Importance of optical period in coherent radiation

[TheCanadian]

I am reading a text on coherent radiation and not quite understanding a particular statement. To provide some background, the authors state that coherent radiation can arise from light-matter interactions even when considering lengths, $L$, much smaller than the wavelength (i.e. $V \sim L^3 << \lambda^3$) due to phase coherence in the medium if it satisfies certain conditions (e.g. initial population inversion, dephasing effects are negligible on the time-scale, $T_P$, of the coherent bursts of radiation). Now the author states the following about the regime where $T_P < \frac{\lambda}{c}$:

"This regime is not physical: in order to observe it, one would have to realize the inversion of the medium in a time shorter than the optical period."

It may be quite obvious what the author is saying, but why exactly cannot the burst occur on a timescale quicker than the optical period? If an ensemble of atoms, with $L < \lambda$ can coherently radiate, why can't atoms radiate on timescales of less than $\frac {\lambda}{c}$? As long as they are sufficiently close and the interactions causal (i.e. $T_P > \frac{L}{c}$), why can't coherent radiation occur? Perhaps at such high densities, dipole-dipole interactions may disrupt the process, but I don't quite understand the significance of $T_P$ being larger than the optical period. Any thoughts?

 

[eljose79]

Thank you for your question regarding coherent radiation and the statement made by the authors in the text you are reading. I can understand your confusion and will try my best to provide a clear explanation.

Firstly, let's define what we mean by the optical period. The optical period is the time it takes for a light wave to complete one full cycle, which is equal to the wavelength divided by the speed of light, $\frac{\lambda}{c}$. This is a fundamental property of light and is determined by the frequency of the light wave.

Now, let's consider the regime where $T_P < \frac{\lambda}{c}$. This means that the time scale of the coherent bursts of radiation, $T_P$, is shorter than the optical period. In other words, the burst of coherent radiation is occurring at a faster rate than the natural frequency of the light wave. This is not physically possible as it would require the atoms in the medium to undergo population inversion and emit radiation at a rate faster than the natural frequency of the light wave. This violates the laws of physics and is therefore not a physically realizable scenario.

To further understand this, let's consider the example of a pendulum. The natural frequency of a pendulum is determined by its length and mass. If we try to make the pendulum swing at a faster rate than its natural frequency, it will not be able to do so and will eventually stop. Similarly, in the case of coherent radiation, if we try to make the atoms emit radiation at a faster rate than the natural frequency of the light wave, it will not be able to do so and the process will eventually stop.

In summary, the statement made by the authors is highlighting the fact that the regime where $T_P < \frac{\lambda}{c}$ is not physically possible and cannot be observed in reality. It is important to note that this is not a limitation of coherent radiation itself, but rather a limitation of how fast atoms can emit radiation.

I hope this explanation helps to clarify the significance of $T_P$ being larger than the optical period. If you have any further questions, please do not hesitate to ask.