribution for waveguide without pattern and last part is to introducing of pattern and calculate its effect on light distribution.

And I'll definitely use either Zemax in the way I have mentioned, either one of numerous free optical packages. One of the reason is that such task cant' be solved analytically by methods you have mentioned.

>Maybe you know any resources which trade the stuff mentioned by you (such as "blazing" and "shadowing" effect) in general? Would be really interesting for me to read and learn more about that.

These information is well-known, you can find it into many optical textbooks, especially deals with diffraction gratings calculations. Sorry, for the moment I don't have direct references.

I'm pretty sure that even Google scholar by key words "blazing grating" will give you many references.

Dear Mr. Sterligov,

just can not thank you enough. I appreciate your time a lot.

I tried to look for indicatrice, but I have not found much about that. Can you maybe tell me roughly what that represents?

Within my company the R&D-Department right now uses LightTools. So far I have not a lot of experience with that. Do you know, if that simulation program does a good job (compared to Zemax), too?

Thanks Mr. Sterligov

Best regards

Giuseppe

Indicatrice is single word which means angular (space) distribution of scattered/emitted/transmitted etc. light intensity. So you need to know it for your LED unit.

>Within my company the R&D-Department right now uses LightTools.

I don't have experience with such package, but I'm pretty sure that it can be used for solving your task.

Good luck

You can see publication about calculations of optical system, very close to yours:

Article High-efficiency directional backlight design for an automotive display

Dear Mr. Sterligov,

thanks a lot for your time. I appreciate your help a lot.

Best regards,

Giuseppe