Explaining linear spectroscopy from first principles

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    Linear Spectroscopy
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Discussion Overview

The discussion revolves around understanding linear spectroscopy from first principles, particularly in the context of absorption experiments. Participants explore the relationship between laser intensity and the population of excited states, while also touching on concepts like Rabi oscillations and the implications of saturation effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the relationship between laser frequency and transmitted intensity in absorption experiments, seeking a first-principles understanding.
  • Another participant questions the definition of a "typical" absorption experiment, asking whether it involves a single light beam or a more complex setup like saturated absorption spectroscopy.
  • A participant notes that in their experience, relative absorption remains constant with laser power unless saturation or carrier-carrier interactions are considered.
  • There is a discussion about whether the focus is on relative or absolute absorption, with one participant clarifying that they are interested in absolute absorbed intensity, which is proportional to excited state population.
  • One participant explains that in the linear regime, each absorption event can be considered statistically independent, leading to a linear relationship between absorption and intensity.
  • Another participant introduces the concept of the linear absorption coefficient and references Beer's law, noting that assumptions about thermal equilibrium and uniform absorption are necessary for its validity.
  • A new topic is introduced regarding pump-probe spectroscopy, with a request for guidance on calculating probe absorption when both beams address the same levels.

Areas of Agreement / Disagreement

Participants express varying perspectives on the nature of absorption experiments, particularly regarding the effects of laser intensity and the conditions under which linear absorption is valid. There is no consensus on the specifics of the absorption process or the implications of different experimental setups.

Contextual Notes

Limitations include assumptions about thermal equilibrium and the uniformity of the absorber, as well as the potential breakdown of Beer's law at high radiation intensities. The discussion does not resolve these complexities.

Who May Find This Useful

Readers interested in spectroscopy, particularly those exploring the fundamentals of absorption processes and the implications of laser intensity in experimental setups.

photon stew
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Hi! I'm a little confused about simple spectroscopy. In typical absorption experiments, we scan the laser frequency w and get a anti-peak/dip in the transmitted intensity I(w) around a resonance frequency. The size of the dip, i.e. the population of the excited level, usually depends linearly on the laser intensity. How can this be understood from first principles?

I know about Rabi oscillations in optically driven two level systems, but these are of course quite different. I have also studied more advanced descriptions -density matrices, master equations like the optical Bloch equations, etc.- but I'm still kind of stuck with this simple question.

Thanks in advance!
photon stew
 
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What is a "typical" absorption experiment from your point of view?

Are you just interested in the absorption of a single light beam or is it rather something like saturated absorption spectroscopy using pump-probe geometry?
 
Cthugha said:
Are you just interested in the absorption of a single light beam or is it rather something like saturated absorption spectroscopy using pump-probe geometry?
At first, I'm interested in the former.
 
In this case I am a bit puzzled. In all simple absorption experiments I ever did, the relative absorption (transmitted intensity divided by incoming intensity) is constant with laser power unless one exits the regime where saturation or carrier-carrier interaction needs to be taken into account.

Or are you interested in the absolute absorbed intensity (which is indeed proportional to the excited state population) varying linearly with the incoming intensity?
 
Cthugha said:
Or are you interested in the absolute absorbed intensity (which is indeed proportional to the excited state population) varying linearly with the incoming intensity?
Yes. This is the reason why this kind of spectroscopy is called linear, isn't it? Ultimately, I'm interested in nonlinear stuff but I realized that I don't understand linear spectroscopy very well, so I wanted to learn more about it first.
 
photon stew said:
Yes. This is the reason why this kind of spectroscopy is called linear, isn't it?

I was rather asking whether you are interested in relative or absolute absorption.

Never mind. The intensity is proportional to the photon number per time interval present in the beam. Each photon has some chance of being absorbed on or near resonance. In the linear regime you can consider each absorption process as statistically independent of each other and the amount of absolute absorbed photons is just the absorption probability times the number of photons present which is necessarily linear in intensity.

Is this the kind of explanation you seek or is it something deeper?
 
I believe it is linear under some basic assumptions, one of them being that the absorption process is random, so that the amount of absorption is proportional to the amount of incident radiation. The constant of proportionality should be the linear absorption coefficient, and you get some differential equation like dI = -k*I*dL, for intensity I, coefficient k and path length L. Integrating this gives you Beer's law which is valid for linear absorption, I/I0 = exp(-kL) for some uniform absorber of length L.

To get to this stage you need to assume the absorber is in thermal equilibrium, which means it has a Boltzmann state population and is surrounded by blackbody radiation of the same temperature. Once you start using very high radiation intensities, you alter the state population of the material, so the above assumption fails and Beer's law becomes inaccurate.

At least that's my understanding!
 
Pump probe spectroscopy in two level system

Hi,
Can someone tell me how to calculate the probe absorption when both pump and probe beams are addressing to same levels.
 

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