I am not sure what you mean.  If you have a physical system with two or more modulations with incommensurate wavevectors in your system, k1and k2then you will in principle see scattering at all wavevectors n1k1+n2k2, n1, n2 integers.  This can result from two distinct physical processes: multiple scattering of the probing radiation or interactions between the various "waves" or modulations in your sample.  Multiple scattering is rather common for electrons, rather uncommon for most other scattering but can still matter, and, well, look up multiple scattering. 

The other possible source for these terms is interactions between modulations.  If you have an interaction between n1 modulations with wavevector k1 and n2 modulations with wavevector k2 then the resultant modulation will have wavevector n1 k1+n2 k2 (and the obvious generalizations.)  And, of course, these "induced" modulations can themselves interact with other modulations to result in yet more modulations, but only changing the integers in the formula k= n1 k1 + n2 k2 .  Generally, if you choose your initial wavevectors well, e.g. so that they are the ones with the largest scattering or (better) the most physics, then the amount of modulation will decrease with increasing |n1|+|n2|.  There are two reasons for this:

1) many systems are close to linear, and for large n1, n2, you need many non-linear or a few high order (power) non-linear interactions

2) it is common that if there is a sharp modulation peak at k1, then there is some finite width modulation near k1.  This modulation with finite width will also have interactions, resulting in increasingly wide modulation near n1 k1 +n2 k2 for large |n1|+|n2|.  And, this increasingly wide modulation makes it harder and harder for there to be sharp peaks.  I know that this is vague, but without a specific example, it sort of has to be.  Look up e.g. the Debye Waller factor in X-ray scattering from solids, for an example.

Dear Prof. Petschek,

Thanks for you answer. I have observed up to five orders of satellite reflections in may system (under electron diffraction), and the intensities of these satellites are strong. Can I address that the modulation is very strong? And what is the main factor inducing such strong modulation (if it is)? This is my key concern.

 You provided that the high order satellites may comes from the multiple scattering or interactions of the modulations. But my system is one-dimension modulation with only one vector k, so the higher orders may not come from the n1k1+n2k2. In term of the multiple scattering, it may be, but why donot this multiple scattering appear in other composition that have the same structure-type?

Many thanks!

Heck, I don't know.  Tell me about your system.  The story really does not depend on the number of wavevectors (examples with one wavevector are known, as are examples with 6 - e.g. icosahedra quasicrystals.)  If there is one wavevector k and you see strong satellites at 2k, 3k, 4k, and 5k and are convinced this is not multiple scattering (I can not be sure from what you say, but it would be my expectation you are correct in thinking that), then there are, ultimately, a number of possibilities.  Hmm.

First, the underlying modulation must be very "sharp" with rather small scattering near it.  I suspect that you know or can test this easily, you are doing scattering as a function of wavevector, yes?  Other than this the possibilities are:

a) The modulation of the fundamental is very big, so that a "natural" non-linearity makes for large satellites.

b) The system is very "soft" (has a high susceptibility) at the wavectors of the satellites, so that even small non-linearities of the system result in large satellites.

c) The system is very non-linear so that even rather small modulations result in rather large satellites.

d) combinations of the above.

What is happening in your system, I don't know.  It might be possible to be more definitive if there were more details.

Oh, looking at the pattern of the satellites can also be interesting.  In some systems, only satellites with odd indices (k, 3k, 5k) are "allowed" and ones with "even" indices (2k, 4k, 6k) are allowed, and there can be more complicated patterns.  This is usually for reasons of symmetry.  Cann't tell from what you provide, but that would be interesting information. 

In some ways, what you are saying need not be surprising.  An ordinary crystal will typically have a few 10's or 100's of scattering peaks in X-ray scattering, with reasonably large n, particularly at low temperatures where fluctuations are small.  It might be surprising in some contexts, however, I just don't know the context.

Dear Prof. Petschek, I have sent an email to you about the details. Thanks!