Toward robust and practical interband cascade laser frequency combs: A perspective

The standard rate equations for a single-lateral-mode semiconductor laser, with photon and carrier densities averaged over the cavity length and round trip time for photons, predict that for any current sufficiently above the lasing threshold, a Fabry–Pérot device with typical gain curvature should operate in a single longitudinal mode, with spectral linewidth inversely proportional to the output power.^1,2 However, many longer-wavelength lasers do not behave this way in practice. Instead, as the current increases above threshold, they lase in multiple longitudinal modes with spectral envelopes that are difficult to predict. The primary culprit is spatial hole burning (SHB, sometimes referred to as population grating), which reduces the gain and carrier density near cavity-axis antinodes of the standing-wave mode with the highest stimulated emission rate.^3,4 The resulting carrier grating for that mode has the same periodicity as the mode intensity, $λ m/ 2 n m$⁠, where $λ m$ is the mode's wavelength and $n m$ is the modal index. As the output power and the rate for stimulated emission into this mode rise, other nearby modes experience higher gain because their antinodes do not coincide with those of the dominant mode, despite their small spectral detuning from the gain peak. This behavior is governed by the ratio of carrier diffusion length (⁠ $D a τ c$⁠) to $λ m/ 4 n m$⁠, where $D a$ is the ambipolar diffusion coefficient (typically, slightly lower than twice the hole diffusion coefficient) and $τ c$ is the carrier lifetime (including stimulated emission). For large diffusion lengths, single-mode lasing is expected because diffusion strongly limits the amplitude of the carrier grating.⁵ In the opposite limit, however, carrier diffusion is too slow to overcome the periodic gain depletion.

SHB is indeed ubiquitous in mid-infrared (mid-IR) semiconductor lasers that employ standing-wave cavities and particularly those with a short recombination lifetime, such as the quantum cascade laser (QCL).^6,7 The resulting multimode emission can take a wide variety of forms. One intriguing occurrence is that the emission spectrum sometimes comprises a large number of phase-locked equidistant modes with a high degree of coherence over the entire emission spectrum.^8–10 While the mode spacing is trivially equidistant if the group velocity dispersion (GVD) $β 2≡ ∂ 2 k ∂ ω 2= ∂ ∂ ω n g c$ (where $n g$ is the group index) vanishes, in practice frequency combs are supported under the much weaker condition of sufficiently low GVD.⁹ 

Here, we focus on the routes to frequency combs that do not require active modulation of the cavity gain or loss. One strategy is to lock the phases of the modes by incorporating a short saturable absorber (SA) section,¹¹ which absorbs light at low intensities but transmits at high intensities. In the ideal scenario, all modes acquire the same phase, which manifests as a short pulse in the time domain so long as the bandwidth is limited, as must be the case in any practical system. The pulse develops as a balancing act between pulse-narrowing (bandwidth-broadening) by the SA and pulse-broadening (bandwidth-narrowing) in the gain section (which produces more gain near the peak than farther away).^11,12 Figure 1(a) illustrates a narrow-ridge laser cavity, defined by cleaved-facet mirrors, in which intracavity passive mode locking (PML) is realized by dividing the cavity into these two independently biased sections. SHB is not a significant concern for PML, because the short propagating pulse rarely encounters any counter-propagating light (except in short regions near the facets). Theory shows that this constant-phase single-pulse solution becomes unstable when the SA section is removed.⁵ 

The second type of passive frequency comb, which does not generate short pulses,^5,8–10 can appear spontaneously in a single-section Fabry–Pérot cavity.^3,13,14 This is the so-called frequency-modulated (FM) comb, which is characterized by a parabolic variation of the phase profile over the spectral bandwidth $φ m∝ m 2/ f B W$ (⁠ $where m$ is the mode number),¹³ as shown in Fig. 1(b), as well as by rapid temporal variation of the intensity around a steady-state value. The instantaneous frequency $d φ d t$ is linear in time over a round trip, i.e., the device exhibits linear chirp¹⁰ with $d φ d t$ spanning the entire bandwidth of the comb over each round trip. While QCL FM combs exhibit a very short upper-state lifetime,^15,16 similar FM behavior has also been observed in interband active regions with much longer carrier lifetimes.^17–21 Considerable progress toward understanding the FM comb characteristics has recently occurred through the application of mean-field theory, which generates a nonlinear Schrödinger equation with a phase potential.^22,23 The analysis finds that a large discontinuity in the optical field, due to weak reflection at one or both of the mirrors, is a prerequisite for comb operation.²³ The gain of the instability has its origin in nonlinear four-wave mixing, which is inherent in the common gain pool shared by modes at different wavelengths,¹⁴ and potentially influenced by the GVD.²³ While the same model with multiple phase discontinuities in a single round trip can also describe harmonic FM combs,²⁴ the harmonic state occurs only when the gain for unstable components has peaks at frequencies separated from the initial lasing mode by multiples of the free spectral range (⁠ $FSR= c 2 n g L cav$⁠).²⁵ Although both types of combs induce a narrow beatnote at the FSR frequency [see Fig. 1(d)], e.g., extracted via a bias tee from the SA section, the observation of a beatnote does not prove the presence of a comb, nor can it be used in isolation to discriminate between the PML (also sometimes referred to as AM) and FM comb types. However, note that the beatnote may be significantly stronger when a single high-intensity pulse is generated by PML.²⁶ 

A number of theoretical studies have explored the conditions necessary for stable PML in two-section semiconductor lasers.^27–30 The first requirement is a relatively long carrier lifetime in the gain section $( τ c)$⁠. When it is shorter than the round trip time (⁠ $τ c≪1/FSR$⁠), as in QCLs with lifetimes < 1 ps, the gain is much higher in regions of low intensity. This favors quasi-continuous-wave (quasi-cw) operation over the generation of short pulses, a phenomenon dubbed “fast saturable gain.”¹⁴ Second, the cavity's SA section should display unsaturated transmission between 1 and 30%,²⁹ as well as carrier removal faster than the photon round trip time (⁠ $τ S A<1/FSR$⁠) so the SA can recover strong absorption before the next pulse arrives.²⁷ The saturation energy in the SA section [defined as $E sat , S A=M ℏω w r/ Γ d g d n | S A$⁠, see also the supplementary material, where $M$ is the number of stages (typically, 5–7 in-state-of the-art ICLs), $w r$ is the mode width (of the order of the ridge width, which should not exceed ≈5 μm in order to maintain single-lateral mode operation well above threshold), and $Γ d g d n | S A$ is the modal differential gain in two-dimensional units] should also be at least a few times lower than that in the gain section $E sat , gain$⁠. The last condition applies to slow SAs (interband lasers that typically feature $τ S A$ exceeding the pulse length).

It was mentioned above that QCLs are unfavorable for PML due to the rapid relaxation of their upper lasing level, although both active and hybrid mode locking have been induced by modulating the current pumping the gain or SA section, respectively, at the cavity round trip frequency FSR.^31,32 On the other hand, interband semiconductor lasers with carrier lifetimes up to three orders of magnitude longer than in a QCL are more suitable for PML.^4,33 Here, we focus on the interband cascade laser (ICL), whose interband active transitions in narrow-gap antimonide quantum wells are incorporated into the power-efficient cascade geometry of a QCL, as illustrated in Fig. 2(a).^33–36 ICLs provide efficient cw emission at room temperature in the 3–4 μm spectral range, which remains challenging for QCLs and conventional diode lasers, while expending remarkably low electrical input power. Recent work has begun to explore the potential of ICLs as mid-IR frequency combs,^19,37,38 which when implemented in dual comb spectroscopy^39,40 and other configurations are expected to provide a powerful tool for rapid, broadband sensing of trace gases, such as methane, carbon monoxide, formaldehyde, in ambient air.

The carrier lifetime in a typical ICL active core is limited almost entirely by Auger recombination,⁴¹ which in the non-degenerate limit exhibits a cubic dependence on carrier density. While at threshold, the typical lifetime [500–800 ps in the λ = 3.3–3.8 μm spectral range, depending on the device geometry, confinement factor, and cavity length, see also Fig. 2(d)]^33,35 is somewhat shorter than in near-IR lasers (up to a few ns), it still handily exceeds the round trip time of 50–100 ps for cavities with typical length 2–4 mm. Thus, PML should in principle be achievable. However, the initial ICL frequency combs demonstrated by Jet Propulsion Laboratory (JPL) and Naval Research Laboratory (NRL),³⁷ with spectral bandwidth 35 cm⁻¹ centered at λ ≈ 3.6 μm, did not emit clean short pulses. In fact, they are now believed to have functioned as FM combs despite the presence of the SA section.³⁸ Subsequently, the FM operation of ICL combs was independently confirmed by TU Wien with other collaborators using the so-called shifted wave interference Fourier transform spectroscopy (SWIFTS),⁴² which can unambiguously differentiate between short-pulse and quasi-cw emission.¹⁹ Meanwhile, SUNY reported mid-IR cascaded structures employing type-I InGaAsSb quantum wells [in place of the type-II “W” wells illustrated in Fig. 2(a)] that demonstrated PML and relatively short pulses at wavelengths in the 2.7–3.25 μm range, albeit with limited bandwidth and strong chirp.^43,44

The goal of this Perspective is to clarify how the unique physics of the ICL affects its operation as a frequency comb. In particular, we present simulations that illuminate the relationship between device design and the resulting properties, such as GVD, temporal pulse width, and spectral bandwidth. This allows us to identify modifications that may potentially produce PML as well as improved FM comb operation in ICLs, for a new generation of chemical sensing devices.

A first matter of concern is that an ICL waveguide is inherently leaky. This is because state-of-the-art ICLs are grown on GaSb substrates with higher refractive index than the modal index of the laser waveguide (in fact, higher than for any other layer in the structure). Thus, if the bottom cladding is insufficiently thick, reflection from the back substrate surface can weakly modulate the gain spectrum with period $1 2 n GaSb 2 − n m 2 d sub$ (in wavenumber units), where $d sub$ is the substrate thickness.^45,46 The geometry responsible for this periodic feedback is illustrated in Fig. 2(b), top panel. This gain modulation appears clearly in the subthreshold electroluminescence (EL) spectrum, as well as in the power spectrum of the fourier-transform infrared (FTIR) interferogram's first satellite for many ICLs, as shown in Fig. 2(c), where the observed period of 13.5 cm⁻¹ compares with the expected value of $≈16$ cm⁻¹ for the 280-μm-thick substrate in the present experiment. In the early stages of ICL development, the major concern was higher optical loss associated with mode leakage to the substrate, which was mitigated by increasing the thickness of the InAs/AlSb superlattice bottom cladding layer to ≈2.6 μm for an emission wavelength of λ = 4.2 μm.⁴⁵ However, we will see below that even when the leakage is too weak to induce any significant loss, the gain modulation can nonetheless induce rapid sinusoidal variation of the GVD,⁴⁷ typically with detrimental impact on the generation of a frequency comb. The amplitude of the oscillating contribution is proportional to the reflectivity of the substrate back surface multiplied by $exp − 4 π n m 2 − n clad 2 d clad / λ m$⁠, where $d clad$ is the thickness of the bottom clad. Therefore, the following measures should mitigate the effects of the mode leakage: (1) increase the thickness of the superlattice bottom clad; (2) incorporate a heavily doped layer with low index and significant loss between the cladding and the substrate; (3) use a heavily (>10¹⁸ cm⁻³) doped p-type GaSb substrate to maximize free-carrier absorption; and (4) roughen the back surface of the substrate on a microscale to scatter the reflected light (so there is little in-phase feedback), as shown in Fig. 2(b), bottom panel. To date, most practical efforts have focused on the final approach. It will be seen below that it did not fully suppress substrate leakage on its own. Nevertheless, we believe that combining this approach with one or more of the other methods will result in sufficient suppression.

Another challenge is to ensure fast carrier extraction from the active wells in the SA section. In both standard quantum-well lasers and type-I ICLs, the extraction speeds up at higher reverse bias. On the other hand, state-of-the-art type-II ICL designs are optimized for efficient injection of the electrons and holes rather than their extraction, as well as for approximate balance of the electron and hole densities at threshold.^35,48 In particular, it is unclear whether the usual arrangement shown in Fig. 2(a), with semimetallic interface and very thin hole injector, is compatible with sufficiently rapid extraction of the holes. One recent experimental study found only a weak reduction in the apparent extraction time with reverse bias up to −3 V.⁴⁹ Furthermore, reverse biasing a type-II ICL sometimes leads to catastrophic device failure, possibly by activating low-density extended defects. Fortunately, however, wholesale redesign may be unnecessary. Instead, proton (or other ion) bombardment of the SA section³⁷ can reduce its carrier lifetime (via the generation of defects and Shockley-Read-Hall recombination at those defects) to below the cavity round trip time of 50–100 ps.⁵⁰ Provided the bombardment can be performed reproducibly, this solution allows ICL gain section designs that are already optimized for low threshold and high output power to be retained. Figure 2(d) shows the estimated carrier lifetime at threshold for broad-area ICLs bombarded with proton doses ranging from 2 × 10¹² to 2 × 10¹³ cm⁻². An even higher dose of 6 × 10¹³ cm⁻² suppressed lasing at all current densities up to at least 3 kA/cm², which implies that the carrier lifetime was ≤ 40 ps in that case.

At the operating point of a quantum-well laser, the differential gain is typically much lower in the gain section than in the reverse-biased SA, which follows from the approximately logarithmic shape of the gain curve. The typical relation $E sat , gain/ E sat , S A≈3$ for near-IR lasers is sufficient to produce PML,³⁰ as discussed above. However, because state-of-the-art ICL designs typically attempt to minimize the material gain required to reach the lasing threshold, in order to combat the strong dependence of recombination lifetime on carrier density, $E sat , gain/ E sat , S A≈2.4$ if we ignore the effect of applied field on the optical matrix element. Moreover, this ratio is degraded even further by the use of asymmetric type-II “W” active wells in designs, such as that shown in Fig. 2(a). Therefore, for application in frequency combs, it may be beneficial to modify the design such that the wells are symmetric or even biased slightly in the opposite direction (with the well on the right in the figure being slightly wider than that on the left). Of course, this expression for the saturation energy strictly applies only to transitions between two levels. For interband transitions in a semiconductor, a more complete picture should also account for the nonlinear dependence of the optical gain/loss on carrier density and the detuning of the peak lasing energy from the absorption edge in the SA.²⁷ For example, if the absorption edge is at much lower energy, saturation becomes quite difficult. Fortunately, for interband transitions in two-section ICLs, the combination of blue shift due to the injection of carriers and red shift due to applied field and lattice heating in the gain section leads to <20 meV offset between the band edges in the SA and gain sections.

To provide initial guidance in identifying the best operating region for a mode-locked ICL, we performed finite-difference simulations of pulse propagation in a single-lateral-mode cavity divided into gain and SA sections. The calculations include the effects of second-order and third-order GVD,⁵¹ gain bandwidth in a parabolic approximation, and gain-index coupling quantified by the linewidth enhancement factor (LEF).^29,30,52 The carrier lifetime in the SA section is assumed constant due to Shockley-Read processes, whereas in the gain section, it is dominated by Auger recombination with a coefficient $γ=$ 2.5 × 10⁻¹⁵ cm²/s characteristic of state-of the-art ICLs.^35,48 Details of the model are described in the supplementary material. While the reflections at uncoated end facets are included, the phase boundary conditions are not enforced so individual cavity modes are not resolved. Also, the detailed scattering dynamics of the quantum-well states generating optical gain and loss on the likely timescale of ≈100 fs is not considered. Nevertheless, the simulations find that under some conditions, a single stable pulse makes a full round trip, indicating that a dense frequency comb is generated from the initial condition of a chirped Gaussian pulse. We verified that after 2000 round trips, the width, shape, and chirp of the initial pulse do not affect the final comb properties discussed below.

Figure 1(a) shows a snapshot of light intensity and gain vs position at a point in time where the pulse has propagated midway along the cavity length (from right to left in the figure). Here, the length of the uniformly pumped (⁠ $J=$ 1 kA/cm²) gain section is 3.8 mm, while that of the unpumped (⁠ $J=0$⁠) SA section is 200 μm. In practice, the two sections are electrically isolated by etching a narrow (at least a few tens of μm) trench through the top contact layer and more heavily doped portion of the top cladding.^43,44 Figure 1(a) shows that in the wake of the propagating pulse, the optical gain is reduced by stimulated emission. With the SA recovery time set to $τ S A=$ 50 ps, as compared to the cavity round trip time $1 FSR≈100$ ps, at the moment of the snapshot, the absorption (negative gain) in the SA section at right has not recovered to its full value of 140 cm⁻¹ following passage of the pulse. We find that the full width at half maximum (FWHM) pulse width, which in this case is $≈0.5$ ps, and peak power tend to stabilize after several hundred round trips. However, a slow periodic variation in the peak power can persist. Considering the limited physical content of the simulation, it is unclear whether this predicts a real-world instability. For realistic LEF values between 1 and 3, the resulting pulse approaches the transform limit for the soliton-like hyperbolic secant shape (within 5%–20%), even when the initial condition is a severely chirped (here, $C=10$⁠) Gaussian pulse. This markedly contrasts the observation of pulses much wider than the transform limit in the recent experiments on type-I ICL frequency combs,^43,44 although we must note that the present model does not yet include the full complexity of the transport through the ICL active core and scattering into and from the states involved in optical gain.

When the SA section is too short and the current density too high (e.g., 100 μm and $>1.2$ kA/cm², respectively), the initial single pulse breaks up into multiple pulses as shown in Fig. 3(a). This occurs when a high pulse intensity easily saturates the absorption in the short SA, so the trailing portion of the pulse is insufficiently attenuated. Assuming the existence of a mechanism that stabilized the relative positions of the pulses, the behavior would manifest as a harmonic comb in the frequency domain with the period in FSRs equal to the number of pulses. On the other hand, if the SA section is long and the current density relatively low (e.g., 200 μm and $J<0.7$ kA/cm²), the peak power per pulse shows extreme variation, with nearly all of the stored energy saved for a substantial pulse that appears every fifth or sixth round trip. This “effective Q switching”²⁷ scenario occurs when saturation of the SA requires more energy than can be accumulated in a single round trip. Based on these results and assuming current ICL waveguide designs with active-core confinement factor  $≈$ 15%, there appears to be little reason to increase the SA section length beyond ≈200 μm.

The simulations confirm that reliable comb generation requires a shorter recovery time in the SA than the photon round trip time, as discussed above and also reported in previous studies.²⁷ We find that the pulses become unstable whenever $τ S A$ increases to 150–200 ps, which can be avoided by ion bombarding the state-of-the-art ICL active stages, as discussed above. As in frequency combs based on type-I InGaAsSb quantum wells,^43,44 a strong reverse bias may also expedite the extraction of carriers from the active wells.

Figure 3(b) shows simulated dependences of the pulse width (red points, right scale) and spectral bandwidth (blue points, left scale) on the second-order GVD. While the GVD's effect is modest for values < 1000–1500 fs²/mm, at the other end of the spectrum, no stable pulses are predicted for GVD > 2700 fs²/mm. Although the exact boundaries naturally depend on the structure and details of the simulation (in particular, the higher-order dispersion discussed below), these results highlight the importance of reducing the GVD. We note that while this simulation based on a conventional ICL design predicts a FWHM bandwidth < 35 cm⁻¹, even when the GVD is reduced to zero, ICLs with chirped stages designed for broadened gain spectrum (discussed below) are predicted to have comb bandwidths extending to at least a few times that value. It should also be mentioned that the useful frequency comb bandwidth may be several times the FWHM value, depending on the exact application and technique employed.

Although the pulse formation is somewhat tolerant of second-order GVD, the introduction of higher-order dispersion (as described in the supplementary material) leads to pulse broadening/bandwidth narrowing followed by numerical instability that indicates that pulses are not supported in the two-section cavities. Figure 3(c) shows the broadening due to positive third-order dispersion $β 3≡ ∂ 3 ω ∂ k 3>0$⁠, where the bandwidth is reduced by a factor of 2.2 when $β 3=1.2× 10 6$ fs³/mm. While numerical instabilities can occur for similar absolute values with $β 3<0$ (characteristic of the gain/absorption spectra in ICLs), it is likely that strong higher-order dispersion degrades the performance in a manner similar to Fig. 3(c). Additional modeling is needed to further explore the dependences. We note that in the context of microresonator frequency combs, the behavior with general higher-order dispersion does not appear to differ qualitatively from that due to third-order dispersion alone.⁵³ 

Somewhat surprisingly, a higher LEF value can increase the spectral bandwidth and reduce the temporal width of the pulse, as shown in Fig. 3(d). Positive LEF indicates that the leading edge of the pulse in the gain section experiences a lower modal index than the trailing edge, which corresponds to self-focusing. (The opposite is true in the SA section.) It remains to be seen whether the comb bandwidth can in fact be extended by deliberately designing the active core for higher LEF. Experimental values from 1.1 to 2.2 for ICLs have been reported,^54,55 while theoretical modeling of the gain-index coupling alone predicts a smaller value LEF ≈ 0.8 at the gain peak for an ICL with a typical threshold gain of 10 cm⁻¹ at room temperature.

The modeling results and other considerations indicate that PML with quite attractive performance should be possible in type-II ICLs. What then explains the absence of any experimental demonstrations to date? One factor may be that the SA extraction time and saturation of the absorption have not been fast enough. However, the most likely suspect seems to be the strong variation of GVD with wavelength in the structures used, thus, far³⁸ [see also Fig. 4(a)], in view of the rapid degradation with second- and third-order dispersions shown in Figs. 3(b) and 3(c). In view of its critical importance, we next examine in greater detail what is known experimentally and theoretically about the GVD in ICLs.

Figure 4(a) shows the experimental GVD spectrum for an ICL with standard design and substrate roughening. This GVD spectrum was determined from the phase profile of the Fourier-transformed first satellite peak of the FTIR interferogram.^10,56 The red curve represents a fit of the extracted phase profile to a fourth-order polynomial, which indicates the large-scale structure of the dispersion. Note that in this case, the subthreshold EL spectrum superimposed on the plot does not display significant oscillations [compare with Fig. 2(b)], presumably due to the roughening. Nonetheless, we still observe oscillations with period ≈ 23 cm⁻¹ due to substrate leakage. Although the leakage effect was reduced by lower reflection of the roughened surface, it also increased because the roughening process thins the substrate. The oscillations appear somewhat suppressed near the peak emission at 3000 cm⁻¹ but become much more pronounced near the tails of the spectrum. We conclude that the observation of a relatively smooth EL spectrum does not confirm full suppression of the substrate leakage, so that the additional measures discussed above will be necessary.

Even in the absence of substrate leakage, the typical GVD in an ICL is significantly larger than in a QCL.¹⁰ Because the contribution from the active core is more complex and strongly varying, we discuss first all the GVD contributions arising outside of the active core, which we call the ICL-waveguide GVD. It is dominated by the relatively strong positive mid-IR dispersion of GaSb, which is due to its relatively narrow energy gap of approximately twice the mid-IR photon energy. In state-of-the-art ICL designs, GaSb forms the bulk of the waveguide core because relatively thick (0.5–0.8 μm) GaSb separate confinement layers (SCLs) are inserted both above and below the active gain stages. The SCL contribution to the GVD is further exacerbated by the large (0.4–0.5) index contrast with the InAs/AlSb superlattice claddings, which compresses the mode profile along the vertical axis. The simulations yield ICL-waveguide GVDs of 1300–1400 fs²/mm for standard designs (with GaSb SCLs) emitting at λ = 3.4 μm. The red (ridge width 4 μm) and blue (20 μm) curves in Fig. 4(b) indicate a weak trend toward lower values as the wavelength increases. Input parameters for the simulations are the optical constants for GaSb, the InAs/AlSb superlattice claddings, and Al_0.4Ga_0.6As_0.03Sb_0.97, which were measured by spectroscopic ellipsometry (see the supplementary material).

An additional factor is that the small aspect ratio between vertical (∼1 μm) and lateral (4–5 μm) extent of the ICL lasing mode limits the freedom in designing the GVD. The plot in Fig. 4(c) of the simulated ICL-waveguide GVD vs ridge width at λ = 3.3–3.4 μm (blue curve for GaSb SCLs) indicates that narrowing the ridge can in principle lower the GVD, although below ≈4 μm the laser performance often suffers due to excessive leakage current and/or optical scattering loss at the sidewalls.⁵⁷ 

While the simulations nominally project pulse formation when the (average) GVD is 1500–2000 fs²/mm near the peak of the ICL gain spectrum [see Fig. 4(a)], such large values may be incompatible with the formation of stable, low-noise ICL combs that are useful in practical applications. One potential solution is to replace the GaSb SCLs with AlGaAsSb. We see from the green curves in Figs. 4(b) and 4(c) that the lower index contrast and wider gap of AlGaAsSb are projected to reduce the ICL-waveguide GVD to the much more promising range of 500–600 fs²/mm.

An alternative approach is to deposit a multilayer dispersion-compensating Gires–Tournois coating on one of the facets, as has been demonstrated for QCLs.⁹ However, the thick coatings have a tendency to peel off, which must be mitigated if the yield is to remain high enough for practical applications.

The active core contribution to the GVD can be computed from the gain/absorption spectrum of the active wells. While the active region includes additional absorption band edges at higher energies, their effects on the GVD and its trend with wavelength should be small. Figure 4(d) depicts the GVD spectrum simulated at a peak gain of 10 cm⁻¹, for profiles with different amplitudes of the gain modulation associated with the substrate leakage discussed above. The GVD including the active contribution is no longer nearly second-order, since a strong decrease (hence, a large third-order term of ≈−10⁶ fs³/mm) is observed somewhat below the gain peak. As discussed above, this higher-order dispersion may be large enough to prevent short pulse formation on its own. While the experimental spectrum in Fig. 4(a) also displays a decreasing GVD trend with frequency, it appears that substrate leakage must be suppressed almost completely before the calculation can be validated quantitatively. Note also that the slope of the GVD is sensitive to the gain broadening magnitude obtained by fitting the typical photoluminescence linewidth at room temperature (which yields FWHM = 13 meV for transitions between individual states).

The active GVD contribution can be reduced by decreasing the confinement factor, e.g., by employing only three active stages. Even when the threshold modal gain is held fixed at 10 cm⁻¹, this produces a blue shift in the gain peak and reduces the higher-order dispersion near the peak (corresponding to $β 3≈$ −3 × 10⁵ fs³/mm). While the threshold current density $J t h$ for this design choice will increase, owing to the strong dependence of Auger recombination on carrier density, it will be compensated to some extent by a lower threshold voltage due to fewer stages.

The preceding examples assumed a gain FWHM bandwidth at threshold of ≈15 meV (≈120 cm⁻¹), as derived from numerical calculations for typical state-of-the-art ICLs.⁴ As the gain spectrum broadens at higher currents (corresponding to higher threshold gains), our simulations project a 66% increase in the comb bandwidth once the gain bandwidth is doubled. However, as before the advantage of higher material gain has the undesired side effect of raising $J t h$⁠. Alternatively, the gain spectrum can be broadened by chirping the active well widths in successive stages, which also comes at the expense of higher $J t h$⁠.

As discussed above, it has been demonstrated experimentally^19,38 that even if PML is not achieved, a single-section semiconductor laser may still operate as a dense or harmonic FM comb. (An electrically isolated second section may still be used to monitor the RF component of the photocurrent.) It also appears possible to use the same wafer material (and potentially even the same device structure) to observe both PML with short pulses and quasi-cw FM combs.²⁶ This leads to an obvious question: What are the potential advantages and disadvantages of PML over FM combs? While some gaps in the understanding remain, a few interesting results are already available. Recall that for active mode locking, the achievable comb bandwidth is roughly the geometric average of the filtering functions due to: (1) the gain spectrum and (2) the modulation spectrum with bandwidth one FSR.¹² Because the gain spectrum in a semiconductor laser encompasses a large number of FSRs, active mode locking leads to relatively narrow combs. On the other hand, the comb bandwidth for passive mode locking, which depends on the pump level, GVD, and other parameters as discussed above, can reach a significant fraction of the gain bandwidth. It was recently shown that the bandwidth of an FM QCL comb can theoretically approach that of a PML comb if the gain spectrum is relatively flat.¹⁶ This consideration may be important to spectroscopic applications that probe either the broad absorption features of large molecules or simultaneous multispecies detection. Second, both PML and FM combs have been injection locked by applying a microwave signal near the repetition frequency to the gain section.^38,58 This procedure may offset minor fluctuations in the device temperature and operating current (in the absence of active stabilization measures), as well as the timing jitter of PML pulses that arise from the random nature of spontaneous emission. Even though considerable improvement in the spectral bandwidth and robustness to feedback have been observed, injection locking also often increases the optical linewidth in FM combs.⁵⁹ 

The details of the mechanism that induces harmonic rather than dense FM combs operation also remain to be established. Linear stability analysis indicates that the harmonic state can be self-supporting and stable in a certain range of pump levels and does not require a particular level of second-order GVD.²⁵ Dense combs are required for spectroscopic applications in which the analyte absorption lines are very narrow (e.g., in trace gas sensing), which emphasizes the importance of this open question. The dependence of FM locking on various parameters is also incompletely understood.²³ 

In conclusion, we believe that the simulations and analyses presented above confirm that state-of-the-art ICLs are amenable to passive mode locking with picosecond pulses and near-transform-limited bandwidths. However, this will require care to assure a sufficiently short recovery time in the SA section, minimization of GVD oscillations associated with substrate leakage, and redesign of the ICL active stages and waveguide to minimize the GVD “background.” PML has not been reported to date because these conditions were not satisfied.

In this work, we have identified promising technical fixes, involving practical measures, which address each of these issues. For example, the SA section recovery time can be reduced by ion bombardment and/or applying a reverse bias, both of which have already been implemented experimentally.^37,44,49 The GVD oscillations due to substrate leakage can be minimized by roughening the bottom surface, thickening the bottom clad layer, and/or increasing free carrier absorption in the region between the bottom clad and the substrate. While implementation of the first of these eliminated significant oscillations in the raw EL spectrum [inset to Fig. 4(a)], this measure alone did not sufficiently minimize the GVD oscillations [Fig. 4(a)] so additional measures will be required. The magnitude of the GVD can be reduced substantially by replacing the high-index GaSb SCL layers in current ICL designs with AlGaAsSb, and the active core contribution can be minimized by reducing the number of active stages. It is also beneficial to narrow the ridge waveguide to the minimum practical width that does not induce excessive scattering loss or current leakage at the sidewalls. Finally, the length of the SA section should be optimized to avoid Q-switching if it is too long and multi-pulsing if it is too short. The full implementation of all these measures may come at the cost of somewhat higher threshold current density.

It appears that the design and processing modifications discussed in this work will make it quite feasible to meet all of the conditions for passive mode locking with short-pulse output. Therefore, we anticipate that future research will produce broadband and stable ICL frequency combs that are ideal for dual-comb spectroscopy to sense greenhouse gases and harmful chemicals in the 3–4 μm spectral range, as well as other applications. The basic ICL structure can also function as an (integrated) high-speed detector when operated near zero bias, which overcomes the difficulties associated with the relative paucity of such detectors in the mid-IR spectral range.^38,60