Semiconductor optical amplifier (SOA)

A semiconductor optical amplifier (SOA) is a laser diode chip whose facets are anti-reflection coated, angled, or both, so that light entering one end is amplified by stimulated emission in a single pass and leaves the other end without the chip lasing. It is pumped by the same forward current that drives a laser, it is a millimeter-scale chip or a section of a photonic integrated circuit, and on InP the composition of its active layer places the gain anywhere from about 1.3 to 1.6 µm, including the O-band, where erbium provides none; GaAs-based devices, such as the tapered amplifiers of atomic physics, cover shorter wavelengths. Typical telecom devices give 15–30 dB of gain, a saturation output power of +8 to +13 dBm and a noise figure of 7–10 dB.

Among optical amplifiers, the usual comparison is with the erbium-doped fiber amplifier (EDFA). The SOA is noisier, its gain depends on polarization unless the active region is designed against it, and its gain recovers in a fraction of a nanosecond, fast enough to follow the data. That speed produces patterning and crosstalk between channels, and it is also what makes the SOA useful as an optical gate and as a wavelength converter. The number-by-number comparison with EDFA and Raman amplifiers, and the choice between the three, is in Optical Amplifiers Compared: SOA vs EDFA vs Raman.

Structure and facet reflectivity

The gain medium is a bulk double heterostructure or a stack of quantum wells of InGaAsP or InGaAlAs grown on InP, inside a ridge or buried waveguide that guides a single transverse mode. Injected current raises the carrier density until the separation of the quasi-Fermi levels exceeds the photon energy, the condition for population inversion in a semiconductor, and from there on a guided signal gains power as it travels. With modal gain $\mathrm{\Gamma }g$, internal loss ${\alpha }_{\text{int}}$ and length $L$, the single-pass chip gain is

$$G=\exp \text{\hspace{0.17em}⁣}[(\mathrm{\Gamma }g-{\alpha }_{\text{int}})L]\mathrm{.}$$

A cleaved facet reflects about 30% (the Fresnel reflectance $((n-1)\mathrm{/}(n+1){)}^2$ is 0.27 for $n=3.2$ and 0.31 for $n=3.5$), which is enough to make the same chip a Fabry-Perot laser. Whatever reflectivity remains, $R_1$ and $R_2$ at the two facets, forms a weak cavity, and the gain ripples with wavelength at the chip's longitudinal mode spacing, with a peak-to-valley ratio

$$\mathrm{\Delta }G={\left(\frac{1+G\sqrt{R_1{R}_2}}{1-G\sqrt{R_1{R}_2}}\right)}^2\mathrm{.}$$

The ripple stays below 3 dB while $G\sqrt{R_1{R}_2}<0.17$ and below 0.5 dB while $G\sqrt{R_1{R}_2}<0.029$; at $G\sqrt{R_1{R}_2}=1$ the chip reaches lasing threshold. The allowed reflectivity therefore falls in proportion to the gain:

Reflectivities of ${10}^{-4}$ and below across the whole gain band are hard to reach with a coating alone. Production devices combine a multilayer coating with a waveguide tilted away from the facet normal, so that the reflected light misses the guided mode, and often add a short unguided window region in front of the facet, in which the beam spreads before it is reflected. The coatings themselves are treated in Anti-Reflection Coating Design. A chip with deliberately partial reflectors, a Fabry-Perot amplifier, has higher gain at its cavity resonances but only within narrow bands; the traveling-wave SOA, with negligible feedback, is the standard device.

Gain and gain bandwidth

Gain appears once the current passes the transparency current and grows as the carrier density rises (the material gain goes roughly as the logarithm of the carrier density), until heating and Auger recombination flatten the rise. The chip gain in decibels is proportional to length, but in a long chip the amplified spontaneous emission grows strong enough to deplete the carriers near the facets, and this self-saturation limits the gain one section can deliver. Packaged devices are specified fiber to fiber: the chip gain less the input and output coupling losses, each 2–6 dB for fiber-to-chip coupling.

Gain exists for photon energies between the bandgap and the quasi-Fermi-level separation, $E_g<h\nu <\mathrm{\Delta }{E}_F$ (the Bernard-Duraffourg condition). A higher current raises $\mathrm{\Delta }{E}_F$, which widens the gain band and moves its peak to shorter wavelengths (band filling); a higher temperature narrows the bandgap, moves the gain to longer wavelengths and lowers it. The 3 dB gain bandwidth of telecom SOAs is typically 50–80 nm, which is 6.2–10.0 THz at 1550 nm and 8.7–14.0 THz at 1310 nm, against 4.4 THz for the 35 nm of a C-band EDFA.

Saturation output power and gain compression

At high signal power, stimulated emission removes carriers faster than the current replaces them, and the gain falls (gain saturation). The figure a datasheet quotes is the 3 dB saturation output power $P_{\text{sat,out}}$: the output power at which the gain has dropped to half its small-signal value $G_0$, 3 dB below it. For an amplifier that saturates homogeneously, with internal loss neglected, the gain obeys

$$G=G_0\exp \text{\hspace{0.17em}⁣}[-\frac{(G-1)P_{\text{in}}}{P_{\text{sat}}}],$$

where $P_{\text{sat}}$ is the saturation power of the medium. Setting $G=G_0\mathrm{/}2$ gives

$$P_{\text{sat,out}}=\frac{G_0\ln 2}{G_0-2}{P}_{\text{sat}},$$

which approaches $0.69P_{\text{sat}}$ at high gain, independent of $G_0$; the saturation power entry has the derivation. The same model fixes the other compression points. At high gain the output at $x$ dB of compression is $(x\ln 10\mathrm{/}10)P_{\text{sat}}$, so the 1 dB compression output is one third of $P_{\text{sat,out}}$, 4.8 dB below it. For $G_0=25$ dB and $P_{\text{sat,out}}=+10$ dBm, the gain is 24 dB at an output of +5.2 dBm (input $-18.8$ dBm) and 22 dB at +10.0 dBm (input $-12.0$ dBm).

The saturation power of the medium is

$$P_{\text{sat}}=\frac{h\nu {\sigma }_m}{a\tau },$$

where ${\sigma }_m=wd\mathrm{/}\mathrm{\Gamma }$ is the cross-section of the active region ($w$ wide, $d$ thick) divided by the confinement factor, roughly the area of the guided mode, $a=dg\mathrm{/}dN$ is the differential gain and $\tau$ the carrier lifetime. Designs for higher output power therefore use a low confinement factor, so that the mode is large compared with the active layer, flare the waveguide toward the output facet, or run at a higher current, which shortens $\tau$ and moves the operating point to where the differential gain is smaller. The same short lifetime sets the speed of the gain dynamics described below.

Noise figure

Every amplifier adds amplified spontaneous emission, and the noise figure measures how much the amplifier degrades the signal-to-noise ratio. For gain $G$ and population inversion factor $n_{\text{sp}}$,

$$F=2n_{\text{sp}}\frac{G-1}{G}+\frac{1}{G},$$

which tends to $2n_{\text{sp}}$ at high gain. Full inversion, $n_{\text{sp}}=1$, gives $F=2$: the 3 dB quantum limit of a phase-insensitive amplifier at high gain. Three effects keep an SOA above it.

Incomplete inversion. At photon energy $h\nu$ the inversion factor of a semiconductor is

$$n_{\text{sp}}=\frac{1}{1-\exp \text{\hspace{0.17em}⁣}[(h\nu -\mathrm{\Delta }{E}_F)\mathrm{/}{k}_{B}T]},$$

and it approaches 1 only when $\mathrm{\Delta }{E}_F$ exceeds the photon energy by several $k_{B}T$ (25.9 meV at 300 K). A margin of $k_{B}T$ gives $n_{\text{sp}}=1.58$ and a high-gain noise figure of 5.0 dB; $2k_{B}T$ gives 1.16 and 3.6 dB; $3k_{B}T$ gives 1.05 and 3.2 dB. The margin is smallest on the short-wavelength side of the gain band, so the noise figure rises toward shorter wavelengths, and it falls as a higher current raises $\mathrm{\Delta }{E}_F$.

Internal loss. Waveguide loss removes signal photons that the gain must then replace, so more spontaneous emission is generated for each unit of net gain, and the high-gain noise factor is multiplied by $\mathrm{\Gamma }g\mathrm{/}(\mathrm{\Gamma }g-{\alpha }_{\text{int}})$. An internal loss of one fifth of the modal gain adds 1.0 dB.

Input coupling loss. A loss ahead of the gain adds to the noise figure decibel for decibel, $\text{NF}=L_{\text{in}}+{\text{NF}}_{\text{chip}}$ in dB, by the Friis formula. A loss after the gain costs output power and almost no noise figure: less than 0.1 dB for output losses up to 6 dB behind 20 dB or more of chip gain. A chip with a noise figure of 5 dB behind 3 dB of input coupling loss therefore measures 8 dB from its input fiber, within the typical 7–10 dB. The OSNR and Noise Figure Calculator evaluates such cascades of losses and gains.

For a single amplifier at high gain, the output OSNR in a reference bandwidth $B_{\text{ref}}$ is $P_{\text{in}}-\text{NF}+C$ in decibels, with $P_{\text{in}}$ in dBm and $C=-10{\log }_{10}(h\nu B_{\text{ref}}\mathrm{/}1\text{ mW})$. For $B_{\text{ref}}=0.1$ nm, $C$ is 58.0 dB at 1550 nm and 55.8 dB at 1310 nm, where both the photon energy and the frequency width of 0.1 nm are larger. An O-band preamplifier with an 8 dB noise figure receiving $-20$ dBm therefore gives an OSNR of 27.8 dB.

Polarization dependence

The gain generally differs between the TE and TM modes of the waveguide (TE and TM polarization), and two effects favor TE. A wide, thin active region confines the TE mode, whose electric field lies in the plane of the layers, more strongly than the TM mode, so ${\mathrm{\Gamma }}_{\text{TE}}>{\mathrm{\Gamma }}_{\text{TM}}$. In unstrained or compressively strained quantum wells, the top of the valence band is the heavy-hole band, whose transitions couple to TE light only. The difference, the polarization-dependent gain (PDG), matters wherever the input polarization is uncontrolled: at the end of a standard single-mode fiber the polarization drifts, and PDG converts the drift into gain fluctuations.

Since the gain in decibels is proportional to the net modal gain, the PDG equals the fractional mismatch between the TE and TM net modal gains times the gain in decibels. A 4% mismatch on a chip with 25 dB of gain is 1.0 dB of PDG, and holding 0.5 dB at that gain needs the two to match within 2%. Designs reduce the mismatch in three ways:

• a bulk active region with a near-square cross-section, which makes the two confinement factors nearly equal;
• a small tensile strain in a bulk active layer, which raises the TM material gain enough to offset the lower TM confinement;
• quantum wells under tensile strain, alone or alternating with compressive wells, in which light-hole transitions supply gain that favors TM.

Typical PDG is 0.5–2 dB, against less than 0.5 dB for an EDFA. An SOA on a photonic integrated circuit normally carries only the TE mode of its waveguide, so it is built for TE gain alone, usually with compressively strained wells, which give more gain per unit current.

Gain dynamics, patterning and crosstalk

The gain follows the carrier density, and the carrier density returns to its steady value with an effective carrier lifetime of 0.1–1 ns. That is shorter than the spontaneous lifetime of the same material because stimulated emission, by the signal and by the ASE, also removes carriers, and it shortens further at higher current. The gain therefore follows changes in input power slower than about $1\mathrm{/}(2\pi \tau )$, which is 160 MHz for $\tau =1$ ns and 1.6 GHz for 100 ps, and averages faster ones. In an EDFA the upper-state lifetime is about 10 ms, and the pump and the signal shorten the effective lifetime to roughly 0.1–1 ms, which puts the same corner between about 160 Hz and 1.6 kHz, far below any data rate.

For an on-off keyed signal at 10 Gb/s a bit lasts 100 ps, and a run of ten identical bits lasts 1 ns, as long as the carrier lifetime or longer. A long run of ones compresses the gain, so the bits that follow see less of it; a run of zeros lets the gain recover, so the next ones see more. The result is a pattern-dependent amplitude that thickens the upper level of the eye diagram and grows with the output power relative to $P_{\text{sat,out}}$. What matters is the part of the signal's power spectrum below $1\mathrm{/}(2\pi \tau )$, which long runs of identical bits supply at any bit rate, so shorter bits (40 ps at 25 Gb/s) do not remove the effect.

Several channels share the gain, which responds to their total power, so the intensity pattern of each channel is imprinted, inverted, on the others (cross-gain modulation), and beating between channels drives four-wave mixing products. The fast gain dynamics make SOAs unsuitable as in-line amplifiers in WDM systems: gain saturation by one channel reduces the gain for the others within nanoseconds, causing crosstalk. Far below saturation a few channels are handled well. In 100GBASE-ER4 modules for 40 km, an SOA preamplifier ahead of the receiver amplifies the four LAN-WDM lanes near 1310 nm together (see pluggable optics).

The usual remedies are to run further below saturation; to clamp the gain with an integrated laser oscillating outside the signal band, which pins the carrier density at the cost of some gain; or to inject a continuous holding beam, which shortens the effective lifetime.

Wavelength conversion and other nonlinear uses

The effects that impair linear amplification are also the basis of all-optical signal processing in SOAs.

Cross-gain modulation. A data signal at ${\lambda }_1$ and a continuous probe at ${\lambda }_2$ enter together. The signal's ones compress the gain, so the probe leaves carrying an inverted copy of the data at the new wavelength. The scheme is simple and works for any probe wavelength within the gain band; the converted signal is chirped, its extinction ratio is limited by how far the input can compress the gain, and its speed by the gain recovery.

Cross-phase modulation. A change in carrier density changes the refractive index along with the gain, in a ratio set by the linewidth enhancement factor $\alpha$: the phase shift is $\mathrm{\Delta }\varphi =-(\alpha \mathrm{/}2)\mathrm{\Delta }\ln G$. This is the SOA's counterpart of cross-phase modulation in fiber, with the index change coming from the carriers instead of the Kerr effect. With $\alpha =5$, a gain compression of 5.5 dB shifts the phase by $\pi$; with $\alpha =3$ it takes 9.1 dB. An SOA in each arm of a Mach-Zehnder interferometer converts the phase shift into an intensity change, which gives converters and gates of either polarity with a higher extinction ratio than cross-gain modulation, at lower control power. In differential schemes a delayed control pulse in the second arm cancels the slow tail of the recovery, so the switching window is set by the delay and can be shorter than the carrier lifetime. The steep transfer function of the same interferometers is used for signal regeneration.

Four-wave mixing. A pump and a signal detuned by $\mathrm{\Delta }f$ beat and modulate the carrier density at $\mathrm{\Delta }f$, and the resulting gain and index gratings scatter the pump into an idler at $2f_p-f_s$. Carrier-density pulsation follows detunings only up to about $1\mathrm{/}(2\pi \tau )$; beyond that the mixing comes from faster intraband processes, spectral hole burning and carrier heating, which extend it to terahertz detunings at lower efficiency. The idler is the phase conjugate of the signal, spectrally inverted, so it carries both the amplitude and the (conjugated) phase and the conversion is transparent to the modulation format, at the price of an efficiency that falls with detuning and a pump that must be filtered out afterward.

Uses: booster, preamplifier, gate and reach extender

SOAs operating in the O-band fill a niche EDFAs cannot serve. Praseodymium- and bismuth-doped fiber amplifiers also work near 1310 nm but are far less widely deployed, so SOAs are the usual choice where an O-band link or PIC needs gain.

Booster. After a laser or modulator, an SOA raises the launch power or makes up the losses of modulators, splitters and fiber coupling. Monolithic InP circuits integrate SOAs beside lasers, modulators and detectors, and silicon photonic circuits add them by heterogeneous integration of III-V material, because silicon's indirect bandgap gives no useful gain. Some monolithic tunable lasers integrate an SOA after the laser section to set the output power and to blank the output while the wavelength changes.

Preamplifier. Ahead of a PIN photodiode, an SOA lifts the signal above the thermal noise of the receiver electronics, the role an avalanche photodiode plays in other receivers. The receiver sensitivity is then limited by beat noise between the signal and the ASE, which is why the noise figure matters most in this position. The 100GBASE-ER4 receiver above is a commercial example.

Switch and gate. Biased on, an SOA amplifies; unbiased, its active region absorbs. Switching between the two takes nanoseconds, set by the drive electronics and the carrier lifetime, so SOA gates serve in fast optical switch fabrics for packet and burst switching, where the millisecond reconfiguration of a MEMS optical circuit switch is too slow.

Reach extender for passive optical networks. In a passive optical network, a 1:64 split alone costs about 18 dB. The GPON wavelengths, 1310 nm upstream and 1490 nm downstream, both lie outside the erbium band, as does the 1270 nm upstream of XG(S)-PON; ITU-T G.984.6 specifies reach extenders for GPON, including a type built on optical amplifiers, and SOAs can supply the gain in both directions. Upstream traffic arrives in bursts from near and far subscribers at different powers; the SOA's gain follows each burst within its sub-nanosecond recovery, where an EDFA's slow gain would surge between bursts, and gain compression can narrow the spread of burst powers that the burst-mode receiver has to handle.

Related devices. A chip with one facet anti-reflection coated and the other highly reflecting is a reflective SOA, used as a colorless transmitter in WDM-PON (see injection locking); the same half-coated chip, with an external filter closing the cavity, is the gain element of an external-cavity laser. A superluminescent diode amplifies its own spontaneous emission into a broadband, low-coherence source for optical coherence tomography.

SOA compared with an EDFA

Compared to EDFAs, SOAs are:

• More compact: chip-scale rather than meters of fiber
• More broadband: gain bandwidth typically 50–80 nm (vs 35 nm for C-band EDFA)
• Faster: sub-nanosecond gain dynamics (vs millisecond for EDFA)
• Higher noise: typical NF 7–10 dB (vs 4–6 dB for EDFA)
• Polarization-dependent: gain difference of 0.5–2 dB between TE and TM (vs $<$ 0.5 dB for EDFA)
• Lower saturation power: typically +8 to +13 dBm (vs about +20 dBm for EDFA)
• Higher coupling loss: fiber-to-chip coupling adds 2–6 dB on each side

Raman amplification, and when each of the three amplifiers is the right choice, is covered in SOA vs EDFA vs Raman.

Typical values

Datasheet values hold at a stated current, wavelength, temperature and input power; an amplifier driven into compression has neither its small-signal gain nor its quoted noise figure.

Common questions

What is the difference between an SOA and a laser diode?

The chip is the same, but an SOA has its facet feedback suppressed by anti-reflection coatings, angled facets or both, so light makes one amplified pass instead of building up in a cavity. The residual reflectivity must keep $G\sqrt{R_1{R}_2}$ well below 1: below 0.17 for less than 3 dB of gain ripple.

Why is the noise figure of an SOA higher than that of an EDFA?

Inversion in a semiconductor is incomplete at the signal photon energy ($n_{\text{sp}}>1$), internal waveguide loss raises the effective inversion factor further, and the fiber-to-chip coupling loss at the input adds to the noise figure decibel for decibel. Typical SOAs measure 7–10 dB, against 4–6 dB for an EDFA.

What is the saturation output power of an SOA?

The output power at which the gain has fallen 3 dB below its small-signal value, typically +8 to +13 dBm (6.3–20 mW). In the homogeneous saturation model the 1 dB compression point lies 4.8 dB lower.

Can an SOA amplify several WDM channels?

Far below saturation, yes: the SOA preamplifier in a 100GBASE-ER4 receiver handles four lanes. Near saturation the gain follows the total power within a fraction of a nanosecond, so the channels modulate one another's gain and generate four-wave mixing products, which is why SOAs are not used as in-line amplifiers in WDM line systems.

Why use an SOA in the O-band instead of a fiber amplifier?

Erbium gives no gain near 1310 nm. Praseodymium- and bismuth-doped fiber amplifiers work there but are far less widely deployed, so SOAs are the usual choice where an O-band link or a PIC needs gain.

References: M. J. Connelly, Semiconductor Optical Amplifiers (Kluwer Academic, 2002). G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010). L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012). M. G. A. Bernard and G. Duraffourg, "Laser conditions in semiconductors," Physica Status Solidi 1, 699 (1961). N. A. Olsson, "Lightwave systems with optical amplifiers," Journal of Lightwave Technology 7, 1071 (1989). G. P. Agrawal and N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE Journal of Quantum Electronics 25, 2297 (1989). T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen and K. E. Stubkjaer, "All-optical wavelength conversion by semiconductor optical amplifiers," Journal of Lightwave Technology 14, 942 (1996). ITU-T Recommendation G.984.6, Gigabit-capable passive optical networks (GPON): Reach extension.