How to increase the angle of light (without going from a higher to lower index of refraction)?

Question

I would like a device to spread out/increase the angle of rays in a light source. In other words, I would like to reproduce the behaviour of light traveling from an area of higher to lower index of refraction. The problem with this simple method is that my light is coming from air, so there is no material I can find with a lower index of refraction. I investigated converging and diverging lenses but these bend on-axis rays to focus them. Instead, I want to leave on-axis rays untouched and spread everything else out, by a strong factor (multiplying the angle by at least a factor of 10).

My light source is 2.4GHz, nearly monochromatic, 5cm*5cm in spot size, and the rays are coming from all different directions.

Answer 1

Although JQK gave a good answer, this post is more of a comment rather than an answer, but it would not fit as a comment, so I post it as an answer instead.

Firstly I would like to ask: what is your actual purpose with the device? Because to me it seems that you are asking for some MEANS that you thought of to reach SOMETHING as an end result, while there might be a much better way to this "SOMETHING". Could you please specify your something instead of your thought of means to achieve it? (If this is not clear enough, an analogy: your end result (the something): painting a wall; your question "I would like something that intakes paint and shoots it in a cone" (basically what you thought of as means to achieve your something). However, as obvious from this example, there are 100s of ways on how to paint a wall).

Of course that there is a chance that I am wrong and what you ask here is literally the only solution to your problem after a lot of thought and knowledge about what you are doing. But it just seems to me that it is the former.

1:

I investigated converging and diverging lenses but these bend on-axis rays to focus them. Instead, I want to leave on-axis rays untouched

If you checked "diverging" lenses, than you should have seen that the focus is virtual, behind the lens, actually on axis rays remain unchanged. More on this later.

2:

I want to leave on-axis rays untouched and spread everything else out, by a strong factor (multiplying the angle by at least a factor of 10).

It seems to me that you are instead interested in isolating just a part of your incoming radiation, to separate those that are "on-axis" from other sources. This goes from my initial remark regarding your question not being clear about your intentions. If this is the case: you want to separate on axis from other sources than there is a much simpler solution: an aperture!

Simply take an aperture of 5x5cm² and make it long enough so that you have the desired angular cut-off. As I would assume that you still need some separation from your device to whatever you are doing next, as you need to be sure that you have enough separation between the on-axis and off-axis components, you can also make this quite longer, or use 2 apertures as on-axis singling out devices. HOWEVER, this now constitutes a waveguide and you need to look into waveguide physics.

Answer 2

2,4 GHz is typically knows as RF, and usually not referred to as light.

You may want to look into negative index of refraction materials that arise using meta materials.

Metamaterials str structures engineered to have properties not found in naturally occurring materials snf can achieve a negative index of refraction. This property comes about through structures at the sub-wavelength scale. Metamaterials can be constructed using a variety of elements like split-ring resonators, wires, and other small components to manipulate electromagnetic waves in unusual ways.

In a material with a negative index of refraction, some very counterintuitive things happen. For instance:

Negative Phase Velocity: The direction of energy flow (group velocity) is opposite to the direction of phase velocity.

Reversed Snell's Law: Light bends in the "wrong" direction when entering the material, which is the opposite of what you would expect based on Snell's law for materials with positive refractive indices.

Reversed Doppler Effect: A source moving toward an observer will appear to be red-shifted rather than blue-shifted.

Hyperbolic Dispersion: The wave vectors can take on hyperbolically-shaped contours in the dispersion relation, leading to interesting properties like negative refraction and superlensing.