The relation between the power delivered at the output of the detector to the power input to the laser is:
Where is the slope of the laser diode characteristic curve, is the responsivity of the photo-diode and is the loss in the fiber. The total loss is the combination of losses due to attenuation in the fiber, splices, bending of the fiber and couplers. Measurements show that the optical losses of the links vary between 0.3 to 8.7 dB for the various antenna stations.
In addition to this change in signal power level, the link also introduces noise. Noise is introduced by the laser diode, the photo- diode as well as all resistive elements in the signal path.
The laser diode introduces noise due to quantum fluctuations
even under conditions of constant bias current. This is called
Relative Intensity Noise (RIN) and is define as:
where are the fluctuations in the laser diode output power, and is the instantaneous laser diode output power. The laser diode noise is also often characterized by the Equivalent Input Noise (EIN) which is defined as where is the input current fluctuation that would correspond to the output power fluctuations . It can be shown that EIN , where is the input resistance.
The noise generated within the the photo detector is called shot noise. As the name suggests, it is due to the discrete nature of light and its interaction of photons with materials. Shot noise is present in the detector even in the absence of illumination and increases with illumination of the detector with light. All resistive elements contribute to thermal noise. The total noise power(N) is the sum of the laser, shot and thermal noise components. The Signal to Noise Ratio (SNR) of the link can be shown to be
where is the noise figure of the detector amplifier, is the temperature of the resistive elements, is the bandwidth of the link, is the dark current, is the average output power of the laser, and is the electron charge. The analog optical fiber communication system of the GMRT has been designed to ensure a minimum SNR of 20 dB .
In addition to this intrinsic additive noise, there are various other imperfections in the fiber optic link. Discontinuities in the refractive index near the connectors, couplers, bends in the fiber and impurities along the length of the fiber could cause part of the light to get reflected back into the laser. This leads to the formation of a resonant cavity between the discontinuity and the laser hence to ghosts. To overcome this problem, optical isolators and low reflection connectors are used. An optical isolator is a unidirectional device with highly reduced signal transmission in the reverse direction. Low reflection connectors are special devices with refractive index matching and focusing arrangements.
The other important characteristic of the optical link, apart from the SNR is the dynamic range, i.e. the range over which its response is linear. The dynamic range of the GMRT optical fiber link is dB were the input to be purely Gaussian random noise, and dB for quasi-sinosidal input.