Undergrad About creating standing wave with laser

[KFC]

Hi all,
I remember the standing wave is introduced in a chapter of mechanical wave in my undergraduate physics times ago. It is said that two waves of the same frequency propagating the opposite directions will form a standing wave in space. I wonder if it is possible to produce the standing wave with laser (light) also. I read something about laser, takes 780nm single-mode laser as example, I wonder if the light is always in the form of sinusoidal wave or not. If should does it mean we only have to split the laser beam from the same source into two and use two mirrors to change the path of the light such that they moves in opposite direction to get the standing wave? If this's the idea, I have something confusing me. In my book, a mechanical wave has both wave vector and frequency. Assuming two waves forming the standing wave has the same frequency (f) but opposite wave vector, we will see a standing wave with amplitude is oscillating in the frequency f. In laser, what's that frequency and where does it come from?

This is confusing because I am reading a book introducing laser and it seems that the laser beam is pretty much just spatial sinusoidal wave. I didn't see the frequency discussed. If there is frequency for a laser beam, what's the typical value of it. It is any way to make that frequency low enough so we can see the optical standing wave with amplitude oscillating in visible way.

Thanks.

 

[DrClaude]

You can produce standing wave using superpositions of laser beams, which are called optical lattices. The result is a periodic oscillating potential for an atom, either because of a spatially varying amplitude or polarization. If you want to learn more, and have institutional access, I really recommend this review article: http://dx.doi.org/10.1016/S0370-1573(01)00017-5

As for the frequency of a laser, it is simply $\nu = c/\lambda$.

 

[KFC]

Thanks DrClaude. Let say the laser beam is of the form

$$y(x) = A\cos(kx + \omega t)$$

So by adding two counter-propagating waves, we have
$$
A\cos(kx + \omega t) + A\cos(-kx + \omega t) = 2\cos(\omega t)\cos(kx)
$$

If the laser frequency is $\omega=2\pi c/ \lambda$, it will have the order of $10^{14}$Hz, it so big. So if it is oscillating that fast, the $\cos(\omega t)$ will be averaged to zero so does it mean there is not observable standing wave?