I am modulating an optical signal with carrier frequency (1 GHz to 20 GHz). At lower carrier frequency (1 GHz), the side-bands are separated by low distance. But the distance becomes higher when the carrier frequency increased (20 GHz). How can I explain this phenomena with Fourier transform?
To explain what is happening you should first describe the modulated waveform. Is it a pure sinusoidal modulation? Are you modulating the intensity of the envelope or the amplitude and phase of the optical field?
From a time-domain expression for the modulated field, calculate the integral Fourier transform, or use a discrete Fourier transform (FFT) and examine the spectral components present in the frequency-domain result.
For pure sinusoidal modulation of the optical field amplitude, we can use simple trigonometric identities rather than a complex Fourier transform.
Abramowitz & Stegun, Handbook of Mathematical Functions (1964), eq. 4.3.32, http://people.math.sfu.ca/~cbm/aands/page_72.htm
cos(x) cos(y) = { cos(x+y) + cos(x-y) } / 2
So a modulated field E = (A + a cos(wm t) ) cos(w0 t)
Becomes: E = A cos(w0t) + a/2 cos(w0 + wm)t + a/2 cos(w0 - wm)t
There are spectral components at the optical carrier frequency w0, and at modulation sidebands separated from the carrier by the modulation frequency wm.
Thank you very much Dr. Robinson.
My specific question is:
Why the side-bands are shifted gradually for incremental modulation frequency?
@Siam Uddin: "Why the side-bands are shifted gradually for incremental modulation frequency?"
Sideband separation in GHz is equal to modulation frequency in GHz. If the modulation frequency increases gradually, the sideband separation increases gradually by the same amount.
In terms of wavelength:
Separation = wavelength2 x modulation_frequency / velocity_light
At wavelength 1550 nm and 20 GHz modulation frequency, sideband separation is 0.16 nm. How does this compare with your simulations or measurements?
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