Optical path length change due to absorption

In summary: I confused specific heat with thermal conductivity. Specific heat is a property of a material that describes how much energy is needed to raise the temperature of a substance by 1 degree Celsius. Thermal conductivity is the ability of a material to dissipate heat.
  • #1
stevenjones3.1
25
0
Hey, so I am trying to figure out the optical path length change of an optical fiber due to absorption. I'll post what I have so far and let me know if I have done anything wrong or if you have suggestions.

so the optical path length is
[itex]L' = nL[/itex]
(L' is optical path length, n is refractive index and L is the length)

the change in length is
[itex]dL' = L dn + n dL \approx L_0 n_0 \beta \Delta T + n_0 L_0 \alpha \Delta T [/itex]
Where [itex]\beta=1.28\times10^{-5} /^{\circ}C[/itex] is the change in refractive index with temperature
[itex] \alpha = 5.5\times10^{-7}/^{\circ}C[/itex] is the thermal expansion coefficient
[itex] L_0 = 700\text{m}[/itex] is the original length and [itex] n_0 = 1.4585 [/itex] is the original refractive index

this all gives [itex]dL' = (14.763\times 10^{-3} m/^{\circ} C)\Delta T [/itex]

For the temperature change I know the attenuation is 0.2dB/km so for 700m that is 0.14dB and if the output is 0dBm (1mW) then this gives an absorbed amount of power of 0.14dB or 0.9683mW

(this next part is where I am a little unclear)

The change in temperature would be equal to
[itex] \Delta T = \frac{\text{Power Dissapated}}{\text{Thermal Conductivity}\times\text{Length}} = \frac{P}{TC \times L_0} [/itex]
the thermal conductivity of fused silica is 1.3W/mK

This would give a temperature change of
[itex] \Delta T = 1.064 \times 10^{-6} C[/itex]


But there is a problem here, time is not involved, my system is running for close to 12 hours and should be constantly increasing in temperature (minus the dissipated heat but I am assuming that is not much of a factor as the cable is insulated)

How do I factor in time to determine the rate of temperature change which would then give me the change in length per hour?


Any help is greatly appreciated, Cheers!
 
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  • #2
I got different results from you- we agree until

stevenjones3.1 said:
For the temperature change I know the attenuation is 0.2dB/km so for 700m that is 0.14dB and if the output is 0dBm (1mW) then this gives an absorbed amount of power of 0.14dB or 0.9683mW

0.14 dB power loss means 0.968 mW is *transmitted* through the fiber (with 1 mW initial power)- only 0.03 mW is absorbed. Then, instead of:

stevenjones3.1 said:
This would give a temperature change of
[itex] \Delta T = 1.064 \times 10^{-6} C[/itex]

I get a temperature change of 2.3*10^-5 mK (thermally isolating the fiber form the environment). In any case, the reason there is no time dependence is because you started with a time-independent equation: it was ΔT, not T(t).

Does this help?
 
  • #3
Oh thanks for the correction on the first part, that was a silly mistake.

The amount of energy absorbed by the fiber is instantaneous and continuous right. So if the system absorbs 0.03mW of the optical power, there should be a way to make an approximation an figure out the increase in temperature over a period of 12 hours, right?
 
  • #4
Sure: 0.03 mW * 12 hrs = 2.6 J. Now all you need is the specific heat of the fiber and anything in thermal contact with the fiber.
 
  • #5
Thanks!
 
  • #6
Except I think its 1.3J
 
  • #7
Andy Resnick said:
Sure: 0.03 mW * 12 hrs = 2.6 J. Now all you need is the specific heat of the fiber and anything in thermal contact with the fiber.

stevenjones3.1 said:
Except I think its 1.3J

Oopsy...
 

1. What is optical path length change due to absorption?

Optical path length change due to absorption is a phenomenon that occurs when light passes through a medium and some of the light's energy is absorbed by the material. This results in a change in the distance that the light travels through the medium, known as the optical path length.

2. How does absorption affect the optical path length?

Absorption can cause a decrease in the optical path length, as some of the light's energy is converted to heat and not transmitted through the material. However, in some cases, absorption can also lead to an increase in the optical path length due to the material's refractive index changing with the absorbed energy.

3. What factors affect the amount of optical path length change due to absorption?

The amount of optical path length change due to absorption depends on the properties of the material, such as its thickness and refractive index, as well as the wavelength of the light being used. Additionally, the concentration of light-absorbing molecules in the material and the path length of the light through the material can also impact the amount of absorption and therefore the change in optical path length.

4. How is optical path length change due to absorption measured?

There are various techniques for measuring optical path length change due to absorption, such as interferometry or spectroscopy. These methods involve directing a beam of light through the material and comparing the phase or intensity of the light before and after it passes through the material to determine the change in optical path length.

5. What are some applications of studying optical path length change due to absorption?

Studying optical path length change due to absorption can provide insights into the properties of materials, such as their absorption coefficients and refractive indices. This information is useful in fields such as materials science, biomedical imaging, and environmental monitoring. Additionally, understanding optical path length change due to absorption is crucial for developing and optimizing optical devices and technologies.

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