Can I adapt a retarder for use with a specific wavelength other than the design wavelength?

A retarder can be used at a different wavelength than the design wavelength and still maintain its phase, if it is tilted about its fast or slow axis. If tilted about the fast axis, the design wavelength can only be changed to a shorter wavelength. If tilted about the slow axis, the design wavelength can only be changed to a longer wavelength. To determine the amount of tilt required, use the following equation:

θ = sin^-1 (λ_new / λ_design) , where

θ = the angle on the output side of the retarder from the optical axis to the back surface of the retarder

Example: If a ¼λ retarder is tilted about the fast axis and it is designed at 1064nm, then it can still be used as a ¼λ retarder for a 670nm source if it is tilted by 39 degrees.

If on the other hand the retarder is not tilted and a wavelength other than the design wavelength is used, there will be a phase shift. A ¼λ retarder has a phase shift of 90°. A ½λ retarder has a phase shift of 180°. To determine the amount of the phase shift, use the following equation:

δ = 360° (Δ n τ / λ ) , where

δ = the retardation angle

Δ n = the birefringence factor

τ = the thickness of the sheet

λ = the wavelength of light

Example: For a ¼λ retarder, since the phase shift (δ ) is 90°, Δ nτ = ¼ = 140nm (for λ =560nm). So if a source at 850nm is used for a ¼λ retarder with a design wavelength of 560nm, then δ = 360° multiplied by (140nm/850nm)= 59.29°. Solving now for Δ nt is (δ λ / 360°)= λ (59.29° / 360°) = 0.165λ » λ /6, the phase shift.