Since it has been asked in the comments a couple of times I'll give my answer about the opaque beam.
First off, I agree with The Photon's answer and other comments about that the modulated spectrum is the convolution of the original spectrum (monotone at the lasers optical frequency - this is the carrier tone) and the signal, that is the pulse train at much lower frequency.
21joanna12 then raises what I think be an interesting question which is how can we get NEW frequencies of light simply by modulating a laser beam? I think this question is motivated by the knowledge that it is typically difficult to shift the frequencies of light. We must send the light through some non-linear medium which typically involves high intensities, careful alignment, etc., yet this seems to be a way to change the frequency of light without needing a non-linear medium.
Here is an attempt to reconcile these two notions of frequency shifting of light. A non-linear medium is characterized by having a non-linear electric susceptibility. If the susceptibility is linear then you know that passing through the medium will not shift the frequency of light. That is why you need a non-linear susceptibility for non-linear optics.
There are other ways to think about the non-linearity however. One way to think about the non-linearity is that it means a pulse of light entering the medium alters the medium in a way that light coming in shortly after the first pulse will experience the medium differently. This shows that there is some time dependence of the response of the medium.
In other words, I am trying to draw an equivalence between a time varying response function of an optical medium and a non-linear susceptibility for the medium.
I'll summarize in the next section explaining how the frequency shifting properties of both a non-linear medium and an opaque modulated sheet can be viewed in both of these ways.
First, viewing both as a time varying response.
-In other answers/comments you have learned how modulating the signal gives rise to new frequencies because of the Fourier components of the new signal. This is how the time varying response of the opaque sheet gives you new frequencies.
-I have argued above that the non-linearity of a non-linear medium means the medium actually has a time-varying response. If you followed everything carefully you could see how the time-varying response of the medium is processing the incident light field and misshaping it from being a perfect sinusoid at one frequency to being a sinusoid at two more different optical frequencies. Clearly the material must be able to response very quickly to alter the light field on such short time scales, but electrons in materials can respond very quickly.
Second, viewing both as an optical non-linearity
-In the case of a non-linear medium there are many references explaining how a non-linear susceptibility function "mixes" two signal and gives you new signals at sum and difference frequencies. This is the usual explanation for optical non-linearities.
-How do we view the opaque sheet as a non-linear medium? Well, above I was trying to draw some kind of equivalence between a non-linear medium and a medium with a time-varying susceptibility. Consider the volume of air in the region where the opaque sheet is being modulated. Much of the time this volume of air has the response function of air, basically it doesn't change anything about the light field. But some of the time it has the response function of the opaque material. That is to say, the response function of this volume of space is modulated in time. We could certainly cast this is a time-varying susceptibility and it may be possible to derive some sort of non-linear frequency susceptibility for this sort of system.
In any case, the reason I've gone into such detail here is to try to illustrate that (perhaps with some extreme stretching of the formalism/imagination) it is actually the same thing going on when either a modulated opaque sheet or a non-linear medium changes the frequencies of a beam of light. That is, both processes can be analyzed in either the time or frequency domain. This may be a bit confusing but maybe it can shed light on both why a modulated sheet CAN add new frequencies to a light beam and also WHY a non-linear medium adds new frequencies to a beam of light.