## SPR 4-Phase Fresnel Reflectivity 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 (R) of p-polarized and s-polarized light as a function of incident angle (t) from a four phase thin film dielectric stack. These calculations are used in predicting the shift in the SPR angle (i.e., the angle at which a minumum in reflectivity is observed in an SPR scanning angle experiment. The four phases are typically:

1. prism (BK7 or SF10 glass)
2. gold or silver thin film
3. monolayer film
4. water or air

For this calculation, you need to supply the angle range over which you wish to perform the calculation, the wavelength of light used in the SPR experiment, the indices of refraction for the 4 phases, and the thicknesses of the two thin films. The prism can only have a real index of refraction, but all of the other phases can be complex (i.e., absorbing). 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 BK-7 and gold at the HeNe laser wavelength of 632.8 nm.

The calculations closely follow those published in the article by Wilford Hansen, J. Opt. Soc. Am. 1968, 58, 380-390. Although the equations follow Hansen's N-phase method, this particular calculation is written to perform only a 4-phase calculation. 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 t-R data will be returned in an x-y table.

Good Luck! If you run into any problems, please email us at: ucispr@gmail.com

#### 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

• Start Angle: degrees
• Final Angle: degrees
• Angle Increment:

1 degrees

0.1 degrees

0.01 degrees

0.001 degrees

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. If you choose 0.01 degrees you will only be allowed 50 degrees.

#### Wavelength, Indices of Refraction and Film Thicknesses

Wavelength of the Calculation: nm

Index of Refraction and Film Thickness:

• Phase #1:

• Phase #2: + i

Thickness: nm

• Phase #3: + i

Thickness: nm

• Phase #4: + i

#### Electric Field Calculation

• Electric field at the interface:

1

2

3

• Above or below the interface:

Above the surface

Below the surface

TIP: If you want to perform a 3 phase calculation, just set the indices of refraction of the third and fourth phases to the same values.