How Does Thin Film Thickness Affect Interference Patterns?

[Gauss M.D.]

Trying to get my head around constructive/destructive interference in thin film optics. The book does a good job of throwing formulas at you but I want some intuition.

If we shine a laser with λ = 600 nm on a thin film of a material with refractive index 1.5, at what thicknesses will we get constructive/destructive interference?

The transmitted light should have a λ of 400 nm. So if the film is 400 nm thick, the light will complete exactly one oscillation before bouncing back, completing another one INSIDE the film - and then rejoining for maximum constructive interference.

But just from doodling oscillations, it seems as if it will reach maximum constructive interference if the film is 200 nm thick aswell. And maximum destructive interference at 100 nm and 300 nm... Is this correct? The mathematical derivation was very confusing. When does max interference occur?

 

[Doc Al]

Trying to get my head around constructive/destructive interference in thin film optics. The book does a good job of throwing formulas at you but I want some intuition.

If we shine a laser with λ = 600 nm on a thin film of a material with refractive index 1.5, at what thicknesses will we get constructive/destructive interference?

The transmitted light should have a λ of 400 nm. So if the film is 400 nm thick, the light will complete exactly one oscillation before bouncing back, completing another one INSIDE the film - and then rejoining for maximum constructive interference.

Don't forget the phase change upon reflection: When light reflects from a medium of higher index of refraction there is a 180° phase shift; when reflecting from a medium of lower index of refraction there is no phase shift.

So you would be correct if the medium that the film is on top of had an index of refraction greater than 1.5.

But just from doodling oscillations, it seems as if it will reach maximum constructive interference if the film is 200 nm thick aswell.

Sure. As long as 2 times the film thickness is an integral multiple of the wavelength in the material.

And maximum destructive interference at 100 nm and 300 nm... Is this correct?

Yes. For destructive interference, with your assumptions, you'll need 2 times the film thickness to equal 0.5, 1.5, 2.5, etc., times the wavelength.

 

[Gauss M.D.]

Don't forget the phase change upon reflection: When light reflects from a medium of higher index of refraction there is a 180° phase shift; when reflecting from a medium of lower index of refraction there is no phase shift.

So you would be correct if the medium that the film is on top of had an index of refraction greater than 1.5.


Sure. As long as 2 times the film thickness is an integral multiple of the wavelength in the material.


Yes. For destructive interference, with your assumptions, you'll need 2 times the film thickness to equal 0.5, 1.5, 2.5, etc., times the wavelength.

Ah, that's what messed me up - the formula wasn't clear on the "2 times" part.