  Nonlinear optical methods are becoming ubiquitous in many areas of modern
photonics. They are, however, often limited to a certain range of input
parameters, such as pulse energy and average power, since restrictions arise
from, for example, parasitic nonlinear effects, damage problems and geometrical
considerations. Here, we show that many nonlinear optics phenomena in gaseous
media are scale-invariant if spatial coordinates, gas density and laser pulse
energy are scaled appropriately. We develop a general scaling model for
(3+1)-dimensional wave equations, demonstrating the invariant scaling of
nonlinear pulse propagation in gases. Our model is numerically applied to
high-order harmonic generation and filamentation as well as experimentally
verified using the example of pulse post-compression via filamentation. Our
results provide a simple recipe for up-or downscaling of nonlinear processes in
gases with numerous applications in many areas of science.
