Performance of DFB Semiconductor Lasers

This is a continuation from the previous tutorial - DFB (distributed feedback) semiconductor lasers.

In the previous tutorial, we briefly discussed the heterostructures used to make a DFB semiconductor laser. The purpose of this section is to describe their performance by considering the continuous wave (CW) and pulsed modes of operation.

The features to be considered are the \(L-I\) curves and their temperature dependence, the longitudinal-mode spectra and the extent of side-mode suppression, and the modulation-response characteristics such as modulation bandwidth and frequency chirp.

In the previous series tutorials we discussed these features for an FP semiconductor laser. We shall refer to them in comparing the performances of FP and DFB semiconductor lasers.

1. CW Operation

The \(L-I\) curves at different temperatures characterize the CW performance of a semiconductor laser and are useful for indicating how the threshold current \(I_\text{th}\) and the differential quantum efficiency \(\eta_\text{d}\) degrade as the device temperature increases.

Figure 7-11 shows the \(L-I\) curves of a 1.55-μm DFB laser with the DCPBH structure [see Figure 7-2 in the DFB semiconductor lasers tutorial].

This device has a first-order grating (\(\Lambda=240\) nm) and the corrugation depth after regrowth is estimated to be 30 nm. The cavity length is about 300 μm with both facets cleaved.

Figure 7-11 should be compared with Figure 5-26 [refer to the strongly index-guided lasers tutorial] obtained for an FP-type DCPBH laser.

Several features of the \(L-I\) curves are noteworthy. At room temperature the threshold current is about 30 mA and the slope is nearly constant up to a power level of 10 mW from each facet.

The two-facet differential quantum efficiency \(\eta_\text{d}\) at room temperature is typically 30-40% for these devices. From the temperature dependence of the threshold current, the characteristic temperature \(T_0\) [refer to the temperature dependence of threshold current of semiconductor lasers tutorial] is estimated to be 67 K at room temperature.

The performance of these DFB lasers is comparable to DCPBH FP lasers as far as \(L-I\) curves are concerned.

However, DFB lasers are expected to outperform conventional FP lasers with respect to their spectral purity. This is shown in Figure 7-12 where the longitudinal-mode spectra at \(I=1.5I_\text{th}\) are shown at several temperatures for the device of Figure 7-11.

The DFB laser maintains the same longitudinal mode in the entire temperature range of \(20-108^\circ\text{C}\). By contrast, an FP semiconductor laser would exhibit several mode jumps over this temperature range because of the temperature-induced shift of the gain peak.

The stability of the DFB longitudinal mode is due to the built-in grating whose period determines the lasing wavelength [see Equation (7-2-1) in the DFB semiconductor lasers tutorial].

In Figure 7-12 the wavelength changes slightly with temperature at a rate \(\text{d}\lambda/\text{d}T\approx0.09\text{ nm}/^\circ\text{C}\). This happens because the mode index \(\bar{\mu}\) in Equation (7-2-1) [refer to the DFB semiconductor lasers tutorial] varies with temperature.

However, the wavelength shift for a DFB laser is considerably smaller compared with that of an FP laser, where \(\text{d}\lambda/\text{d}T\approx0.5\text{ nm}/^\circ\text{C}\).

The calculated value of of \(\text{d}\lambda/\text{d}T\) for the DFB laser is about \(0.1\text{ nm}/^\circ\text{C}\) after including the temperature dependence of the carrier-induced contribution to the refractive index and is in agreement with the experimental value.

The mode-suppression ratio (MSR), defined as the ratio of the power of the main mode to that of the most intense side m ode, plays an important role in characterizing the spectral purity.

For the FP laser, an MSR greater than 50 is difficult to achieve; typical values fall in the 10-20 range. For the DFB laser, MSR values of \(\sim1000\) (30 dB) are readily obtained at power levels of a few milliwatts. For example, the MSR for the laser in Figure 7-12 was over 35 dB at a 5-mW output level.

To understand the origin of such a high degree of spectral purity in DFB laser, we consider the multimode analysis of the longitudinal-mode spectrum part of the steady-state characteristics of semiconductor lasers tutorial.

If we use Equation (6-3-9) to obtain the powers \(P_0\) and \(P_1\) for the main mode and the most intense side mode, respectively, the MSR is given by

\[\tag{7-4-1}\text{MSR}=\frac{P_0}{P_1}=\frac{\gamma_1-G_1}{\gamma_0-G_0}\]

where

\[\tag{7-4-2}\gamma_i=v_\text{g}(\bar{\alpha}_i+\alpha_\text{int})\]

is the photon decay rate and

\[\tag{7-4-3}G_i=\Gamma{v_\text{g}}g(n,\omega_i)\]

is the net rate of stimulated emission for the mode lasing at the frequency \(\omega_i\).

In contrast to an FP laser, the photon decay rate is different for different modes because of the frequency-selective feedback provided by the grating. This is evident in Figures 7-4 to 7-6 [refer to the DFB semiconductor lasers tutorial], where the mode-gain coefficient \(\bar{\alpha}\) is lowest for the main mode.

If we define \(\Delta\gamma\) and \(\Delta{G}\) as \(\Delta\gamma=\gamma_1-\gamma_0\) and \(\Delta{G}=G_0-G_1\), Equation (7-4-1) becomes

\[\tag{7-4-4}\text{MSR}=1+\left(\frac{\Delta\gamma+\Delta{G}}{\gamma_0\delta}\right)\]

where \(\delta=1-G_0/\gamma_0\) and is a small dimensionless parameter whose value is \(\sim10^{-4}\) and decreases with an increase in the main-mode power [see Equation (6-3-11) in the steady-state characteristics of semiconductor lasers tutorial].

For an FP laser, \(\Delta\gamma=0\) and \(\Delta{G}\) alone, arising from the gain roll-off, provides mode discrimination. However, \(\Delta{G}/G_0\) for the two adjacent longitudinal modes is typically less than 0.5% and the \(\text{MSR}\le50\).

For a DFB laser the relative change \(\Delta\gamma/\gamma_0\) in the photon decay rates can be made \(\sim10\%\) with a proper design, and MSR values of \(\sim1000\) can be achieved. The required loss margin depends on \(\delta\) and is \(4-5\text{ cm}^{-1}\) when \(\delta=5\times10^{-5}\).

The performance of the DCPBH DFB lasers shown in Figures 7-11 and 7-12 was achieved with the use of a first-order grating.

The use of a second-order grating can also lead to high-performance DFB lasers. However, since the coupling coefficient is generally smaller for a second-order grating [see Figure 7-8 in the DFB semiconductor lasers tutorial], the mode discrimination between the lowest-gain DFB mode and the FP mode (closest to the gain peak) is likely to be poor unless the gain peak is made to nearly coincide with the Bragg wavelength. This can be understood from Equation (7-4-4) by noting that \(\Delta{G}\lt0\) in the case of gain-peak deviation from Bragg resonance.

Furthermore, since the gain peak shifts with the drive current and the temperature, such DFB lasers may exhibit high MSRs only over a limited current and temperature range.

Their performance can be improved by making one or both facets low-reflecting; this increases the losses for the FP modes, which results in making \(\Delta\gamma\) in Equation (7-4-4) larger. Reduced facet reflectivity can be achieved by etching or burying the facet or by using an antireflection coating.

The use of a low-reflectivity facet, however, increases the device threshold, as can be seen by comparing Figures 7-5 and 7-6 [refer to the DFB semiconductor lasers tutorial].

High-performance DCPBH lasers with a second-order grating, one cleaved facets dn one low-reflectivity facet have been demonstrated at both 1.3-μm and 1.5-μm wavelengths. The threshold current is typically 50-60 mA. At the 1.3-μm wavelength, a relatively high power (over 55 mW) at room temperature has been achieved under CW operation, and the laser exhibited CW operation up to a temperature of \(105^\circ\text{C}\) while maintaining the single longitudinal mode. At the 1.55-μm wavelength, the corresponding reported values of power and temperature are 20 mW and \(75^\circ\text{C}\). Comparable performance has also been achieved using other buried-heterostructure-type lasers.

The performance of DFB lasers is quite sensitive to the facet reflectivities. As discussed in the DFB semiconductor lasers tutorial and shown in Figures 7-5 and 7-6, the loss margin \(\Delta\gamma\), or the difference \(\Delta\alpha\) in the threshold gain of the main and side modes, depends not only on the facet reflectivities but also on the grating phases \(\phi_1\) and \(\phi_2\) at the two facets.

In particular, the gain margin \(\Delta\alpha\) becomes quite small for some specific phase combinations, indicating that those DFB lasers will not oscillate in a single longitudinal mode.

Since \(\phi_1\) and \(\phi_2\) can vary randomly from device to device, the performance of DFB lasers can be characterized only in a statistical sense. The "yield" of acceptable devices can be estimated numerically by finding the fraction of phase combinations for which \(\Delta\alpha\) exceeds a certain value.

Figure 7-13 shows the numerically calculated yield as a function of \(\Delta\alpha{L}\) for several combinations of the facet reflectivities \(R_1\) and \(R_2\) (given in parentheses) for a DFB laser with \(\kappa{L}=2\).

Typically \(\Delta\alpha{L}\) should exceed 0.2 for the satisfactory performance of a DFB laser. The dashed curve in Figure 7-13 shows that the yield of acceptable devices for this value of \(\Delta\alpha{L}\) is below 50% for a laser with uncoated facets (\(R_1=R_2=32\%\)). However, it can be made to exceed 80% by a proper combination of the facet reflectivities.

Many other laser characteristics such as the threshold current \(J_\text{th}\), the differential quantum efficiency \(\eta_\text{d}\), and the laser line width, also depend on the facet reflectivities and the grating phases.

Yield curves similar to those shown in Figure 7-13 can be generated by considering the phase combinations that satisfy not only the gain-margin condition but also preset conditions on \(J_\text{th}\), and \(\eta_\text{d}\).

The numerical results show that it is possible to achieve an overall yield of 80-90% by a proper choice of values for the parameters \(\kappa{L}\), \(R_1\), and \(R_2\). In particular, a combination of low-reflection (\(\sim1\%\)) and high-reflection (\(80-90\%\)) coatings on the laser facets has provided DFB lasers of high output powers with high yield.

2. Modulation Performance

For their application in high-bit-rate optical communication systems, the performance of DFB semiconductor lasers under high-frequency direct modulation is of significant interest.

Conventional FP lasers suffer from one drawback: they become essentially multimode (MSR \(\sim1\)) under direct modulation even when the side modes are reasonably suppressed during CW operation.

Unless dispersion-shifted fibers are used, the large source bandwidth, combined with fiber dispersion at the 1.55-μm wavelength, severely limits the allowable bit rate for long-distance optical transmission through silica fibers.

DFB semiconductor lasers are expected to overcome this limitation by virtue of their design.

Figure 7-14 shows the measured powers in the main mode and the most intense side mode of a buried-heterostructure laser with a second-order grating and a tilted (nonreflecting) facet.

Solid curves were obtained under a sinusoidal modulation of 500 MHz with a peak-to-peak amplitude of 14 mA. Dashed curves show for comparison the mode powers under CW operation.

The DFB laser maintains an MSR of about 30 dB in a large current range. The lowest value of MSR (~ 16 dB) occurs at the 67-mA bias current corresponding to a 100% depth of modulation.

Similar behavior has been observed for other DFB structures. A properly designed, state-of-the-art DFB semiconductor laser can maintain the single-longitudinal-mode operation with an MSR greater than 30 dB under direct modulation in the gigahertz range. It is this property that makes the DFB laser an ideal candidate for high-bit-rate optical communication systems.

The multimode rate equations (6-2-25) and (6-2-26) [refer to the rate equations for semiconductor lasers tutorial] can be used to simulate the longitudinal-mode spectra of DFB lasers under transient conditions after using Equation (7-4-2) for the photon decay rates.

The numerical results show that coupling-coefficient values as small as \(\kappa{L}=0.15\) significantly reduce the side-mode power at the first relaxation-oscillation peak when compared with the FP case (\(\kappa=0\)), where the main and side modes are almost equally intense [see Figures 6-7 and 6-8 in the transient response of semiconductor lasers tutorial]. The side mode remains suppressed by more than 20 dB at all times when \(\kappa{L}=1\).

These results suggest that for a 250-μm-long laser a coupling coefficient \(\kappa\) of \(40\text{ cm}^{-1}\) is large enough to provide dynamic side-mode suppression. Such values of \(\kappa\) are readily achieved with both first- and second-order gratings. Numerical simulations using the multimode rate equations under 2 Gb/s direct modulations also show that an MSR of 30 dB is maintained as long as the relative loss difference [\(\Delta\gamma/\gamma_0\) in Equation (7-4-4)] is greater than ~ 10%.

Similar to the experimental data of Figure 7-14, the MSR depends on the bias level. Figure 7-15 shows the MSR calculated by solving the rate equations numerically as a function of the relative loss difference \(\Delta\gamma/\gamma_0\) at several bias levels.

The MSR is defined as the ratio of the pulse energies for the main and side modes. In general, the modulation performance of a DFB laser is superior in the sense of maintaining high MSR when the laser is biased slightly above threshold.

The direct modulation also leads to wavelength chirping that shifts the laser wavelength over a wide range during each modulation cycle. This range is usually referred to as the chirp and is typically ~ 0.1 nm under practical conditions.

The wavelength chirp leads to a significant dispersion penalty in optical communication systems and is often the limiting factor in their performance.

The origin of the chirp relates to the carrier-induced index change accompanying the modulation-induced gain variations.

Since carrier-induced index changes are about the same for FP and DFB lasers operating under identical conditions, the wavelength chirp for DFB lasers is expected to be comparable to that observed for FP lasers. Measurements of the chirp for DFB lasers have shown that this is indeed the case.

However, the amount of chirp is dependent to some extent on the device structure [see Figure 6-15 in the noise characteristics of semiconductor lasers tutorial]. With a proper design, DFB lasers with a chirp of only 0.4 nm under 2-GHz modulation were realized as early as 1985.

Another important characteristic that should be considered is the modulation bandwidth \(\nu_\text{B}\). Under ideal conditions it is determined by the relaxation-oscillation frequency \(\nu_\text{R}\), which can be increased by increasing the bias power \(P_\text{b}\) since \(\nu_\text{R}\propto{P}_\text{b}^{1/2}\).

However, in practice electrical parasitics can decrease the modulation response by more than 3 dB for frequencies well below \(\nu_\text{R}\), thereby significantly reducing the modulation bandwidth. The bandwidth of early DFB lasers was often limited to below 5 GHz because of electrical parasitics.

Advances in packaging technology resulted in considerable improvement after 1985. A DFB laser exhibited a modulation bandwidth of 14 GHz in 1987. Figure 7-16 shows the modulation response of this laser at several bias levels. The 3-dB bandwidth exceeds 14 GHz when the laser is biased at \(I_\text{b}=7.69I_\text{th}\).

A modulation bandwidth of 17 GHz was realized in 1989 by using a phase-shifted DFB laser. Since phase-shifted DFB lasers have several advantages over conventional design, we turn to their discussions in the next subsection.

3. Phase-Shifted DFB Lasers 

As discussed in the longitudinal modes and threshold gain section of the DFB semiconductor lasers tutorial, DFB lasers designed such that they experience an extra phase shift in the middle of the laser cavity have a low-threshold mode (the so-called gap mode) whose frequency lies inside the stop band associated with conventional DFB lasers.

In the case of \(90^\circ\) or \(\pi/2\) phase shift, the mode lies at the center of the stop band and its wavelength coincides exactly with the Bragg wavelength. At the same time, the gain margin between this mode and the neighboring modes is so large (\(\gt20\%\)) that side modes of such a laser are likely to remain suppressed (by more than 30 dB) even when the laser is directly modulated at high speeds in the GHz range. Such phase-shifted DFB lasers are referred to as \(\lambda/4\)-shifted DFB lasers since the \(\pi/2\) phase shift is realized by shifting the grating by a quarter wavelength.

Several schemes were proposed around 1984-85 to realize such a phase shift during the grating fabrication. Since then, phase-shifted DFB lasers have been extensively studied. This section reviews the performance issues associated with such devices.

The advantages of phase-shifted DFB lasers can be understood by considering the threshold characteristics such as the gain of the lowest-loss mode, the gain margin \(\Delta\alpha\) between the main and the side modes, and the detuning of various modes from the Bragg wavelength.

These quantities can be calculated by solving the coupled-mode equations, Equations (7-3-15) and (7-3-16) [refer to the DFB semiconductor lasers tutorial], with the appropriate boundary conditions. 

The main difference from the theory of the DFB semiconductor lasers tutorial is the the parameter \(\Delta\beta\) is no longer constant along the entire cavity length because of the abrupt phase shift occurring in the middle of the cavity.

Since \(\Delta\beta\) is constant in the two sections on each side of the phase-shift region, a simple approach applies the analytic solution of the DFB semiconductor lasers tutorial to each section and connects the two solutions in the middle through the phase shift.

Such an approach is referred to as the matrix method since propagation through each section is governed by a \(2\times2\) matrix. It can be readily extended to study devices with multiple phase shifts or multisection devices with different grating parameters in each section.

In the case of \(\lambda/4\)-shifted DFB laser with negligible facet reflectivities the lowest-loss mode is found to be located exactly at the Bragg wavelength.

The gain margin \(\Delta\alpha\) depends on the coupling coefficient \(\kappa\), but is much larger than that for conventional DFB lasers. For example, \(\Delta\alpha{L}\) exceeds \(1\) when \(\kappa{L}=2\). It is this property of phase-shifted DFB lasers that makes them attractive since the MSR can remain quite large even under high-speed modulation for such large values of the gain margin.

However, similar to the case of conventional DFB lasers, the gain margin is very sensitive to the facet reflectivities. Generally speaking, both facet reflectivities should be quite small (\(\ll1\%\)) and the coupling coefficient should not be too high before the yield of \(\lambda/4\)-shifted DFB lasers is at an acceptable level.

There are two main problems associated with \(\lambda/4\)-shifted DFB lasers.

First, as discussed in the threshold behavior section of the DFB semiconductor lasers tutorial, the gain margin between the TE and TM modes is generally small in DFB lasers compared with FP lasers. This problem becomes especially severe for \(\lambda/4\)-shifted DFB lasers since the loss differential resulting from different facet reflectivities of TE and TM modes is absent. Phase-shifted DFB lasers need to be carefully designed to enhance the gain margin between the TE and TM modes.

The second problem rests from a phenomenon referred to as longitudinal spatial-hole-burning.

The mode intensity in \(\lambda/4\)-shifted DFB lasers is highly nonuniform and peaks in the center of the cavity where the phase-shift region is located. Because of enhanced stimulated emission occurring near the cavity center, the gain, or equivalently the carrier density, is depleted more in the center than near the cavity ends, as if a spatial hole were burnt in the axial profile of the carrier density.

Since the refractive index of the optical mode depends negatively on the carrier density, a lower carrier density implies an increase in the local refractive index. This change translates into an extra power-dependent phase shift near the cavity center that adds to the built-in phase shift.

Since the gain margin depends on the amount of phase shift and is maximum for a shift of \(\pi/2\), it degrades with an increase in the output power. Eventually the side mode becomes strong enough that the laser no longer qualifies as a single-longitudinal-mode laser.

The extent of degradation depends on nonuniformity of the axial intensity profile which in turn depends on the coupling coefficient. Numerical results show that longitudinal spatial-hole burning is particularly severe for large values of \(\kappa{L}\). In particular, the intensity profile is least nonuniform for \(\kappa{L}=1.25\). For this reason, \(\lambda/4\)-shifted DFB lasers often employ low values of \(\kappa{L}\) in the range of \(1-1.5\).

Several schemes can be used to counteract the impact of spatial-hole burning in phase-shifted DFB lasers.

For example, the laser can be designed with a nonoptimum built-in phase shift \(\phi_\text{sh}\lt\pi/2\). Even though the gain margin is reduced near threshold, spatial-hole burning initially improves the gain margin before it comes so severe that the gain margin nearly vanishes. The net result is to enhance the range of single-mode operation.

A similar effect can be achieved by injecting the current nonuniformly such that the carrier density at threshold is higher in the center than near the cavity edges. Spatial-hole burning burns the hole, but the laser can be operated to higher powers before its impact becomes too severe.

Another technique consists of designing DFB lasers with multiple phase-shift regions. The number, the location, and the amount of phase shift then provide additional control over the extent of spatial-hole burning since they affect the intensity distribution of the lasing mode.

Figure 7-17 compares the axial distribution of mode intensity when the number of phase-shift regions \(N_\text{sh}\) varies from 1 to 3.

The phase shift in each region is assumed to be the same, and the phase-shift regions are located symmetrically with equal spacing. Thus, phase shifts occur with a spacing of \(L/(N_\text{sh}+1)\) for a cavity of length \(L\).

The amount of phase shift \(\phi_\text{sh}\) is optimized for each value of \(N_\text{sh}\) to obtain the maximum gain margin (\(\phi_\text{sh}=90^\circ,50^\circ,\text{and }65^\circ\) for \(N_\text{sh}=1,2,\text{and }3\), respectively).

In all cases the mode intensity peaks at the location of the phase-shift regions. However, the intensity distribution is considerably more uniform for \(N_\text{sh}=2\) and \(3\) compared with \(N_\text{sh}=1\), resulting in reduced spatial-hole burning.

Spatial-hole burning can also be reduced by making the coupling coefficient nonuniform such that it is smallest in the central portion of the cavity.

In another approach, the corrugation pitch of the gating is made larger in the central region of the cavity so that the phase shift is distributed over a wider region. The length of the central region and the pitch difference are chosen such that the optical field experiences a phase shift of \(\pi/2\). Such lasers are called corrugation-pitch-modulated DFB lasers.

4. Multiquantum-Well DFB Lasers

The use of a multiquantum-well (MQM) design has several advantages over conventional semiconductor lasers with a single, relatively thick (~ 0.1 μm) active layer. It is thus natural to consider its use for DFB lasers as well.

Even though DFB lasers with an MQW active region were fabricated as early as 1985 by using LPE, their development had to wait until the use of the MOVPE and MBE growth techniques became practical.

Such DFB lasers are called MQW DFB lasers and have been extensively studied since 1988. This section briefly reviews their performance.

The advantages of the MQW structure stem from a fundamental change in the density of states associated with the conduction and valence bands of a thin layer (thickness ~ 10 nm) because of the quantum-size effects.

Both the gain and refractive index are affected by changes in the density of states. In particular, the differential gain, quantified by the parameter \(a\), is larger by about a factor of 2 while, at the same time, the line-width enhancement factor \(\beta_\text{c}\), is smaller by about a factor of 2. These changes favorably affect many laser characteristics such as the threshold current, modulation bandwidth, frequency chirp, and the laser line width.

The use of an MQW structure in a phase-shifted DFB laser has considerably improved the performance of DFB lasers operating at 1.55 μm. Most of the improvements occur because of a lower value of the line-width enhancement factor \(\beta_\text{c}\) in MQW lasers compared with the conventional DFB lasers.

In the case of a phase-shifted MQW DFB laser, lower values of \(\beta_\text{c}\) reduce the degradation caused by the spatial-hole burning, a major benefit as far as the yield issue is concerned.

This benefit can be understood by noting that the reduction in the carrier density near the phase-shift region caused by spatial-hole burning results in a smaller change in the refractive index (or the phase shift) in MQW DFB lasers simply because the index change is proportional to \(\beta_\text{c}\). As a result, values of the MSR as large as 40-50 dB can be maintained over a large current range.

Such lasers can provide 20-30 mW of output power with a high MSR while maintaining a line width below 1 MHz. In fact, line widths as small as 170 kHz have been obtained by using lasers with a 1.2-mm cavity length.

Figure 6-15 [refer to the noise characteristics of semiconductor lasers tutorial] shows the line width of an 800-μm MQW DFB laser as a function of the output power. This laser attains a 270-kHz line width at an output power of only 13.5 mW.

MQW DFB laser also show excellent modulation characteristics. The small-signal bandwidth can attain a value as large as 14 GHz with an optimization of the number and thickness of quantum wells. Such lasers can be modulated at bit rates as high as 10 Gb/s and exhibit ultralow values of the frequency chirp because of relatively low values of \(\beta_\text{c}\).

Strained-layer MQW DFB lasers have also been developed since a proper amount of strain can further lower the line-width enhancement factor \(\beta_\text{c}\) and result in even better performance.

MQW DFB lasers have been used in many transmission experiments. These experiments shows the potential application of such lasers in 1.55-μm lightwave systems operating at 10 Gb/s.

5. Gain-Coupled DFB Lasers

Distributed feedback in most DFB lasers is generated by introducing a periodic variation of the modal refractive index. However, distributed feedback can also occur when the modal gain varies periodically along the cavity length. Such lasers are called gain-coupled DFB lasers since the coupling between the forward- and backward-propagating waves is provided by the gain in place of the refractive index.

Their properties were analyzed by Kogelnik and Shank in 1972. Attempts were made soon after to fabricate gain-coupled DFB lasers by etching the active layer to provide a periodic modulation of its thickness. Such attempts were not very successful because of the defects introduced during the etching process.

Interest in gain-coupled DFB lasers revived in the late 1980s because of the yield problems associated with index-coupled DFB lasers (see Figure 7-13). Extensive studies began and have shown there are many properties that make gain-coupled DFB lasers superior to index-coupled DFB lasers.

The coupled-mode equations introduced in the coupled-wave equations section of the DFB semiconductor lasers tutorial can be used to understand the performance advantages of gain-coupled DFB lasers.

The main difference is that the coupling coefficient \(\kappa\) is no longer real, but becomes complex. It can be written as \(\kappa=\kappa_\text{r}+\text{i}\kappa_\text{i}\), where \(\kappa_\text{r}\) and \(\kappa_\text{i}\) represent the contributions of index and gain gratings, respectively.

In the case of pure gain coupling, \(\kappa_\text{r}=0\) and \(\kappa\) is imaginary. The lowest-threshold mode of such a laser lies exactly at the center of the stop band associated with index-coupled DFB lasers.

The gain margin \(\Delta\alpha{L}\) depends on the value of \(\kappa_\text{i}L\) and exceeds \(0.2\) even for its relative low values (\(\kappa_\text{i}L\gt0.5\)). This feature is similar to the case of phase-shifted DFB lasers.

However, in contrast with phase-shifted DFB lasers the gain margin is not very sensitive to facet reflections or to the grating phases at the facets. As a result, a relatively high yield can be obtained even for lasers whose facets are left as cleaved.

The impact of spatial-hole burning is also reduced in gain-coupling DFB lasers. These advantages are maintained even in the case of partial gain coupling, a case commonly encountered in practice, as long as \(\kappa_\text{i}\) is properly optimized (in the range \(1.5-2\)). With a proper design, the yield of gain-coupled DFB lasers can exceed 80% even after taking into account the effect of spatial-hole burning.

The simplest way to induce gain coupling in a DFB laser is to insert an absorbing layer between the transparent cladding layer and the substrate [see Figure 7-7 in the DFB semiconductor lasers tutorial] before the grating is etched. The absorbing layer is partially etched away during the grating formation, resulting in an internal absorption that has the grating periodicity.

Indeed, this was the approach adopted for the demonstration of a gain-coupled DFB laser in 1989. Periodic modulation of the internal loss is equivalent to gain modulation along the cavity length since the gain has to be higher in the high-loss region to overcome the cavity losses at threshold.

Such a gain grating is invariably accompanied by an index grating since the structure is basically the same as the one used for index-coupled DFB lasers. The coupling coefficient \(\kappa\) is not only complex but is generally dominated by the index coupling (\(\kappa_\text{r}\gg\kappa_\text{i}\)). The experimental data revealed that even small values of \(\kappa_\text{i}\) improve the device performance significantly.

It is possible to design a DFB laser in which the mode coupling is almost completely provided by the gain (\(\kappa_\text{r}\ll\kappa_\text{i}\)). The basic idea is to grow the cladding and active layers on top of the etched grating in such a way that the thickness of both layers is spatially modulated along the cavity length, resulting in two gratings.

The bottom grating provides only index coupling (\(\kappa_\text{i}=0\)), but the top grating formed by thickness variations of the active layer has a complex coupling coefficient because both the gain and the index are periodically modulated.

Furthermore, the two index gratings are not in phase, making it possible nearly to cancel their contributions with a proper design. Such a DFB laser has almost pure gain coupling and has a number of attractive features.

Gain-coupled 1.55-μm DFB lasers with a corrugated active layer have been found to have excellent operating characteristics with threshold currents as low as 12 mA and an MSR as high as 55 dB.

The same technique can also be used to produce gain-coupled single-quantum-well lasers by growing an ultrathin active layer whose thickness is periodic along the cavity length.

The main advantage of gain-coupled DFB lasers is that their performance is relatively unaffected by the facet reflections, and they can be used without requiring an antireflection coating at the facets.

The insensitivity to facet reflections results in a high yield since the grating phases at the facets do not play an important role in determining the laser performance. Such lasers are also relatively immune to the external feedback.

This insensitivity to the facet or external reflections can be understood qualitatively by noting that the laser can adjust its axial intensity distribution to take advantage of the gain grating. A gain-coupled DFB laser uses its gain most effectively if the intensity is high in the high-gain regions and low in the low-gain regions. Thus, the intensity distribution is determined by the gain grating in contrast with index-coupled lasers where facet reflections and phase-shift locations determine the intensity distributions.

For this reason, spatial-hole burning is less important in gain-coupled DFB lasers. The effective line-width enhancement factor \(\beta_\text{c}\) is also affected by the gain grating and can be made quite small under certain conditions. These properties of gain-coupled DFB lasers make them an ideal device for many applications in the field of lightwave technology.

The next tutorial discusses about DBR (distributed Bragg reflector) semiconductor lasers.