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Correction to the Beer-Lambert-Bouguer law for optical absorption
Haim Abitan1, Henrik Bohr, Preben Buchhave
1The QUP Centre and the Optics Group, Fysik Institute, DTU Lyngby 2800, Denmark. abitan@fysik.dtu.dk
Applied Optics
|October 11, 2008
Summary
This study introduces a general absorption law, exact for optical media, by incorporating stimulated and spontaneous emission. It extends Beer's law to higher power densities using the Lambert W-function.
Area of Science:
- Optics and Photonics
- Quantum Optics
- Laser Physics
Background:
- The Beer-Lambert-Bouguer law (Beer's law) is limited to low power densities.
- Higher power densities cause Beer's law to fail due to neglected emission processes.
- Previous models addressing emission lacked analytical solutions.
Purpose of the Study:
- To develop a general absorption law valid at high power densities.
- To analytically solve the two-level energy rate equation model.
- To account for absorption, stimulated emission, and spontaneous emission.
Main Methods:
- Utilized the Lambert W-function for analytical solutions.
- Solved the two-level energy rate equation model.
- Derived a generalized absorption law.
Main Results:
- An exact general absorption law was obtained, valid beyond Beer's law limitations.
- The general law reduces to Beer's law at low power densities.
- A criterion for the application of the new law was established.
Conclusions:
- The derived general absorption law provides an accurate description of light absorption in optical media.
- This model overcomes the limitations of Beer's law at high power densities.
- Experimental validation supports the applicability of the generalized absorption law.
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