This leaves only two design parameters whose optimum values were investigated in a 2005 study using Gaussian-shaped pulses and a Gaussian transfer function for the filter. The performance of an SPM-based regenerator depends on three parameters: the maximum nonlinear phase shift φ NL ≡ γP 0L eff, the filter-passband offset ω f, and the filter bandwidth δω, which must be large enough to accommodate the entire signal so that the width of optical pulses remains intact. Where F is the Fourier-transform operator and H f(ω-ω f) is the transfer function of a filter offset from the carrier frequency of pulses by ω f. As an optical filter acts in the spectral domain, the optical field after the filter can be written as Where L eff = (1 - e -αL)/α is the effective length for a fiber of length L with the loss parameter α, P 0 is the peak power of pulses, and U(0, t) represents bit pattern of the input bitstream. To understand the operation of SPM-based regenerators, one may employ the analysis given in the basic concepts of optical receivers tutorial. If we neglect the dispersive effects within the highly nonlinear fiber, only the phase of the optical field is affected by SPM within the fiber such that
![3r regenerator optisystem 3r regenerator optisystem](http://cdn.optiwave.com/wp-content/uploads/2013/07/25085521/Optical-System-Fiber-%2B-EDFA-span.jpg)
The noise level of 1 bits is also reduced because a small change in the peak power does not affect the pulse spectrum significantly, resulting in a much cleaner output bitstream. In practice, this offset is chosen such that pulses representing 1 bits pass through the filter without much distortion. If the passband of the optical filter is offset enough from the peak of the input spectrum, this noise would be blocked by the filter. However, it is easy to see why this scheme would remove noise from the 0 bits. It may appear surprising at first sight that spectral filtering of a bitstream whose phase has been modified nonlinearly improves the signal in the time domain.
![3r regenerator optisystem 3r regenerator optisystem](https://optiwave.com/wp-content/uploads/2017/05/Transmitters-library-768x501.jpg)
It is subsequently passed through a bandpass filter (BPF), whose center wavelength is chosen judiciously, resulting in an output bitstream with much-reduced noise and much-improved pulse characteristics.
![3r regenerator optisystem 3r regenerator optisystem](https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-981-10-7293-2_28/MediaObjects/454211_1_En_28_Fig3_HTML.gif)
The distorted noisy signal is first amplified by an EDFA before it propagates through a highly nonlinear fiber, where its spectrum broadens considerably because of SPM-induced frequency chirp. The following figure shows the underlying idea behind this scheme. An SPM-based 2R regenerator, proposed in 1998 for regenerating RZ signals, has been studied extensively in recent years. Fiber-Based 2R RegeneratorsĪll three major nonlinear effects, SPM, XPM, and FWM, can be employed for optical regeneration.
![3r regenerator optisystem 3r regenerator optisystem](https://optiwave.com/wp-content/uploads/2017/05/Transmitters-library-600x391.jpg)
However, the use of SOAs is also being pursued in view of their low-power requirements. As nonlinear effects in optical fibers respond at femtosecond time scales, highly nonlinear fibers are often employed for such devices. Since 2R and 3R regenerators have to work at time scales shorter than the bit slot in order to carry out pulse reshaping and retiming, they must operate at time scales of 10 ps or less, depending on the bit rate of the optical signal. Devices that perform the first two functions are called 2R regenerators. With this terminology, optical amplifiers can be classified as 1R regenerators because they only reamplify the bitstream. Such devices are referred to as 3R regenerators to emphasize that they perform all three functions. An ideal optical regenerator transforms the degraded bitstream into its original form by performing three functions: reamplification, reshaping, and retiming. An important application of optical signal processing is for regenerating optical signals degraded during transmission through fibers and amplifiers.