Photonics - peak temperature / thermal diffusivity

[nadeemo88]

Homework Statement

Estimate the peak temperature for a 1 ns versus a 1 ms optical pulse with a total energy of 1 J in a 1 cm^2 spot is incident on a sheet of metal. The metal is 20 thou ( 20 thou = 0.5 m). The metal sheet is mounted on a copper block which is held at room temperature. The thermal diffusivity is, D = 0.1 cm^2/s. The absorbtion coefficient at the relevant wavelength (0.37 $$\mu$$m) is $$\alpha$$ = 8000 cm$$^{-1}$$

Homework Equations

x bar = (Dt)^1/2
I(x) = Ie^($$^{-\alpha}$$X)
dI/dx = -$$\alpha$$I

The Attempt at a Solution

this is for my general engineering phsycis class, the prof gave us a 4th year photonics assignment, i have no idea how to even approach it..

 

[Jhero]

Dear student,

Thank you for your post. This is a challenging problem, but I will try to provide some guidance on how to approach it.

First, we need to understand the physical principles involved in this problem. We have an optical pulse with a total energy of 1 J and a duration of 1 ns or 1 ms. This pulse is incident on a sheet of metal, which is mounted on a copper block at room temperature. The thermal diffusivity of the metal is given as 0.1 cm^2/s, which tells us how quickly heat can spread through the material. The absorption coefficient at the relevant wavelength is also provided, which tells us how well the metal absorbs the incident light.

To estimate the peak temperature, we need to consider the energy absorbed by the metal and how it is distributed over time and space. We can use the equations you have provided in your post to help us with this.

First, we can use the equation x bar = (Dt)^1/2 to find the distance traveled by heat in time t. This will give us an idea of how far the heat has spread in the metal after the pulse is incident on it.

Next, we can use the equation I(x) = Ie^(^{-\alpha}X) to determine the intensity of the light at a particular depth x in the metal. This will help us understand how the intensity of the light changes as it travels through the metal.

Finally, we can use the equation dI/dx = -\alphaI to find the rate of change of intensity with respect to depth. This will give us an idea of how quickly the intensity decreases as the light travels through the metal.

Using these equations, we can estimate the temperature at different depths in the metal and determine the peak temperature. It may also be helpful to consider the specific heat capacity of the metal and the size of the spot where the light is incident, as these factors will also affect the temperature.

I hope this helps you get started on solving this problem. If you have any further questions, please don't hesitate to ask. Good luck with your assignment!