# Optical Amplifiers

This is a continuation from the previous tutorial - ** vertical-cavity surface-emitting lasers (VCSELs)**.

## 1. Background Information

Optical amplifier, as the name implies, is a device that amplifies an input optical signal. The amplification factor or gain can be higher than 1,000 (>30 dB) in some devices.

There are two principal types of optical amplifier: the semiconductor-laser amplifier (SLA), and the fiber amplifier. In an SLA, light is amplified when it propagates through a semiconductor medium fabricated in the form of a waveguide. In a fiber amplifier, light is amplified when it travels through a fiber doped with rare-earth ions (such as Nd^{+}, Er^{+}, etc.).

SLAs are typically less than 1mm in length whereas fiber amplifiers are typically 1-100m in length. The operating principals, design, fabrication and performance characteristics of SLAs and fiber amplifiers are described in this tutorial.

In a lightwave transmission system, as the optical signal travels through the fiber, it weakens and gets distorted. Regenerators are used to restore the optical pulses to their original form.

Figure 11-1(a) shows the block diagram of a typical lightwave regenerator. Its main components are an optical receiver, an optical transmitter, and electronic timing and decision circuits.

Optical amplifiers can nearly restore the original optical pulses. This increases their transmission distance without using conventional regenerators. An example of a semiconductor amplifier that functions as a regenerator is shown schematically in Figure 11-1(b).

Semiconductor amplifiers need external current to produce gain and fiber amplifiers need pump lasers for the same purpose. Because of its simplicity, an optical amplifier is an attractive alternative for a new lightwave system.

## 2. General Concepts

Optical amplifiers amplify incident light through stimulated emission, the same mechanism used by lasers. Indeed, an optical amplifier is nothing but a laser without feedback.

Its main ingredient is the optical gain realized when the amplifier is pumped (optically or electrically) to achieve population inversion. In general, the optical gain depends on the frequency (or wavelength) of the incident signal, and on the local beam intensity at any point inside the amplifier.

Details of the frequency and intensity dependence of the optical gain depend on the amplifier medium. To illustrate the general concepts, let us consider the case in which the gain medium is modeled as a homogeneously broadened two-level system.

The ** gain coefficient** of such a medium can be written as

\[\tag{11-2-1}g(\omega)=\frac{g_0}{1+(\omega-\omega_0)^2T_2^2+P/P_\text{s}}\]

where \(g_0\) is the peak value of the gain determined by the pumping level of the amplifier, \(\omega\) is the optical frequency of the incident signal, \(\omega_0\) is the atomic transition frequency, and \(P\) is the optical power of the signal being amplified. The ** saturation power** \(P_\text{s}\) depends on the gain-medium parameters such as the fluorescence time \(T_1\) and the transition cross section; its expression for different kinds of amplifiers will be given in the following sections.

The parameter \(T_2\) in Equation (11-2-1) is known as the dipole relaxation time and is typically quite small (0.1 ps - 1 ps). The fluorescence time \(T_1\) is also called the population relaxation time and varies in the range 100 ps - 10 ms depending on the gain medium used to make the amplifier.

Equation (11-2-1) can be used to discuss important characteristics of optical amplifiers, such as the gain bandwidth, amplification factor, and the output saturation power.

We begin by considering the case in which \(P/P_\text{s}\ll1\) throughout the amplifier. This is referred to as the ** unsaturated region**, as the gain remains unsaturated during amplification.

**Gain Spectrum and Bandwidth**

By neglecting the term \(P/P_\text{s}\) in Equation (11-2-1), the gain coefficient is given by

\[\tag{11-2-2}g(\omega)=\frac{g_0}{1+(\omega-\omega_0)^2T_2^2}\]

This equation shows that the gain is maximum when the incident frequency \(\omega\) coincides with the atomic transition frequency \(\omega_0\).

The gain reduction for \(\omega\ne\omega_0\) is governed by a Lorentzian profile that is a characteristic of homogeneously broadened two-level systems.

As discussed later, the gain spectrum of actual amplifiers can deviate considerably from the Lorentzian profile.

The ** gain bandwidth** is defined as the full width at half maximum (FWHM) of the gain spectrum \(g(\omega)\). For the Lorentzian spectrum the gain bandwidth is given by \(\Delta\omega_\text{g}=2/T_2\) or by

\[\tag{11-2-3}\Delta\nu_\text{g}=\frac{\Delta\omega_\text{g}}{2\pi}=\frac{1}{\pi{T_2}}\]

As an example, \(\Delta\nu_\text{g}\sim3\text{ THz}\) for semiconductor laser amplifiers for which \(T_2\sim0.1\text{ ps}\).

Amplifiers with a relatively large bandwidth are preferred for optical communication systems, since the gain is then nearly constant over the entire bandwidth of even a multichannel signal.

A related concept of ** amplifier bandwidth** is commonly used in place of the gain bandwidth. The difference becomes clear when one considers the

**\(G\), also known as the**

*amplifier gain***and defined as**

*amplification factor*\[\tag{11-2-4}G=P_\text{out}/P_\text{in}\]

where \(P_\text{in}\) and \(P_\text{out}\) are the input and output powers of the continuous-wave (CW) signal being amplified.

We can obtain an expression for \(G\) by using

\[\tag{11-2-5}\frac{\text{d}P}{\text{d}z}=gP\]

where \(P(z)\) is the optical power at a distance \(z\) from the input end.

A straightforward integration with the initial condition \(P(0)=P_\text{in}\) shows that the signal power grows exponentially as

\[\tag{11-2-6}P(z)=P_\text{in}\exp(gz)\]

By noting that \(P(L)=P_\text{out}\) and using Equation (11-2-4), the amplification factor for an amplifier of length \(L\) is given by

\[\tag{11-2-7}G(\omega)=\exp[g(\omega)L]\]

where the frequency dependence of both \(G\) and \(g\) is shown explicitly.

Both the amplifier gain \(G(\omega)\) and the gain coefficient \(g(\omega)\) are maximum when \(\omega=\omega_0\) and decrease with the signal detuning \(\omega-\omega_0\). However, \(G(\omega)\) decreases much faster than \(g(\omega)\) because of the exponential dependence of \(G\) on \(g\).

The amplifier bandwidth \(\Delta\nu_\text{A}\) is defined as the FWHM of \(G(\omega)\) and is related to the gain bandwidth \(\Delta\nu_\text{g}\) as

\[\tag{11-2-8}\Delta\nu_\text{A}=\Delta\nu_\text{g}\left(\frac{\ln2}{g_0L-\ln2}\right)\]

As expected, the amplifier bandwidth is smaller than the gain bandwidth, and the difference depends on the amplifier gain itself.

**Gain Saturation**

The origin of gain saturation lies in the power dependence of the gain coefficient in Equation (11-2-1). When \(P\ll{P}_\text{s}\), \(g(\omega)\) reduces to Equation (11-2-2) and is referred to as the ** small-signal gain** since the incident signal power should be small and remain small during amplification.

Since \(g\) is reduced when \(P\) becomes comparable to \(P_\text{s}\), the amplification factor \(G\) is also expected to decrease. To simplify the discussion, let us consider the case in which incident signal frequency is exactly tuned to the atomic transition frequency \(\omega_0\) to maximize the small-signal gain.

The detuning effects can be incorporated in a straightforward manner: by substituting \(g\) from Equation (11-2-1) in Equation (11-2-5), we obtain

\[\tag{11-2-9}\frac{\text{d}P}{\text{d}z}=\frac{g_0P}{1+P/P_\text{s}}\]

This equation can be easily integrated over the amplifier length. By using the initial condition \(P(0)=P_\text{in}\) together with \(P(L)=P_\text{out}=GP_\text{in}\), we obtain the following implicit relation for the large-signal amplifier gain:

\[\tag{11-2-10}G=G_0\exp\left(-\frac{G-1}{G}\frac{P_\text{out}}{P_\text{s}}\right)\]

where \(G_0=\exp(g_0L)\) is the unsaturated value of the amplification factor (\(P_\text{out}\ll{P}_\text{s}\)).

Equation (11-2-10) shows that the amplification factor \(G\) decreases from its unsaturated value \(G_0\) when \(P_\text{out}\) becomes comparable to \(P_\text{s}\).

A quantity of practical interest is the ** output saturation power** \(P_\text{out}^\text{s}\), defined as the output power for which the amplifier gain \(G\) is reduced by a factor of 2 (or by 3 dB) from its unsaturated value \(G_0\).

By using \(G=G_0/2\) in Equation (11-2-10), \(P_\text{out}^\text{s}\) is given by

\[\tag{11-2-11}P_\text{out}^\text{s}=\frac{G_0\ln2}{G_0-2}P_\text{s}\]

\(P_\text{out}^\text{s}\) is smaller than \(P_\text{s}\) by about 30%. Indeed, by noting that \(G_0\gg2\) in practice (\(G_0=1,000\) for 30 dB amplifier gain) \(P_\text{out}^\text{s}\approx(\ln2)P_\text{s}\approx0.69P_\text{s}\). As seen by Equation (11-2-11), \(P_\text{out}^\text{s}\) becomes nearly independent of \(G_0\) for \(G_0\gt20\text{ dB}\).

**Amplifier Noise**

All amplifiers degrade the signal-to-noise ratio (SNR) of the amplified signal because of spontaneous emission that adds to the signal during its amplification.

The SNR degradation is quantified through a parameter \(F_\text{n}\), called the ** amplifier noise figure** in analogy with the electronic amplifiers, and defined as

\[\tag{11-2-12}F_\text{n}=\frac{(\text{SNR})_\text{in}}{(\text{SNR})_\text{out}}\]

where SNR refers to the electrical power generated when the signal is converted to electrical current by using a photodetector.

In general, \(F_\text{n}\) would depend on several detector parameters which govern the shot noise and thermal noise associated with the detector. One can obtain a simple expression for \(F_\text{n}\) by considering an ideal detector whose performance is limited by shot noise only.

Consider an amplifier with the amplification factor \(G\) so that the output power is related to the input power by \(P_\text{out}=GP_\text{in}\). The SNR of the input signal is given by

\[\tag{11-2-13}(\text{SNR})_\text{in}=\frac{\langle{I}\rangle^2}{\sigma_\text{s}^2}=\frac{(RP_\text{in})^2}{2q(RP_\text{in})\Delta{f}}=\frac{P_\text{in}}{2h\nu\Delta{f}}\]

where \(\langle{I}\rangle=RP_\text{in}\) is the average photocurrent, \(R=q/h\nu\) is the responsivity of an ideal photodetector with unit quantum efficiency, and

\[\tag{11-2-14}\sigma_\text{s}^2=2q(RP_\text{in})\Delta{f}\]

is the shot noise. Here \(\Delta{f}\) is the detector bandwidth.

To evaluate the SNR of the amplified signal, one should add the contribution of spontaneous emission to the receiver noise.

The spectral density of spontaneous-emission-induced noise is nearly constant (white noise) and can be written as

\[\tag{11-2-15}S_\text{sp}(\nu)=(G-1)n_\text{sp}h\nu\]

where \(\nu\) is the optical frequency.

The parameter \(n_\text{sp}\) is called the ** spontaneous-emission factor** or population-inversion factor. Its value is \(1\) for amplifiers with complete population inversion (all atoms in the excited case), but becomes \(\gt1\) when the population inversion is incomplete.

For a two-level system,

\[\tag{11-2-16}n_\text{sp}=N_2/(N_2-N_1)\]

where \(N_1\) and \(N_2\) are the atomic populations for the ground and excited states respectively.

The effect of spontaneous emission is to add fluctuations to the amplified power which are converted to current fluctuations during the photodetection process.

It turns out that the dominant contribution to the receiver noise comes from beating of spontaneous emission with the signal itself. This beating phenomenon is similar to heterodyne detection in the sense that spontaneously emitted radiation mixes coherently with the amplified signal at the photodetector and produces a heterodyne component of the photocurrent.

The variance of the photocurrent can then be written as

\[\tag{11-2-17}\sigma^2=2q(RGP_\text{in})\Delta{f}+4(GRP_\text{in})(RS_\text{sp})\Delta{f}\]

where the first term is due to shot noise and the second term results from signal-spontaneous emission beating. All other contributions to the receiver noise have been neglected for simplicity.

The SNR of the amplified signal is thus given by

\[\tag{11-2-18}(\text{SNR})_\text{out}=\frac{\langle{I}\rangle^2}{\sigma^2}=\frac{(RGP_\text{in})^2}{\sigma^2}\approx\frac{GP_\text{in}}{4S_\text{sp}\Delta{f}}\]

where the last relation was obtained by neglecting the first term in Equation (11-2-17) and is valid for \(G\gg1\).

The amplifier noise figure can now be obtained by substituting Equations (11-2-13) and (11-2-18) in Equation (11-2-12). If we also use Equation (11-2-15) for \(S_\text{sp}\), we obtain

\[\tag{11-2-19}F_\text{n}=2n_\text{sp}(G-1)/G\approx{2n_\text{sp}}\]

This equation shows that the SNR of the amplified signal is degraded by a factor of \(2\) (or 3 dB) even for an ideal amplifier for which \(n_\text{sp}=1\). For most practical amplifiers, \(F_\text{n}\) exceeds 3 dB and can be as large as 6-8 dB. For its application in optical communication systems, an optical amplifier should have \(F_\text{n}\) as low as possible.

**Amplifier Applications**

Optical amplifiers can serve several purposes in the design of fiber optic communication systems.

As already mentioned in the introduction, an important application for long-haul systems is in replacing electronic regenerators with optical amplifiers. Such a replacement can be carried out as long as the system performance is not limited by the cumulative effects of dispersion and spontaneous emission.

The use of optical amplifiers is particularly attractive for multichannel lightwave systems, since electronic regeneration requires demultiplexing of channels before each channel signal is regenerated using separate receiver and transmitters, a rather costly procedure. Optical amplifiers can amplify all channels simultaneously. When optical amplifiers are used to replace electronic regenerators, they are called ** in-line amplifiers**.

Another way to use optical amplifiers is to increased the transmitter power by placing an amplifier just after the transmitter. Such amplifiers are called ** power amplifiers** or boosters, as their main purpose is to boost the transmitted power. A power amplifier increases the transmission distance by 10-100 km depending on the amplifier gain and the fiber loss.

Transmission distance can also be increased by putting an amplifier just before the receiver to boost the received power. Such amplifiers are called ** preamplifiers**.

Another application of optical amplifiers is to use them for compensating distribution losses in local-area networks. Distribution losses often limit the number of nodes in a network, particularly in the case of bus topology.

Further applications use optical amplifiers in photonic switching systems.

## 3. Semiconductor Laser Amplifiers

The SLA is a device very similar to a semiconductor laser. Hence its operating principle, fabrication and design are also similar. The basic laser structure can be used to study light amplification. When the injection current is below threshold, the laser acts as an optical amplifier for incident light waves, and above threshold it undergoes oscillation.

Initial optical amplifier studies were carried out on GaAs homostructure devices in the mid 1960s. Extensive work on AlGaAs laser amplifiers was carried out in the 1980s. These amplifiers used an index guiding structure and are therefore closer to a practical device.

SLAs can be classified into two categories: the Fabry-Perot (FP) amplifier, and the traveling-wave (TW) amplifier.

An FP amplifier has considerable reflectivity at the input and output ends, resulting in resonant amplification between the end mirrors. Thus, an FP amplifier exhibits very large gain at wavelengths corresponding to the longitudinal modes of the FP cavity.

The TW amplifier, by contrast, has negligible reflectivity at each end, resulting in signal amplification during a single pass. The optical gain spectrum of a TW amplifier is quite broad and corresponds to that of the semiconductor gain medium. Most practical TW amplifiers exhibit some small ripple in the gain spectrum arising from residual facet reflectivities.

TW amplifiers are more suitable for system applications. Therefore much effort has been devoted over the last few years to fabricate amplifiers with very low facet reflectivities. Such amplifier structures either utilize special low-reflectivity dielectric coatings, or have tilted or buried facets. Fabrication and performance of these devices are described later.

Much of the experimental work on semiconductor optical amplifiers has been carried out using the InGaAsP material system with the optical gain centered around 1.3 μm or 1.55 μm. The interest in these wavelength regions is primarily due to low loss and low dispersion of silica fibers which are extensively used as the transmission medium for the optical fiber transmission systems.

The amplifiers used in lightwave system applications, either as preamplifiers in front of a receiver or as in line amplifiers as a replacement of regenerators, must also exhibit equal optical gain for all polarizations of the input light.

In general, the optical gain in a waveguide is polarization dependent although the material gain is independent of polarization for bulk semiconductors. This arises from unequal mode confinement factors for light polarized parallel to the junction plane (TE mode) and that for light polarized perpendicular to the junction plane (TM mode).

For thick active regions, the confinement factors of the TE and TM modes are nearly equal. Hence the gain difference between the TE and TM modes is smaller for amplifiers with a thick active region. Figure 11-2 shows the calculated gain difference as a function of cavity length for different active layer thicknesses.

In general, the gain difference increases with increasing cavity length since the overall gain increases.

**Impact of Facet Reflectivity**

In an ideal TW amplifier the optical beam should not experience any reflection at the facets. In practice, facets with antireflection (AR) coatings generally exhibit some residual reflectivity and form an optical cavity.

An example of the transmission characteristics of a TW amplifier with antireflection-coated cleaved facets is shown in Figure 11-3. The output exhibits modulations at longitudinal modes of the cavity simply because the optical gain is a few decibels higher at the modes than in between modes.

The phase and amplitude transfer functions of an SLA can be characterized by a change in phase and change in amplitude of \(G\). For an amplifier with facet reflectivities \(R_1\), \(R_2\), the gain \(G\) is given by

\[\tag{11-3-1}G=\frac{(1-R_1)(1-R_2)G_\text{s}}{(1+\sqrt{R_1R_2}G_\text{s})^2+4\sqrt{R_1R_2}G_\text{s}\sin^2\phi}\]

where \(G_\text{s}\) is the single-pass gain, and the phase shift \(\phi\) is given by

\[\tag{11-3-2}\phi=\phi_0+\frac{g_0L\beta_\text{c}}{2}\left(\frac{P}{P+P_\text{s}}\right)\]

where \(\phi_0=2\pi{L}\mu/\lambda\) is the nominal phase shift, \(L\) is the length of the amplifier, \(\mu\) is the index, \(\beta_\text{c}\) is the line-width enhancement factor, \(g_0\) is the unsaturated gain, and \(P\) and \(P_\text{s}\) are the total internal power and saturation power, respectively.

The \(\sin^2\phi\) term in Equation (11-3-1) is responsible for the modulation of the output signal at cavity modes. The case of practical interest is one of low reflectivities, i.e., \(R_1\) and \(R_2\le10^{-3}\). In this case, the effect of residual facet reflectivities appears as small ripples (Figure 11-3) superimposed on an envelope function. The envelope function is essentially the gain spectrum of the semiconductor material.

The peak-to-valley ratio of the intensity ripple is given by

\[\tag{11-3-3}V=\left[\frac{1+\sqrt{R_1R_2}G_\text{s}}{1-\sqrt{R_1R_2}G_\text{s}}\right]\]

For an ideal TW amplifier both \(R_1\) and \(R_2\rightarrow0\); \(V\) equals \(1\), i.e., no ripple occurs at cavity mode frequencies.

The quantity \(V\) is plotted as a function of \(\sqrt{R_1R_2}\) (reflectivity) in Figure 11-4 for different values of gain.

A practical amplifier should have \(V\lt1\text{ dB}\). To realize such low values of \(V\), reflectivities of \(\lt10^{-4}\) are needed. Three principal schemes exist for achievement of such low reflectivities. They are

**Ultra-low-reflectivity dielectric-coated amplifiers****Buried-facet amplifiers****Tilted-facet amplifiers**

**Amplifier Designs**

**1. Low-Reflectivity Coatings**

A key factor for good performance characteristics (low gain ripple and low polarization selectivity) for TW amplifiers is very low facet reflectivity. The reflectivity of cleaved facets can be reduced by dielectric coating.

For plane waves incident on air air interface from a medium of refractive index \(n\), the reflectivity can be reduced to zero by coating the interface with a dielectric whose refractive index equals \(n^{1/2}\) and whose thickness equals \(\lambda/4\).

However, the fundamental mode propagating in a waveguide is not a plane wave and therefore the above \(n^{1/2}\) law only provides a guideline for achieving very low (\(\lt10^{-4}\)) facet reflectivity by dielectric coating.

In practice, very low facet reflectivities are obtained by monitoring the amplifier performance during the coating process. The effective reflectivity can then be estimated from the ripple at the FP mode spacings, caused by residual reflectivity, in the spontaneous emission spectrum.

The result of such an experiment is shown in Figure 11-5. The reflectivity is very low (\(\lt10^{-4}\)) only in small range of wavelengths.

Laboratory experiments have been carried out using amplifiers that rely only on low-reflectivity coatings for good performance, but thickness is critical. Good antireflection coatings have a limited wavelength range, so alternatives to coatings have been investigated. Several schemes are discussed below.

**2. Buried-Facet Amplifiers**

Also known as window devices, the principal feature of buried-facet optical amplifiers relative to AR-coated cleaved-facet devices is a polarization-independent reduction in mode reflectivity. This is because the buried facet gives better control over achieving polarization-independent gain.

A schematic cross section of a buried-facet optical amplifier is shown in Figure 11-6.

Current confinement in this structure is provided by semi-insulating Fe-doped InP layers grown by metal-organic chemical vapor deposition (MOVPE). It is fabricated similar to ta laser.

The first four layers are shown on a (100)-oriented \(n\)-type InP substrate by MOVPE. These layers are

- an \(n\)-type InP buffer layer
- an undoped InGaAsP (\(\lambda\sim1.55\) μm) active layer
- a \(p\)-type InP cladding layer
- a \(p\)-type InGaAsP (\(\lambda\sim1.3\) μm) layer

Mesas are then etched on the wafer along the [110] direction with 15-μm-wide channels normal to the mesa direction using a SiO_{2} mask. The latter is needed for buried-facet formation.

Semi-insulating Fe-doped InP layers are then grown around the mesas by MOVPE with the oxide mask in place. The oxide mask and \(p\)-type InGaAsP layer are removed and a \(p\)-type InP and \(p\)-type InGaAsP (\(\lambda\sim1.3\) μm) contact layer is then grown over the entire wafer by the MOVPE growth technique.

The wafer is processed using standard methods and cleaved to produce 500-μm-long buried-facet chips with ~ 7-μm-long buried facets at each end. Chip facets are then AR-coated using a single-layer film of ZrO_{2}.

Fabrication of cleaved-facet devices follows the same procedure as described above, except that the mesas are continuous with no channels separating them. The latter is needed for defining the buried-facet regions. The semi-insulating layer, in both types of devices, provides current confinement and lateral index guiding. For buried-facet devices it also provides the buried-facet region.

The effective reflectivity of a buried facet decreases with increasing separation between the facet and the end of the active region. The effective reflectivity of such a facet can be calculated by using a Gaussian-beam approximation for the propagating optical mode. It is given by

\[\tag{11-3-4}R_\text{eff}=R/[1+(2S/kw^2)^2]\]

where \(R\) is the reflectivity of the cleaved facet, \(S\) is the length of the buried-facet region, \(k=2\pi/\lambda\), where \(\lambda\) is the optical wavelength in the medium, and \(w\) is the spot size at the facet.

The calculated reflectivity is plotted in Figure 11-7 using \(w=0.7\) μm and \(R=0.3\) for an amplifier operating near 1.55 μm. A reflectivity of \(10^{-2}\) can be achieved for a buried-facet length of about 15 μm.

Although increasing the length of the buried-facet region decreases the reflectivity, if the length is too long the beam emerging from the active region will strike the top metalized surface, producing multiple peaks in the far-field pattern, a feature not desirable for coupling into a single-mode fiber.

The beam waist \(w\) of a Gaussian beam after traveling a distance \(z\) is given by the equation

\[\tag{11-3-5}w^2(z)=w_0^2\left[1+\left(\frac{\lambda{z}}{\pi{w_0^2}}\right)^2\right]\]

where \(w_0\) is the spot size at the beam waist and \(\lambda\) is the wavelength in the medium.

Since the active region is about 4 μm from the top surface of the chip, it follows from Equation (11-3-5) that the length of the buried-facet region must be less than 12 μm for single-lobed far-field operation.

The optical gain is determined by injecting light into the amplifier and measuring the output. The internal gain of an amplifier chip as a function of current at two different temperatures is shown in Figure 11-8.

Open circles and squares represent the gain for a linearly polarized incident light with the electric field parallel to the \(p-n\) junction in the amplifier chip (TE mode). Solid circles represent the measured gain for the TM mode at 40°C.

Measurements were done for low input power (-40 dBm), so that the observed saturation is not due to gain saturation in the amplifier, but rather to carrier loss caused by Auger recombination. Note that the optical gain for the TE input polarization is nearly equal to the optical gain for TM input polarization.

Figure 11-9 shows the measured gain as a function of input wavelength for TE-polarized incident light. The modulation in the gain (gain ripple) with a periodicity of 0.7 nm is due to residual facet reflectivities.

The measured gain ripple for this device is less than 1 dB. The estimated facet reflectivity from Equation (11-3-3) by using the measured gain ripple of 0.6 dB at 26 dB internal gain is \(9\times10^{-5}\). The 3-dB bandwidth of the optical gain spectrum is 45 nm for this device.

It has been shown that the ripple and polarization dependence of the gain correlate well with the ripple and polarization dependence of the amplified spontaneous-emission spectrum. Measurements of amplified spontaneous emission are much simpler to make than gain measurements, and provide a good estimate of the amplifier performance.

**3. Tilted-Facet Amplifiers**

Another way to suppress the resonant modes of the FP cavity is to slant the waveguide (gain region) from the cleaved facet so that the light incident on it internally does not couple back into the waveguide.

The process essentially decreases the effective reflectivity of the tilted facet relative to a normally cleaved facet. The reduction in reflectivity as a function of the tilt angle is shown in Figure 11-10 for the fundamental mode of the waveguide.

A schematic of a tilted-facet optical amplifier is shown in Figure 11-11. Waveguiding along the junction plane is weaker in this device than that for the strongly index guided buried-heterostructure device. Weak index guiding for the structure of Figure 11-11 is provided by a dielectric defined ridge. The fabrication of the device follows a procedure similar to that described previously.

The measured gain as a function of injection current for TM- and TE-polarized light for a tilted facet amplifier is shown in Figure 11-12. Optical gain as high as 30 dB have been obtained using tilted-facet amplifiers.

The effective reflectivity of the fundamental mode decreases with increasing tilt of the waveguide. But the effective reflectivity of the higher order modes increases, and this may cause higher-order modes to appear at the output, especially when the ridge widths is large. (Higher-order modes at the output may reduce fiber-coupled power significantly.)

**Amplifier Characteristics**

The amplification characteristics of SLAs have been discussed extensively. As seen in Figure 11-3, the measured amplifier gain exhibits ripples reflecting the effects of residual facet reflectivities. Gain ripples are negligibly small when the SLA operates in a nearly TW mode.

The 3-dB amplifier bandwidth depends on the injected current and is typically 50-60 nm. As discussed above, this bandwidth reflects the relatively broad gain spectrum, \(g(\omega)\), of SLAs. The gain spectrum of semiconductor lasers has been considered in the radiative recombination in semiconductors tutorial; the same discussion applies to SLAs.

The gain spectrum becomes broader with an increase in the injection current. This feature is clearly seen in Figure 11-3. Figures 11-8 and 11-12 show how the measured peak gain increases with the injected current.

To discuss gain saturation, we consider the peak gain and assume that it increases linearly with the carrier population \(N\) [refer to the steady-state characteristics of semiconductor lasers tutorial]. The gain is then given by Equation (6-3-3) or, equivalently, by

\[\tag{11-3-6}g=(\Gamma{a}/V)(N-N_0)\]

where \(\Gamma\) is the confinement factor, \(a\) is the differential gain coefficient, \(V\) is the active volume, and \(N_0\) is the value of \(N\) required at transparency.

The carrier population \(N\) changes with the injection current \(I\) and the signal power \(P\) according to the rate equation (6-2-20) [refer to the rate equations for semiconductor lasers tutorial]. By expressing the photon number in terms of the optical power, this equation can be written as

\[\tag{11-3-7}\frac{\text{d}N}{\text{d}t}=\frac{I}{q}-\frac{N}{\tau_\text{e}}-\frac{a(N-N_0)}{\sigma_\text{m}h\nu}P\]

where \(\tau_\text{e}\) is the carrier lifetime and \(\sigma_\text{m}\) is the cross-sectional area of the waveguide mode.

In the case of a CW beam, or pulses much longer than \(\tau_\text{e}\), the steady-state value of \(N\) can be obtained by setting \(\text{d}N/\text{d}t=0\) in Equation (11-3-7). When the solution is substituted in Equation (11-3-6), the optical gain is found to saturate as

\[\tag{11-3-8}g=\frac{g_0}{1+P/P_\text{s}}\]

where the small-signal gain \(g_0\) is given by

\[\tag{11-3-9}g_0=(\Gamma{a}/V)(I\tau_\text{e}/q-N_0)\]

and the saturation power \(P_\text{s}\) is defined as

\[\tag{11-3-10}P_\text{s}=h\nu\sigma_\text{m}/(a\tau_\text{e})\]

A comparison of Equations (11-2-1) and (11-3-8) shows that the SLA gain saturates in the same way as that of a two-level system. We can therefore use the analysis of the gain saturation section in the **General Concepts** part above. In particular, the output saturation power \(P_\text{out}^\text{s}\) is given by Equation (11-2-11) and \(P_\text{s}\) is given by Equation (11-3-10). Typical values of \(P_\text{out}^\text{s}\) are in the range of 5-10 mW.

The noise figure \(F_\text{n}\) of SLAs is larger than the minimum value of 3 dB for several reasons.

The dominant contribution comes from the population-inversion factor \(n_\text{sp}\), which represents the ratio of spontaneous to net stimulated emission rate. For SLAs, \(n_\text{sp}\) is obtained from Equation (11-2-16) by replacing \(N_2\) and \(N_1\) by \(N\) and \(N_0\), respectively.

An additional contribution results from nonresonant internal loss \(\alpha_\text{int}\) (such as free-carrier absorption or scattering loss) which reduce the available gain from \(g\) to \(g-\alpha_\text{int}\). By using Equation (11-2-19) and including this additional contribution, the noise figure can be written as

\[\tag{11-3-11}F_\text{n}=2\left(\frac{N}{N-N_0}\right)\left(\frac{g}{g-\alpha_\text{int}}\right)\]

Residual facet reflectivities increase \(F_\text{n}\) by an additional factor that can be approximated by \(1+R_1G\), where \(R_1\) is the reflectivity of the input facet. In most TW amplifiers \(R_1G\ll1\), and this contribution can be neglected.

Typical values of \(F_\text{n}\) for SLAs are in the 5-7 dB range.

An undesirable characteristic of SLAs is their polarization sensitivity. The difference in amplifier gain \(G\) between TE and TM polarization is as much as 5-8 dB simply because both \(\Gamma\) and \(a\) are different for the two polarizations in the gain expression.

This feature makes the amplifier gain dependent on the polarization state of the input beam, a property undesirable for lightwave system applications where the polarization state changes with propagation along the fiber (unless polarization-preserving fibers are used).

Several schemes have been devised to reduce the polarization sensitivity.

In one scheme, the amplifier is designed such that the width and the thickness of the active region are comparable. A gain difference of less than 1.3 dB between TE and TM polarizations has been realized by making the active layer 0.26-μm thick and 0.4-μm wide.

Another scheme makes use of a large-optical-cavity structure; a gain difference of less than 1 dB has been obtained with such a structure.

Several other schemes reduce the polarization sensitivity by using two amplifiers or two passes through the same amplifier. Figure 11-13 shows three such configurations.

In Figure 11-13(a) the TE-polarized signal in one amplifier becomes TM polarized in the second amplifier, and vice versa. If both amplifiers have identical gain characteristics, the twin-amplifier configuration provides signal gain that is independent of the signal polarization. A drawback of the series configuration is that residual facet reflectivities lead to mutual coupling between the two amplifiers.

In the parallel configuration shown in Figure 11-13(b) the incident signal is split into a TE- and TM-polarized signal, each of which is amplified by separate amplifiers. The amplifier TE and TM signals are then combined to produce the amplified signal with the same polarization as that of the input beam.

The double-pass configuration of Figure 11-13(c) passes the signal through the same amplifier twice, but the polarization is rotated by 90° between the two passes. Since the amplified signal propagates in the backward direction, a 3-dB fiber coupler is needed to separate it from the incident signal. In spite of a 6-dB loss occurring at the fiber coupler (3 dB for the input signal and 3 dB for the amplified signal) this configuration provides high gain from a single amplifier, as the same amplifier supplies gain on the two passes.

**Multichannel Amplification**

One of the advantages of using optical amplifiers is that they can be used to amplify several channels simultaneously as long as the carrier frequencies of multiple channels lie within the amplifier bandwidth.

Ideally the signal in each channel should be amplified by the same amount. In practice, several nonlinear phenomena in SLAs induce interchannel cross talk, an undesirable feature that should be minimized for practical lightwave systems.

Two such nonlinear phenomena are cross-saturation and four-wave mixing. They both originate from the stimulated recombination term in the carrier rate equations. In the case of multichannel amplification, the power \(P\) in Equation (11-3-7) corresponds to

\[\tag{11-3-12}P=\frac{1}{2}\left|\sum_{j=1}^MA_j\exp(-\text{i}\omega_jt)+\text{c.c.}\right|^2\]

where \(\text{c.c.}\) stands for complex conjugate, \(M\) is the number of channels, \(A_j\) is the (complex) amplitude, and \(\omega_j\) is the carrier frequency for the \(j\)th channel.

Because of the coherent addition of individual channel fields, Equation (11-3-12) contains a time-dependent term resulting from beating of the signal in different channels, that is,

\[\tag{11-3-13}P=\sum_{j=1}^MP_j+\sum^M_{j\ne{k}}\sum^M_{j\ne{k}}2\sqrt{P_jP_k}\cos(\Omega_{jk}t+\phi_j-\phi_k)\]

where \(A_j=\sqrt{P_j}\exp(\text{i}\phi_j)\) is assumed together with \(\Omega_{jk}=\omega_j-\omega_k\).

When Equation (11-3-13) is substituted in Equation (11-3-7), the carrier population \(N\) is also found to oscillate at the beat frequency \(\Omega_{jk}\). Since the gain and the refractive index both depend on \(N\), they are also modulated at the frequency \(\Omega_{jk}\); such a modulation is referred to as the creation of gain and index gratings by the multichannel signal.

These gratings induce interchannel cross talk by scattering a part of the signal from one channel to another. This phenomenon can also be viewed as four-wave mixing.

The origin of cross-saturation is also evident from Equation (11-3-13). The first term on the right side shows that the power \(P\) in Equation (11-3-8) should be replaced by the total power in all channels. Thus, the gain of a specific channel is saturated not only by its own power but also by the power of neighboring channels, a phenomenon known as cross-saturation. Such a cross-saturation has been observed in several experiments.

It is undesirable for direct-detection or amplitude-shift keying (ASK) coherent systems in which the channel power changes with time depending on the bit pattern. The signal gain of one channel then changes form bit to bit, and the change depends on the bit pattern of neighboring channels. The amplified signal appears to fluctuate more or less randomly. Such fluctuations degrade the effective SNR at the receiver.

The cross-saturation-induced interchannel cross talk occurs regardless of the extend of the channel spacing. It can only be avoided by operating SLAs in the unsaturated regime.

It is also absent for phase-shift keying (PSK) and frequency-shift keying (FSK) coherent systems, since the power in each channel, and hence the total power, remains constant with time.

Interchannel cross talk induced by four-wave mixing, on the other hand, can occur for all multichannel coherent communication systems irrespective of the modulation format used. However, in contrast with cross-saturation, it occurs only when the channel spacing is not too large and becomes negligible when channel spacing exceeds 10 GHz simply because carrier population is not able to respond when \(\Omega\tau_\text{e}\gg1\), where \(\Omega\) is the channel spacing.

Figure 11-14 shows the gains of two channels for an SLA with 25-dB small-signal gain when the input channel powers are \(-30\) and \(-25\) dBm (1 and 3.2 μW respectively).

Dashed lines shows the equal channel gain expected in the absence of four-wave mixing. The gain of the low-frequency channel is enhanced and the gain of the high-frequency channel is reduced as a result of energy transfer initiated by four-wave mixing.

The channel gains can differ by more than 5 dB for large input powers and small channel spacing. Such gain variations result in cross talk penalty and degrade the system performance considerably.

The cross talk penalty was measured in a system experiment where three channels spaced 2 GHz apart were transmitted through a 50-km-long fiber by using an FSK coherent scheme. The bit rate was 560 Mbps. The bit-error-rate (BER) degraded severely as a result of four-wave mixing with a large penalty (> 2 dB) at \(10^{-9}\).

The performance could be improved by reducing the channel powers or by increasing the channel spacing. A channel spacing of 10 GHz or more is necessary to reduce the effect of carrier-density modulation and the associated four-wave mixing in SLAs.

**Pulse Amplification**

The large bandwidth of TW-type SLAs suggest that they are capable of amplifying ultrashort optical pulses (as short as a few picoseconds) without significant pulse distortion.

However, when the pulse width \(\tau_\text{p}\) becomes shorter than the carrier lifetime \(\tau_\text{e}\), gain dynamics play an important role, since both \(N\) and \(g\) in Equation (11-3-6) become time dependent. Ultrashort pulse amplification in SLAs has been extensively studied both theoretically and experimentally.

The study of pulse propagation in SLAs requires that both spatial and temporal evolution is included by considering a partial differential equation for the amplitude \(A(z,t)\) of the pulse envelope. In its simplest form this equation is given by

\[\tag{11-3-14}\frac{\partial{A}}{\partial{z}}+\frac{1}{v_\text{g}}\frac{\partial{A}}{\partial{t}}=\frac{1}{2}(1+\text{i}\beta_\text{c})gA\]

where carrier-induced index changes are included through the line-width enhancement factor \(\beta_\text{c}\).

The time time dependence of \(g\) is governed by Equations (11-3-6) and (11-3-7). The two equations can be combined to yield

\[\tag{11-3-15}\frac{\partial{g}}{\partial{t}}=\frac{g_0-g}{\tau_\text{e}}-\frac{gP}{E_\text{s}}\]

where the saturation energy \(E_\text{s}\) is defined as

\[\tag{11-3-16}E_\text{s}=h\nu(\sigma_\text{m}/a)\]

and \(g_0\) is given by Equation (11-3-9).

Equations (11-3-14) and (11-3-15) govern amplification of optical pulses in SLAs. They can be solved analytically for pulses whose duration is short compared with the carrier lifetime (\(\tau_\text{p}\ll\tau_\text{e}\)). The first term on the right-hand side of Equation (11-3-15) can then be neglected during pulse amplification.

By introducing the reduced time \(\tau=t-z/v_\text{g}\) together with \(A=\sqrt{P}\exp(\text{i}\phi)\), Equations (11-3-14) and (11-3-15) can be written as

\[\tag{11-3-17}\frac{\partial{P}}{\partial{z}}=g(z,\tau)P(z,\tau)\]

\[\tag{11-3-18}\frac{\partial{\phi}}{\partial{z}}=-\frac{1}{2}\beta_\text{c}g(z,\tau)\]

\[\tag{11-3-19}\frac{\partial{g}}{\partial{\tau}}=-\frac{1}{E_\text{s}}g(z,\tau)P(z,\tau)\]

Equation (11-3-17) is identical with Equation (11-2-5) except that the gain \(g\) depends on both \(z\) and \(\tau\). It can be easily integrated over the amplifier length \(L\) to provide the output power as

\[\tag{11-3-20}P_\text{out}(\tau)=P_\text{in}(\tau)\exp[h(\tau)]\]

where \(P_\text{in}(\tau)\) is the input power and \(h(\tau)\) is the total integrated gain defined as

\[\tag{11-3-21}h(\tau)=\displaystyle\int\limits_0^Lg(z,\tau)\text{d}z\]

If we integrate Equation (11-3-19) over the amplifier length after replacing \(gP\) by \(\partial{P}/\partial{z}\), we obtain

\[\tag{11-3-22}\frac{\text{d}h}{\text{d}\tau}=-\frac{1}{E_\text{s}}[P_\text{out}(\tau)-P_\text{in}(\tau)]=-\frac{P_\text{in}(\tau)}{E_\text{s}}(\text{e}^h-1)\]

where Equation (11-3-20) was used to relate \(P_\text{out}\) to \(P_\text{in}\).

Equation (11-3-22) can be easily integrated to obtain \(h(\tau)\). The quantity of practical interest is the amplification factor \(G(\tau)\) related to \(h(\tau)\) by \(G=\exp(h)\). It is given by

\[\tag{11-3-23}G(\tau)=\frac{G_0}{G_0-(G_0-1)\exp[-E_0(\tau)/E_\text{s}]}\]

where \(G_0\) is the unsaturated amplifier gain and

\[E_0(\tau)=\displaystyle\int\limits_{-\infty}^{\tau}P_\text{in}(\tau)\text{d}\tau\]

is the partial energy of the input pulse defined such that \(E_0(\infty)\) equals the input pulse energy \(E_\text{in}\).

The solution (11-3-23) shows that the amplifier gain is different for different parts of the pulse. The leading edge experiences the full gain \(G_0\), as the amplifier is not yet saturated. The trailing edge experiences the least gain, since the whole pulse has saturated the amplifier gain.

The final value \(G_\text{f}\) of \(G(\tau)\) after passage of the pulse is obtained from Equation (11-3-23) by replacing \(E_0(\tau)\) by \(E_\text{in}\). The intermediate values of the gain depend on the pulse shape.

Figure 11-15 shows the shape dependence of \(G(\tau)\) for super-Gaussian input pulses by taking

\[\tag{11-3-24}P_\text{in}(\tau)=P_0\exp[-(\tau/\tau_\text{p})^{2m}]\]

where \(m\) is the shape parameter. The input pulse is Gaussian for \(m=1\) but becomes nearly rectangular as \(m\) increases.

For comparison purposes the input energy is held constant for different pulse shapes by choosing \(E_\text{in}/E_\text{s}=0.1\).

The shape dependence of the amplification factor \(G(\tau)\) implies that the output pulse is distorted when compared with the input pulse, and distortion is itself shape dependent.

Figure 11-16 shows the pulse distortion occurring when a super-Gaussian input pulse of energy such that \(E_\text{in}/E_\text{s}=0.1\) is amplified by an SLA with 30-dB small-signal gain.

Different curves correspond to different pulse widths \(\tau_0\). Pulses shorter than the carrier lifetime \(\tau_\text{e}\) are distorted the most since \(G(\tau)\) is the most nonuniform for such pulses.

Interestingly enough, the energy gain \(G_\text{E}\), defined as \(G_\text{E}=E_\text{out}/E_\text{in}\), does not depend on the pulse shape. It depends only on the initial gain \(G_0\) and the final gain \(G_\text{f}\) through the relation

\[\tag{11-3-25}G_\text{E}=\frac{\ln[(G_0-1)/(G_\text{f}-1)]}{\ln[(G_0-1)/(G_\text{f}-1)]-\ln(G_0/G_\text{f})}\]

The above discussion applies to any kind of amplifier. However, SLAs differ in one important aspect from other amplifiers. The difference comes from Equation (11-3-18), which shows that gain saturation leads to a time-dependent phase shift across the pulse.

The total phase shift is found by integrating Equation (11-3-18) over the amplifier length and is given by

\[\tag{11-3-26}\phi(\tau)=-\frac{1}{2}\beta_\text{c}\displaystyle\int\limits_0^Lg(z,\tau)\text{d}z=-\frac{1}{2}\beta_\text{c}h(\tau)=-\frac{1}{2}\beta_\text{c}\ln[G(\tau)]\]

Since the pulse modulates its own phase through gain saturation, this phenomenon is referred to as saturation-induced self-phase modulation.

Physically, gain saturation leads to temporal variations in the carrier population, which in turn change the refractive index through the line-width enhancement factor \(\beta_\text{c}\). Changes in the refractive index modify the optical phase.

The frequency chirp is related to the phase derivative as

\[\tag{11-3-27}\Delta\nu_\text{c}=-\frac{1}{2\pi}\frac{\text{d}\phi}{\text{d}\tau}=\frac{\beta_\text{c}}{4\pi}\frac{\text{d}h}{\text{d}\tau}=-\frac{\beta_\text{c}P_\text{in}(\tau)}{4\pi{E_\text{s}}}[G(\tau)-1]\]

where Equation (11-3-22) was used.

Figure 11-17 shows the chirp profiles for several input pulse energies when a Gaussian pulse is amplified in an SLA with 30-dB unsaturated gain. The frequency chirp is larger for more energetic pulses simply because gain saturation sets in earlier for such pulses.

Self-phase modulation and the associated frequency chirp can affect lightwave systems considerably. The spectrum of the amplified pulse becomes considerably broad and contains several peaks of different amplitudes. The dominant peak is shifted toward the red side and is broader than the input spectrum. It is also accompanied by one or more satellite peaks.

Figure 11-18 shows the expected shape and spectrum of amplified pulses when a Gaussian pulse of energy such that \(E_\text{in}/E_\text{s}=0.1\) is amplified by SLAs. The temporal and spectral changes depend on amplifier gain and are quite significant for \(G_0=30\) dB.

The experiments performed by using picosecond pulses from mode-locked semiconductor lasers confirm the expected qualitative behavior. In particular, the spectrum of amplified pulses is found to be shifted toward the red side by 50-100 GHz depending on the amplifier gain.

Spectral distortion in combination with the frequency chirp would affect the transmission characteristics when amplified pulses are propagated through optical amplifiers.

It turns out that the frequency chirp imposed by the SLA is opposite in nature compared with that imposed by directly modulated semiconductor lasers. If we also note that the chirp is nearly linear over a considerable portion of the amplified pulse (see Figure 11-17), it is easy to understand that the amplified pulse would pass through an initial compression stage when it propagates in the anomalous-dispersion region of optical fibers.

Figure 11-19 shows the input pulse, the amplified pulse, and the compressed pulse when a Gaussian pulse is first amplified in an SLA with 30-dB small-signal gain and then propagated through an optical fiber of length \(0.3L_\text{D}\), where \(L_\text{D}\) is the dispersion length. The pulse is compressed by about a factor of 3 because of the frequency chirp imposed on the amplified pulse by the SLA.

Such a compression was observed in an experiment in which 40-ps optical pulses were first amplified in a 1.52-μm SLA and then propagated through 18 km of single-mode fiber with a dispersion of 15 \(\text{ps}/(\text{km}\cdot\text{nm})\).

This compression mechanism can be used to design fiber-optic communication systems in which in-line SLAs are used to compensate simultaneously for fiber loss and dispersion by operating SLAs in the saturation region so that they impose frequency chirp on the amplified pulse.

The basic concept was demonstrated in 1989 in an experiment in which the signal was transmitted over 70 km at 16 Gb/s by using an SLA. Figure 11-20 shows the pulse shapes measured by a streak camera at the fiber output with and without SLA.

In the absence of an SLA or when the SLA was operated in the unsaturated regime, the system was dispersion-limited to the extent that signal could not be transmitted over more than 20 km.

**System Applications**

Several experiments have demonstrated the potential of SLAs as optical preamplifiers. In this application, the signal is optically amplified before it falls on the receiver. The preamplifier boots the signal to such a high level that the receiver performance is limited by shot noise rather than by thermal noise.

The basic idea is similar to the case of avalanche photodiodes (APDs), which amplify the signal in the electrical domain. However, just as APDs add additional noise, preamplifiers also degrade the SNR through spontaneous-emission noise. The relatively large noise figure of SLAs (\(F_\text{n}=5-6\) dB) makes them less attractive as preamplifiers.

Nonetheless, they can improve the receiver sensitivity considerably. In an 8-Gb/s transmission experiment, the use of an SLA preamplifier resulted in a 3.7 dB improvement over the best sensitivity achieved by using APD receivers.

SLAs can also be used as power amplifiers to boost the transmitter power. It is, however, difficult to achieve powers in excess of 10 mW because of a relatively small value (~ 5-7 mW) of the output saturation power.

SLAs have been used as in-line amplifiers in several system experiments. In one experiment, signal at 1 Gb/s was transmitted over 313 km by using four cascaded SLAs. This experiment used the conventional IM-DD (intensity modulation with direct detection) technique for signal transmission.

In a coherent transmission experiment four cascaded SLAs were used to transmit 420-Mb/s FSK signal over 370 km. In a 140-Mb/s coherent experiment, the transmission distance was extended to 546 km by using 10 cascaded SLAs.

Recently, SLAs have been employed to overcome distribution losses in local-area networks. In one experiment an SLA was used as a dual-function device. It amplified five FSK channels multiplexed by using the subcarrier multiplexing technique, improving the power budget by 11 dB.

At the same time, the SLA was used to monitor the network performance through a baseband control channel. The 100-Mb/s baseband control signal modulated the carrier density of the amplifier to produce a corresponding electric signal that was used for monitoring.

Although the potential of SLAs for lightwave system applications has been demonstrated, SLAs need to overcome several drawbacks before their use becomes practical. Among the drawbacks are polarization sensitivity, interchannel cross talk, and a large coupling loss.

Even though SLAs can have a chip gain as high as 30-35 dB, the usable gain is reduced by 8-10 dB because of a large coupling loss occurring at the input and output ends.

Fiber amplifiers are preferable from this standpoint, since their coupling loss (due to fusion splice) is negligible. They are also nearly polarization insensitive and have negligible interchannel cross talk.

SLAs would nonetheless find some applications, as they can be monolithically integrated within the transmitter or receiver. Of particular interest are multiquantum-well (MQW) amplifiers discussed in the next section.

**Multiquantum-Well Amplifiers**

For some applications the polarization independence of gain is not important. An example is a power amplifier following a laser. Since light from the laser is TE polarized, the parameter of interest in this application is high TE gain and high saturation power.

Optical amplifiers with a multiquantum-well (MQW) active region (which have strongly polarization dependent gain) satisfy both of these requirements and therefore ideally suited for this application.

The anisotropic nature of the optical transition in a quantum well makes the TE-mode gain of an MQW amplifier much higher (by more than 10 dB) than the TM-mode gain. MQW amplifiers are capable of much higher output power than regular double-heterostructure (DH) amplifiers.

The output power of an amplifier is limited by gain saturation. If \(P_\text{s}\) is the saturation power in the gain medium, the output saturation power can be approximated by \(P_0=P_\text{s}/\Gamma\) where \(\Gamma\) is the confinement factor of the optical mode.

For MQW amplifiers whose active region consists of a few (generally 3-4) quantum wells 5-10 nm thick, the confinement factor is considerably smaller than that for a regular DH amplifier. This effect results in high saturation power. However, since the signal gain is given by \(G=\exp[(\Gamma{g}-\alpha)L]\) where \(g\) is the material gain, the MQW amplifiers have lower gain than DH amplifiers for the same cavity length.

Gain-saturation characteristics of an optical amplifier are obtained by plotting the measured gain as a function of output power. This is shown in Figure 11-21 for both a DH and an MQW amplifier. Both devices amplify signals near 1.55 μm.

The DH amplifier had a 0.4-μm-thick active region, was 500-μm long and exhibited <1 dB gain difference between TE and TM polarizations. The MQW amplifier result is shown for the TE mode. It had 4 active-layer wells, each 7-nm thick, and barrier layers also 7-nm thick. Saturation powers as high as 100 mW have been reported for MQW amplifiers.

The density of states function for electrons and holes in a quantum well is independent of energy. This features results in a broad spontaneous-emission spectrum and hence a broad gain spectrum of an MQW amplifier.

The measured gain spectrum of a device at two different currents is shown in Figure 11-22(a) while Figure 11-22(b) shows the corresponding output saturation power.

Since the MQW amplifier is ideally suited for amplifying the output power of a semiconductor laser, it is useful to combine amplifier and laser on a single chip and thereby eliminate coupling losses. MQW amplifiers have been integrated with both distributed-feedback (DFB) and distributed-Bragg-reflector (DBR) lasers (see Figure 11-23).

A grating provides the frequency-selective feedback resulting in single-mode operation of the laser. MQW layers grown over the InP substrate serve as the active region for both the laser and the amplifier.

The effectiveness of the amplifier can be seen from Figure 11-24 which shows the \(L-I\) characteristics of the laser with the amplifier biased at 170 mA. The slope of the \(L-I\) curve (2 mW/mA) is about a factor of 10 higher than that for a typical DBR laser without an amplifier.

## 4. Fiber Amplifiers

Amplification of light in a fiber by the interaction of a pump with a signal can be accomplished in a number of ways. These include nonlinear optical phenomena such as Raman amplification and Brillouin amplification or by the stimulated emission from an excited state of a rare-earth ion within the fiber.

Nonlinear methods have been shown to be useful, but they are generally less efficient in transferring energy from pump to signal. The method of placing rare-earth ions in the core of an optical fiber as an amplifying medium was first demonstrated in 1964 by Koester and Snitzer. They observed 40 dB of gain at 1.06 μm in a flashlamp-pumped neodymium-doped fiber 1 m in length. Amplification of light in the wavelength region of minimum loss for a silica-based optical fiber (1.5 μm) using transitions of the erbium ion was demonstrated more than twenty years later.

**Energy Levels**

Fundamental to all rare-earth-doped amplifier systems is the ability to invert the population of ions from the ground state to an excited state. The excited state acts as a storage of pump power from which incoming signals may stimulate emission.

The pumping schemes are broadly classified as either 3- or 4-level systems as shown in Figure 11-25. Erbium is considered a 3-level system. Notable in the 3-level system is an absorption at the signal wavelength when the system is not inverted or underpumped.

The energy levels of the Er^{3+} ion in the glass fiber are shown in Figure 11-26. The local electric field acts as a small perturbation on the erbium ion which results in a splitting of each level of the ion into a number of closely spaced levels (shown for \(^4I_{13/2}\)). The splitting between these levels is usually much smaller than the energy separation between the discrete levels of the ion.

Each of the closely spaced levels are further broadened by their characteristic lifetimes and inhomogeneities in the glass host. This results in the observation of broad absorption and fluorescence spectra. The amplification process involves generation of a sufficiently large number of Er^{+} ions in the excited state using an external laser source. For efficient transfer of energy the wavelength of the external source (pump laser) should match one of the energy levels of the Er^{+} ion.

A laser emitting near 1480 nm will populate directly the first excited state. The most commonly used pump lasers at present emit near 1480 nm and 980 nm. Semiconductor lasers emitting near 1480 and 980 nm are most desirable pump sources.

Pumping at 980 nm is believed to be very efficient and also results in less noise. The main elements of a fiber amplifier are schematically shown in Figure 11-27. The pump power and signal are combined using a wavelength-division multiplexer (WDM). High-power semiconductor lasers emitting at 980 nm and 1480 nm are used as pump sources for fiber amplifiers. Lasers at these wavelengths have been fabricated using InGaAs-GaAs and InGaAsP-InP material systems.

**Fiber Amplifier Performance**

A principal characteristic for a device such as an optical fiber amplifier is optical gain. The measured small-signal gain at two different signal wavelengths as a function of pump power is shown in Figure 11-28. Note that the saturation power is quite high relative to that for a semiconductor amplifier. The pump-laser wavelength is 1.476 μm and the fiber length is 19.5 m. The gain increases rapidly at pump powers near threshold and increases slowly at high pump powers, where almost all the erbium ions along the length of the fiber are inverted.

A figure of merit commonly used to describe the amplifier is the slope of the tangent to the gain-versus-pump-power curve (in dB/mW). Large values indicate a low threshold and a steep rise in gain with pumping. Pump efficiencies vary with pumping wavelength and can be as high as 5.9 dB/mW for 1.48-μm pumping, 11.0 dB/mW for 0.98-μm pumping and 1.3 dB/mW for 0.82-μm pumping.

An important characteristic of an amplifier is the noise figure defined by Equation (11-2-12). The noise figure for a fiber amplifier is given by

\[\tag{11-4-1}F_\text{n}=\frac{1}{\eta_\text{in}}\frac{2n_\text{sp}(G-1)+\frac{1}{\eta_\text{out}}\frac{1}{\eta_\text{det}}}{G}\]

where \(\eta_\text{in}\) and \(\eta_\text{out}\) are the input and output coupling efficiencies, \(\eta_\text{det}\) is the detector quantum efficiency, \(G\) is the gain of the fiber amplifier, and \(n_\text{sp}\) is the spontaneous-emission factor. Under ideal conditions, \(\eta_\text{in}=1\), \(G\gg1\) and \(n_\text{sp}=1\) which results in \(F_\text{n}\approx2n_\text{sp}\approx3\) dB. The measured values of \(F_\text{n}\) for 1.48-μm, 0.98-μm, and 0.82-μm pumping are 4.1 dB, 3.2 dB, and 4.0 dB, respectively. The noise figure is lowest for 0.98-μm pumping.

Erbium-doped fiber amplifiers are relatively well developed. Amplifiers operating near 1.3 μm are also being investigated. Optical gain has been reported in fluorozirconate fibers doped with 560 ppm of Pr^{3+} and pumped at 1.007 μm. The measured gain at 1.3 μm as a function of the launched pump power is shown in Figure 11-29. These initial results are promising, even though the pump power is considerably higher than that for an erbium-doped fiber amplifier. Availability of commercial-grade fiber amplifiers at 1.3 μm will have a strong impact on the design of lightwave systems.

The next tutorial discusses about ** Photonic Integrated Circuits (PIC)**.