Comparison of Gain Measurement Techniques for Characterization of Quantum Dot Lasers

This paper presents a comparative analysis of three gain measurement methods which are H&P (Hakki & Paoli), SC (Segmented-Contact) and IA (Integrated-Amplifier) for the gain characterization of 1300nm (O-band) InAs/GaAs QD (Quantum Dot) laser devices. In this case, during continuous mode operation at a fixed heat-sink temperature of 17oC, the experimental conditions, measured spectral ranges and signal to noise ratio are compared and advantages are discussed. The devices used for the analysis are fabricated as multi-section, single mode structures. Before self-heating, each of the methods show identical results but SC proved to be better in terms of accuracy of internal loss measurement. The H&P method has been shown the only choice for high current density gain measurements at a fixed junction temperature under consideration. The method to remove self-heating effects via H&P is also discussed and via this method a high current density gain analysis upto 5.5kA/cm2(~ 8e-h pairs)is performed under 30oC fixed junction temperature condition. In comparison to other methods, the IA method has shown to be advantageous in terms of low current density measurements exhibiting the capability of accessing wider spectral ranges and performing the gain characterization where laser material operates in loss.


Mehran University Research
T he commercial applications of QD laser devices in the areas of optical coherence tomography [1], fiber optic: O-band communication [2] is largely due to their cost effectiveness and temperature independent turn on [3][4]. An understanding of the spectral relationship between gain and current density is not only integral to the device engineering but also crucial to determine the performance of semiconductor laser devices [5].
Optical gain measurement is a fundamental requirement for the characterization of lasers and amplifiers owing to This paper presents a comparative, empirical analysis of H&P [11], SC [12] and IA methods [13] for gain measurement. The analysis being presented here would mainly contribute towards the understanding of many body effects at high carrier/current densities and evolution of states at comparatively lower carrier/current densities. This is made possible by utilizing various InAs/

DEVICE STRUCTURE AND FABRICATION
The QD laser structure fabricated for the analysis as shown in Fig. 1(a) is grown by Innolume. In this case ten Then, the laser structure is fabricated as multi-section narrow ridge laser devices with deep etch having each section width as 3μm and length as 500μm .
A bi-layer InAs/GaAs QD laser structure as shown in between the paired layers results in preferential nucleation of QDs in the second layer above QDs in the first (seed) layer, so that the seed layer acts as a base for QD growth in the second layer, which fixes the QD density [14]. This allows suitable growth conditions for the second QD layer to be chosen to achieve an extension in room temperature emission from the QD ground state beyond 1300 nm while maintaining a reasonable QD density. The small separation between the paired layers allows efficient electronic coupling between the layers so that emission occurs from the second, longwavelength QD layer. Full details of the epitaxial structure are provided elsewhere [15].

Hakki &Paoli Method
The H&P [11]  The modulation depth, as calculated by knowing the peak and trough of the electro-luminescence spectra allows the gain to be calculated as a function of each of the wavelengths. Due to high spectral resolution requirements for the method the signal to noise ratio is low. The gain values obtained become unreliable when troughs approach the noise floor. These factors result in longer data acquisition times and make low current density measurements very difficult. Fig. 2 shows the modulation depth an electro-luminescence spectrum and can be calculated by Equation (1) [11].
In case of H&P method the net modal gain at each wavelength can be calculated via Equation (2) [11]. Other than modulation depth modal gain shows its dependence upon the laser cavity length and the reflectivity at facets which is usually 33%.
In order to accurately determine the modal gain it needs a fully resolved electro-luminescence spectrum. For the purpose the resolution was adjusted to be 10pm and electro-luminescence spectra are retrieved. Fig. 3 indicates the experimental set up used for the H&P analysis [5]. In this case a current source is used as an input to the laser device. The temperature controlled condition for the laser device under test is achieved via placing it on a heat sink with a feed back control system to maintain a required temperature at each current density level. A 3-axis tracking system is used which is feedback controlled and is placed before the laser device which moves the single mode lensed fiber and actively aligns it according to the maximum output power from the laser. 99% of the coupled power is sent to the optical spectrum analyzer and 1% is fed back to the tracking stage to remain aligned for the maximum input power.

Segmented-Contact Method
The schematic for pumping a multi-section device for SC gain measurement method [12] is shown in Fig. 4. In this case, the gain is evaluated via finding the ratio of the amplified spontaneous emissions obtained by pumping the sections of lengths L and 2L with the same current density.
Via optical spectrum analyzer and utilizing the Lab-view as a data acquisition tool electro-luminescence spectra were retrieved from the sections as mentioned before which enabled the modal gain to be determined as given by Equation (3)

. AMPLIFIED SPONTANEOUS EMISSION FROM SECTION LENGTHS L AND 2L OF A MULTI-SECTION LASER DEVICE DRIVEN AT THE SAME CURRENT DENSITY AT CONSTANT HEAT-SINK TEMPERATURE OF 17 O C UNDER CW MODE OF OPERATION
The SC gain measurement method is applicable to both multi-modal and single mode laser devices provided higher order modes are entirely eliminated by either spatial filtering [12] or an additional device length is left un-pumped [16] in the front of pumped sections. In our case the second option is used and an un-pumped section length of the order of 250μm is left at the front as an unguided spontaneous emission filter.
The measurement set up for the technique is shown in Fig. 6 [5]. This experimental schematic can be employed for both SC and IA gain measurement methods. As can be observed that the experimental set up requirements are less stringent than the H&P. The difference mainly is that instead of single mode lensed fiber as in case of H&P method, a multi-mode fiber is used. So, the alignment requirements are not very critical as in case of the H&P method. Coupling efficiencies are also higher in comparison. Furthermore, less resolution data acquisition requirements make analysis much quicker than the H&P method.

Integrated-Amplifier Method
The IA gain method [13] is a variant of SC method. Here its importance in predicting the gain of a QD laser device at low current/carrier densities is discussed. This method allows the gain spectrum to be measured at lower current densities where material usually operates in loss and therefore can act as an alternate method to quantitatively determine the absorption in the QD states. It has an additive advantage to access wider spectral ranges in comparison to existing conventional gain measurement techniques [11][12] as well. In order to deduce the gain spectrum by integrated amplifier method, initially the emission spectrum with only the amplifier sections is measured, in our case this is with driving the front two contact segments at a current density of JA. This intensity, IA, is subtracted from the intensities IL (driving a single contact at a given current density) and I2L (driving two contacts at a given current density). The net modal gain in this case can be deduced using Equation

QUANTUM DOT LASER DEVICE SELECTION
For sake of comparison between H&P and SC methods at high current densities, the laser lengths were 'as cleaved' as 300μm and 4.75mm respectively. In each of the cases, the laser cavity width was 3μm. In first case for H&P method as shown in Fig. 8(a) optical power vs. current density characteristics confirms the non lasing characteristics of the laser device even at high current densities. This is further confirmed via electroluminescence characteristics as shown in the inset to Fig. 8(a) at 5kA/cm 2 . For SC method the amplified spontaneous emissions from lengths, L and 2L are shown in Fig. 8(b) at 5kA/cm 2 which also show the non-lasing characteristics in this case. Hence both of the devices were well suited for the empirical analysis.
For low current density measurement the SC and IA gain measurement techniques are compared. To fulfill the requirement a bi-layer multi-section device: 10mm long, 7 ?m wide with 1mm long isolated contacts was used. The multi-section device is shown in Fig. 9.
The I-V characteristics of the individual sections were essentially identical. It is therefore assumed that the L-J characteristics of the individual sections are also identical. All the acquisition parameters (resolution, sensitivity, integration times and coupling efficiency) were selected to be same for both techniques.
The amplified spontaneous emission characteristics for SC and IA are shown in inset to Fig. 8(b). For the latter case the amplifier section was derived at 1.42kA/cm 2 .

RESULTS AND DISCUSSION
The comparative gain analysis at high current densities between H&P and SC was performed in current density range: 0.03-1.67kA/cm 2 at a constant heat sink temperature of 17 o C under CW operational mode.
For low current density comparison the techniques were tested out to access wider spectral ranges and absorption measurement. The bi-layer material was found to be more optically efficient in comparison to the Innolume material therefore was used to perform low current density analysis. The analysis was performed for the current density range: 7-300A/cm 2 .

Net Modal Gain Empirical Comparison at High Current Densities
Net modal gain spectra for H&P and SC techniques for the given carrier density at a constant heat sink temperature of 17 o C are shown in Fig. 10(a-b) respectively.
The comparative analysis [5] indicates an initial blue shift and then a red shift of the modal gain spectra. In this case the blue shift is attributable to the state filling effects [16] and red shift is due to the combined self heating and free carrier effects.
In case of H&P method, net modal gain spectra are observed to be noisier towards shorter and longer wavelengths. This observed noise is attributable to the valleys of the electro-luminescence spectra touching the noise floor rendering the data unreliable. Hence a lesser signal to noise ratio towards these wavelengths is obtained.
In Fig. 10(b) for SC method, the internal loss (?i) value can be clearly identified at longer wavelengths in comparison to the H&P method. This is attributable to the less resolution requirements for the method which not only improves the signal to noise ratio but also makes data acquisition times much shorter i.e. upto 15 times. Due to a higher signal to noise ratio achieved via this method, is suggestive of accessing lower current densities in comparison. Further suggestion towards fulfillment of the purpose is via longer integration times i.e. higher resolution settings in addition [5].
The overlapping comparative analysis of the two said techniques is performed before onset of self heating effects in Fig. 11. Fig. 11(a), at low current density range: 0.13-2-0.5kA/cm 2 shows identical results for both techniques with the net modal gain variation within the range of ±0.5/cm. However, the noisier H&P net modal gain spectra make internal loss determination more difficult due to the valleys touching the acquisition system's noise floor which is not the case for the SC method. The same the case is observed for high current densities as shown in Fig. 11(b). In this case wider/more reliable net modal gain spactra are obtained in case of SC method comparison to the H&P method.
With the on-set of self heating, the comparison of the techniques become impossible due to the different degree of self heating produced in the cavities due to the difference in their corresponding lengths.

FIG. 9. THE MULTI-SECTION DEVICE SELECTED FOR THE COMPARATIVE EMPIRICAL GAIN ANALYSIS OF SEGMENTED-CONTACT AND INTEGRATED-AMPLIFER TECHNIQUES
It is already known that via short length laser devices the longitudinal modes can be clearly resolved. Therefore, the H&P method suggests the consideration of a single longitudinal mode as a junction temperature monitor to entirely remove the self heating/ Joule heating effects from the laser device making possible for laser devices to be analyzed for the free-carrier effects solely

Temperature Calibration for Hakki & Paoli Method
The self heating effects are considered to play a major role in modifying the modal gain spectral results and mask other important effects to be analyzed. For the purpose, a method [5] is presented here, via employing itself heating effects are entirely removed and device can be analyzed at a fixed junction temperature of interest even at high current densities. The steps employed for the method are clearly shown in Fig. 12.
The Fig. 12(a)  observed. It is attributable to the laser length elongation or may be due to refractive index variation as a function of temperature.
The inset to Fig. 12 Via employing temperature calibration methodology, the gain spectra are plotted as shown in Fig. 13 upto high current densities such as 5.5kA/cm 2 at a constant junction temperature of 30 o C. In this case, the evolution of the gain spectra can be explained in terms of free carrier effects.

Net Modal Gain Comparison at Low Current Densities
Generally with SC method, the gain spectrum can only be determined at wavelengths at which spontaneous emission occurs. It may not be obtained over shorter wavelengths where spontaneous emission is week. The purpose of amplifier section is to compensate for loss providing the positive net modal gain in this spectral region. It may in turn increase the spectral range over which the gain/loss can be deduced.
Comparison of the gain spectra deduced using the two measurement schemes is shown in Fig. 14  between the different spectra in Fig. 14 is unlikely to be due to spatial in homogeneity of the sample.

ACKNOWLEDGEMENT
The author is obliged to University of Engineering & Technology, Kala Shah Kaku Campus, Lahore, Pakistan, for their support in writing this paper.