Chapter 13: Optical Amplifiers
Source: Hunsperger, sixth edition (2009), Problems 13.1–13.8, printed pages 273–274.
Problem 13.1 — Three semiconductor amplifier architectures
Working. A traveling-wave amplifier suppresses facet reflections so the signal is amplified predominantly in one transit. A Fabry–Perot amplifier retains reflecting facets and reinforces resonant signals through repeated passes, while remaining below threshold. An injection-locked amplifier is a laser biased above threshold whose oscillation locks to a suitably matched injected optical signal.
Answer. Traveling-wave, Fabry–Perot, and injection-locked amplifiers. They differ in feedback strength and whether the unseeded device oscillates.
Check. All obtain added optical energy from the electrical supply. An above-threshold injection-locked device is not described by the same unsaturated linear formula as a below-threshold amplifier.
Problem 13.2 — Select EDFA pump wavelengths
Working. Pumping must overlap an erbium absorption band that feeds the metastable upper laser manifold. The useful 980 nm band has finite width, so 982 nm can also excite it; the 1480 nm band directly pumps the upper laser manifold.
Answer. 980 nm, 982 nm, and 1480 nm are the intended useful choices. The listed 855 and 1350 nm values are not the conventional ground-state pump bands for the illustrated silica EDFA.
Check. Pump absorption depends on host, temperature, and the actual absorption spectrum. A transition band is not a delta function, so rejecting 982 nm merely because it differs from 980 nm is incorrect.
Problem 13.3 — Signal gain with ASE separated
Working. Amplified spontaneous emission is added noise, not amplified signal. Using 900 mW signal output and 1 mW signal input,
Answer. Signal gain is approximately 29.54 dB.
Check. Adding the 50 mW ASE would give total output power 950 mW but would overstate useful signal gain. If “stimulated power” denotes only newly generated power, including the transmitted 1 mW changes the result slightly to \(10\log_{10}(901)\).
Problem 13.4 — Third-harmonic modelocking
Working. A linear two-mirror cavity of length 2 m has \(T_{\rm rt}=2n_gL/c\). With negligible dispersion, \(n_g\simeq1.75\), so
Answer. Approximately 128.5 MHz.
Check. A ring cavity would have a different round-trip length. The optical carrier wavelength does not set the repetition rate once optical path length is specified.
Problem 13.5 — Amplifier wavelength ranges
Working. Gain bandwidth depends on the active transition or Raman shift, not just the presence of a waveguide.
Amplifier |
Interpretation |
|---|---|
SOA |
Different semiconductor compositions span roughly 0.8–1.6 micrometres; one device covers only its material gain band. |
EDFA |
Roughly 1.52–1.60 micrometres across C/L-band implementations; strongest conventional gain is near 1.55 micrometres. |
Raman |
Pump-selectable Stokes gain, with silica’s main peak near \(\nu_s=\nu_p-13.2\,{\rm THz}\). |
TDFA |
The book discusses S-band systems around 1.48–1.52 micrometres and a pumping scheme with a broader 1.43–1.50 micrometre response. |
Answer. Give a range together with host, pumping scheme, and device family; Raman amplification has no single universal absolute band.
Check. Stokes Raman gain is at lower frequency and longer wavelength than the pump. A 1500 nm pump cannot generate a 1480 nm Stokes signal; that numerical passage in the chapter is inconsistent.
Problem 13.6 — Check the proposed Fabry–Perot amplifier first
Working. The net single-pass power gain is
For equal facet reflectivity 0.33, the round-trip power factor is \(R^2G_s^2\), and \(RG_s=1.38588>1\).
Answer. (a) The specified unsaturated device is already above lasing threshold. There is no stable small-signal Fabry–Perot amplifier gain at that operating point without saturation or a changed bias. (b) With negligible facet reflection and the assumed same material gain, the traveling-wave gain is 4.19965, or about 6.23 dB.
Check. Algebraically evaluating \((1-R)^2G_s/(1-RG_s)^2\) above threshold produces a number outside the formula’s physical domain. Carrier density may also change when feedback is removed at fixed injection current.
Problem 13.7 — Stimulated photon generation rate
Working. Divide stimulated optical power by one photon’s energy:
Answer. Approximately \(6.57\times10^{18}\) photons/s.
Check. Use watts rather than milliwatts. This is a generation rate, not the stored number of photons in the amplifier.
Problem 13.8 — A second above-threshold amplifier specification
Working. With \(G_s=15\) and \(R=0.65\), the round-trip power multiplier is
Answer. The unsaturated specification is far above threshold, so it does not define a stable linear Fabry–Perot amplifier. Stable operation would require \(G_s<1/R=1.53846\).
Check. The squared denominator in the formal resonant-gain expression does not make the above-threshold solution physical. Gain clamping or injection-locking would require additional information.