Speckle and Modal Noise in Optical Fibres Theory and Experiment

Abstract

Modal noise has been observed in optical fibres excited by partially coherent sources . In this paper the theory of this noise is presented . Following the basic guidelines of the speckle theory, the statistical properties of the fluctuations of the power transmitted through a circular aperture of arbitrary size are evaluated . It is found that, for fibres having an a-exponent index-profile, the maximum attainable signal-to-noise ratio, when the receiving aperture area is equal to the core area, is given by the square root of the number of the guided modes . The hypotheses on which the theory is based are discussed and an experiment, confirming the theoretical results, is presented .

Modal noise prediction in fibre spectroscopy - I. Visibility and the coherent model

“…According to Daino et al (1980), the number of excited modes is equal to the number of speckles that can be counted when observing the fibre under monochromatic light. A standard He–Ne laser instead of the white light source.…”

“…The SNR derives from theoretical considerations as follows. According to Goodman & Rawson (1981) the SNR can be calculated from speckle statistics and geometrical considerations, given the number of speckles (which is equal to the number of excited modes M , see Daino et al 1980) and the area fraction ρ 2 of the illuminated fibre end face that is transmitted to the detector surface (see Fig. 1): Note that the truncation described by ρ 2 is not necessarily generated by a slit at, for example, the spectrograph entrance, but also by overfilling the grating or any other spatially filtering process (e.g.…”

Statistical properties of modal noise in fiber–laser systems

“…At this point it is worthwhile to note that it is usually possible to write (4) the matching of the two fields at z = L, V(')(r, z = L, t) = II)(r, z = L, t) yields, taking advantage of the orthogonality condition of the guided modes (among themselves and with the radiation modes),…”

Self-phase modulation and modal noise in optical fibers

“…(4) can be as sumed to be zero, and, one takes advantage of the relation The set of Eqs. (9) shows that the phase of each mode con tains nonlinear contributions proportional to the powers carried by the various modes and that will exhibit, as a con sequence, temporal variations strictly connected to the ones undergone by the modal powers. Thus, if the amplitude of the input signal fluctuates, each mode field acquires, besides an obvious amplitude modulation, a phase modulation that adds to that induced by the frequency fluctuations of the source.…”