The amount of light absorbed by a substance under normal single photon conditions is given by Beer’s Law, in which the amount of absorbed light is (in the weak absorption limit) proportional to the absorption cross-section of the molecule, s, the pathlength, l, and the concentration of absorbing species, C. In Two Photon Absorption (2PA), the absorption is proportional to the square of the light intensity. As a consequence, 2PA occurs only for very intense light, which, in common application, occurs at the focus of a laser beam. The photo at right shows fluorescence of a dye following 1PA and 2PA. The laser at the top of the cuvette is exciting the dye by 1PA causing yellow fluorescence emission. The emission can be seen clearly along the whole focussed laser path. The laser at the bottom of the cuvette is exciting the dye by 2PA, which causes the same yellow fluorescence. This time emission only occurs at the focal point of the laser because of the (intensity)2 dependence of the 2PA.
Simulated effects of excitation wavelength and numerical aperture on the dimensions of the 2PA volume. a, Normalized distributions of laser intensity-squared in the x-y and x-z plane for three different numerical apertures of water-immersion objective lenses at an excitation wavelength of 850 nm. Intensities-squared at lateral (x,y,0) and axial (x,0,z) positions were calculated using an ellipsoidal Gaussian approximation to the diffraction limited focus7,11 and expressed as the fraction of the intensity-squared at the focal point [I(0,0,0)2=1]. Color-coded contour plots depict isointensity lines in the x-z and x-y plane at the levels of 0.1, 0.3, 0.5, 0.7, and 0.9 of I(0,0,0)2. Note different scales for each panel. b, Dependence of 2PA volume on numerical aperture of the objective lens and illumination wavelength. Values were obtained by approximating the intensity-squared distribution as a three-dimensional Gaussian volume.12 For all calculations, it is assumed that the objective lens is uniformly illuminated (overfilled) and that no saturation of the fluorescence excitation process occurs. NA indicates numerical aperture.
Figure right provides a simplified illustration of the difference between single photon and two-photon activated processing. A material is polymerized along the trace of the moving laser focus, thus enabling fabrication of any desired polymeric 3D pattern by direct “recording” into the volume of photosensitive material. In a subsequent processing step the material, which was not exposed to the laser radiation, and therefore, stayed unpolymerized, is removed and the fabricated structure is revealed. The material sensitive in the UV range (λUV) can be polymerized by irradiation with the infra-red light of approximately double wavelength (λIR=2λUV), under the condition that the intensity of the radiation is high enough to initiate two-photon absorption.