Sources, Modulators, and Detectors For Fiber-Optic Communication Systems Part 2

OPERATING CHARACTERISTICS OF LASER DIODES

A forward-biased pn junction injects carriers into the active region. As the drive current increases, the carrier density in the active region increases. This reduces the absorption from an initially high value (at thermal equilibrium the absorption coefficient a = 500 cm-1) to zero, at which point the active layer becomes transparent at the prospective laser wavelengths. An active layer is characterized by its carrier density at transparency Ntr. Typically, Ntr ~ 1018 cm-3. Above this carrier density, stimulated emission occurs, with a gain proportional to the diode carrier density above transparency. The gain depends on the detailed device design, taking into account the issues enumerated in the previous section and the materials involved. The gain is sizeable only in direct-band semiconductors (semiconductors based on the III-V or II-VI columns of the periodic table).

Laser Threshold

Threshold is given by the requirement that the round-trip optical gain due to stimulated emission must equal the round-trip optical loss due to the sum of the transmission out the end facets and any residual distributed loss. Gain occurs only for light that is actually in the active region, and not for the fraction of waveguided light that extends outside the active region. Typically, the local gain per unit length GL is defined as that experienced locally by light inside the active region. (The modal gain per unit length is gL = r GL.) Near transparency, the gain depends linearly on carrier density N:

where aL is the proportionality constant in units of lengthWhen

which is the loss per unit length in the unpumped active region (assuming the gain is linear in N). Typically,

The current density (J) is related to the carrier density through

where t is the lifetime of the electron-hole pairs. The transparency current density for d = 0.15 |im, Nlr = 1018 cm-3, and t = 2 ns is 1200 A/cm2. The threshold condition can be found by taking the natural logarithm of Eq. (3):

where am is the mirror reflectivity amortized over length,represents any internal losses for the laser mode, also amortized over length.

Combining Eqs. (2) through (6), along with the fact that a laser diode with stripe width w and length L will have a current I = JwL, gives

where the waveguide V parameter is from Eq. (1) with d = dg. Note that when the internal losses are small, the threshold current is independent of device length L, but depends on the reflectivity of the facets. Note also that the longer the spontaneous lifetime, the lower the threshold current density (although this may make a long turn-on delay, as discussed later). Finally, as expected by the relation between current and current density, a thinner stripe width w will lower the threshold current (consistent with appropriate spatial output, as discussed later). The current density at transparency Ntr is a basic property of the gain curve of the active region. It is smaller for quantum well lasers (discussed later) than for thicker active regions.

Note that because V is linearly proportional to d there is an optimal active layer thickness, a trade-off between increasing the carrier density as much as possible, but not so much as to lose optical confinement. The optimum thickness for 1.3-^.m lasers is 0.15 |im; for 1.55-^m lasers it is comparable (0.15 – 0.18 |im). Threshold currents for broad-area DH lasers can be under -500 A/cm2 at 1.3 |im and -1000 A/cm2 at 1.55 |im. Confining carriers and light separately can beat this requirement, a trick used in designing quantum well lasers.

Light Out Versus Current In (the L-l Curve)

Below laser threshold only spontaneous emission is observed, which is the regime of the LED, as discussed in Sec. 4.8. In the spontaneous regime, the output varies linearly with input current and is emitted in all directions within the active region. As a result, a negligible amount of light is captured by the single-mode fiber of telecom below threshold.

Above threshold, the electrical power is converted to optical power. In general, the light will come out of both facets, and the amount of light reflected out the front facet depends on the rear facet reflectivity. When 100 percent mirror is placed on the back facet, the optical power at photon energy hv (wavelength X = c/v) emitted out the front facet is

where n is the internal quantum efficiency, which is the fraction of injected carriers that recombine by radiative recombination (usually close to unity in a well-designed semiconductor laser), and IL is any leakage current. This equation indicates a linear dependence between light out and current above threshold (for constant quantum efficiency). The power out will drop by a factor of 2 if the back facet has a reflectivity equal to that of the front facet, since half the light will leave out the back.

From Eq. (8) can be calculated the external slope efficiency of the LD, given by This allows the differential quantum efficiencyto be calculated:

This expression assumes thatincludes the power out both facets.

The internal quantum efficiency depends on the modes of recombination for carriers. The rate of carrier loss is the sum of spontaneous processes, expressed in terms of carrier density divided by a lifetime Te, and stimulated emission, expressed in terms of gain per unit time GT and photon density P:

The spontaneous carrier lifetime is given by:

which includes spontaneous radiative recombination, given by BN. (The dependence on N results from needing the simultaneous presence of an electron and a hole, which have the same charge densities because of charge neutrality in undoped active regions.) The nonradia-tive recombination terms that decrease the quantum efficiency below unity are a constant term Anr (that accounts for all background nonradiative recombination) and an Auger recombination term (with coefficient C) that depends on the square of the carrier density and comes from processes involving several carriers simultaneously. This term is particularly important in long-wavelength lasers where the Auger coefficient C is large. Stimulated emission is accounted for by gain in the time domain GT, which depends on N (approximately linearly near threshold). The group velocity vg converts gain per unit length GL into a rate GT (gain per unit time),We can define a gain coefficient in the time domainso that

The internal quantum efficiency in a laser is the fraction of the recombination processes that emit light:

Referring to Eq. (9), the external quantum efficiency depends on the sources of intrinsic loss. In long-wavelength lasers, this is primarily absorption loss due to intervalence band absorption. Another source of loss is scattering from roughness in the edges of the waveguide.

Figure 5 shows a typical experimental result for the light out of a laser diode as a function of applied current (the so-called L-I curve) for various temperatures. It can be seen that the linear relation between light out and current saturates as the current becomes large enough, particularly at high temperatures. Three main mechanisms have been proposed for the decrease in external slope efficiency with increasing current, each of which can be seen in the form of Eq. (9):

1. The leakage current increases with injection current.

2. Junction heating reduces recombination lifetime and increases threshold current.

3. The internal absorption increases with injection current.

When there is more than one laser mode (longitudinal or transverse) in the LD, the L-I curve has kinks at certain current levels. These are slight abrupt reductions in light out as the current increases. After a kink the external slope efficiency may be different, along with different spatial and spectral features of the laser. These multimode lasers may be acceptable for low-cost communication systems, but high-quality communication systems require single-mode lasers that do not exhibit such kinks in their L-I curves.

Temperature Dependence of Laser Properties

The long-wavelength lasers are more typically sensitive to temperature than are GaAs lasers. This sensitivity is usually expressed as an experimentally measured exponential dependence of threshold on temperature T:

where To is a characteristic temperature (in degrees Kelvin) that expresses the measured thermal sensitivity.

FIGURE 5 Typical experimental result for light out versus current in (the L-I curve). These results are for diodes operating at 1.3 |im, consisting of strained layer multiple quantum well InGaAsP lasers measured at a series of elevated temperatures.3

This formula is valid over only a limited temperature range, because it has no real physical derivation, but it has proved convenient and is often quoted. The data in Fig. 5 correspond to To ~ 80 K. The mechanisms for this sensitivity to temperature depend on the material system begin used. In long-wavelength double heterostructure lasers, To appears to be dominated by Auger recombination. However, in short-wavelength GaAs lasers and in strained layer quantum wells, where Auger recombination is suppressed, To is higher and is attributed to intervalence band absorption and/or carrier leakage over the heterostructure barrier, depending on the geometry. Typical long-wavelength DH lasers have To in the range of 50 to 70 K. Typical strained layer quantum well lasers have To in the range of 70 to 90 K, although higher To can be achieved by incorporating aluminum in barriers, with as high as 143 K reported.4 This temperature dependence limits the maximum optical power that can be obtained because of the phenomenon of thermal runaway, as shown at the highest temperatures in Fig. 5. While the power is usually increased by increasing the current, the junction temperature also increases (due to ohmic losses), so the threshold may increase and the output power may tend to decrease.

Various means for increasing To have been explored. The most effective way to increase To has proven to be the use of tensile strained quantum wells (discussed in Sec. 3.6). The result has been to increase To from -50 K to as high as 140 K, comparable to that measured in GaAs. In double heterostructures, losses by carrier leakage can be reduced by using a dual active region for double carrier confinement, which has been demonstrated to achieve To values as high as 180 K in 1.3-^m InP lasers.5

In practice, many long-wavelength lasers require thermoelectric coolers to moderate the temperature. The temperature dependence of long-wavelength lasers may limit their performance at high temperatures, which in turn limits where they can be used in the field.

Spatial Characteristics of Emitted Light

Light is emitted out of the facet of the laser diode after it has been guided in both directions. It will diverge by diffraction, more strongly in the out-of-plane dimension, where it has been more strongly waveguided. The diffracting output is sketched in Fig. 1. The spatial characteristics of the output can be estimated by fitting the guided light to a gaussian beam and then calculating the far-field pattern. The out-of-plane near-field profile for the lowest order mode in an optical confinement layer of width dg can be fit to a gaussian distribution by6:

where V is from Eq. (1). The far-field diffraction angle can be found from the Fourier transform multiplied by the obliquity factor, resulting in a slightly different gaussian fit. The gaussian half-angle in the far field is given by6:

where

Experimental data can be compared to the gaussian beam formula by remembering that the full-width half-maximum power FWHM = w(2 ln 2)1/2. For a typical strongly index-guided buried heterostructure laser, the far-field FWHM angle out of plane is ~1 rad and in-plane is ~1/2 rad. These angles are independent of current for index-guided lasers. Separate confinement heterostructure lasers can have smaller out-of-plane beam divergences, more typically ~30°.

Single-mode lasers that are index guided in the lateral direction (buried heterostructure and ridge waveguide) will obey the preceding equations, with lateral divergence angles varying from 30° to 10°, depending on design. This beam width will also be independent of current. When lasers are gain guided laterally, the spatial variation of the gain leads to a complex refractive index and a curved wavefront. The result is that the equivalent gaussian lateral beam seems to have been emitted from somewhere inside the laser facet. The out-of-plane beam, however, is still index guided and will appear to be emitted from the end facet. This means that the output of a gain-guided laser has astigmatism, which must be compensated for by a suitably designed external lens if the laser is to be focused effectively into a fiber.

If the laser emits a diverging gaussian beam with waist w, a lens can be used to focus it into a fiber. An effective thin lens of focal length f placed a distance d1 after the laser facet will focus to a new waist w’ given by:

where

The distance d2 from the lens to the new beam waist is given by:

where

This new waist must be matched to the fiber mode. Because of the large numerical aperture of laser light, simple lenses exhibit severe spherical aberration. Fiber systems usually utilize pigtailed fiber, butt coupled as close as possible to the laser, without any intervening lens. Typical coupling efficiencies are only a few percent. Alternatively, a ball lens may be melted directly onto a fiber tip and placed near the laser facet. Sometimes graded index (GRIN) lenses are used to improve coupling into fibers.

Gain-guided lasers with electrode stripe widths of >5 |im usually emit multiple spatial modes in the in-plane direction. These modes interfere laterally, producing a spatial output with multiple maxima and nulls. Such spatial profiles are suitable for multimode fiber applications, but cannot be coupled into single-mode fibers with high efficiency. They will diffract at an angle given by setting w equal to the minimum near-field feature size. If the stripe is narrow enough, gain-guided lasers are always single mode, but the double-lobed far-field spatial profile (from the complex refractive index in the gain medium) cannot be conveniently coupled into single-mode fibers.

Spectral Characteristics of Laser Light

In principle, a Fabry-Perot laser has many frequency modes with frequencies vm, given by requiring standing waves within the laser cavity. Since the mth mode obeyswhere n is the refractive index experienced by the guided laser mode, then

Taking the differential, the frequency difference between modes is

where the effective group refractive indexFor typical semiconductor lasers,

so that whenthe frequency difference between modes is Av =

150 GHz, and since. the wavelength spacing is AX = 1 nm.

At any given instant in time, a single spatial mode emits in only one spectral mode. However, in multimode lasers, considerable mode hopping occurs, in which the LD jumps from one spectral mode to another very rapidly. Most spectral measurements are time averages and do not resolve this mode hopping, which can occur in nanoseconds or less. Explanations for the mode-hopping typically involve spatial hole burning or spectral hole burning. Hole burning occurs when the available carrier density is momentarily depleted, either spatially or spectrally. At that time an adjacent mode with a different (longitudinal or lateral) spatial profile or a different resonance wavelength may be more advantageous for laser action. Thus, the laser jumps to this new mode. The competition between different modes for available gain is a strong mechanism for creating lasers with multiple wavelength modes.

One way to provide a single spectral mode is to ensure a single (lateral) spatial mode. It has been found that single spatial mode lasers usually have single spectral modes, at least at moderate power levels. The only way to ensure a single-frequency LD is to ensure a single longitudinal mode by using distributed feedback, as discussed in Sec. 5.7.

Polarization

The emitted light from a typical semiconductor laser is usually linearly polarized in the plane of the heterostructure. While the gain in a semiconductor has no favored polarization dependence, the transverse electric (TE) waveguide mode (polarized in-plane) is favored for two reasons. First, the TE mode is slightly more confined than the transverse magnetic (TM) mode (polarized out-of-plane). Second, the Fresnel reflectivity off the cleaved end facets is strongly polarization sensitive. As waveguided light travels along the active stripe region, it can be considered to follow a zig-zag path, being totally internally reflected by the cladding layers. The total internal reflection angle for these waves is about 10° off the normal to the cleaved facets of the laser. This is enough to cause the TM waveguide mode to experience less reflectivity, while the TE-polarized mode experiences more reflectivity. Thus, laser light from LDs is traditionally polarized in the plane of the junction.

However, the introduction of strain (Sec. 4.6) in the active layer changes the polarization properties, and the particular polarization will depend on the details of the device’s geometry. In addition, DFB and DBR lasers (Sec. 4.7) do not have strong polarization preferences, and they must be carefully designed and fabricated if well-defined single polarization is required.

TRANSIENT RESPONSE OF LASER DIODES

When laser diodes are operated by direct current, the output is constant and follows the L-I curve discussed previously. When the LD is rapidly switched, however, there are transient phenomena that must be taken into account. Such considerations are important for any high speed communication system, especially digital systems. The study of these phenomena comes from solving the semiconductor rate equations.7

Turn-on Delay

When a semiconductor laser is turned on abruptly by applying forward-biased current to the diode, it takes time for the carrier density to reach its threshold value and for the photon density to build up, as shown in the experimental data of Fig. 6. This means that a laser has an unavoidable turn-on time. The delay time depends on applied current and on carrier lifetime, which depends on carrier density N,as shown in Eq. (11). Using a differential analysis, the turn-on time for a laser that is switched from an initial current I just below threshold to I just above threshold is

where

is a differential lifetime given by

When Ii = 0 and I >> Ith, the turn-on delay has an inverse current dependence:

When radiative recombination dominates, thenas seen by comparing the middle terms of Eqs. (11) and (22). For a 1.3-|m laser,

Thus,ns and a typical turn-on time at 1.5 times threshold current is 3 ns. The increase in delay time as the current approaches threshold is clearly seen in the data of Fig. 6. As a result, to switch a laser rapidly, it is necessary to switch it from just below threshold to far above threshold. However, Fig. 6 shows that under these conditions there are large transient oscillations, discussed next.