Gain bandwidth (gain spectrum)
The range of wavelengths or frequencies over which a gain medium or optical amplifier provides gain, usually quoted as the full width at half maximum of its gain spectrum or, for an amplifier, the 3 dB width of its gain. A C-band erbium-doped fiber amplifier covers about 35 nm (4.4 THz); Nd:YAG about 0.45 nm (120 GHz).
The gain bandwidth of a laser medium or optical amplifier is the width of its gain spectrum, the range of optical frequencies that it amplifies. It is usually quoted as the full width at half maximum of the gain coefficient or, for an amplifier, as the 3 dB width of its gain in decibels, and it may be given in nanometers or in hertz. It sets how far a laser can be tuned, how many WDM channels an amplifier can carry and the shortest pulse a mode-locked laser can produce. Values span five orders of magnitude:
| Gain medium | Gain bandwidth | In frequency |
|---|---|---|
| He-Ne, 633 nm | Doppler width | 1.5 GHz |
| Nd:YAG, 1064 nm | 0.45 nm | 120 GHz |
| Er fiber, C-band | 1530–1565 nm | 4.4 THz |
| SOA, 1550 nm | 50–80 nm (3 dB) | 6.2–10 THz |
| Yb fiber | about 1030–1100 nm | 19 THz |
| Ti:sapphire | 650–1100 nm | 189 THz |
The Ti:sapphire and ytterbium figures are tuning ranges; their FWHM gain widths are narrower. The conversion between wavelength and frequency widths is , so 35 nm at 1547.5 nm is 4.4 THz.
Origin of the gain spectrum
The gain spectrum is the lineshape of the laser transition, weighted by the population inversion. In a gain medium with homogeneous broadening, every atom or ion has the same line, and the gain saturates uniformly across the spectrum; Nd:YAG at room temperature, broadened by lattice phonons, is the standard example. In an inhomogeneously broadened medium, such as the Doppler-broadened neon of a helium-neon laser, different groups of emitters see different center frequencies, and a strong signal saturates only its own part of the spectrum, which shows up as spectral hole burning. Erbium in glass lies in between: its line is mostly homogeneous at room temperature, and a strong channel burns only a shallow hole a few tenths of a decibel deep.
In a semiconductor the material gain exists between the bandgap energy and the separation of the quasi-Fermi levels. Raising the carrier density widens the gain band and moves its peak to shorter wavelengths; raising the temperature shrinks the bandgap and moves the peak to longer wavelengths, by about 0.4–0.5 nm/K in InP-based lasers near 1310 nm. Quantum-well gain spectra are typically tens of nanometers wide, and telecom semiconductor optical amplifiers reach 3 dB bandwidths of 50–80 nm.
Measurement
An amplifier's gain spectrum is measured with a tunable laser or a broadband source and an optical spectrum analyzer, taking the ratio of output to input signal and subtracting the amplified spontaneous emission. In a semiconductor laser below threshold, the fringe contrast of the amplified spontaneous emission gives the net optical gain at each Fabry-Perot mode (the Hakki-Paoli method), from which the gain spectrum and its width follow.
Bandwidth and pulse duration
A pulse of duration (FWHM) has a spectral width of at least
with for a Gaussian and 0.315 for a sech² pulse, the time-bandwidth product of a transform-limited pulse. A mode-locked laser can produce pulses no shorter than its gain bandwidth supports. A bandwidth of 100 nm centered at 800 nm is
which supports a Gaussian pulse of 9.4 fs or a sech² pulse of 6.7 fs. The 120 GHz of Nd:YAG supports about 3.7 ps, and the 4.4 THz of erbium about 100 fs. Dispersion, gain narrowing and the finite bandwidth of mirrors lengthen the shortest pulse further; a Ti:sapphire laser reaches few-femtosecond pulses only with careful dispersion control.
Gain bandwidth of amplifiers for WDM
For an erbium-doped fiber amplifier, the useful gain bandwidth is where the gain is flat enough to carry channels with similar power, typically the 35 nm of the C-band. Gain-flattening filters trade some gain for flatness across the band. L-band amplifiers with longer erbium fiber extend the range to about 1625 nm.
Gain-bandwidth product of electronic amplifiers
The same words also name a different quantity. In an avalanche photodiode or an operational amplifier, the gain-bandwidth product (GBW) is the product of the low-frequency gain and the 3 dB electrical bandwidth, which stays roughly constant when the gain is changed. An avalanche photodiode with a gain-bandwidth product of 200 GHz is limited to about 10 GHz at a multiplication factor of 20, because the avalanche takes longer to build up at high gain. The op-amp GBW sets the bandwidth of a transimpedance amplifier. Neither has anything to do with the optical gain spectrum.
Common questions
What is the gain bandwidth of an EDFA?
About 35 nm, 1530–1565 nm, for a C-band amplifier, equal to 4.4 THz; L-band designs cover roughly 1565–1625 nm.
Is gain bandwidth the same as gain-bandwidth product?
No. Gain bandwidth is the optical spectral width of a gain medium; gain-bandwidth product is an electrical figure of merit of an amplifier or APD.
References: A. E. Siegman, Lasers (University Science Books, 1986); O. Svelto, Principles of Lasers, 5th ed. (Springer, 2010); E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, 1994); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012).