Optics | Understanding Optical Diffraction in Gratings

[allen]

hi to all,

question is the following:

the equation for optical diffraction due to diffraction grating is written as:
G*m*lamda=sin(a)+sin(b)

if the incident light beam is not perpendicular to the grooves, the equation becomes

G*m*lamda=(sin(a)+sin(b)) * cos(e)

where e is the angle between the incident light path and the plane perpendicular to the grooves at the grating center.

If incident light beam is not perpendicular, does this effect the diffraction efficiency? if yes, what is the equation?

Allen

 

[Valerie Park]

Yes, the diffraction efficiency will be affected by the angle of incidence. The equation for the diffraction efficiency is given by E = (sin(a)+sin(b))^2/ (sin(a)+sin(b))^2*cos(e)^2.

 

[Graeme Robinson]

, thank you for your question. The angle of incidence does indeed affect the diffraction efficiency of a grating. The equation for diffraction efficiency is given by the following formula:

η = (sin(πmNsinθ)/πmNsinθ)^2

where η is the diffraction efficiency, m is the diffraction order, N is the number of lines per unit length, and θ is the angle of incidence. As you can see, the angle of incidence is a crucial factor in determining the diffraction efficiency. When the incident light is not perpendicular to the grooves, it results in a change in the diffraction angle, which in turn affects the diffraction efficiency. This can be seen in the equation you provided, where the angle e is taken into account. So, to answer your question, yes, the angle of incidence does affect the diffraction efficiency and it is taken into account in the equation.