Evanescent Field Penetration Depth
In total internal reflection fluorescence microscopy (TIRFM), a small portion of the reflected light penetrates through the interface and propagates parallel to the surface in the plane of incidence creating an electromagnetic field in the liquid adjacent to the interface. This field is termed the evanescent field, and is capable of exciting fluorophores residing in the immediate region near the interface.
This tutorial explores penetration depth of the evanescent field as a function of refractive index differences between the two phases surrounding the interface, the critical angle of incident illumination, and the laser excitation wavelength.
The tutorial initializes with glass (refractive index, n = 1.52) as medium one and water (refractive index, n = 1.33) representing medium two. The default wavelength is 445 nanometers and the incident light beam angle is 61 degrees, approximately equal to the critical angle. Use the Incident Angle slider to adjust the angle of the virtual laser beam, which will simultaneously change the evanescent wave penetration depth (d, recorded in nanometers and displayed in the applet window). As the incident angle is increased, the penetration depth decreases through a range of 606 nanometers at the highest incident angle (61 degrees), to 51 nanometers at an incident angle of 80 degrees. The Wavelength slider can also be employed to alter the penetration depth, with longer wavelengths producing greater degrees of penetration. To change the refractive index difference between the two media surrounding the interface, use the Refractive Index pull-down menus. Increasing the refractive index of medium one (n(1), the medium of higher refractive index) produces a corresponding decrease in both critical angle and penetration depth at a constant value for medium two (n(2), the medium of lesser refractive index). Likewise, increasing the refractive index of medium two produces larger values for the penetration depth when the refractive index of medium one (n(1)) is held constant.
For a light beam having a finite width, the evanescent wave created at the interface can be described as partially emerging from the solid into the liquid medium and traveling for some distance before re-entering the solid phase. This propagation distance, called the Goos-Hänchen shift, can be measured when the beam width is restricted to one or several wavelengths. The size of this shift ranges from a fraction of a wavelength when the incident light is perpendicular to the interface, to infinite at the critical angle, which corresponds to the refracted beam skipping along the surface. Wider beams (those having a width much larger than a few wavelengths) produce an evanescent field whose intensity can be measured in units of energy per unit area per second. The evanescent field intensity decays exponentially with increasing distance from the interface according to the equation:
where I(z) represents the intensity at a perpendicular distance z from the interface and I(o) is the intensity at the interface. The characteristic penetration depth (d) at λ(o), the wavelength of incident light in a vacuum, is given by:
The penetration depth, which usually ranges between 30 and 300 nanometers, is independent of the incident light polarization direction, and decreases as the reflection angle grows larger. This value is also dependent upon the refractive indices of the media present at the interface and the illumination wavelength. In general, the value of d is on the order of the incident wavelength, or perhaps somewhat smaller. When the incident angle equals the critical value, d goes to infinity, and the wavefronts of refracted light are normal to the surface.