Thermal Blooming

A high powered laser going through the air will cause the air to heat up. If the laser beam lasts longer than a small fraction of a second, the hot air will expand and become less dense. Less dense air has a lower index of refraction, so the density gradient across the beam acts like a lens, which in this case makes the beam expand. This expansion is called thermal blooming. The phenomenon is non-linear - if you try to compensate for not enough intensity on target by increasing the beam power without also making the beam wider to compensate, you can just end up heating the air more and actually reducing the beam intensity.

If there is wind, or if you are moving quickly through the air (like if you are flying an airplane), or your target is (like if you are shooting at missiles or artillery shells), you are continually getting fresh air into your beam. This makes the air that has been in your beam for longer hotter than the newer air, forming a lens which bends your beam in addition to expanding it.

Adaptive optics methods can help to solve this, but would-be laser engineers need to be careful because a straightforward implementation just ends up making the problem worse (to counteract the expansion, you focus the beam more which heats up the air more which makes your beam diverge even more). Alternatively, you can use high power laser pulses that are so short that the air does not have time to expand.

Does your beam need to worry about thermal blooming? For relatively long duration beams moving relative to the air you can compute the thermal distortion factor, $N$, to find out (Warning! Math ahead!)

${\begin{array}{lll}N_{c}&=&{\dfrac {16{\sqrt {2}}}{\pi }}{\dfrac {\beta \,P\,R^{2}}{R_{a}\,v\,D^{3}}}\\N_{E}&=&R/R_{0}\\f&=&\left\{{\begin{array}{ll}1&{\mbox{if }}N_{E}=0\\{\dfrac {2}{N_{E}^{2}}}\,\left(N_{E}-1+\exp[-N_{E}]\right)&{\mbox{otherwise}}\end{array}}\right.\\N_{E}&=&{\dfrac {\pi }{4}}\,n\,{\dfrac {D}{S}}\\q&=&\left\{{\begin{array}{ll}1&{\mbox{if }}N_{F}=1\\{\dfrac {2\,N_{F}^{2}}{N_{F}-1}}\,\left(1-{\dfrac {\ln[N_{F}]}{N_{F}-1}}\right)&{\mbox{otherwise}}\end{array}}\right.\\N_{V}&=&v_{T}/v\\s&=&\left\{{\begin{array}{ll}1&{\mbox{if }}N_{V}=1\\{\dfrac {2}{(N_{V}-1)^{2}}}\,\left(N_{V}\ln[N_{V}]-(N_{V}-1)\right)&{\mbox{otherwise}}\end{array}}\right.\\N&=&N_{c}\,f\,q\,s\end{array}}$

where $S$ is the beam spot size diameter at the target, $D$ is the beam diameter at the aperture, and $R$ is the range to the target. $P$ is the beam power. The relative wind speed to the beam is $v$ at the aperture and $v_{T}$ at the target. $R_{a}$ is the characteristic absorption length of the wavelength of light you are using for the given atmospheric conditions, and $R_{0}$ is the net attenuation length including both absorption and scattering. Remember that $R_{a}$ is the absorption length, not the total attenuation length, so primarily scattering phenomena like clouds or fog or mist won’t change it much.

The parameter $\beta$ is the atmospheric thermal coefficient

$\beta ={\frac {(-dn/dT)}{\rho \,C_{P}}}$

where $n$ is the refractive index of the air, $dn/dT$ is the rate of change of the refractive index with increasing temperature, $\rho$ is the air’s mass density, $C_{P}$ is the specific heat capacity of the air at constant pressure, and $\beta$ in sea level air on earth under typical conditions at visible and near visible wavelengths is around $\beta =8.3\times 10^{-10}{\mbox{m}}^{3}/{\mbox{J}}$.