Reverse saturable absorption. Rate equations.

In summary: This approach is commonly used in the literature when solving these types of equations numerically. In summary, to solve the rate equations for a reverse saturable absorber, a change of variable is necessary to account for the refraction in the medium.
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ale_yoman
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Hello to all. Nice forum. Really like it. I hopee you'll can help me.

The rate equaition in the case of reverse saturable absorber, with a long-lived strongly absorbing excited state (T0) which is rapidly populated from a ground state (S0), are given as:
[itex]\frac{dS_{0}}{dt} = - \sigma_{01} S_{0} \phi + k_{30}T_{0} [/itex]

[itex]\frac{dT_{0}}{dt} = \sigma_{01} S_{0} \phi - k_{30}T_{0} [/itex]

[itex]\frac{d \phi}{dz} = - \sigma_{01} S_{0} \phi - \sigma_{34} T_{0} \phi [/itex]

[itex]\phi[/itex] is the photon flux, [itex]\sigma_{ij} [/itex] - ij-transition cross-section.

Thу last equation describes the light absorption in the sample depth. To solve these equations numerically with RK-method it is necessary to reduce the last one to the form [itex]\frac{d \phi}{dt}[/itex].

In the literature i met the change of variable which led to [itex]\frac{1}{c}\frac{d \phi}{dt}[/itex]. Why is it correct? What is about refraction in the sample?
 
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  • #2
In order to solve the last equation numerically with RK-method, it is necessary to transform it into an equation of the form \frac{d \phi}{dt}. This can be done by making a change of variables, such as \phi = \frac{\tilde{\phi}}{c}, where c is the speed of light in the medium. This change of variable has the effect of accounting for refraction in the medium, since the rate of change of the photon flux is now a function of the speed of light in the medium.
 

1. What is reverse saturable absorption?

Reverse saturable absorption is a phenomenon where the absorption of light by a material decreases as the intensity of the incident light increases. This is in contrast to saturable absorption, where the absorption increases with increasing light intensity.

2. How does reverse saturable absorption occur?

Reverse saturable absorption occurs when a material undergoes a nonlinear optical process in response to intense light. This process can be described by rate equations which govern the energy levels and transitions of the material.

3. What are rate equations?

Rate equations are mathematical equations that describe the dynamics of a physical system. In the context of reverse saturable absorption, rate equations describe the rate at which energy is absorbed and emitted by a material in response to light.

4. What are some applications of reverse saturable absorption?

Reverse saturable absorption has a variety of applications in fields such as optical limiting, optical switching, and laser technology. It can also be used for the protection of sensitive optical components from high-intensity light.

5. How is reverse saturable absorption studied?

Reverse saturable absorption can be studied using various experimental techniques, such as transient absorption spectroscopy and Z-scan measurements. These techniques involve measuring the changes in light absorption as a function of intensity, allowing for the characterization of the material's properties and the determination of rate equations.

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