Gain-flattening filter (gain equalization)
A passive optical filter whose loss spectrum is the inverse of an optical amplifier's gain spectrum, so that all WDM channels leave with equal gain. In an erbium amplifier it removes several dB of excess gain near the 1530 nm peak and leaves a ripple below about 1 dB across the C-band.
A gain-flattening filter (GFF), also called a gain-equalizing filter, is a fixed filter placed inside an optical amplifier so that the amplifier's overall gain is the same at every wavelength in its band. An erbium-doped fiber amplifier has a gain spectrum with a strong peak near 1530 nm and a broader, lower region from about 1540 nm to 1560 nm, so without correction the channels near the peak gain several dB more than the others. The filter's insertion loss is designed as the mirror image of that excess: high where the gain is high, near zero where it is lowest. With it, the gain ripple of a C-band amplifier is typically below 1 dB peak to peak, at the cost of a few dB of output power. The broader context of amplifier types and their specifications is under optical amplifier.
Filter shape
In decibels, the required filter transmission is the target flat gain minus the unfiltered gain,
Suppose an amplifier stage measured without the filter gives 26 dB at 1532 nm and at least 20 dB everywhere else in the band. A 20 dB flat target then needs a filter with 6 dB of loss at 1532 nm, a little loss across the shoulders, and almost none at the gain minimum. The flat gain equals the lowest point of the raw curve, so flattening always costs the difference between the peak and the minimum in output power at the peak wavelengths, which the amplifier must make up with pump power.
The quality of a filter is stated as its error function, the residual difference between its actual and its target loss spectrum, typically a few tenths of a dB. In a long link the residual errors add: if the same 0.5 dB error appears at one wavelength in each of 20 amplifiers, that channel ends up 10 dB off; uncorrelated errors would add only to about 2.2 dB (0.5 dB × √20). Systematic errors are the ones that matter, and long-haul systems correct them every several spans with an adjustable equalizer.
Implementations
Thin-film filters. A multilayer dielectric stack, designed with many layers to synthesize an arbitrary smooth loss curve, and packaged between fiber collimators like a thin-film filter for WDM. These are compact, temperature-stable and the most common form.
Long-period fiber gratings. A grating with a period of hundreds of micrometers couples the core mode into forward-propagating cladding modes, which are then lost, at wavelengths satisfying
An effective-index difference of 0.0031 and a 500 µm period put the resonance at 1550 nm. Each resonance is a broad loss dip tens of nanometers wide, and cascading several gratings builds the inverse-gain shape in the fiber itself, with very low back-reflection.
Dynamic gain equalizers. A spatially dispersed channel array with a liquid-crystal or MEMS attenuator per wavelength slice, closely related to the wavelength-selective switch in a ROADM, applies an adjustable loss spectrum and corrects accumulated ripple in service.
Placement and noise figure
The filter usually sits between the two stages of a two-stage amplifier. Loss placed before the first stage adds directly to the noise figure; loss placed after it is divided by the first stage's gain. For a 4 dB first stage with 20 dB gain, a 5 dB filter and a 5 dB second stage, the cascade formula gives
a total of 4.15 dB, against 4.04 dB with no filter. The same 5 dB filter at the input would raise the noise figure to 9.0 dB.
Tilt and inversion
The shape of an erbium gain spectrum depends on the average population inversion along the fiber, which is set by the operating gain. A filter is the exact inverse of the gain shape at one design gain only. When the amplifier runs at a higher gain, the short-wavelength side gains more and the spectrum tilts toward the blue; at a lower gain it tilts toward the red. Amplifiers therefore hold the erbium stages at the design gain with automatic gain control and use an internal variable optical attenuator to absorb differences in span loss, or they add a separate adjustable tilt control. Stimulated Raman scattering between channels adds its own tilt, transferring power from short to long wavelengths, which a dynamic equalizer can also correct.
Common questions
Why does an EDFA need a gain-flattening filter?
In a WDM link the channels pass through many amplifiers in cascade, and any gain difference compounds. Without flattening, channels at the gain peak would grow and the others shrink until the weakest fell below the receiver's OSNR limit, and the strongest drove the fiber into nonlinearity.
Is gain flattening the same as gain equalization?
The terms are used interchangeably for the fixed filter. "Dynamic gain equalization" refers to the adjustable, per-wavelength devices used to correct accumulated ripple and tilt.
References: E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, 1994); P. C. Becker, N. A. Olsson and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic Press, 1999); A. M. Vengsarkar et al., "Long-period fiber gratings as band-rejection filters," Journal of Lightwave Technology 14, 58 (1996).