We report the observation of photoluminescence produced by the recombination of free carriers generated via continuous-wave (CW) two-photon absorption (TPA) in a packaged, low-confinement (Γ~0.5%) InGaAsP/InP quantum-well slab-coupled optical waveguide amplifier (SCOWA) having a saturation output power of 0.8 W and 1/e-mode-field diameters of 5×7 μm. Photoluminescence power measured at the wavelength corresponding to the bandgap wavelength of the SCOWA’s InGaAsP waveguide (λG~1040 nm) exhibits a quadratic dependence on the amplifier’s 1540-nm output power. Comparison between measured and simulated CW gain saturation data reveals that the combination of TPA and TPA-generated free-carrier absorption (FCA) limits the CW output intensity of high-power, low-confinement semiconductor optical amplifiers and semiconductor lasers.
©2008 Optical Society of America
Two-photon absorption (TPA) has long been known to limit the optical intensity that can be transmitted through a semiconductor optical waveguide . In addition to directly depleting the optical field, TPA also results in the creation of free carriers that can further attenuate the field through free-carrier absorption (FCA). Due to the high intensities required to produce TPA, these effects are more often observed under short-pulse excitation . However, continuous-wave (CW) TPA can also present a significant power limitation in waveguide devices having small mode dimensions and requiring high optical power, such as wavelength shifters based on four-wave mixing  and silicon-waveguide Raman amplifiers . Additionally, it has also been conjectured that nonlinear gain compression observed in semiconductor lasers may be caused by TPA [5,6].
The saturation output power Po,sat of a semiconductor optical amplifier (SOA) is defined as the output power where the SOA device gain G has decreased to Go/2, where Go is the gain under small-signal excitation. In the conventional rate-equation analysis, where G is reduced by the depletion of injected carriers caused by stimulated emission, Po,sat can be shown to be proportional to w∙d/Γ, where w and d are the width and thickness of the SOA’s active region, and Γ=Γxy is the transverse optical confinement factor, defined as the normalized overlap integral between the transverse optical mode field and the active region . Thus, two approaches to increase Po,sat are (i) increase the area of the active region, A=w∙d, and (ii) decrease Γ. Much work has been reported on increasing Po,sat by increasing w through the use of a tapered or flared waveguide [8,9]. Tapered SOAs with Po,sat>1 W have been demonstrated. The performance of tapered SOAs has been limited by the spatial properties of the output mode which is asymmetric (~1×200 μm), astigmatic, and unstable due to filamentation in the tapered section.
The second approach to increasing Po,sat is to decrease the optical confinement factor Γ. In conventional SOAs, Γ is on the order of 3–10%. By reducing Γ to 0.5% in a slab-coupled optical waveguide amplifier (SCOWA) structure, we have realized 1.5-μm InGaAsP/InP quantum-well (QW) SOAs exhibiting record device and fiber-coupled Po,sat values of 0.9 W and 0.8 W, respectively . Other researchers have reported device Po,sat as large as 0.25 W in 1.5-μm InGaAsP/InP QW SOAs by reducing Γ to ~1% . SOAs based on InAs/InP quantum dots (QDs) have demonstrated device Po,sat=0.37 W at 1.5 μm . The high value of Po,sat in QD SOAs is due to a combination of small confinement (Γ<1%) and small differential gain at high injection current .
The amount by which Γ can be reduced to increase Po,sat is limited by the decrease in modal gain that also occurs as Γ is reduced. The net gain coefficient of a waveguide SOA can be written as gnet=Γgo-αi (cm-1), where go is the active-material gain coefficient and αi is the average internal loss. To obtain useful optical gain from a low-Γ SOA, αi must be kept smaller than Γgo and the SOA length must increase as gnet decreases. Several loss mechanisms contribute to αi, including FCA associated with carriers in the doped waveguide and cladding regions, FCA associated with injected carriers in the active region, and waveguide scattering losses. By centering the optical mode in a relatively low-doped n-type InGaAsP waveguide and grading the p- and n-doping profiles, we have been able to achieve αi~0.5 cm-1 in InGaAsP QW slab-coupled optical waveguide lasers (SCOWLs) at threshold current conditions .
Recently, the impact of nonlinear absorption on pulse amplification in low-Γ structures has been investigated. In ultrafast pump/probe measurements performed on InGaAsP QW SCOWAs, we have observed transient gain compression that is proportional to the peak intensity of the pump pulse . This nonlinearity is attributed to TPA. Recent theoretical work has also revealed that the output pulse energies of low-Γ SOAs can be limited by TPA for short-pulse (<10 ps) amplification .
In this paper, we report the observation of photoluminescence from the InGaAsP waveguide (λG~1040 nm) of a packaged InGaAsP QW SCOWA under 1540-nm high-power CW excitation. The photoluminescence power exhibits a quadratic dependence on the amplifier’s 1540-nm output power, indicating that the photoluminescence results from the radiative recombination of TPA-generated carriers. Measured CW gain saturation data is then compared with results from a steady-state SOA simulation which includes the effects of both TPA and TPA-generated FCA. This comparison shows that TPA-generated FCA is required to reproduce the abrupt CW output-power limiting observed in high-power SCOWAs. These results provide evidence that TPA limits the CW output intensity of low-Γ SOAs and semiconductor lasers.
2. Two-photon absorption loss mechanisms
As described above, TPA introduces both primary and secondary optical loss mechanisms to the propagation of an optical signal through a semiconductor waveguide. The primary mechanism, associated with the direct depletion of the optical field due to the absorption of two photons, is described by the TPA absorption coefficient
where IS=PS/Amode,NL is the effective optical signal intensity, PS is the optical signal power, Amode,NL=(∬|E(x,y)|2 dxdy)2/∬|E(x,y)|4 dxdy is the nonlinear modal area , E(x,y) is the transverse mode field, and βTPA is the TPA coefficient.
The secondary TPA loss mechanism results from FCA associated with the TPA-generated carriers. The TPA nonlinear absorption process creates equal densities of electrons and holes nTPA=pTPA=NTPA. Ignoring carrier diffusion, the rate equation governing the generation and recombination of the TPA-generated carriers is approximated by
where hν is the photon energy of the fundamental optical signal, and τ 2 is the lifetime of the TPA-generated carriers. Assuming that τ 2 is independent of NTPA, the steady-state value of NTPA can be obtained from Eq. (2) as
The absorption coefficient due to TPA-generated FCA can then be written as
where σ 2FCA is the FCA cross section of the TPA-generated carriers. The TPA-generated FCA is dominated by intervalence band absorption (IVBA) of the TPA-generated holes.
3. TPA photoluminescence measurement description
CW photoluminescence measurements were performed by exciting a packaged SCOWA with a fixed wavelength (λ=1540 nm), variable power CW optical signal (Fig. 1). The SCOWA DC bias current was 4.5 A and the thermo-electric cooler (TEC) controlled baseplate temperature was 16 °C. A variable optical attenuator was used to adjust the input signal power. The polarization of the input signal was adjusted using a paddle-type fiber polarization controller to maximize the SCOWA output signal. An optical power meter was used to measure the 1540-nm output power directly from the SCOWA. The output power ranged from 0.21 to 0.82 W as the input power was varied. After calibrating the 1540-nm output power values, the SCOWA output was filtered using an optical bandpass filter (λC=1000 nm, Δλ~100 nm) to attenuate the strong 1540-nm signal. The filtered signal was characterized using an optical spectrum analyzer (OSA) with a 100-nm span centered at 1050 nm, near the room-temperature peak photoluminescence wavelength of the SCOWA waveguide layer (1039 nm). The OSA resolution and video bandwidth were 2 nm and 10 Hz, respectively. For the range of SCOWA output power values used in the experiment (0.21–0.82 W), the filter attenuation was 47 dB. Therefore, the 1540-nm leakage power injected into the OSA ranged from 4.2 to 16.4 μW over the measurement power range.
Details of the SCOWA material design  and device fabrication  have been reported previously. Here, the aspects that are relevant to the present investigation are summarized. The high output power and large transverse optical mode of the SCOWA structure are realized by using a very thick waveguide layer with offset QWs to attain low Γ. For the SCOWA reported here, the lattice-matched InGaAsP waveguide layer has a bandgap wavelength of λG~1040 nm, a thickness of 5-μm, and is lightly n-type doped (5×1016 cm-3, S). The measured room-temperature photoluminescence from the waveguide layer had a peak wavelength of 1039 nm and a width of Δλ=34 nm. The nominally undoped multiple quantum well (MQW) active region contains five 8-nm compressively strained (1%) InGaAsP quantum wells with tensile-strained (0.3%) InGaAsP (λG~1210 nm) barriers (8 nm) and bounding (12 nm) layers. The composition of the InGaAsP wells was adjusted to attain a peak photoluminescence wavelength of 1530 nm. The thicknesses and indices of the waveguide, MQW region, and cladding layers were chosen to obtain Γ~0.5%. Lateral mode confinement was obtained by etching a 5.7-μm-wide rib to an etch depth that enabled stable, fundamental mode operation with 1/e-dimensions of 5×7 μm. The fabricated SCOWA was cleaved to a length of 1 cm and anti-reflection (AR) coatings were deposited on the 5-degree-angled facets. The reflectivity of the AR coating at 1540- and 1050-nm is ~0.1% and 5%, respectively. The device was mounted junction-side down to a Cu-W submount using AuSn solder. Fiber pigtailing was achieved using lensed fibers and laser-welding. The spot size of the lensed fibers (6.5 μm) was chosen to match the mode dimensions of the SCOWA.
At a bias current of 5 A and a wavelength of 1540 nm, the packaged, fiber-pigtailed SCOWA has a small-signal gain of Go=13.8 dB, a saturation output power of Po,sat=0.8 W, a spectral bandwidth > 100 nm (~1450–1550 nm), and a maximum electrical-to-optical conversion efficiency of ηE-O=11%, neglecting the TEC power . The maximum 1540-nm output power obtained from the device was 0.93 W at a saturated gain of 6.7 dB. The lensed-fiber to SCOWA coupling efficiency was estimated to be ηC=90% (-0.5 dB). At 5-A bias and 1550-nm, the noise figure was measured to be 5.5 dB.
4. TPA photoluminescence measurement results
The OSA spectra (Fig. 2) reveal the presence of a broad optical signal having a center wavelength of ~1055 nm and a magnitude that increases with increasing 1540-nm SCOWA output power. We attribute this optical signal to the radiative recombination of carriers in the waveguide region that are generated by TPA. When the 1540-nm input signal power is zero and the SCOWA is only producing amplified spontaneous emission (ASE), the measured spectrum (black curve in Fig. 2) is indistinguishable from the OSA noise-floor spectrum (not shown). As the input power is increased, the 1055-nm signal rises above the OSA noise floor. The 1055-nm peak wavelength of the observed signal is about 16-nm larger than the peak wavelength of the measured room-temperature photoluminescence from the SCOWA waveguide layer. The observed wavelength red-shift under forward-bias operation is attributed to a reduction of the InGaAsP waveguide bandgap due to a combination of heating  and bandgap renormalization .
To confirm that the observed optical signal is due to the recombination of TPA-generated carriers, we plotted the 1055-nm power, averaged from 1050 to 1060 nm, as a function of the 1540-nm SCOWA output power (Fig. 3). For each data point, the average value of the OSA noise-floor power (0.38 pW) was subtracted from the 1055-nm average power. The relationship between the 1055-nm optical signal and the 1540-nm SCOWA output power has a strong quadratic dependence. Assuming that the recombination of TPA-generated carriers is radiative with carrier-density-independent lifetime τ 2, the TPA-carrier photoluminescence power from a volume ΔV can be shown to be P 2=βTPAI 2 SΔV=βTPA(PS/Amode,NL)2ΔV. Therefore, the quadratic dependence observed in Fig. 3 provides strong evidence that the observed 1055-nm signal is due to the recombination of the TPA-generated carriers. We note that the assumption of a carrier-density-independent radiative lifetime is likely since the waveguide is doped n-type (n=5×1016 cm-3). Therefore, the photoluminescence power is generated by the radiative recombination of TPA-generated holes and the background electron population. For completeness, we note that the photoluminescence signal does not result from hole leakage from the QW region into the waveguide region since it is not present when no light is injected (ASE condition) and the carrier density would be at its largest.
5. Comparison of measured and simulated CW gain saturation
Previously, we reported a comparison of measured and simulated gain-saturation data from a low-confinement InGaAsP QW SCOWA . The simulation is based on the steady-state model presented in . The main results of this comparison were (i) the Po,sat of an SOA is directly related to the shape of the material gain coefficient g(n), which quantifies the relationship between the material gain and the injected carrier density n, (ii) the often used linear g(n) approximation is not adequate for quantifying the trade-off between Go and Po,sat, and (iii) the trade-off between Go and Po,sat becomes increasingly dependent on the optical loss as Γ is reduced. Direct comparison of measured and simulated gain vs. output power data showed excellent agreement in the Go and Po,sat values. However, the measured gain saturation vs. output power was much more abrupt than the simulated curves at high bias current and high output power.
In this work, we extend the steady-state waveguide SOA simulation to include the effects of both TPA and TPA-generated FCA. In the simulation, the SOA is divided into M sections along its length and rate equations are solved self consistently to determine the carrier density and optical signal power as a function of injection current and input optical power. The simulation includes the following optical loss mechanisms: (i) α0, the injected-carrier-independent loss due to free-carrier absorption in the doped regions and waveguide scattering loss, (ii) αQW, the IVBA due to injected holes in the quantum wells, (iii) α2, the absorption due to TPA, and (iv) α2FCA, the FCA due to TPA-generated carriers. The loss mechanisms introduced in the extended model were given earlier in Eqs. (1) and (4).
Similar to , the single-QW material gain coefficient used in the simulation was g(n)=g 0ln(n+nS/nTR+nS), where n is the injected QW carrier density, g0=415 cm-1, nTR=1.65×1018 cm-3 is the transparency carrier density, and nS=-1.43×1018 cm-3 is an additional fitting parameter. The values of g0, nTR, and nS were determined from the measured small-signal gain of the packaged SCOWA at 1540 nm at several bias currents. Calculation of the carrier density n from the injected current density was obtained by solving the carrier-density rate equations under the small-signal, steady-state condition. The simulated optical mode was a 2-dimensional Gaussian distribution with 1/e-mode-field diameters of 5 and 7 μm in the vertical and lateral directions, respectively. For these mode dimensions, Amode,NL=27.5 μm2. Other important simulation parameters are the optical confinement factor Γ=0.5%, waveguide width w=5.7 μm, active region thickness d=40 nm=5×8-nm QWs, length L=1 cm, and fiber-to-waveguide coupling efficiency ηC=90%.
Figure 4 provides a comparison of the measured and simulated fiber-to-fiber gain vs. output power characteristics of the packaged SCOWA described above. The only parameter that was varied in generating the five simulated curves was the DC bias current. The TPA coefficient βTPA used in the simulations for the 1.04-μm InGaAsP waveguide material was 60 cm/GW. This value of βTPA was estimated from the dependence of βTPA on the inverse cube of the bandgap energy EG -3  and assuming βTPA=32 cm/GW for InP . The fixed simulation values of σ2FCA=2×10-17 cm2 and τ2=8 ns were chosen to make the Po,sat of the measured and simulated data equal at a bias current of 5 A only. These values agree well with those reported in . No other fitting or adjustment parameters were used. The data of Fig. 4 reveal remarkable agreement between the simulated and measured gain-saturation characteristics. We expect good agreement between the small-signal gain values since the simulation’s material-gain coefficient expression is derived from measured small-signal gain data. In addition to this agreement, both the saturation output power Po,sat values and the roll-off shapes of the gain-saturation curves are almost identical. In our previous work where we did not include the effects of TPA and TPA-generated FCA , we were not able to obtain the correct roll-off shape at high bias current and corresponding high output power. From the simulation, we estimate that the TPA-generated carrier density becomes as large as NTPA=3.6×1016 cm-3 at 5-A bias current and at Po=Po,sat=0.8W. At this value of NTPA and Po, the TPA and TPA-generated FCA coefficients are α2=0.18 and α2TPA=0.72 cm-1, respectively. These results indicate that (i) the density of TPA-generated holes is smaller than the background electron density in the n-doped waveguide (5×1016 cm-3), and (ii) the nonlinear loss is dominated by the TPA-generated FCA.
The relative impact of TPA and TPA-generated FCA at high bias current (IDC=5 A) can be clearly seen in the simulated results shown in Fig. 5. When both TPA and TPA-generated FCA are included in the simulation, the fiber-coupled Po,sat=0.8 W and the output power saturates abruptly. When neither of these effects is included, Po,sat increases by 40% (1.5 dB) to 1.13 W and the saturation is more gradual. When the amplifiers are driven deep into saturation (G ~ 6 dB), the output powers with and without TPA are 0.98 W and 1.74 W, respectively, a ratio of 2.5 dB. Figure 5 also shows the intermediate case when only TPA is included. These results show that mitigation of TPA effects should result in significantly higher output power, especially at high bias current.
The SCOWA band-diagram schematic in Fig. 6 summarizes our interpretation of the TPA and TPA-generated FCA physics implied by our photoluminescence observation and the excellent agreement between measured and simulated gain-saturation data. Under forward-bias, electrons and holes are injected into the SCOWA’s QW region from the n-doped waveguide and p-doped cladding region, respectively. When the QW carrier density is large enough to provide gain, optical signals injected into the SCOWA at wavelengths within the gain bandwidth are amplified through stimulated emission. In the SCOWA design, most of the optical mode is confined to the waveguide region and it is evanescently coupled to the QW region. When the amplified signal power becomes large, electron-hole pairs are generated via TPA in the waveguide where the mode intensity is largest. This TPA mechanism acts to directly deplete the optical field. The TPA-generated carriers, primarily the holes, introduce an additional loss mechanism through FCA. The holes then recombine radiatively with the background electron concentration in the n-doped waveguide to generate photoluminescence at a wavelength corresponding to the bandgap wavelength (~1040 nm) of the waveguide material. The TPA and TPA-generated FCA optical loss mechanisms limit the maximum intensity that can be produced by the amplifier.
To our knowledge, the effects of TPA have not been directly observed or analyzed for a SOA amplifying a CW optical signal or from a semiconductor laser producing a CW signal. The recent theoretical work by Tseng et al.  studying pulse amplification in SOAs revealed that the saturation output pulse energy Eo,sat of an SOA can be limited by either carrier depletion or by TPA depending on several device parameters including Γ, Amode,NL, βTPA, and the temporal width of the pulse. For traditional high-Γ SOAs, Eo,sat is usually limited by carrier depletion. However, for low-Γ structures such as the SCOWA, TPA effects can limit Eo,sat before significant carrier depletion can occur. The analysis presented in  was restricted to pulse amplification and the impact of TPA-generated FCA was not considered. In this work, we have observed the photoluminescence from TPA-generated carriers during CW amplification. We have also performed a comparison of measured and simulated CW gain saturation that revealed that TPA-generated FCA has a larger effect on limiting SOA CW output power than TPA alone. It is likely that TPA-generated FCA has limited the CW gain and output power of previously reported SOAs and semiconductor lasers, especially those having small Γ. This work also provides evidence that nonlinear gain compression, which describes the reduction in material gain at high optical intensity, is partially due to TPA.
Several techniques may be applied to mitigate the effect of TPA on the output power of low-Γ SOAs and lasers. First, the size of the optical mode could be increased to decrease the optical intensity, thereby decreasing α2 [see Eq. (1)]. Second, the waveguide could be designed from a material having a bandgap energy that is at least twice the photon energy so that TPA would be effectively eliminated. Third, non-radiative recombination centers could be introduced into the waveguide through low-temperature growth or proton bombardment. These recombination centers would reduce the lifetime τ 2 of the TPA-generated carriers, thereby decreasing the associated FCA [see Eq. (4)]. And fourth, the waveguide could be designed so that the peak of the optical mode was in the high-field region of a p-i-n diode. Sweepout of the TPA-generated carriers would again reduce τ 2.
The authors would like to thank Dr. Stephen Pappert of the Defense Advanced Research Projects Agency (DARPA) Microsystems Technology Office (MTO) for support. They would also like to acknowledge Dr. Daniel Sparacin of Booz Allen Hamilton for helpful discussions. This work is sponsored by the DARPA MTO under Air Force contract number FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors, and are not necessarily endorsed by the United States Government.
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