Gain-Guided Lasers

This is a continuation from the previous tutorial - broad-area lasers.

Most injection lasers intended for commercial applications have a built-in feature that restricts current injection to a small region along the junction plane.

This restriction serves several purposes:

1. It allows continuous-wave (CW) operation with reasonably low threshold currents (10-100 mA) compared with an unacceptably high value (~ 1 A) for broad-area lasers;
2. It can allow fundamental-mode operation along the junction plane, which is necessary for applications where the light is coupled into an optical fiber
3. The requirements for heat sinking are considerably less severe than those for a broad-area laser
4. The low operating current allows operation at high temperatures and increases the operating life of the device.

The simplest current-restricting structure is an oxide-stripe device, originally fabricated by Dyment and used to study the transverse-mode structure along the junction plane in AlGaAs injection lasers.

A variation of the above structure, the proton-stripe AlGaAs laser, has become the workhorse for many commercial applications in systems employing AlGaAs lasers.

Figure 5-5 shows three gain-guided laser structures fabricated using the InGaAsP material system. There are

1. The oxide-stripe laser, where an SiO₂ layer on the p contact confines the injected current flow to a small region through an opening in the dielectric
2. The proton-stripe or deuteron-stripe laser, where the implanted protons or deuterons create a region of high resistivity that restricts the current flow to an opening in the implanted region
3. The junction-stripe laser, where Zn diffusion converts a small region of the top n-type layer into p type, thus providing a current path while the reverse-biased junction over the remaining region provides current confinement.

Variations of the above structures can also be found in the literature.

In all these structures, the active region is planar and continuous. The stimulated-emission characteristics of such a laser are determined by the carrier distribution (which provides optical gain) along the junction plane.

Since the optical mode distribution along the junction is determined by the optical gain, these lasers are called gain-guided lasers. The physics behind the gain-guiding mechanism has been discussed in the waveguide modes in semiconductor lasers tutorial.

Figure 5-6(a) shows the typical light-current (L-I) characteristics of a gain-guided deuteron-stripe InGaAsP laser (\(\lambda=1.3\) μm). These devices were fabricated using an 8-μm-thick wire as a bombardment mask.

The 250-μm long lasers had threshold currents in the range 100-150 mA. Similar threshold current values have been reported for other types of gain-guide lasers.

Typical spectral emission characteristics of these lasers are shown in Figure 5-6(b). The laser emits at several wavelengths, each of which corresponds to a different longitudinal mode of the laser cavity, as discussed in the threshold condition and longitudinal modes in semiconductor lasers tutorial.

Note that the longitudinal modes shift toward longer wavelengths as the drive current increases. This is a consequence of the temperature-induced shift of the gain peak as a result of device heating at high currents.

We now discuss some specific characteristics (generally undesirable) of gain-guided lasers.

Kinks in Light-Current Characteristics

As the current through the laser is increased, the L-I characteristics of a gain-guided laser often exhibit a "kink", or nonlinearity.

The nonlinearity can be associated with a movement of the optical mode along the junction plane, a transition to higher-order modes, or a transition from the TE to the TM mode.

Such a nonlinear response can severely alter the amount of light coupled into an optical fiber and thus limits the usefulness of the laser in an optical communication system.

Figure 5-7 shows an example of the kink for an oxide-stripe laser.

The lasers with narrow stripes exhibit kinks at higher operating powers than do lasers with wide stripes, as observed for AlGaAs proton-stripe lasers.

Pulsations

Many gain-guided injection lasers exhibit sustained oscillations or pulsations; i.e., the emitted light pulsates at a certain frequency (typically in the range of 200-500 MHz).

Figure 5-8 shows an example of a self-pulsing laser. The bottom trace shows the long duration current pulse, and the top trace shows the emitted light pulses at a repetition rate of ~ 200 MHz.

The self-pulsing phenomenon has been extensively studied for AlGaAs proton-stripe gain-guided lasers. Similar characteristics have been observed for InGaAsP lasers.

In general, the pulsation frequency increases with increasing drive current, approximately obeying the simple relation

\[\tag{5-3-1}\Omega_\text{R}\propto\left(\frac{I}{I_\text{th}}-1\right)^{1/2}\]

where \(\Omega_\text{R}\) is the pulsation frequency, \(I_\text{th}\) is the threshold current, and \(I\) is the injection current.

It will be seen in a later tutorial that \(\Omega_\text{R}\) is the relaxation-oscillation frequency of an intrinsic laser resonance.

Self-pulsing semiconductor lasers have found commercial applications in optical-disk systems (e.g., compact-disk players) because of their relative insensitivity to external optical feedback.

Several models exist in the literature that explain the observation of pulsation in injection lasers. A saturable-absorption model proposed by Joyce and Dixon satisfactorily accounts for pulsations.

This model relies on a fundamental nonlinear relation between the optical gain and the injected carrier density in semiconductor lasers. This relation is shown schematically in Figure 5-9.

The pulsation phenomenon can be understood in the following qualitative way.

Consider an injection laser that has a nonuniform carrier density along the cavity length. Such nonuniformity is generally localized and can arise from defects in the active layer, nonradiative recombination at mirror facets, or local variation in current injection caused by processing defects.

The carrier density in these regions is smaller than the average value across the cavity length. Let \(n_1\) denote the carrier density at the defects and \(n_0\) be the average carrier density.

When a current \(\Delta{I}\) is injected into the laser, the carrier density \(n_1\) changes by \(\Delta{n}_1\) and the average carrier density \(n_0\) changes by \(\Delta{n}_0\) (see Figure 5-9).

The corresponding changes in the gain or loss are \((\text{d}g/\text{d}n_0)\Delta{n}_0\) and \((\text{d}g/\text{d}n_1)\Delta{n_1}\). If \(l\) is the length of the defective region and \(L\) is the length of the laser, a net optical gain results if

\[\tag{5-3-2}l\left(\frac{\text{d}g}{\text{d}n_1}\right)\Delta{n_1}\gt{L}\left(\frac{\text{d}g}{\text{d}n_0}\right)\Delta{n_0}\]

The condition can be satisfied for some values of \(l\) and \(L\) since \(\text{d}g/\text{d}n_1\gt\text{d}g/\text{d}n_0\) as seen in Figure 5-9.

If Equation (5-3-2) is satisfied, an increase in the injected current results in a net increase in the above-threshold gain, which causes the stimulated emission to rise suddenly.

This sudden increase in stimulated emission causes a depletion of carriers to a below-threshold value, and the stimulated emission stops.

Stimulated emission begins when the carrier density is replenished to an above-threshold value by the injected current and the process repeats itself.

Thus Equation (5-3-2) may be viewed as the condition for pulsation in an injection laser. Central to this model is the nonlinear-gain-versus-carrier-density relation, which makes regions with smaller carrier density act as saturable absorbers.

A discussion of the pulsation instability based on the rate equations is given in a later tutorial.

The regions near the cleaved facets of an injection laser are generally regions where carrier density is depleted by surface recombination. The recombination rate at a surface is usually expressed in terms of surface recombination velocity \(S\) [refer to the nonradiative recombination in semiconductors tutorial], which is the product of the defect density \(N_\text{d}\), capture cross section \(\sigma\), and carrier velocity \(v\), i.e.,

\[\tag{5-3-3}S=N_\text{d}\sigma{v}\]

Nash et al. have shown that the surface recombination velocity of a cleaved GaAs surface can be reduced by coating the surface with \(\text{Al}_2\text{O}_3\), which also reduces the rate at which pulsations occur in AlGaAs lasers.

The occurrence of pulsation is generally more frequent in AlGaAs lasers than in long-wavelength InGaAsP lasers. This is generally attributed to the fact that a cleaved InP surface has a smaller surface recombination velocity (\(\sim10^5\text{ cm/s}\)) than does a GaAs surface exposed to air (\(\sim10^7\text{ cm/s}\)).

Van der Ziel has studied the self-focusing (contraction of the beam diameter near the pulse center) associated with pulsations in AlGaAs proton-stripe gain-guided lasers.

Figure 5-10 shows the similar self-focusing behavior for 1.3-μm InGaAsP lasers. The top trace shows the light pulse and the bottom trace shows the measured near-field width during the evolution of the optical pulse.

As a consequence of self-focusing, the width decreases as the light intensity increases. Lang has shown that index guiding along the junction can reduce the self-focusing effect by stabilizing the optical mode and can also reduce the probability of pulsations. His analysis agrees with the performance of strongly index-guided InGaAsP lasers, which generally do not exhibit pulsations.

Electrical Derivative Characteristics

Electrical characterization, especially the measurement of current-voltage derivatives, is a useful way of understanding various current paths in an injection laser.

The electrical characteristics of injection lasers were first developed for the study of stripe-geometry gain-guided lasers.

Below threshold, the current-voltage characteristic of a broad-area junction laser is similar to that of a diode with a series resistance \(R\). The series resistance accounts for the contact resistance and that of the various layers.

The current-voltage characteristics of a diode are given by the Shockley equation

\[\tag{5-3-4}I=I_\text{s}[\exp(\beta{V_\text{d}})-1]\]

where \(\beta=q/\eta{k_\text{B}}T\), \(V_\text{d}\) is the voltage across the diode, \(I_\text{s}\) is the saturation parameter, \(k_\text{B}\) is the Boltzmann constant, \(T\) is the absolute temperature, \(q\) is the electron charge, and \(\eta\) is called the ideality factor.

Usually \(\exp(\beta{V_\text{d}})\gg1\), so that the second term in Equation (5-3-4) can be neglected.

Above threshold, the voltage across the laser diode saturates because the carrier density saturates. The measured voltage \(V\) across the laser diode then is

\[\tag{5-3-5}V=V_\text{d}+IR\]

From Equations (5-3-4) and (5-3-5), it follows that

\[\tag{5-3-6}I\frac{\text{d}V}{\text{d}I}=\begin{cases}\frac{\eta{k_\text{B}T}}{q}+RI\quad\qquad{I\lt{I_\text{th}}}\\RI\qquad\qquad\qquad{I\gt{I_\text{th}}}\end{cases}\]

The quantity \(I\text{d}V/\text{d}I\) drops by \(\eta{k}_\text{B}T/q\) at threshold for an injection laser. Measurement of this quantity can provide information about the junction characteristics of the laser diode.

Figure 5-11 shows the measured optical and electrical characteristics of a stripe-geometry gain-guided laser. A kink at threshold in the \(I\text{d}V/\text{d}I\) curve is in agreement with Equation (5-3-6).

Equation (5-3-6) is modified in the presence of carrier leakage over the heterojunction [refer to the how to estimate the threshold current density of a semiconductor laser tutorial]. The modified equation shows that observation of sublinearity in the above-threshold variation of \(I\text{d}V/\text{d}I\) with \(I\) is an indication of heterobarrier leakage.

Wright et al. have examined the electrical characteristics in the presence of a shunt path across the laser diode. Such shunt paths can arise in strongly index-guided lasers.

For simplicity, we consider a resistive shunt path. Figure 5-12 shows the \(I\text{d}V/\text{d}I-I\) characteristic of a laser with a resistive shunt.

The slow turn-on of the \(I-V\) curve is due to the current flowing through the resistive shunt, and its slope at low currents equals the shunt resistance.

The corresponding \(I\text{d}V/\text{d}I-\text{versus}-I\) curve shows a "bump" before threshold is reached. Observation of such a bump in the measured \(I\text{d}V/\text{d}I-\text{versus}-I\) characteristic of a laser diode indicates the presence of a shunt path.

Optical characteristics also manifest themselves through the measured electrical derivative characteristics. For example, a kink in the \(L-I\) characteristic is generally associated with a kink in the \(I\text{d}V/\text{d}I-I\) characteristic.

This can be understood as follows.

An \(L-I\) kink is usually associated with a change in the optical mode (mode movement, mode transition, or appearance of additional higher-order modes) along the junction plane.

This also changes the average carrier density in the active region, which in turn changes the Fermi energies. Since the voltage across the diode equals the separation of the quasi-Fermi levels in the conduction and valence bands, a change in voltage occurs with a change in the optical mode along the junction plane.

The voltage change appears as a kink in the \(I\text{d}V/\text{d}I-\text{versus}-I\) characteristic.

The sustained oscillation of the emitted light or pulsations are often associated with sharp kinks in the electrical derivative characteristics. An example of such behavior is shown in Figure 5-13.

The pulsation-induced sharp spike in the \(\text{d}L/\text{d}I\) curve manifests as a sharp dip in \(I\text{d}V/\text{d}I\).

Note that the \(I\text{d}V/\text{d}I\) curve near threshold is lower than what would be expected from the series resistance alone. Thus the device apparently exhibits negative resistance. This type of negative-resistance behavior was first reported by Anthony et al.

During pulsation, the average carrier density oscillates rapidly, which leads to an oscillation in voltage across the diode. This rapidly oscillating voltage appears as an apparent negative resistance in the measured electrical derivative characteristics.

The next tutorial discusses about weakly index-guided lasers.