CHAPTER 1 INTRODUCTION
1.4 Organization of Thesis
The organization of this thesis is as follows. In Chapter 2, the physics of quantum dot lasers and optical waveguide theory will be introduced separately. We also present the theoretical comparison between non-metallic waveguides and metallic-coated waveguides to understand their fundamental differences. Theoretical results indicates group index of metallic waveguides behaves very differently from that of conventional dielectric waveguides. In Chapter 3, we present the fabrication and the structure of the quantum dot plasmonic laser. At the end of this chapter, we show the evidence for lasing action of this plasmonic device. In Chapter 4, we present theoretical and experimental studies on the net modal gain, refractive index change, linewidth enhancement factor, and group index of the quantum dot plasmonic Fabry-Perot laser.
Our investigations includes both CW and pulsed current operations to distinguish the optical characteristics from thermal effects. In Chapter 5, we will summarize major achievements of this thesis and discuss further possible research.
CHAPTER 2
PHYSICS OF QD FABRY-PEROT PLASMONIC LASER
2.1 QD Lasers
Effects of size quantization occurs when the size of confinement structures is comparable with de Broglie wavelength of carriers. In bulk semiconductor structures, carriers are free to move in all directions so that quantized effects do not occur. To restrict movement of one dimension of carriers, quantum well (QW) structure is proposed to confine carriers in planes perpendicular to the growth direction during layer-by-layer or Frank-Van der Merwe type of growth. By the end of 1980s, the technique of growing quantum wells and superlattices were well developed; hence, scientists in semiconductor area turned to investigate structures with less dimensionality - quantum wires and quantum dots (QDs). Quantum-wire material has a additional restriction along another dimensional to quantum quantum-well structure, and yields a 1-D semiconductor active layer. In addition to quantum-wire structure, QD structures can provide three-dimensional confinement for carriers and localize carriers in the QDs, which breaks down the classical model of a continuous dispersion of energy as a function of momentum. The comparison of the bulk (3-D), quantum well (2-D), quantum wire (1-D), and quantum dots (0-D) with associated density of states (DOS) are shown in Fig. 2.1. The resulting density of states of
Fig 2.1 Physical structure and density of states for a bulk semiconductor, QW, Q-Wire, and QD structures. [15]
quantum dots are delta-function like and discrete, like in atomic physics. Therefore, the physical properties of quantum dot structures respected resemble an atom in a cage. Fig. 2.2 shows the size comparison between bulk, quantum dots and atoms.
The most attracting property of QDs is its completely discrete transition energy level because of the delta-function-like density of states. Therefore, if we use QDs as gain medium to fabricate lasers, carriers can be efficiently utilized because of the delta-function-like density of states. Thus, the threshold gain is easy to reach by effectively using usage of injecting carriers.
Wavelength of light
Macroscopic De Broglie
Wavelength at 300K
Waveguide Volume
Semiconductor
Quantum Dot Atom
1cm 1 m 10 nm 1
AoFig 2.2 Schematic comparison of typical dimensions of bulk material, waveguide for visible light, quantum dots, and atoms.
Hence, QD lasers feature ultra low threshold density and ultrahigh temperature threshold stability, which are two of the main advantages over conventional QW lasers or bulk lasers [16,17]. The lasing spectra stability with temperature and ultra high differential gain are also guaranteed by the sharp gain spectrum of QDs.
The first concept of QD semiconductor laser was proposed by Dingle and Henry in 1976 [18]
and later by Arakawa and Sakaki in 1982 [17]. Experimentally, the growth of QDs had been realized by the self-organized Stranski-Krastanov (S-K) growth method, as shown in Fig 2.3. The S-K method can be carried out by using either metal-organic chemical vapor deposition (MOCVD) or molecular beam-epitaxy (MBE) growth method. However, size and shape of QDs fabricated by the S-K method fluctuate randomly, resulting in the inhomogeneous broadening in
Fig 2.3 Stranski-Krastanov (SK: layer-plus-island) mode of thin film growth. [19]
gain spectrum. This real situation would induce temperature dependence of threshold properties and broaden linewidth of laser devices.
2.2 Optical Waveguide Theory
In order to understand fundamental differences between dielectric and metallic waveguides, this section presents 1-D model for both dielectric and metallic waveguides. Numerical examples are also given to compare their difference on group index.
Dielectric Slab Waveguide [20]
Consider a slab waveguide as shown in Fig. 2.4. From the wave equation [20],
(2.1)
(2) E 0
Fig 2.4 A simple slab waveguide structure for waveguide analysis.
the electric field can be solved. We assume the structure is symmetric waveguide and the waveguide width w is far larger than the thickness d; hence the field dependence on y direction is negligible. The permittivity and permeability of the cladding layers are and , respectively.
The permittivity and permeability of the waveguide are 1 and 1, respectively. We assume
1 1
Since both TE and TM polarized light exist in the waveguide, we first consider only TE-polarized light modes of the waveguide. After the TE modes are obtained, TM modes can be easily obtained by using the duality principle [18].
/ 2
For TE polarization, the electric field of the even modes can be written
(2.2) By substituting Eq. (2.2) into Eq. (2.1), we obtain
(2.3) After manipulation for Eq. (2.3), we get
(2.4) Where eik zz stands for the guided waves propagate in the z direction, is the decay constant in the cladding layer, and cosk x is chosen to be the standing wave solution. From the x boundary condition, we can get
(2.5) By manipulating Eq. (2.5), we have
(2.6) From Eq. (2.4) and Eq. (2.6), one can solve k and z . As the decay constant and propagation constant kz are solved, the normalize parameters C , 0 C , 1 C , can be obtained. 2 Than, the electric and magnetic wave of the TE even modes in this structure are well analyzed.
Ey eikzz
(2.7) From the boundary condition, we have
By manipulating Eq. (2.8a) and Eq. (2.8b), we obtain
(2.9) Using the same procedures, electromagnetic waves in this structure can be obtained.
For TM polarization, we can apply the duality principle into the above equations: replacing the field solution E and H by H and -E, respectively, and the permittivity and permeability change the symbol to each other.
The effective index and group index for the guided mode are expressed as
(2.10)
Surface Plasmon Waveguide [18]
The surface Plasmon waveguide theory follows Professor Chuang’s book, second edition [18].
The permittivity of the metal can be expressed as
(2.12) where p is the plasma frequency and 0 is the vacuum permittivity. In the range of optical frequency, the permittivity of the metal becomes negative since optical frequency is far smaller than plasma frequency and leads to a significant field attenuation when electromagnetic waves propagate in metal.
Consider a thin metallic slab waveguide as shown in Fig. 2.5. We assume the structure is a symmetric waveguide and the waveguide width w is far larger than the thickness d; hence the field dependence on y direction is negligible. The permittivity of the dielectric medium and metal are 1 are p, respectively.
For TM polarization, the magnetic field for the even mode can be written as
(2.13) Substituting Eq. (2.13) into Eq. (2.1) gives
(2.14)
Fig 2.5 A metallic slab waveguide structure for waveguide analysis.
where 1 and 2 are decay constant in the dielectric and metal, respectively. From the boundary conditions, we obtain
(2.15) Thus, manipulating Eq. (2.15) gives
(2.16)
From Eq. (2.14) and Eq. (2.16), one can solve the decay constant 1 and 2. Then, the other parameters k , z C , 0 C can also be obtained. 1
For TM polarization, the magnetic field for the odd modes can be written as C0 C1cosh (2 d
(2.17) From the boundary conditions, we have
(2.18) By manipulating Eq. (2.18), we have
(2.19)
Using the same procedure, electric and magnetic fields in this structure can be obtained.
2.3 Plasmonic Effects
Group index is a good property to investigate plasmonic effects. To see clear difference of group index between dielectric and metallic waveguides, we consider a slab
0.35 0.65 / / 0.35 0.65
Al Ga As GaAs Al Ga As waveguide and a slab Au/GaAs/Au metallic waveguide
with identical waveguide width w.
In Fig 2.6, we plot the effective refractive index neff( ) of the TM even mode versus wavelength of a slab Al0.35Ga0.65As GaAs Al/ / 0.35Ga0.65As waveguide. The waveguide width w is set as 50 nm. The material dispersion is considered in the simulation.
Hy eikzz
900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500
Fig 2.6 Simulation results of the effective refractive index neff( ) versus wavelength of a slab
0.3 0.7 / / 0.3 0.7
Al Ga As GaAs Al Ga As waveguide.
Fig 2.7 shows the numerical results of the group index ng( ) versus wavelength of a slab
0.35 0.65 / / 0.35 0.65
Al Ga As GaAs Al Ga As waveguide obtained from Eq. (2.11). It is clear to see the
value of group index falls between the refractive index of GaAs and the refractive index of
0.35 0.65
Al Ga As . In Fig 2.8, we plot the TM even mode of effective refractive index neff( ) versus wavelength of a plasmonic Au GaAs Au/ / waveguide. The structure of the width w is set as the same number, 50nm, and the permittivity of gold is -14.8.
n
GaAs0.35 0.65
Al Ga As
n
n
eff950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500
Fig 2.8 Simulation results of the effective refractive index neff( ) versus wavelength of a
1000 1100 1200 1300 1400 1500
2
Fig 2.9 Simulation results of the group index ng( ) versus wavelength of a Au GaAs Au / / plasmonic waveguide.
Fig 2.9 shows the group index ng( ) versus wavelength of the slab plasmonic waveguide, which can be obtained from Eq. (2.11). It is clear to see the group indices are larger than that of
GaAs . This means that plasmonic effects modify the dispersion relation of the guided modes resulting in an extremely high group index.
2.4 Conclusion
950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 0
We has described the fundamental properties of 3-D (bulk), 2-D (quantum well), 1-D (quantum wire), and 0-D (quantum dot) materials. The main advantages of the QD lasers over QW lasers and bulk lasers are ultra low threshold density, temperature insensitivity, discrete energy levels, and delta-like shape density of states. Furthermore, the optical waveguide theory for dielectric waveguide and metal-semiconductor-metal waveguide is derived to understand the fundamental difference between the two types of waveguide. The given numerical examples for comparison between dielectric and metallic waveguide indicates that the group index will be increased when plasmonic effects affect the guided modes.
CHAPTER 3
QD PLASMONIC LASER GROWTH, STUCTURE, AND LASING ACTION
In this chapter, we present the design structure and fabrication of a QD with sidewall-coated metallic waveguide. The luminescence is also included in the content. Despite metals are lossy media, we observed clear lasing action and a low threshold density current.
3.1 Structure and Growth
Fig. 3.1 shows the cross section of the fabricated QD plasmonic laser by Chien-Yao Lu in Professor Chuang’s group at the University of Illinois. A series of Fabry-Perot lasers were fabricated with the sample containing InAs/GaAs quantum dots as the active medium. Ten stacks of QD layer are sandwiched between 1.5m thick Al0.35Ga0.65As cladding layers and covered with a 5-nm-thick In0.15Ga0.85As quantum-well cap layer [21]. A 500 nm SiN layer was x deposited by plasma-enhanced chemical vapor deposition and was then patterned by photolithography to define the dry etching mask for the ridge waveguides. Inductive coupled plasma reactive ion etching (ICP-RIE) technique was used to produce a 2m deeply-etching ridge waveguide with vertical sidewalls. A thin SiN passivation layer serving as the x
p -Al0.35Ga0.65As
n -Al0.35Ga0.65As InAs/GaAs QD x10
p - GaAs
2
1290 nm QD Layer structure
Fig 3.1 The cross section structure of the fabricated QD plasmonic laser. The device was fabricated by Chien-Yao Lu in Professor Chuang’s group at the University of Illinois.
Fig 3.2 SEM image of the waveguide. (Photos taken by C. Y. Lu at UIUC).
electrical isolator was then deposited on the sidewall followed by a conformal metallic coating (100 nm Au / 5 nm Ti). Fig 3.2 shows the scanning electron microscope (SEM) image of the waveguide cross section view. The whole sample was lapped down to about 100 m
Au SiNx
Poly Poly
p
n
contact
contact
Active medium
(a) (b) 2 m waveguide
the easy cleaving of device facets before the deposition of the n-type contacts on the backside of the sample. The sample was then cleaved to several devices with various waveguide lengths.
3.2 Lasing Action
The laser device was mounted on the copper heat sink by indium and conductive epoxy for the measurements. The device was operated at 293 K under DC current operation with a fiber tip to collect the emitted light from the device. The device temperature was kept constant by thermo-electric cooler (TEC) with feedback control signal from the thermal couple sensor. Fig. 3.3 shows our experimental setup for measuring the steady-state light emission of the QD plasmonic laser.
The current source (ILX LDC-3900) and TEC controlled via Labview program are used to drive and sustains the temperature of the plasmonic QD laser. The optical power meter is used to collect light emission for intensity analysis and also can be controlled by Labview program. Fig.
3.4 shows the control front panel of the Labview program. We use both lens-fiber and fiber tip to collect light from the device. The fiber tip has a better ability to extract light from the facet of the plasmonic laser than the lens-fiber. However, lens fiber has the advantage of reducing feedback and eliminate the external cavity effects. Fig. 3.5 (a) shows the plot of emission intensity versus different injection current (L-I curve) and Fig. 3.5 (b) shows the voltage versus different injection current (I-V curve) of the 1150-m-long laser device, respectively. A clear onset of LI curve is evident for lasing action.
Fig. 3.6 shows our experimental setup for measuring the amplified spontaneous emission of the QD plasmonic laser in steady state. The same current source is used to drive the plasmonic
Fig 3.3 The diagram of the experimental setup used in obtaining the steady-state light emission of the QD plasmonic laser.
QD laser controlled via global parallel interface bus (GPIB) computer surface and it can be precisely operated to A level. The TEC also sustains the temperature of the QD plasmonic laser which is mounted on the copper heat-sink stage and set in the current controlled device steering by the GPIB interface. Fig. 3.7 shows the vi. of Labview program that we use for the
Labview Computer
ILX-3900
Current / Temperature control
HP 8153A Power Meter
QD Plasmonic Laser
Lens Fiber
0 5 10 15 20 25 30 35 40 45 Fig 3.4 Schematic of LIV measurement by using Labview control front panel
Fig 3.5 (a) Emission intensity versus different injection current (L-I curve) of the QD plasmonic laser. (b) Voltage versus different injection current (I-V curve) of the QD plasmonic laser.
experiment. The Optical Spectrum Analyzer (OSA) is used to collect light emission for spectrum analysis and can be controlled by Labview program. The resolution of OSA (ADVANTEST Q8347) can be down to 5.7 pm and sensitivity has the limitation to -95dBm. The fiber shown in Fig. 3.8 is manufactured by balled lens fiber type using fusion splicing technique. This designed setup reduces feedback and eliminates the external cavity effects of conventional methods.
Moreover, it improves the coupling efficiency of collecting light from the device under test.
Fig 3.6 The diagram of the experimental setup used for obtaining the ASE spectrum from the QD plasmonic laser.
Labview Computer
ILX-3900
Current / Temperature control
ADVANTEST Q8347 Optical Spectrum Analyzer
QD Plasmonic Laser
Lens Fiber
Fig 3.7 Schematic of ASE spectrum measurement by using Labview control front panel
Fig 3.8 The amplified spontaneous emission is collected by lens fiber from the facet of our plasmonic QD Fabry-Perot laser
Plasmonic QD FP Laser Injecting carrier (by probe)
Lens Fiber
1220 1240 1260 1280 1300 1320 1340 1360 I=20mA, 20oC
Intensity (a.u.)
Wavelength (nm)
1220 1240 1260 1280 1300 1320 1340 1360 I=18mA, 20oC
Intensity (a.u.)
Wavelength (nm)
1220 1240 1260 1280 1300 1320 1340 1360 I=16mA, 20oC
Intensity (a.u.)
Wavelength (nm)
1220 1240 1260 1280 1300 1320 1340 1360
Intensity (a.u.)
Wavelength (nm) I=14mA, 20oC
The amplified spontaneous emission is collected from the facet of our plasmonic QD Fabry-Perot laser, lens fiber, and finally showed on the OSA screen. The laser device is p-side up. We use Scanning Electron Microscope (SEM) to precisely measure the device length, which is 1150
m. By the means of Labview program, setup control and data analysis on the computer is also available.
Fig 3.9 Amplified spontaneous emission under different injection currents (below threshold) from the QD plasmonic laser.
1220 1240 1260 1280 1300 1320 1340 1360 I=24mA, 20oC
Intensity (a.u.)
Wavelength (nm)
Fig. 3.19 shows the optical spectrum emission under different injected currents below threshold. For the spectrum below threshold, clear amplified spontaneous emission is observed and the clear interference pattern in the spectrum is owing to the Fabry-Perot resonance. As the injected current is larger than the threshold current, stimulated emission takes place and leads to lasing action. The clear resonance peak at 1287nm is depicted in Fig. 3.9. The main lasing wavelength is about 1287 nm, as shown in Fig 3.10. A clear onset of significant stimulated emission is observed. As is shown in Fig. 3.9, the threshold current of the device is about 22.5mA.
Corresponding to a threshold current density is 0.978 kA cm [12], which is comparable to or / 2 even lower than typical quantum well semiconductor lasers.
Fig 3.10 Spectrum of QD plasmonic laser biased at 24mA (above threshold).
CHAPTER4
DC CHARACTERISTICS OF FABRY-PEROT PLASMONIC LASER
4.1 Introduction
In this chapter, we describe the theoretical and experimental techniques for analyzing the optical gain, refractive index change, linewidth enhancement factor, and group index extracted from amplified spontaneous emission spectra of the plasmonic QD Fabry-Perot laser. First of all, we use the Hakki-Paoli method to extract the net modal gain. By changing the injection current, we obtain the change in the refractive index via wavelength shifts of Fabry-Perot peaks and the linewidth enhancement factor. We did the measurements under CW and pulsed mode operations to distinguish the amount of thermal effects. In the last part of this chapter, we show temperature-dependent threshold current of this device.
4.2 Theoretical Analysis of Modal gain, Refractive Index
Change, Group Index, and Linewidth Enhancement Factor
4.2.1 Modal Gain
The Hakki-Paoli (HP) method is one of the most common method to extract net modal gain from amplified spontaneous emission (ASE) spectra. To derive the net modal gain, we first consider a semiconductor laser in a Fabry-Perot cavity, as shown in Fig. 4.1.
When a wave bounces back and forth in a Fabry-Perot cavity, its amplitude after one round trip of distance 2L has to remain at least the same to obtain gain.
(4.1) where is the optical confinement factor. It determines the longitudinal mode spectrum of the Fabry-Perot laser. To obtain lasing action, the modal gain has to overcome the intrinsic loss i
and the mirror loss
1 2
1 1
2 ln
m L R R
. Therefore, the threshold condition of the Fabry-Perot laser
is
Fig 4.1 A simple modal of a Fabry-Perot cavity, which g is the optical gain in active region.
On the other hand, the imaginary part of Eq. (4.1) gives
(4.4) When the phase-matching condition is satisfied, peaks of resonant Fabry-Perot modes are present in the ASE spectrum. Similarly, valleys of Fabry-Perot modes can be obtained from the antiresonance condition. Then, we can have the expression of amplified spontaneous emission for a Fabry-Perot laser [22]
(4.5) where r1 R1 , r2 R2 are the electric field reflection coefficients of each facet. Since
2 0
1r r e1 2 GLei k n Le in the denominator is the only fast-varying term, it dominates the behavior of amplified spontaneous emission. As a result, we can approximate the slowly varying term in Eq.
(4.2) with a constant K 2neL m
IASE() (1 r1r2)[W ()L
GL ](eGL 1)(1 r1r2eGL)
| 1 r1r2eGLei 2 k0neL|2
g
L
R
1R
2(4.6) respectively. After some manipulation, the net modal gain G can be extracted from the adjacent peak and valley of the amplified spontaneous emission spectrum by
(4.8) According to Eq. (4.8), several important parameters are obtainable. First, when the wavelength is far larger from the gain region, modal gain is approximately zero, so that net g modal gain would equal to material loss i, that is, G g i . At or above threshold, G i
will approach the mirror loss m, that is, G g i m, since max
min
I
I approaches to infinity. By measuring the amplified spontaneous emission spectrum, both net modal gain and material loss can be obtained.
4.2.2 Change of Refractive Index
The change in the refractive index, group index, and effective index can be extracted from the amplified spontaneous emission spectra. By considering adjacent longitudinal mode, FP mode spacing FP at single current bias is [20],
(4.9) From the waveguide theory, the group velocity v can be expressed as g
(4.10) Since both n and e are function of . The group index n can be expressed as g
(4.11) From Eq. (4.9) and Eq. (4.11), we can get a compact expression for group index
(4.12) According to Eq. (4.1), we define 1 and 2 as two adjacent peak wavelength in ASE
(4.12) According to Eq. (4.1), we define 1 and 2 as two adjacent peak wavelength in ASE