ABSTRACT
The duality between the paraxial diffraction of beams in spatial domain and the dispersion of ultra-short pulses in time domain offer significant insights into pulse dynamics when propagating through single-mode optical fibers. A quadratic phase modulation in time (time lens) is the analog of a thin lens in space. Furthermore, an analogy between spatial and temporal imaging can be used to obtain the distortion-less expansion or compression of optical pulse sequences. Temporal imaging systems function toward focusing and defocusing the ultra-short pulses after propagating through a length of single-mode optical fiber. A quadratic phase modulator acts as a time lens via the quadratic phase modulation. Ultra-fast photonic signal processing in optical communication has emerged recently for long-haul optical transmission, and temporal imaging is expected to play a key role in the near future in this emerging technology. The significant application of temporal imaging is the adaptive equalization or, effectively, the refocusing of the broadened pulses by feeding them through an optical modulator that changes the phase of the carriers of the pulses to the opposite of the quadratic phase effects. This type of adaptive equalizer could eliminate any quadratic phase distortion, which normally can be compensated using passive devices such as dispersion-compensating fibers (DCFs), polarization-mode dispersion (PMD) compensator, and eliminators for timing jitter effects.
