Thermal Lens Effect
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General introduction to photothermal methods
Parameters for common solvents used in photothermal specteoscopy by Dr. Stephen E. Bialkowski


















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Thermal Lens Effect

The thermal lens effect was discovered when Gordon, et al. (1964) observed transient power and beam divergence changes in the output of a helium-neon laser after placing "transparent" samples in the laser cavity. It is a photothermal effect and results when energy from a laser beam passing through a sample is absorbed, causing heating of the sample along the beam path. The lens is created through the temperature dependence of the sample refractive index. The lens usually has a negative focal length since most materials expand upon heating and the refractive index is proportional to the density. This negative lens causes beam divergence and the signal is detected as a time dependent decrease in power at the center of the beam.    

Thermal lens formation
The total amount of heating depends on how strongly the sample absorbs the laser wavelength and on the power of the laser. For the common case of a Gaussian beam profile, the spatial variation in intensity across the beam is a well-characterized function. The heating caused by absorption of a Gaussian beam has radial symmetry along the laser path which creates a corresponding radial temperature gradient in the sample. The refractive index of most materials decreases with increasing temperature. Therefore, there will be a gradient in the refractive index corresponding to the temperature gradient in the sample, with the refractive index lowest at the center of the beam path. Effectively, then, the laser path is shorter at beam center. This effect, with the radial symmetry, makes a diverging lens out of the sample. The same laser beam which heats the sample to cause lens formation can be observed to diverge, or "bloom," as it passes through the sample. Blooming can be detected visually, or instrumentally with a photodiode positioned on the center of the laser beam axis. When blooming occurs, the diode detects a loss in laser intensity which is proportional to the temperature change. The formation of the thermal lens is shown in Fig. (1).

To detect the thermal lens, another laser beam (probe beam) can be used. There are two methods for that. In one case the probe beam is incident coaxially to the excitation one (pump beam), and in second methode probe beam incident vertical to the pump beam. In both cases, the probe beam is deflected by the thermal lens. As a result, the intensity at the center of the probe beam decreases and the variation depends on the size of the thermal lens.

Another interesting aspect of thermal lens is that the heating and subsequent lens formation is not instantaneous. It takes a finite time to develop, depending on the laser power and the thermal properties of the sample. In solution, the thermal properties of the solvent (heat capacity and thermal conductivity) determine the time for blooming to occur (typically milliseconds). To best observe the "grow-in" of the thermal lens effect, laser light is focused with a lens at a precise position in the sample. The pump laser is turned off and on with a rotating chopper. By correct choice of components, lens formation will occur during the "on" cycle of the pump laser through the chopper, and it will dissipate by cooling during the "off" cycle, so that the effect can be observed repetitively. During the formation of the lens, the probe beam is deflected and it comes back when the lens is destroyed. The variation of the intensity of the probe beam during lens formation is something like shown in Fig. (2).

Lens formation: Intensity trace
Measurements of the change in divergence of a laser beam after formation of the thermal lens allows determination of the absorbances of 10-7 10-6, which correspond to analyte concentrations of 10-11 10-10 mol.L1. Thus, thermal lens spectrometry is 100-1000 times more sensitive than conventional spectrophotometry. The performance characteristics of thermal lens spectrometry is power-based, that is the signal is proportional to light intensity and also it is a geometrical method, that is the signal depends on geometry of the optical scheme design.

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