Chapter 2 Theoretical Fundamentals
2.3 Quantum Dot Laser
2.3.2 Optical Gain and Laser Threshold
When light propagates through a medium, its intensity, Φ , will be attenuated due to light absorption, which is characterized by absorption coefficient α. Mechanisms which contribute to optical loss have various origins. They usually are divided into the output (mirror) loss, αm, caused by light output from the cavity and the internal loss, αi, which combines the effect of all the other mechanisms. However, if population inversion takes place in the medium, the absorption coefficient changes sign to negative due to stimulated emission dominates the light absorption.
To emphasize these two different cases of light absorption or light amplification, optical gain coefficient, G , is introduced. Now we consider the output loss inside a Fabry-Perrot cavity as shown in Fig. 2.4.
Let us assume that light propagating from the left to the right facet has intensity Φ at its initial position at the left facet. Over the length L 0 it becomes to Φ0exp[(G−αi)L]. After partial reflection at right facet having reflectivity R , a beam of intensity 1 R1Φ0exp[(G −αi)L] starts from right to left. In the similar manner, the intensity of the light becomes equal to R1R2Φ0exp[2(G−αi)L] at its initial position after a round trip, where R is the left-facet reflectivity. In steady state (at threshold), this 2
Fig. 2.4 Light propagation and its intensity in a round-trip cycle inside the Fabry-Perrot cavity.
round trip results in no change of the light intensity.
G is the threshold gain. At this moment, the injected current density is th
called the threshold current density Jth. The optical confinement factor Γ should be introduced when we consider the interaction between charge carriers and the light. It is defined as the ratio of the integrated light intensity with the region of inversion population to the total optical intensity throughout the laser structure. Different transverse optical modes will have different overlap with the active region. Therefore, the optical gain in Eq. (2.38) corresponds to a certain mode and is known as the modal gain as opposed to the material gain. Specifically, the modal gain is a product of the Γ - factor of the given q mode and the material th
2.3.3 Characteristics of Quantum Dot Lasers
For an individual self-organized QD, its electronic structure is very similar to the ideal case. There is a set of atomic-like quantum levels composed of several excited states and ground state. However, in contrast to the ideal array of identical QDs, self-organized islands differ greatly from each other in their size , shape, and other parameters affecting the energy of the quantum level. Namely, the quantum energy of real QD arrays is statistically determined rather than the zero-dimensional DOS of the individual QD. The DOS is maximum at the energy that corresponds
to the most probable QD size. In fact, the DOS of the array is characterized by a set of subbands that originates from inhomogeneously broadened quantum level of the GS and ES of individual QDs. Typically, the energy separation between ground state (GS) and excited state (ES) in QD is about 40~70 meV.
Compared to QW laser, the saturated gain, G , of QD laser is sat much lower and proportional to the DOS at the maximum:
Δ
⋅
∝
∝ QDmax i QD/
sat g n
G ρ (2.40) where g is the level degeneracy ( g =1 for the GS and ES is usually i characterized by gi >1), nQD is surface density of QD and Δ is the energy width of the DOS. Real QD array will decrease Gsat due to inhomogeneous broadening. On the other hand, the saturated gain can be increased by means of several QD planes or denser QD arrays in each plane. However, the transparency current density which is also proportional to the total surface density of the QD array will be traded off.
In a word, the competition between the transparency current density and the gain saturation determines the threshold current density at the given cavity loss.
In addition to the GS level, it was observed that one or more ES levels can be thermally populated to give an additional contribution to the threshold current density [41]. With higher degeneracy, these ES levels have higher saturated gain. Thus, the transition of the lasing emissions from the GS to the ES can be observed with increasing total loss. The situation is illustrated in Fig. 2.5, where the gain-current dependence is schematically shown for ideal as well as self-organized QD arrays. By the way, it has been shown that the experimental dependence of the optical modal gain on the threshold current density can be well fitted by the following empirical equation [42]:
)] transparency current density, γ is an additional dimensionless gain parameter which can be treated as a non-ideality factor.
Fig. 2.5 Schematic dependence of the optical gain on the current density for the ideal and real (self-organized) QDs.
Current density, J
Chapter 3
Experimental Techniques
3.1 Coherence Length Measurement
Compared with measuring the spectrum of some light sources, the measurement of coherence length provides a more direct way to judge whether an emitter is suitable or not for OCT application. To achieve the goal, we have set up a fiber-based, delay-tunable Mach-Zehnder interferometer.
3.1.1 Experimental Setup
The automatic, delay-tunable interferometer is re-equipped from the commercial, manually path-tunable MZI-VAR 1300, which is used as the frequency clock in SS-OCT originally and is produced by Thorlabs. Fig.
3.1 shows the scheme of the whole system. Roughly speaking, the system is composed of three components, fiber-based Mach-Zehnder interferometer (MZI), computer-controlled translation stage and signal digitizer. They function as doing interference, providing path difference
Fig.3.1 The scheme of the coherence length measurement system.
Light Source Detector
Fiber Coupler
Fiber Coupler Translation
Stage
Polarization Controller GRIN Lens
Collimator
Built-in Digitizer Computer
and demonstrating signal processing, respectively. Compared to free-space Michelson interferometer, the advantage of the fiber-based MZI is that it doesn’t require aligning the light beams except for the face-to-face collimators.
In short, the MZI is constructed by two 50/50 couplers. A translation stage driven by a computer-controlled actuator is used to change the optical delay in one arm of the MZI. Fig. 3.2 shows the photo of the MZI.
The polarization controller in the other arm of MZI can be used to optimize the polarization status in the fiber and maximize the interference fringe contrast in the detector output. One of the two output ports of the second 50/50 coupler is connected to a photodetector (PD). Then the interference signal from the PD will be sampled by a high-speed digitizer and the data can be saved.
The actuator, Z825, with a maximum traveling range of 25mm and a minimum resolution of 29 nm, is produced by Thorlabs. In other words, only light sources with coherence length shorter than 25 mm can be defined by this system. The high-speed digitizer, NI 5122, with a maximum sampling rate of 100M points per second, is a product of National Instrument. Narrow-shape interferogram can be obtained by means of setting appropriate traveling velocity and enough sampling rate.
Labview software is used to controlled the actuator and digitizer simultaneously and output the digital interferogram data. Fig. 3.3 shows the interface of the control panel.
Followings are some crucial issues that have to be concerned in this system. First, to define the coherence length correctly, the traveling range of the actuator must pass through the point of zero path difference. It can be proved by the characteristic of perfect symmetry of the
Fig. 3.3 The interface of the Labview control panel.
interferogram. Second, the face-to-face collimators must be aligned as good as possible to achieve nearly equal receiving power during translation. Finally, due to the sensitivity of interference, the whole system including all the fibers must remain stationary during the measurement. Any fluctuation will change the polarization state of the fiber output and further make an impact on the interferogram.
3.1.2 The Accuracy of Measurement
The Wiener-Khinchin theorem provides us a method to verify whether our measurement is accuracy enough or not. The interferogram and the power spectrum form a Fourier Transform pair. We measure the power spectra and interferograms of three commercial lasers. They are 1310 nm MQW-FP LD (multiple quantum well - Fabry-Perot laser diode), 1310 nm MQW-DFB (distributed feedback) LD and 1550 nm MQW-DFB LD and then will be abbreviated by LD#1, LD#2 and LD#3, respectively. The measurement of optical spectrum will be discussed later.
In this regard, an issue must be concerned before performing Inverse Discrete Fourier Transform (IDFT) on linear-scaled power spectrum we measured. According to sampling theorem, an analog signal that has been sampled can be perfectly reconstructed without aliasing from the samples only if the sampling rate exceeds two times of the highest frequency in the original signal. On the other hand, the sampling interval in the time domain is the reciprocal of the sampling range in the frequency domain;
the sampling range in the time domain determines the reciprocal of the sampling interval in the frequency domain, and vice versa. In conclusion, to make sure the reconstructed data is without aliasing and is correct, some conditions when measuring the power spectrum must be considered,
such as enough sampling rate and sampling range. By the way, a more efficient algorithm, IFFT (Inverse Fast Fourier Transform), is used to compute the IDFT. More details about these concepts can be referred to textbooks of digital signal processing (DSP) [43].
Fig. 3.4~3.6 show the comparison of (a) the power spectrum in linear scale, (b) IFFT of power spectrum, (c) IFFT of power spectrum in the measurable area (d) envelope detection on IFFT of power spectrum, (e) the experimental interferogram and (f) its detail for the three different light sources. The FWHM of the main peak in the three power spectra (Fig. 3.4~3.6 (a)) are 0.022 nm, 0.012 nm and 0.050 nm, corresponding to theoretical coherence length (Fig. 3.4~3.6 (d)) as long as 64.30 mm, 124.69 mm and 26.82 mm, respectively. As expected, the narrower a spectrum of some light source is, the longer its coherence length will be.
Obviously, due to the limitation of our optical spectrum analyzer (OSA), the power spectrum of LD#2 (Fig. 3.5 (a)) may not accurate enough and should be narrower in reality. In other words, its coherence length should be longer than the value above. Besides, the periodic behavior of the carrier wave in the interferogram will be the other evidence to confirm if what we measured is reasonable. The oscillation period of an interferogram directly depends on the central wavelength of a light source.
It also can be observed from Fig. 3.4~3.6 (f). Though these coherence lengths longer than 25mm can not be defined experimentally with our interferometer, the accuracy of the measurement can be confirmed by the similarity between theory (Fig. 3.4~3.6 (c)) and our experiment (Fig.
3.4~3.6 (e)).
The interferograms we measured here are all obtained when these lasers are under continuous-wave (cw) mode operation. For most broadband lasers, including our CMQD LDs, relatively high current injection is necessary. However, severe thermal effect induced by highly
35
cw pumping will cause great damage to our devices which are unpackaged and without facet coating. Some differences between interferograms measured at cw and pulsed mode will be discussed later.
Fig. 3.4 (a)The power spectrum in linear scale, (b)IFFT of power spectrum, (c) IFFT of power spectrum in the measurable area (d)envelope detection on IFFT of power
(a) (b)
(c) (d)
(e) (f)
022nm .
=0 Δλ
Fig. 3.5 (a)The power spectrum in linear scale, (b)IFFT of power spectrum, (c) IFFT of power spectrum in the measurable area (d)envelope detection on IFFT of power spectrum, (e)the experimental interferogram and (f)its detail for LD#2.
(a) (b)
(c) (d)
(e) (f)
Fig. 3.6 (a)The power spectrum in linear scale, (b)IFFT of power spectrum, (c) IFFT of power spectrum in the measurable area (d)envelope detection on IFFT of power spectrum, (e)the experimental interferogram and (f)its detail for LD#3.
(a) (b)
(c) (d)
(e) (f)
3.2 Characteristics of Laser Diode
3.2.1 Light - Current - Voltage (L-I-V) Characteristic
L-I-V characteristic is the most fundamental characteristic of a LD.
The threshold current (I ), slope efficiency (th η), turn-on voltage (V ) and 0 series resistance (R ) of a LD can be immediately determined from a s measured L-I-V curve. More parameters, such as internal loss (αi), model gain ( G ),...etc, can be obtained by analyzing these basic parameters from devices of different cavity length. Fig. 3.7 shows the schematic diagram for the measurement of L-I-V characteristics.
In our L-I-V measurement, laser device is put on a copper stage which is equiped with a TE-cooler to stabilize the temperature of our device. Keithley 2520 pulsed laser diode test system is used for current injection and photocurrent detection. The light output is detected by a Ge detector and eventually will be calibrated mathematically by a well calibrated power meter. In the meanwhile, electrical information will be feedbacked to Keithley when current injection begins. With GPIB-interfaced connection, the whole measurement can be controlled by the computer.
Fig. 3.7 The schematic diagram for the measurement of L-I-V characteristic.
Computer LDT-5910
Temperature Controller
TE-Cooler KEITHLEY 2520
CW / Pulsed Laser Diode Test System
Probe Station Laser Device GPIB
Detector I
3.2.2 Lasing Spectrum
The same probe system and temperature controller are used. Laser emission is coupled into a single-mode (SM) fiber and then transfered to ANDO AQ-6315E, the optical spectrum analyzer (OSA) with a minimum resolution of 0.05nm. To overcome insufficient coupling efficiency, a lens module composed of an aspheric lens and a well-coated collimator is used. All spectums we measured from our CMQD laser are with resolution of 0.1 nm. Fig. 3.8 illustrate the setup for the measurement of lasing spectrum. With GPIB interface between OSA and computer, measurements can be achieved by program.
3.2.3 Far-Field Pattern
Nowadays, Semiconductor lasers play an more and more important role in the field of fiber-optic communication. To improve the coupling efficiency into the single-mode fiber of some light source, a circle shape and narrow beam divergence of the far-field pattern (FFP) is demanded.
Fig. 3.9 shows the experimental setup used to perform the FFP measurement. The same probe system and temperature controller are used.
Fig. 3.8 The setup for the measurement of lasing spectrum.
LDT-5910 Temperature
Controller
TE-Cooler KEITHLEY 2520
CW / Pulsed Laser Diode Test System
Probe Station
Laser Device
GPIB
I
OSA
Computer Lens Module
SM Fiber
The emitting ligth is focused on the Hamamatsu IR CCD camera (C5840) through the Hamamatsu FFP lens module (A3267-12). Combined with a frame grabber card built in the computer, the signal received by camera can be visulized and analyzed by computer. To prevent the gain saturation of CCD, some attenuators will be used in the high-power measurement case. After appropriate calibration for corresponding wavelength of the light source, the cross-sectional (vertical and lateral) beam divergence angle can be determined conveniently.
Fig. 3.9 The setup for the measurement of FFP.
LDT-5910 Temperature
Controller
TE-Cooler KEITHLEY 2520
CW / Pulsed Laser Diode Test System
Probe Station
Laser Device I
Computer
Lens Module
Camera Adaptor
Chapter 4
Chirped-Multilayer Quantum Dot Lasers
4.1 Introduction
Due to the inhomogeneity in shapes, sizes and composition, self-assembled QDs is subjected to lower saturated optical gain. Stacking multiple QD layers of the same growth condition (uniform-stacked) has been proposed to increase the optical gain for well-performed QD laser in the 1.3 μm region [44]. In other hand, the intrinsic characteristic of broad gain spectrum in QDs, if properly engineered, are promising for low coherence application such as OCT.
Operating at amplified spontaneous emission (ASE) and suppressing stimulated emission, SLD has been one of the candidates for low-coherence application. However, its lower output power may limit the performance on real-time imaging of OCT. Furthermore, the tilted ridge waveguide (RW) configuration for low mirror reflectivity complicates the fiber coupling and increase the package cost. Recently, it was announced that QD lasers, in normal RW configuration, can be managed to lase with a wide emission spectrum [38~40].
In this work, we propose the control of the emission wavelength in the chirped structure by changing the matrix surrounding of the QDs.
Specifically, when the InAs QDs are covered by an InGaAs strain-reducing layer (SRL), a red-shift of the emission wavelength is observed, depending on the composition and thickness of the SRL [20].
The areal density is not significantly affected by the capping, so that the available gain and the wavelength are effectively decoupled. In contrast to other approaches, this technique is reproducible and easy to implement,
since it relies on well-controlled growth parameters.
We have demonstrated 10-layer QD laser with three chirped-wavelength QD-stacks, which we called chirped-multilayer quantum dot laser diode, CMQD LD, once and for all. Some basic parameters of the CMQD LD will be measured and discussed. Empirical gain-current analysis is also performed. The measurement of interferograms will be demonstrated by our delay-tunable Mach-Zehnder interferometer to exhibit how broad a spectrum is in a more different way.
4.2 Device Growth and Fabrication
The CMQD laser structure was based on a typical p-i-n configuration grown on a silicon-doped, (100)-oriented n+-GaAs by the molecular beam epitaxy. Multilayer QD active region with undoped graded-index separate-confinement heterostructure (GRINSCH) of 0.5μm was sandwiched between Si-doped and C-doped Al0.35Ga0.65As cladding layer of 1.5 μm, and followed by heavily C-doped GaAs contact layer of 0.4 μm. The emission wavelength of InAs QDs are tuning by the subsequent In0.15Ga0.85As capping layer of different thickness. Multilayer QDs are spaced by GaAs and centered in the active region also by GaAs. The spacing thickness of 33 nm is chosen so that strain is not accumulated in the multilayer deposition. The wafer growth is credited to the Innolume GmbH in Germany.
To chirp the emission wavelengths of QD active region, three wavelengths designated as QDL, QDM and QDS (stand for longer-, medium- and shorter-wavelength QD stacks, respectively) were engineered in the laser structure, which corresponding to the InAs QDs of 2.6 ML capped by InGaAs of 4 nm, 3 nm and 2.5 nm, respectively. The
stacking numbers for QDL, QDM and QDS were 3, 4 and 3 layers, respectively. The stacking sequence of different capping thickness was interlaced. Fig. 4.1 shows the schematic diagram of chirped-multilayer QD structure.
Ridge waveguide of 3μm width was formed by high-density-plasma dry etching. The etching depth was in situ monitored to stop just above GRINSCH waveguide. Thin oxide was then deposited by plasma-enhanced chemical-vapor deposition. The contact window opening over the narrow ridge was done by double-channel self-aligned process. After p-metallization by Ti/Pt/Au deposition, the substrate was thin down to around 100 μm, and n-type metal of AuGe/Ni/Au was deposited afterwards. As-cleaved and uncoated laser bars with cavity lengths from 0.5 mm to 5 mm were fabricated then evaluated by standard light-current-voltage (L-I-V) and spectrum measurement. Both pulsed and continuous-wave driving conditions are performed under varied heatsink temperature.
Fig. 4.1 The schematic diagram of the chirped multilayer QD structure.
GaAs GaAs
N-AlGaAs cladding P-AlGaAs cladding QDM
QDL
QDM QDS
QDL QDM
QDS
QDL
QDM QDS
N-type : Si 1.5µm
Al0.35Ga0.65As
GaAs
0.5μm P-type : C
1.5µm
InAs QDs InGaAs QW
4.3 Results and Discussion
The areal density of InAs QDs without InGaAs capping was grown separately and characterized by AFM to be around 5*1010 cm-2. Fig. 4.2 shows the AFM image of epitaxial surface immediately following the QD deposition. According to the room-temperature (RT) photoluminescence (PL), the dependence of QD emission wavelength on the thickness of capping InGaAs layer can be determined. Fig. 4.3 illustrates the dependence of GS and ES peaks at RT PL on the thickness of In0.15Ga0.85As capping layer. The peak wavelength of GS for QDL, QDM and QDS in our case is about 1262 nm, 1230 nm and 1215 nm, respectively. The peak wavelength of first ES for QDL, QDM and QDS is
The areal density of InAs QDs without InGaAs capping was grown separately and characterized by AFM to be around 5*1010 cm-2. Fig. 4.2 shows the AFM image of epitaxial surface immediately following the QD deposition. According to the room-temperature (RT) photoluminescence (PL), the dependence of QD emission wavelength on the thickness of capping InGaAs layer can be determined. Fig. 4.3 illustrates the dependence of GS and ES peaks at RT PL on the thickness of In0.15Ga0.85As capping layer. The peak wavelength of GS for QDL, QDM and QDS in our case is about 1262 nm, 1230 nm and 1215 nm, respectively. The peak wavelength of first ES for QDL, QDM and QDS is