Can two interfering light waves create a wave with a different wavelength? I want to know if two light waves were to interfere in opposing directions, not from the same direction, would it be possible for the resulting wave’s wavelength to be different from the two waves put in?
 A: When you add two (plane/spherical/whatever) waves together in a vacuum, the resulting field configuration is not one new wave of the same type, unless the inputs were going in the same direction with the same wavelength. Otherwise, the field of two waves interfering just looks like two waves, different from any single wave, and with sufficiently good measurements you can decompose the field back to its parts.
I.e. the sum of two waves with different wavelengths is almost always just two waves with different wavelengths.
In certain materials, the charged particles of the material may respond specially certain wavelengths of radiation, or combinations of wavelengths. E.g. passing light at two different frequencies $f_1,f_2$ through certain crystals can convert some of the energy to waves at frequencies $f_1+f_2,f_1-f_2.$ This won't happen in vacuum or air. More generally, an optical system cannot produce output at a different frequency from its inputs without involving "nonlinear effects". Most media are linear to a good approximation, and nonlinear effects, when available, are often only achieved at high intensities.
A related phenomenon is beating, which happens with all kinds of waves in all media and is named for the effect of two slightly out-of-tune sounds being played together. This occurs when you have two waves at frequencies $f_1,f_2$ close together. The sum is equivalent to a wave at frequency $(f_1+f_2)/2$ whose amplitude oscillates at frequency $(f_1-f_2)/2.$ Detectors with high enough resolution will resolve the original frequencies $f_1,f_2.$ Detectors of low enough resolution will pick up the average frequency. I.e. the sum of two waves of different wavelengths can temporarily approximate a wave at an intermediate wavelength.
