Two Phase Fresnel Reflectivity and Electric Field Calculation

Brought to you by the Research Group of Prof. Robert M. Corn
at the Dept. of Chemistry, University of California, Irvine.

This page is for calculating the reflectivity of p-polarized and s-polarized light (RefP and RefS) as well as the square of the interfacial electric fields (Es2, Ex2, Ez2) as a function of incident angle (Angle) from a two phase dielectric system. The first phase must be non-absorbing (real refractive index only). The second phase can have both a real and imaginary part. Some typical calculations are:

  1. prism (BK7 or SF10 glass) - air
  2. prism (BK7 or SF10 glass) - water
  3. air - metal (gold or silver typically)
  4. water - metal (gold or silver typically)
  5. liquid -liquid interface (e.g., CCl4-water)

For this calculation, you need to supply the angle range over which you wish to perform the calculation and the indices of refraction for the 2 phases. As mentioned above, the first phase can only have a real index of refraction.

If you don't know the indices of refraction, we have created tables of gold, BK-7, and SF-10, indices of refraction for wavelengths between 500 nm and 2000 nm. The default indices in the form are for air and gold at the HeNe laser wavelength of 632.8 nm.

This particular web page is written to perform only a 2 phase calculation. We also have a web page for a 4 phase Fresnel calculation that uses the N-phase method published in the article by Wilford Hansen, J. Opt. Soc. Am. 1968, 58, 380-390. For more information or a copy of the complete N-phase calculation code, please see our Calculations Page.

To run this calculation, just fill out the form items below and hit the "Submit Parameters" button. Your input data will then be saved, and the calculated Angle-Ref data will be returned in an x-y table.

Good Luck! If you run into any problems, please email us at:

A 3 letter code (your initials, for example):

These 3 letters will be used in generating a unique code for your Fresnel calculation input parameters. These parameters are stored in a common logfile. If you leave them at the default letters ("ABC"), you risk having your parameters overwritten or used by another person.

Angle Range and Increment

The angle range for the calculation can vary between 0 degrees (normal to the surface) and 90 degrees (grazing incidence). The final angle must be larger than the start angle. You have three choices in the spacing of the angles in the calculation: every 0.1 degrees, 0.01 degrees or 0.001 degrees. NOTE: If you choose the finest angle increment of 0.001 degrees, you will only be allowed to have a maximum total range of 5 degrees in your calculation.

Electric Field Calculation

above the interface

below the interface

Indices of Refraction