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Achromatic Waveplate Theoretical Calculation

Theoretical calculations of achromatic waveplates made of quartz crystal and MgF2 crystal

 

The zero-order achromatic waveplate is constructed by aligning the fast axis of a multi-order quartz crystal waveplate with the slow axis of a magnesium fluoride waveplate, resulting in an optical path difference of 1/4 or 1/2 between the fast and slow axes over a wide spectral range. The quartz crystal and magnesium fluoride or ultraviolet sapphire minimize the dependence of phase retardation on wavelength, thus achieving a flat spectral response within the operating range of the achromatic waveplate. Its assembly diagram is shown below.

                                                 

The theoretical calculations for the component parameters of an achromatic waveplate with a quartz crystal + MgF2 crystal structure are as follows:

Quartz crystal refractive index:

Refractive index of MgF2 crystal:

Achromatic waveplate design wavelength and retardation: λ1:=470 λ2:=608 Δ:=1:1π

The retardation of a single crystal waveplate can be expressed as:

The cumulative delay at the two design reference wavelengths can then be expressed as:

  

The process of calculating the thickness of quartz crystal and MgF2 crystal:

  

Based on the above solution module, the thicknesses d1 of the quartz crystal and d2 of the MgF2 crystal that meet the design requirements can be obtained:

  

Substitute the above values ​​into the following formula for calculating the retardation of achromatic waveplates:

The above calculation method is used to solve for the thickness of components of achromatic waveplates made of quartz crystal and MgF2 crystal given the wavelength and retardation.