# Absorption

**Absorption** is physical phenomenon reduction of power of wave during its propagation. Usually, absorption is property of the medium, where the wave propagates.

Also, **absorption** is physical quantity that determines the decrease of amplitude or intensity of the wave in the medium.

Term **absorption** may have many other meanings ^{[1]}.

At propagation of linear waves, absorption $A$ is inverse of the length, at which the intensity reduces with factor 1/e.

The interpretation of this quantity is especially simple, while absorption does not depend on the intensity of the wave, and product of absorption to wavelength is small compared to unity.

For more complicated cases, absorption is parameter that appears in the wave equation; this equation may depend on the kind of wave. Therefore, the exact meaning of this parameter also depends kind of wave. Value of absorption may depend on properties of medium, on wavelength, on the polarization of wave, on its intensity and on and many other parameters of the problem.

## Gain

Negative of absorption is gain or increment, $G=-A$. Positive increment (or negative absorption) may take place for electromagentic wave at the amplification in the gain medium. For optical range of electromagnetic waves, the medium with negative absorption is called laser medium. Negative absorption require the external source of energy, called pump.

## Loss

Absorption is related to loss

- $ \!\!\!\!\!\!\! (1) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~L=\ln(A \ell_0)$,

where $\ell_0$ is unit of length; usually, $\ell_0=1 \rm meter$.

From the loss, the absorption can be calculated as

- $ \!\!\!\!\!\!\! (2) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~A=\exp(L)/\ell_0$,

Historically, there is special unit for loss, called Decibel and abbreviated as dB.

- $ \!\!\!\!(3) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ \displaystyle 1 \mathrm{dB}= \frac{\ln(10)}{10} \approx 0.230258509$

In such a way, loss of one decibel means absorption, at which the intensity per unit of length (say, one meter) changes for one tenth of the order of magnitude.

One may divide the loss by one dB by (1) and say, that the result is loss, measured in decibel. Similarly, one multiply the loss, measured in decibel, by one decibel by (3), and obtain value of loss.

The engineers like to measure the loss in decibels. For some reasons, they do not recognize dB as mathematical constant and try to hide its value from physicists, mathematicians and users. Usually, many examples are suggested
^{[2]}^{[3]} instead of simple definition (3).

Loss, measured in dB, indicates, how many tens of times should the wave pass in order to reduce for one order of magnitude.

Absorption, as loss, can be used as characteristics of material.

As "absorption" term loss may have many other meanings
^{[4]}.