Temperature Performance of Monolithic Passively Mode ... - IEEE Xplore

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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 19, NO. 4, JULY/AUGUST 2013

Temperature Performance of Monolithic Passively Mode-Locked Quantum Dot Lasers: Experiments and Analytical Modeling Jesse K. Mee, Student Member, IEEE, Mark Thomas Crowley, David Murrell, Ravi Raghunathan, and Luke F. Lester, Fellow, IEEE

Abstract—In this paper, a detailed study is presented on a series of quantum dot (QD) passively mode-locked lasers (MLLs) with variable absorber to gain-section length ratios. The effect of temperature on the stability of pulses emitted from the QD ground state is primarily examined and compared to an analytical model that predicts regions of mode-locking stability for a given device layout. The model correctly predicts the temperatures of maximum operability in each device for a variety of absorber voltages. Prediction of the regimes of excited-state operation from the QDs is also included and experimentally verified. For the first time, the unsaturated absorption is identified as a key parameter that strongly influences the range of biasing conditions that produce stable mode-locked pulses. This dataset offers valuable insight into design of future MLL devices for maximum optical pulse quality over a large range of temperature and biasing conditions. Index Terms—Passively mode-locked lasers (MLLs), quantum dots (QDs), semiconductor lasers, temperature performance.

I. INTRODUCTION N RECENT years, increasing challenges in electronic charge transport due to electromagnetic interference effects, fundamental limitations of capacity, and increased power dissipation have led to the investigation of integrating photonics into the backplane of high-speed communication network architectures [1]–[3]. This realization has fueled competition between different laser structures aimed at determining which technology possesses the most superior properties to support these

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Manuscript received November 2, 2012; revised January 7, 2013 and January 18, 2013; accepted January 20, 2013. Date of publication February 25, 2013; date of current version May 13, 2013. This work was supported in part by the Air Force Research Laboratory under Grant FA9453-12-1-0132, in part by the Air Force Office of Scientific Research under Grant FA9550-10-1-0276 and Grant FA9550-10-1-0463, in part by the National Science Foundation under Grant ECCS-0903448, and in part by the Silicon Research Corporation under Contract SRC-2009-HJ-2000. J. K. Mee is with the Air Force Research Laboratories, Kirtland Air Force Base, NM 87117 USA, and also with Center for High Technology Materials, University of New Mexico, Albuquerque, NM 87106 USA (e-mail: [email protected]). M. T. Crowley is with BinOptics Corporation, Ithaca, NY 14850 USA (e-mail: [email protected]). D. Murrell, R. Raghunathan, and L. F. Lester are with the Center for High Technology Materials, University of New Mexico, Albuquerque, NM 87106 USA (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2013.2247571

high-speed applications. Although quantum-well (QW) devices are considered to be at the forefront of this discussion, structures based on quantum dots (QDs) actually possess many superior properties over their QW counterparts. These include low linewidth enhancement factor [4], low threshold current densities, wide gain bandwidth, easily saturated gain and absorption, and temperature-resistant operation [5]–[7]. As a result, generation of ultrashort, ultrahigh repetition rate, optical pulses has been demonstrated in mode-locked lasers (MLLs) based on QD materials [8], [9]. Some of the particular advantages of these QD MLLs include their compact size, lower power consumption, broad operational maps, and improved temperature operation [10]. These attributes have attracted considerable attention in the space electronics community. Satellite missions are often tightly constrained by their power budget. At the same time mission payloads, such as hyperspectral imagers, for example, can produce tens of Gb/s of uncompressed data [11]. The maturity of the QD MLL technology to the point of integration with the data transmission architecture on a satellite could represent a significant reduction in the size, weight, and power (SWaP), while simultaneously improving the capacity. In addition, these devices have the potential to support many terrestrial applications from high bit-rate optical time-division multiplexing (OTDM) for use in data center network architectures [12], to the generation of RF signals [13]. It is expected that these laser devices will need to operate reliably under a variety of environmental conditions. In particular, the ability for the MLL to produce stable pulses over a large range of temperatures is of critical importance, especially for use in data centers or on a processor card in which the device would ideally be located close to the CPU core. Recently, we have focused on understanding and improving the pulse characteristics of two-section QD passively MLLs over broad temperature excursions [10], [14]. In a recent study by Mesaritakis et al., it was shown that the number of QD layers has a considerable impact on the quality of mode-locking [15]. In this paper, we focus on the impact from the absorber length to gain length ratio. As a prerequisite to optimizing pulse characteristics, knowledge of how to construct the cavity layout for two-section MLLs is needed. Our previous work has followed a methodology based on a microwave photonics approach, wherein two characteristic functions describing the boundary for the onset of mode-locking are used to predict regions of mode-locking stability for a given cavity geometry. The strength of this approach lies in the fact that all the parameters appearing in the analytic expressions can

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MEE et al.: TEMPERATURE PERFORMANCE OF MONOLITHIC PASSIVELY MODE-LOCKED QUANTUM DOT LASERS

be measured, namely, the static gain and loss characteristics. The segmented contact method [16], [17] is utilized to measure the loss and gain spectra over a wide temperature range up to 120 ◦ C and over a wide range of gain-section current and saturable absorber-section reverse voltages. The cavity design for passively MLLs based on several distinct material systems has already been realized using this approach [18]–[20]. The path to a QD MLL capable of broader temperature suitable for integration with Si-photonics was discussed in [14] and demonstrated in [10]. In this paper, a complete set of QD MLLs having different absorber lengths for the same fixed cavity length is analyzed. Using the experimental gain and absorption spectra to derive appropriate inputs, a model has been constructed that predicts regions of mode-locking stability for a given cavity geometry. The model is found to be in good agreement with experimentally determined operational maps for each of the devices used in this study. Close examination of the features in the experimental operational maps, correlated with the characteristics of the modal gain and loss spectra, has revealed that the unsaturated absorption strongly impacts the range of injection current and absorber bias conditions that produce short pulses. With this understanding, future devices can be designed to leverage broad gain bandwidths and selective lasing wavelength capabilities to operate in a regime that minimizes the unsaturated absorption and thus maximizes the range of biasing conditions over which the device produces high-quality pulses. This paper is organized as follows. In Sections II and III, the epitaxial growth and processing characteristics of the devices are introduced, and the experimental setup and methodology are given. In Section IV, the measured modal gain and absorption spectra are discussed and the relevant analytical equations for the modeling are given. This approach includes the inputs derived from the gain and loss spectra at the ground state (GS) and excited state (ES) wavelengths of the QDs, and the resulting theoretical stability maps and experimentally obtained operational maps. In Section V, insight is gathered into the above-threshold behavior of the MLLs that is not directly captured by the analytical model. II. DEVICE FABRICATION The active region for the devices used in these experiments is a highly optimized composition of six stacks of InAs QDs embedded in InGaAs QWs, separated by GaAs barriers, otherwise known as the dots-in-a-well (DWELL) laser structure [5]. Standard multisection laser processing was used to fabricate the 5-μm ridge waveguide, and the anode/cathode metal contacts. Each device contains an intracavity saturable absorber that is electrically isolated from the gain section via proton implantation. The total cavity length is a constant 8.0 mm in all cases; however, the length of the intracavity absorber La is varied among the different devices. In this paper, four different devices having La = 0.8 mm, 1.0 mm, 1.4 mm, and 1.6 mm are examined. The resulting absorber to gain-section length ratios are 0.11, 0.14, 0.21, and 0.25, respectively. In these two-section lasers, the facets are HR (95%)/AR(5%) coated with the absorber adjacent to the HR-coated facet. In addition, to enable

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gain and absorption measurements, a multisection laser was processed that has 16 electrically isolated 500-μm sections, and a 3.5-μm ridge waveguide. III. EXPERIMENTAL SETUP The two-section lasers have been individually mounted to AlN carriers for improved thermal conductivity and increased mechanical stability. They are placed on a vacuum stage with a large thermal mass. The temperature of the laser is controlled by a thermoelectric (TE) cooler. An ILX 3811 current source applies current to the anode contact above the ridge waveguide. A reverse bias from 0 to −7 V is applied across the saturable absorber. Light is coupled into a polarization maintaining singlemode fiber using a set of collimating lenses, and an isolator is incorporated to minimize feedback into the laser cavity. A 50-GHz HP 8565E electrical spectrum analyzer enables the characterization of the pulse train in the frequency domain. A high-speed photodiode is used for the optical-to-electrical conversion. The optical domain is characterized with an Ando AQ6317B optical spectrum analyzer. The MLL output is also captured in the temporal domain with a 140-GHz Tektronix DSA 8200 sampling oscilloscope, capable of measuring optical pulse shape in time. The measured pulse width τm from this scope is actually the convolution of the sampling gate, which has a width of 7.1 ps, and the optical pulses. Assuming that both are Gaussian in nature, then the actual pulse width τact can be estimated using the deconvolution formula [21] 2 2 = τm − 50.4. τact

(1)

It is noted that due to the high level of asymmetry in some optical pulses, the approximation in (1) can induce some error; however, the operational maps presented in Section IV are for stable pulse trains that are well approximated by a Gaussian profile. Gain and absorption measurements were conducted on the multisection device using a segmented contact method. In this technique, the gain profile is determined by measuring the emitted amplified spontaneous emission with different pump lengths. The absorption profile is determined in a similar fashion but requires the addition of a variable reverse bias. Details of these measurements and the relevant equations can be found in [16]. IV. RESULTS AND DISCUSSION A. Measured Gain and Absorption Characteristics The analytical model presented in the next section is a useful tool for predicting the regions of mode-locking stability for a given device geometry. In this section, the approach for extracting model parameters from the experimental data is outlined. This model requires inputs derived from static gain and loss characteristics measured directly on the device. In order to perform a full analysis of the QD material used in this study, gain spectra were measured at TE cooler temperatures from 20 to 120 ◦ C over a range of current densities from 229 to 1257 A/cm2 . Total loss spectra were measured for absorber voltages from 0 to −7 V and the same temperature range.

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produce mode-locked pulses from the ES when the absorber was grounded. From the modal gain data presented in Fig. 1 and Tables I and II, the first of the required model inputs can be derived, namely, the modal gain and differential modal gain with respect to current density. For a given temperature and current density J, it is assumed that the MLL emits at the wavelength corresponding to the peak gain. Consequently, the QD peak modal gain behavior in Fig. 1 can be modeled using the following empirical expression: Jtr − J (2) + αi go (J) = gm ax 1 − exp b Fig. 1. Measured modal gain spectra for a constant current density of 857 A/cm2 at 20, 40, 60, 80, 100, 110, and 120 ◦ C. The wavelength of emission from the GS is observed to red shift at an average rate of 0.64 nm/◦ C between 20 and 60 ◦ C, and 0.39 nm/◦ C between 60 and 110 ◦ C

As mentioned previously, the complete set of required model inputs can be derived from gain and absorption spectra. First, the modal gain results are presented. For clarity, the modal gain spectra for selected temperatures between 20 and 120 ◦ C are shown in Fig. 1 at a constant current density of 857 A/cm2 (15 mA applied to a 500-μm × 3.5-μm section). At 20 ◦ C, three primary optical transitions are evident in Fig. 1 corresponding to the GS transition at λ = 1222.2 nm, the first ES transition at λ = 1158.8 nm, and the second ES transition at λ = 1112.2 nm. It is noted that the second ES is not clearly evident for temperatures greater than 20 ◦ C. The measured spectra shown in Fig. 1 were measured at the same current density and only the temperature was varied. From these measurements, the observed spectral variation of the GS gain peak between 20 and 60 ◦ C is 0.64 nm/◦ C, whereas between 60 to 100 ◦ C it is 0.39 nm/o C. The observed red shifting of the GS gain peak is expected to be a combination of both bandgap shrinkage (BGS) and the temperature-dependent shift of the bandgap [22]. For the devices reported here, it is likely that 60 ◦ C represents an activation energy associated with a nonradiative recombination process [23]. As a consequence, fewer carriers would be available for radiative recombination and the contribution to the red shift due to BGS would be reduced [24]. Inspection of the magnitude of the modal gain over temperature reveals that the GS gain degrades from 10.2 to 4.4 cm−1 , while the ES gain degrades more significantly from 14.1 to 4.1 cm−1 . This has been attributed to a reduced radiative efficiency for higher energy transitions at elevated temperature [25]. For completeness, the peak modal gain values and their matching emission wavelengths in the GS are summarized from 20 to 80 ◦ C in Table I in the Appendix. For the temperatures of 100–120 ◦ C, the ES gain peak wavelengths and modal gain values are summarized in Table II. This selection was based on the examination of optical spectra which revealed that for the case of a grounded saturable absorber, the lasing wavelength transitioned from GS to ES between 93 and 98 ◦ C for the device having La = 0.8 mm, and between 80 and 85 ◦ C for La = 1.0 mm. The devices having longer absorber lengths failed to

that has the corresponding differential gain of Jtr − J dgo gm ax = exp dJ b b

(3)

in which go (J) is the modal gain with respect to current density, gm ax is the measured maximum net gain, Jtr is the transparency current density, αi is the internal loss, and b is a fitting parameter which carries units of A/cm2 . The differential gain evaluated at go = 0 cm−1 (J = Jtr ) represents a conservative approximation for the differential absorption and has the convenient result based on the fitting parameters [19]: dao dgo gm ax ≈ . (4) = dJ dJ g o =0 b In Fig. 2(a), the measured modal gain at the GS gain peak as a function of current density over the temperature range 20–80 ◦ C is shown. This represents the range of temperatures wherein lasing occurred from the GS when the saturable absorber was grounded. For the remaining temperatures, the measured modal gain at the ES gain peak is shown in Fig 2(b). The symbols in Fig. 2 are the experimental values from Tables I and II and the solid lines are the fits according to (2). From this, the modal gain, differential modal gain, and differential absorption are determined. As presented in the next section, the unsaturated absorption and internal loss are the only remaining model parameters after the aforementioned analysis of the modal gain spectra. The internal loss can be derived from the net-gain spectra; however, it is most evident by the inspection of the absorption characteristics shown in Fig. 3. In our case, the internal loss was found to be an average of 2.4 cm−1 over the full range of temperatures examined. From Fig. 3, the average differential wavelength shift Δλ/ΔT in the absorption peaks is 0.44 nm/◦ C between 20 and 60 ◦ C, and it reduces to 0.42 nm/◦ C between 60 and 110 ◦ C. Recall that the overall average wavelength shift in the modal gain peak was greater than the aforementioned values for the absorption peak; however, it is noted that this shift reduces more significantly in the gain spectra than in the loss spectra such that for higher temperatures Δλ/ΔT |gain p eak < Δλ/ΔT |abs p eak . This turns out to be a critical detail in understanding the temperature of maximum stability, which will be discussed in more detail in Section V. For convenience, in Table III in the Appendix a complete list of the absorption peak wavelengths


Fig. 2. (a) Measured modal gain peak (symbols) of the GS as a function of current density over the temperature range from 20 to 80 ◦ C. (b) Measured modal gain peak of the ES as a function of current density from 100 to 120 ◦ C. Solid lines denote the resulting fits from (2).

and corresponding maximum absorption values is given in the GS at each temperature for applied voltages from 0 to −7 V. The next step is to determine the values of unsaturated absorption ao for any particular temperature and reverse-bias voltage on the absorber. This is accomplished by projecting the range of gain peak wavelengths (complied in Tables I and II for the full range of current densities) onto the total loss spectra presented in Fig 3. The bands in Fig. 3 represent the range of measured gain peak wavelengths. The unsaturated absorption is found by taking the average absorption value over the region and then subtracting the internal loss. This process is repeated for each temperature and reverse voltage. Unsaturated absorptions values for each temperature and voltage combinations are recorded in Table IV in the Appendix. It is found that the unsaturated absorption reaches a minimum at T = 60 ◦ C. This is a consequence of the variance in the differential wavelength shift of the gain and absorption spectra, which results in the gain peak walking off of the absorption peak. For the case of T = 80 ◦ C, the unsaturated absorption is slightly higher than that of T = 60 ◦ C because the shift in the gain peak is significantly reduced for higher temperatures. The values of ao increase dramatically

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Fig. 3. Measured total loss spectra for absorber reverse bias of 0 V from T = 20 to 80 ◦ C in (a) and from 100 to 120 ◦ C in (b). The shaded bands represent the range of absorber losses possible given the gain peak positions as a function of current density found in Tables I and II. The diagonal lines are the GS gain peak projection, and the cross-hatched lines are the ES gain peak projection (a) and (b), respectively.

at 100 ◦ C or higher, when the MLL is lasing from the ES. Intuitively, this would seem to reduce the likelihood of achieving laser threshold; however, the increase in ao is compensated by an increase in modal gain go at the first ES. B. Analytical Modeling An analytical approach, first introduced by Lin et al. [19] to construct MLLs for room temperature operation and later by Crowley et al. [14] to investigate the path to achieving broad temperature operation of QD MLLs, is used to predict the regions of pulse stability for a given device layout. In the previous section, the method for deriving all of the input parameters that appear in this model from static gain and loss measurements was outlined. The model is based on the idea that the onset of passive mode-locking in a semiconductor laser is bound by two functions. The first was derived from a net-gain modulation phasor approach, describing the onset of passive modelocking as a sinusoidal variation in output intensity [26]. The expressions derived in that study assumed that the gain and loss were uniformly distributed in the cavity. Subsequent work by

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Lin et al. [19] expanded this approach to account for discrete, electrically isolated gain and saturable absorber sections. For convenience, the resulting modified equation is stated here as well 2 dg o go(J ) La dJ > dg o . (5) Lg ao dJ |g o =0 Using the empirical formula from (2), the mode-locked condition expressed previously can be further reduced to the following alternative form: Jtr − J La > exp 2 · Lg b gm ax Jtr − J αi × 1 − exp . (6) + a0 b a0 The second equation which bounds the regions of passive mode-locking is the threshold condition for lasing and can be expressed in terms of the length of the absorber section over the length of the gain section as follows [14]: g o − αm − αi La = . Lg ao + αm + αi

Fig. 4. Mode-locking stability map for 0 V applied reverse bias as determined from (6) and (7) using the measured GS gain and absorption data, solid plots and measured ES gain and absorption data, dashed plots. The horizontal dashed lines represent the absorber to gain length ratios of the devices used in this study.

(7)

Here, αm is the mirror loss described by the classic equation [27] 1 1 αm = ln (8) 2L R1 R2 where R1 and R2 are the reflection coefficients at the laser facets, and L is the cavity length. The mirror loss was calculated based on HR (95%)/AR (5%) coated facets and an 8.0-mm cavity. In contrast to our previous paper, wherein we simply demonstrated the utility of our analytical model as a guide for achieving record temperature operation for a QD MLL [10], here we include a treatment of the ES mode-locking regimes and perform an in-depth study of the physical parameters which most strongly impact pulse stability including methods for optimizing the pulsed output for a wide range of temperatures and biasing conditions. Following this methodology, the stability map in Fig. 4 was generated for the case of 0 V applied to the saturable absorber, over the full range of examined temperatures. The characteristic function describing the threshold conditions for lasing shown in (7) sets the upper bound in Fig. 4 while (6) determines the lower bound. Devices having absorber to gain length ratios that fall within the bounds of the curves in Fig. 4 are predicted to produce mode-locked pulses for a given temperature. This represents the operable range of our stability maps. The dotted horizontal lines then depict the absorber to gain-section length ratios of the QD MLLs used in this study. It is generally noted that the path toward achieving better temperature performance in an MLL involves moving to a shorter absorber length. As a result, the device having La /Lg = 0.11 is anticipated to have the best temperature performance. The analytical model predicts that in all cases, with the exception of 20 ◦ C and La = 0.8 mm, the devices studied are in a region that is limited by the threshold condition rather than the modelocking stability condition in (6). The physical implications of this are discussed in Section IV-C. Stability maps have also been

Fig. 5. Comparison of model predictions from the GS (solid lines) and the ES (dashed lines) for 100–120 ◦ C with grounded saturable absorber.

constructed for the remaining voltages (−1 through −7 V); however, these have been excluded from this paper because the same fundamental conclusions are reached. The dashed boundaries in Fig 4 represent regions where mode-locking from the first ES was observed. In these regions, (2) was fitted to the ES netgain peak, and the values of gm ax and ao reflect the maximum gain and unsaturated absorption in the ES, respectively. A direct comparison of the model predictions at the GS and the ES for higher temperatures is shown in Fig 5. For 100 ◦ C or higher, the model indicates that the devices used in this study fail to meet the threshold condition in the GS. Conversely, for high-current densities, lasing from the ES is expected up to 110 ◦ C for the device having La = 0.8 mm, and up to 100 ◦ C for the device having La = 1.0 mm. One can see that the horizontal dotted lines in Fig. 5, representing the absorber to gain length ratios of these devices, intersect the ES maps only. In the following sections, results are presented from experiments designed to examine the current and voltage biasing regimes that produce stable mode-locking over a wide range of temperatures. In particular, verification of the model predictions for the temperature


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of maximum operation and the regions of ES versus GS modelocking is sought. C. Measured Mode-Locked Operational Maps To examine the accuracy of our predictive model, a detailed characterization of the pulse train output in the temporal domain is performed. At each temperature, and for incremental voltages from 0 to −7 V, the laser injection current was swept from below laser threshold, up to 500 mA—equal to a current density of 1.428 kA/cm2 . This current was selected as a maximum to avoid potential damage to the device. The regions of fundamental mode-locking (5 GHz) were recorded where the measured pulse width (τm ) was less than 20 ps, equal to an actual pulse width τa of ∼18.7 ps according to (1). In addition to the examination of the pulsed output in the temporal domain, the frequency and optical domains were characterized at the key biasing conditions that bounded the contours depicted in Fig. 6. This allows determination of the electronic state from which the device is lasing, the 3-dB bandwidth of the optical spectrum, and provides added insight into the quality of mode-locking. When the fundamental and second harmonics exhibit at least 15–20 dB above the noise in the RF spectrum analyzer, the MLL is assumed to be stable [14]. On average, the RF spectra for these pulses exhibited five to six harmonics with the SNR of the fundamental RF signal being greater than 37 dB. In Fig. 6, the resulting operational maps for each of the four devices used in this study are shown. The regions within the contours represent the current and voltage combinations that produce τa < 19 ps. The laser continued to pulse outside these contours but with longer pulse durations. The symbols in Fig. 6 represent the measured threshold current values for each combination of temperature and absorber bias. Recall that the only case where one of the devices was operating in the regime of (6) is at 20 ◦ C for the device having a 0.8-mm-long saturable absorber. Equation (6) represents the ultimate limit for the onset of mode-locking. Accordingly, the associated range of operational conditions shown in Fig. 6(a), where fundamental mode-locking with temporal FWHM less than 19 ps was observed, is very narrow. In many cases, unusual pulse dynamics such as pulse splitting, pulse doubling, and harmonic mode-locking were observed outside the contours of Fig. 6. A more detailed investigation into these regimes will be reported elsewhere. Comparing experimental results in Fig. 6 to the analytical predictions in Figs 4 and 5, excellent agreement is found, clearly demonstrating the capability to accurately predict the 0 V temperature of maximum operation on each of the device geometries studied in these experiments. Additionally, model predictions for the maximum operating temperature over a wide range of absorber voltages were also demonstrated with a high level of accuracy, further validating the utility of this approach. On examination of the optical spectrum for a grounded saturable absorber, it is found that the application of a reverse bias is generally observed to induce ES mode-locking when operating at temperatures where the switch from GS to ES operation occurs. In general, the onset of pulsing from the GS occurs near threshold, while the onset of pulsing from the ES occurs

Fig. 6. Contour maps depicting the regions of fundamental mode-locking (5 GHz) where the measured FWHM of the optical pulse was less than 19 ps for (a) L a = 0.8 mm, (b) L a = 1.0 mm, (c) L a = 1.4 mm, and (d) L a = 1.6-mm. These absorber lengths are depicted in the modeled mode-locking stability maps in Figs. 4 and 5. The plotted symbols show the threshold current at each temperature and reverse voltage.

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Fig. 7. Pulse train output at T = 60 ◦ C and V a = −5 V for a device with L a = 0.8 mm. Points A to D correspond to the biasing condition displayed in Fig. 6(a).

at injection current values that are well above threshold. This is clearly observed in Fig. 6(a) for the case of 100 and 110 ◦ C, and in Fig. 6(b) for the case of 100 ◦ C where ES pulses are observed at currents significantly above threshold. This result undoubtedly confirms our analytical model predictions shown in Fig. 5 regarding regimes of ES versus GS mode-locking. The voltage dependence of the GS to ES transition is also evident in Fig. 6(a) and (b) at 80 ◦ C, and in Fig. 6(c) at 70 ◦ C wherein the pulses are observed from the GS at 0 V but transition to ES under the application of reverse bias. The typical progression of the pulse train shape is shown in Fig. 7. The points labeled A to D in Fig. 6(a) correspond to the biasing conditions used in Fig. 7. Typically, the shortest pulses are produced at currents close to laser threshold, while increasing the injection current beyond laser threshold results in spectral broadening and pulse broadening due to self-phase modulation [28]. Point D represents a typical pulse train that may be found outside the contours of Fig 6. In this case, pulse breakup is depicted, which typically occurs at currents slightly higher than those within the shaded contours. V. ABOVE THRESHOLD ANALYSIS One of the key observations from Fig. 6 is that the devices which are optimized for broad temperature operation (La /Lg = 0.11 and 0.14) prefer lasing temperature around 60 ◦ C. This is evidenced not only by expanded regions of mode-locked operation, seen in Fig. 6, but also from measurements of the pulse characteristics wherein narrow pulse durations and minimum interpulse noise occurred for the temperatures between 60 and 80 ◦ C. The analytical model from Section IV has demonstrated great utility; however, it fails to capture the dynamics related to improved stability over an increased range of injection currents. Equation (6) is derived in the limit that the pulse train is sinusoidal, while (7) describes the threshold condition for lasing. In addition, the model assumes a uniformly distributed gain and loss everywhere in the cavity, i.e., the variation of

Fig. 8. Experimentally measured unsaturated absorption at the gain peak over the temperature range from 20 to 120 ◦ C for saturable absorber reverse bias of 0 to −7 V. The absorption is found to reach a minimum around T = 60 ◦ C. This is a consequnce of the gain peak/absorption peak walk-off.

the gain and loss characteristics along the length of the device is not accounted for. The effect of lumped gain/loss elements is magnified at currents above threshold and manifests in selfphase modulation and gain saturation. Due to these constraints, the model is best suited to conditions near threshold. Previous studies have shown that mode-locking stability can improve at elevated temperatures due to an increased rate of thermionic emission [29]. In this study, it is shown that there are potentially other factors leading to improved stability with temperature. In particular, a trend in the unsaturated absorption has been found that explains the expanded range of stable operation beyond the onset of mode-locking. In Fig. 8, the unsaturated absorption at the gain peak ao is plotted over the full range of temperatures studied. It was previously noted that the average differential wavelength shift in the gain spectra was larger than that in the absorption spectra resulting in a gain peak/absorption peak walk-off. As seen in Fig. 8, the minimum unsaturated absorption values are measured at 60 ◦ C for all absorber biasing conditions. A reduced value of ao allows for lower modal gain go in the amplifying section of the device as per (7). As a result, the pulse is subjected to less distortion per pass in the gain section, and pulse shaping takes place more gradually. Thus, the pulse widths at 60 ◦ C are generally shorter than those at any other temperature, and the operational conditions yielding pulses below 19 ps expand as observed in Fig. 6. Further evidence of the benefit of lower ao can be found in the variation of the time bandwidth product (TBP) with temperature, which was previously reported in [10, Fig. 4]. There, the same trend was observed with the TBP minimizing in the temperature range between 60 and 80 ◦ C. VI. CONCLUSION In conclusion, using a segmented contact method, the gain and loss characteristics on a six-stack DWELL semiconductor laser structure were measured. The resulting modal gain and absorption spectra were used to derive the input parameters of


an analytical mode-locked model. This model has been shown to effectively predict regions of stable operation in a semiconductor MLL across temperature. Following the generation of the theoretical stability maps, four different two-section MLLs having absorber to gain length ratios of La /Lg = 0.11, 0.14, 0.21, and 0.25 were characterized over temperature. Experimental measurements of the pulsed output in the time domain allowed operational maps to be generated in which the regions within the contours of the maps represented injection current and absorber reverse bias conditions which produced pulses of FWHM less that 19 ps. Excellent agreement between the modeled stability maps and the experimental operational maps was found. For the case of a grounded absorber, the model was able to correctly predict the maximum temperature where mode-locking was observed in each device. From the examination of the experimental results and the gain and loss characteristics, the unsaturated absorption was identified as a critical parameter that strongly influences the range of currents above threshold that produce stable mode-locked pulses. Practically, given the strong wavelength dependence of ao , and the broad gain bandwidth, a grating could be used in the future to select a lasing wavelength to have the minimum unsaturated absorption.

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TABLE III ABSORPTION PEAK WAVELENGTHS AND MAX ABSORPTION

APPENDIX TABLE I GS MODAL GAIN AT PEAK GAIN WAVELENGTH TABLE IV UNSATURATED ABSORPTION VALUES a o (CM−1 ) ASSUMING AVERAGE INTERNAL LOSS OF α i = 2.4 CM−1

ACKNOWLEDGMENT TABLE II ES MODAL GAIN AT PEAK GAIN WAVELENGTH

The authors acknowledge useful discussions with Dr. V. Kovanis of AFRL. REFERENCES [1] J. A. Davis, R. Venkatesan, A. Kaloyeros, M. Beylansky, S. J. Souri, K. Banerjee, K. C. Saraswat, A. Rahman, R. Reif, and J. D. Meindl, “Interconnect limits on gigascale integration (GSI) in the 21st century,” Proc. IEEE, vol. 89, no. 3, pp. 305–324, Mar. 2001. [2] M. Haurylau, C. Q. Chen, H. Chen, J. D. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Topics Quantum Electron., vol. 12, no. 6, pp. 1699–1705, Nov.–Dec. 2006. [3] D. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE, vol. 97, no. 7, pp. 1166–1185, Jul. 2009.

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Jesse K. Mee (S’11) received the B.S. degree (concentrating on microelectronics) and the M.S. degree (Hons. with distinction) from the University of New Mexico (UNM), Albuquerque, USA, in 2009 and 2010, respectively, both in electrical engineering. His research was related to reliability physics of microelectronics for space applications. In particular, he concentrated on the reliability degradation phenomenon known as negative bias temperature instability. He is currently working toward the Ph.D. degree in optoelectronics at the Center for High Tech Materials, UNM, under the guidance of Prof. L. F. Lester. He has been with the Air Force Research Laboratories, Albuquerque, NM, USA, since 2008 and currently focuses on optical backplane design for satellite bus architecture. His research interests include high-temperature operation of passively MLLs, optical pulse compression, and integrated photonics.

Mark Thomas Crowley received the B.Sc. (Hons.) degree in physics from University College Cork, Cork, Ireland, in 2004. During the same year he was an intern with Prof. David Cotter’s Photonic systems group, University College Cork, researching fourwave mixing in highly nonlinear optical fibers. In 2010, he received the Ph.D. degree in physics from Tyndall National Institute, University College Cork, in modeling electronic and optical properties of InGaAs/GaAs QDs under the supervision of Prof. E. O’Reilly. Between 2010 and 2012, he was a Postdoctoral Researcher in Prof. Luke Lester’s group at the Center for High Technology Materials, University of New Mexico. His postdoctoral work concentrated on the device physics, and characterization and modeling/design of semiconductor QD MLLs. He is currently a Design Engineer with BinOptics Corporation, Ithaca, NY, USA.


David Murrell received the B.S. degree in engineering physics and the M.S. degree in applied physics from the Colorado School of Mines, Golden, USA, in 2007 and 2009, respectively. His thesis topic dealt with the electrical examination of deep electronic states in fully depleted CdTe solar cells. He is currently a Research Assistant at the University of New Mexico, Albuquerque, USA, involved in research in the field of semiconductor lasers. He has an extensive interest in optics and integrated devices, developed when working at the Air Force Research Laboratory, Wright-Patterson Air Force Base, OH, USA, during two consecutive internships starting in 2006. His projects at that time involved device characterization of passively mode-locked semiconductor lasers.

Ravi Raghunathan received the Bachelor of Applied Science (Hons.) degree in electrical engineering from the University of Windsor, Windsor, ON, Canada, in 2003, the Master of Science degree in electrical engineering (electrophysics) from the University of Southern California, Los Angeles, USA, in 2006, and the Master of Science degree in optical science and engineering from the University of New Mexico, Albuquerque, USA, in 2010. He is currently working toward the Ph.D. degree in optical science and engineering at the Center for High Technology Materials, University of New Mexico, under the guidance of Prof. L. F. Lester. His current research interests include the theoretical and experimental investigation of various aspects of the device physics and characterization of semiconductor lasers, such as pulse compression and noise performance improvement in passively mode-locked QD lasers, ultrafast pulse characterization, nonlinear dynamical phenomena in semiconductor lasers, and the investigation of novel phenomena, such as nonlinear and quantum optical effects in semiconductor nanostructures.

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Luke F. Lester (S’89–M’91–SM’01–F’13) received the B.S. degree in engineering physics and the Ph.D. degree in electrical engineering in 1984 and 1992, respectively, both from Cornell University, Ithaca, NY, USA. He is a Professor and Interim Chair in the Department of Electrical and Computer Engineering and the Endowed Chair Professor in Microelectronics at the University of New Mexico (UNM), Albuquerque, USA. Prior to his arrival at UNM in 1994, he was an Engineer for the General Electric (Martin Marietta) Electronics Laboratory, Syracuse, NY, USA, for six years where he worked on transistors for millimeter-wave applications. There in 1986 he coinvented the first Pseudomorphic HEMT, a device that was later highlighted in the Guinness Book of World Records as the fastest transistor. By 1991 as a Ph.D. student in Prof. Lester Eastman’s group at Cornell, he researched and developed the first strained quantum-well lasers with millimeter-wave bandwidths. These lasers are now the industry standard for optical transmitters in data and telecommunications. In all, he has 27 years of experience in III–V semiconductor devices and advanced fabrication techniques. In 2001, he was a Cofounder and Chief Technology Officer of Zia Laser, Inc., a startup company using QD laser technology to develop products for communications and computer/microprocessor applications. The company was later acquired by Innolume, GmbH. He has published more than 115 journal articles and more than 240 conference papers. Dr. Lester’s received the following awards and honors: a 1986 IEE Electronics Letters Premium Award for the first transistor amplifier at 94 GHz; the 1994 Martin Marietta Manager’s Award; the Best Paper Award at SPIE’s Photonics West 2000 for reporting a QD laser with the lowest semiconductor laser threshold; and the 2012 Harold E. Edgerton Award of the SPIE for his pioneering work on ultrafast QD MLLs. He is also a Fellow of the SPIE. He was a U.S. Air Force Summer Faculty Fellow in 2006 and 2007. He is an active organizer and participant in the IEEE Photonics Society’s conferences, workshops and journals.