Ultra-fast Spectroscopy of Terahertz Quantum Cascade Lasers
Dissertation zur Erlangung des Grades eines ”Doktors der Naturwissenschaften” (Dr. rer. nat.)
in der Fakult¨atf¨urPhysik und Astronomie der Ruhr-Universit¨atBochum
vorgelegt von Sergej Markmann geboren in Uman
Lehrstuhl f¨urAngewandte Festk¨orperphysik AG Terahertz-Spektroskopie und Terahertz Technologie Bochum, Sommersemester 2016 1. Gutachter: Dr. Nathan Jukam 2. Gutachter: Prof. Dr. Andreas D. Wieck Disputation am: 24.10.2016 “Your theory is crazy, but it’s not crazy enough to be true.”
Niels Bohr
“Science is a wonderful thing if one does not have to earn one’s living at it.”
Albert Einstein
“Fall in love with some activity, and do it! Nobody ever figures out what life is all about, and it doesn’t matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough. Work as hard and as much as you want to on the things you like to do the best. Don’t think about what you want to be, but what you want to do. Keep up some kind of a minimum with other things so that society doesn’t stop you from doing anything at all.”
Richard Feynman To my parents and my brother Contents
Contentsi
Summary ii
Zusammenfassungv
Abbreviations and Symbols viii
1 General introduction1 1.1 Outline of the Thesis...... 3 Bibliography...... 4
2 Spectral emission control of THz QCL with narrow-band THz pulses7 Bibliography...... 22
3 Spectral emission control via broad-band double pulse injection seeding 26 Bibliography...... 37
4 Phase Seeding-Phase Probing technique for investigation of ultra- fast time-resolved laser dynamics 42 Bibliography...... 60
5 Nonlinear spatial gain grating in THz Quantum Cascade Laser 63 Bibliography...... 74
6 Outlook 77
i Appendices 79
A Design strategy of the photoconductive antenna 80
B Electronics used for the injection seeding experiments 87
C THz Quantum Cascade Laser used for the experiments 90
Acknowledgement 94
Curriculum Vitae 96 Summary
The subject of this thesis is to develop new concepts for controlling the spectral emission of THz quantum cascade lasers (QCLs) and to study their gain dynamics in both the time and frequency domains. For this purpose a THz time-domain system is set up. The control of the spectral emission as well as the time-resolved gain dynamics is studied with the injection seeding technique. There are several approaches to control and modify the spectral emission of a THz QCL. Most of these methods are based on the modification of the laser waveguide or the active laser medium. In this work, two new methods are introduced for controlling the spectral emission that do not require any modification of the active region or waveguide. The first method is based on injection seeding of the THz QCL with narrow-band THz pulses. These narrow-band pulses are generated from periodically poled lithium niobate (PPLN) crystals. The frequency of the injected narrow-band THz pulses can be tuned by choosing the proper poling period of the PPLN crystal. In the frequency domain, the injected narrow-band THz pulse can be superimposed with the QCL gain spectrum. The longitudinal modes that have an overlap with the narrow- band THz pulse are selected by injection seeding, while those modes which do not overlap with seed pulses are suppressed. If the broadening of the pulse is smaller than the longitudinal mode spacing, selection of a single mode becomes possible. Only longitudinal modes, that are within the full width at half maximum (FWHM) of the spectral QCL gain, can be selected. The second approach for the spectral emission control involves seeding with two broad-band THz pulses. The spectrum of a single broad-band THz pulse is much larger than the QCL gain spectrum. However, the combined spectrum of two broad-band THz pulses, which are separated by a double pulse delay, has a rapid spectral modulation in the frequency domain. The
iii envelope of the spectral amplitude still has the shape as that of a single THz pulse. By adjusting the double pulse delay and hence the seed modulation in frequency domain, QCL modes can be selected or suppressed depending on the double pulse delay time. It is shown that for a given QCL, the selection of a single longitudinal mode is possible. Moreover, the QCL spectrum can be reversibly switched from multi-mode to a singe mode regime. Also, the mode selection dynamics (evolution of the QCL emission spectrum) for both techniques are studied in time and frequency domain. Besides spectral emission control, a new technique for measuring the time- resolved gain dynamics of the injection seeded THz QCL with weak THz pulses is also presented. The time-resolved gain dynamics is studied on both femto- and pico-second time scales. For this purpose the QCL is injection seeded with the broad-band THz pulses which are then amplified in the cavity. After several round trips in the cavity, the injected seed pulse saturates the QCL gain. At this time a second weak broad-band THz pulse (probe pulse) is injected into the QCL to probe the gain. By adjusting the probe delay with respect to the seed, the gain dynamics as a function of time and hence of the electric field strength is studied. By probing the QCL, a spatial gain grating is observed which has rapid oscillations on femto- second time scales. These gain oscillations are in a good agreement with a developed density matrix model that indicates the existence of the spatial gain grating. This grating is a result of the superposition of forward and backward propagating waves in the cavity. An upper limit for the gain recovery time was extracted from the time domain experiment and is in the order of 20 ps for the bound-to-continuum QCL design. To explain the observed physical effects, a model based on density matrix is developed that can explain a majority of the observed phenomena. The gain is also probe on the large time scale, to study the electric field strength dependence. These measurements demonstrated a complex gain dynamics, where each spectral gain component is modulated with multiple frequencies. This effect is assigned to the nonlinearities in the intersubband systems. Zusammenfassung
Die Ziele dieser Arbeit sind sowohl neue Konzepte der spektralen Emissionskon- trolle von Terahertz (THz) Quantenkaskadenlaser (QKL) zu entwickeln als auch die Dynamik dieser komplexen Systeme im Zeit- und Frequenzbereich zu studieren. F¨urdiesen Zweck wurde ein THz-Zeitbereichs-Spektrometer gebaut, mit dem die oben beschriebenen Aufgabestellungen bearbeitet werden k¨onnen. Es gibt zahlre- iche Methoden f¨urdie spektrale Emissionskontrolle des QKL. Die meisten Metho- den beruhen auf der Modifikation des Laserwellenleiters oder des lichtverst¨arkenden Mediums. In dieser Arbeit werden zwei Methoden zur spektralen Emissionskon- trolle vorgestellt, bei denen weder der Laserwellenleiter noch das lichtverst¨arkende Medium abge¨andertwerden soll. Beide Methoden machen sich ein kleines THz- Signal zu Nutze, das in den QKL injiziert und verst¨arktwird. Bei der ersten Methode werden THz-Pulse mit einer geringen spektralen Bandbreite in den QKL injiziert. Die spektralen schmalbandigen THz-Pulse werden von einem periodisch
gepolten Lithiumniobat (LiNbO3) Kristall (PGLN Kristall) erzeugt. Die Frequenz des erzeugen THz-Pulses wurde eingestellt, indem die Periode des PGLN Kristalls ge¨andertwurde. Ein erzeugter schmalbandiger THz-Pulse wurde mittels parabolis- cher Spiegel in den Laserwellenleiter injiziert. Im Frequenzbereich kann das Spek- trum des erzeugten THz-Pulses mit dem Spektrum des QKL ¨uberlagert werden. Es k¨onnen lediglich die Moden des QKL verst¨arktwerden, die einen spektralen Uberlapp¨ mit dem schmalbandigen THz-Puls haben, ansonsten werden die anderen Moden unterdr¨uckt. Falls die spektrale Verbreiterung des THz-Pulses kleiner ist als der Modenabstand im QKL, so lassen sich einzelne Moden ausw¨ahlen. Es wurde gezeigt, dass nur die Lasermoden selektiert und verst¨arktwerden k¨onnen,die in- nerhalb der spektralen Halbwertsbreite des laserverst¨arkenden Mediums liegen. Die
v zweite Methode der spektralen Emissionskontrolle basiert auf der Injektion von zwei bandbreiten THz Pulsen. Die spektrale Bandbreite eines einzelnen THz-Pulses ist viel gr¨oßerals der spektrale Emissionsbereich des QKLs. Das resultierende Spek- trum von zwei bandbreitigen THz-Pulsen, die durch eine Doppelpulsverz¨ogerung von einander in Zeitbereich separiert sind, weißt eine rapide spektrale Modulation auf. Die spektrale Modulation kann kontrolliert werden, indem die Doppelpulsverz¨ogerung reguliert wird. Die Einh¨ullendedes kombinierten Doppelpulsspektrums entspricht der Einh¨ullendeeines einzelnen THz-Pulses. Durch die Injektion der Doppelpulse in den QKL kommt es zur Uberlagerung¨ des Doppelpulsspektrums und des spektralen Verst¨arkungsprofilsdes QKLs. Auf diese Weise ist es m¨oglich, bestimmte Moden zu verst¨arken bzw. zu unterdr¨ucken. Es wurde gezeigt, dass sowohl einzelne spektrale Moden selektierbar sind als auch das QKL-Spektrum reversibel modifiziert werden kann. Zus¨atzlich zur spektralen Emissionskontrolle wurde ein neues spektroskopis- ches Verfahren entwickelt, mit dem zeitaufgel¨ostePh¨anomenemit schwachen THz- Pulsen studiert werden k¨onnen.Mittels dieses neuen spektroskopischen Verfahrens wurde die Verst¨arkungsdynamikdes QKLs auf dem Femto- und Pikosekunden- Bereich studiert. Es wurden zwei schwache THz-Pulse in den QKL injiziert, deren zeitliche Verz¨ogerungzwischen den THz-Pulsen eingestellt wurden. Der erste THz- Puls wurde in die Facette des QKLs injiziert und verst¨arkt.Nach mehrfachen Re- flektionen und der Verst¨arkungim Laserresonator hatte der THz-Puls die maximale Feldst¨arke erreicht und s¨attigte damit das System. W¨ahrendder S¨attigung des Sys- tems wurde der zweite schwache Puls in den QKL injiziert und in der Transmission (Austritt aus der QKL Facette) detektiert. Durch die Anderung¨ der Zeitverz¨ogerung zwischen den beiden THz-Pulsen wurde die Verst¨arkungsdynamik des QKL als Funktion der Zeit bzw. als Funktion der elektrischen Feldst¨arke studiert. Bei der Untersuchung des QKLs wurde ein r¨aumliches oszillierendes Verst¨arkungsprofil gemessen, das sich rapide im Femtosekunden-Bereich ¨andert. Die Messungen stim- men mit dem entwickelten Modell, das die schnelle r¨aumliche Anderung¨ des Verst¨ar- kungsprofils vorhersagt, ¨uberein. Der physikalische Ursprung der Verst¨arkungsos- zillationen ist die Uberlagerung¨ der vorw¨artsund r¨uckw¨artsausbreitenden Wellen im Laserresonator. Ebenso konnte die Obergrenze der Wiederherstellungszeit der max- imalen Verst¨arkungzu 20 ps aus den Messdaten ermittelt werden. Es wurde dar¨uber hinaus eine spektrale/r¨aumliche S¨attigungdes verst¨arkenden Mediums nachgewiesen und auch eine zeitabh¨angigespektrale Verschiebung des verst¨arkenden Mediums beobachtet. Das auf dem Formalismus der Dichtematrix basierende theoretische Modell, erlaubt eine quantitative Beschreibung zahlreicher beobachteter Ph¨anomene. Abschließend wurde ein intensit¨atsabh¨angiges Modulationsverhalten des verst¨arkenden Mediums erkannt. Jede verst¨arkende spektrale Komponente des QKL wurde mit vielfacher Laserhauptfrequenz moduliert. Dieser Effekt wird den nichtlinearen In- tersubband¨uberg¨angenzugeordnet. Abbreviations and Symbols
Abbreviations
E-Field Electric field
FDTD Finite-difference time-domain method
FT Fourier transform
FTIR Fourier transform infrared spectroscopy
FWHM Full Width at Half Maximum
GVD Group velocity dispersion
LT-GaAs Low temperature grown GaAs
NIR Near-infrared
PGLN Periodisch gepolten Lithiumniobat
PPLN Periodically poled lithium niobate
PSPP Phase Seeding-Phase Probing
QCL Quantum cascade laser
QKL Quantenkaskadenlaser
RF Radio frequency
STFT Short time Fourier transform
TDS Time-Domain-Spectroscopy
viii THz Terahertz
Symbols
χ2 Nonlinear coefficient of second order
∆ν Line width
(ω) Dielectric constant
Γ Dephasing matrix
γ Decay constant
hω¯ UL Laser transition energy h¯ Reduced Planck constant
Λ Poling period
µ0 Vacuum permeability
Ω Emission frequency of PPLN crystal
ω Angular frequency
ρ Density matrix
τl Life times of lower laser
τU Life times of the upper
τIR Duration of NIR pulse c Speed of light
E Electric field g Absorption coefficient
H Hamiltonian
L Length of the PPLN crystal lb Temporal walk-off length in backward direction lw Temporal walk-off length in forward direction
MUL Dipole matrix element
N Number of electrons per unit volume
nGaAs Refractive index of the active medium nIR Refrective index for NIR pulse nT Hz Refrective index for THz pulse
P Polarisation
nl P2 Second order term of the polarisation series
R Pumping rate
T2 Dephasing time
TT Hz,b Period of one THz cycle in backward direction
TT Hz,w Period of one THz cycle in forward direction
Chapter 1
General introduction
One of the fastest growing research areas in the last 20 years is the field of THz science and technology. The aim of THz technology is to cover the gap in the electromagnetic spectrum from 0.1 THz to 10 THz that is caused by the lack of THz sources and detectors. It is difficult for existing electronics to provide efficient sources with electromagnetic radiation above 0.3 THz. This is mainly due to the poor conductivity of metals and semiconductors at higher frequencies. This is a limiting factor for terahertz generation using electronic techniques. The other side of the terahertz spectral gap is due to the lack of optical sources, that cannot ef- ficiently generate THz radiation below 10 THz. Semiconductor lasers are sources of optical an near-infrared radiation that are compact, inexpensive, efficient and reliable. The working principle of these lasers is based on the recombination of electrons and holes in p-n junction. The emission energy of the photon is mainly de- termined by the band-gap of the material in which the recombination proceeds. By taking this physical concept an scaling it to the THz region this would require direct semiconductor materials with band gaps of 1 meV to 40 meV which do not exist. In order to overcome these issues, Kazarinov and Suris proposed lasers based on intersubband transitions in the conduction band during the 70s [1]. Intersubbands can be designed by growing a heterostructure (materials or material composition with unequal energy band gaps), for example a multi quantum well structure with a fixed periodicity which is repeated for several times. By proper design of a period (cascade), energy states are formed and are coupled with each other. In this way an
1 CHAPTER 1. GENERAL INTRODUCTION
electron can be transported through the cascade. The transport from one cascade to the next is caused by energy reduction via photon emission or electron-electron scattering. Lasers based on this concept are called quantum cascade lasers (QCLs). The first laser, based on this principle was demonstrated in 1994 in Bell Laboratories by J´erˆomeFaist et. al. [2]. The laser operated up to 90 K with the emission wave- length of 4.2 µm. Further improvement of mid-infrared QCL structures resulted in continuous wave room temperature [3,4], high power [5], single- [6] and broad-band [7] operation. Eight years later the first operation of a THz QCL was demonstrated by K¨ohleret. al. [8]. The laser operated up to 50 K at 4.4 THz with 2 mW of optical output power. To improve the temperature performance of THz QCL differ- ent active region (lasing region) designs have been developed. As yet, the highest operating temperature of a QCL is 199.5K [9] and there are no THz QCL operating at room temperature. However, THz QCL can achieve output powers higher than 1 W [10] and be operated with compact cryocoolers. The common materials com- positions for THz QCLs growth is AlxGa1−xAs/GaAs due to its high mobility. The emission frequency of THz QCLs is covered from 1.2 THz [11] to 5 THz which is limited for higher frequencies by the Reststrahlen region of GaAs (33 meV-36 meV) [12]. Recently there was a demonstration of octave spanning broad-band THz QCL operation with a gain bandwidth of 1.7 THz [13]. Such lasers may be of interest for implementing terahertz comb spectroscopy and the generation of narrow THz pulses in the time domain. The dynamics of THz QCL is complex and still not understood completely. This complex gain dynamics is due to the lifetimes of intersubband transitions that are on the order of picoseconds and are due to carrier-carrier and phonon scattering. One of the aims of this work is to develop new concepts to con- trol the spectral emission of a THz QCL for spectroscopy application. A further goal is to study time and frequency resolved gain dynamics of the injection seeded THz QCL for studying and understanding the involved mechanisms, which are leading to the fast gain dynamics. This knowledge is the key for further improvement of QCL structures.
2 CHAPTER 1. GENERAL INTRODUCTION 1.1. OUTLINE OF THE THESIS
1.1 Outline of the Thesis
The work is organized as follows: Chapter 2 introduces spectral control of the THz QCL with narrow-band THz pulses. It also gives a brief overview over the generation principles of narrow-band THz pulses originating from periodically poled lithium niobate (PPLN) crystal. The crystal used in this work is characterized in time and frequency domain and is used for the injection seeding experiments on a THz QCL. Besides the spectral control of a THz QCL, a longitudinal mode selection dynamics is also investigated. Chapter 3 proposes an alternative method to control the THz QCL emission spec- tra with broad-band THz pulses. The method is based on injection seeding of two broad-band THz pulses which are separated by a time delay. The resulting spec- trum of two broad-band THz pulses is used for the mode selection in the QCL and is modified by adjusting the time delay between two THz pulses. The dynamics of the mode selection is studied as well. Chapter 4 describes the principles and the techniques for investigation of the THz QCL gain dynamics with two weak THz pulses. The first THz pulse is injected and amplified in the cavity. After several roundtrips in the cavity the amplified THz pulse saturates the gain of the QCL. In the saturation regime the second weak THz pulse (probe) is injected and its transmission is recorded. By varying the delay be- tween the second THz pulse and the saturation regime, the QCL gain dynamics is studied on femto- and picosecond time scale. A density matrix model is developed for modeling and understanding the experimental results. Chapter 5 deals with the electric field strength dependent gain measurements. The gain of the QCL is probed and analyzed in the frequency domain for the verification of the intersubband nonlinearities. Chapter 6 discuss future experiments and theoretical work that can be performed on THz QCLs using the techniques developed in this thesis.
3 BIBLIOGRAPHY BIBLIOGRAPHY
Bibliography
[1] R. Kazarinov and R. A. Suris, Sov. Phys. Semicond. 5, 707 (1971).
[2] J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[3] M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, Science 295, 301 (2002).
[4] A. Lyakh, C. P߬ugl,L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. T.-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, Appl. Phys. Lett. 92, 111110 (2008).
[5] G. Scamarcio, F. Capasso, C. Sirtori, J. Faist, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, Science 276, 773 (1997).
[6] R. Audet, J. MacArthur, L. Diehl, C. Pfl¨ugl, F. Capasso, D. C. Oakley, D. Chapman, A. Napoleone, D. Bour, S. Corzine, G. H¨ofler, and J. Faist, Appl. Phys. Lett. 91, 231101 (2007).
[7] R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchin- son, A. Y. Cho, and H. C. Liu, Science 290, 1739 (2000).
[8] R. K¨ohler,A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, Nature 417, 156 (2002).
[9] S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. Wasilewski, S. R. Laframboise, D. Ban, A. M´aty´as,C. Jirauschek, Q. Hu, and H. C. Liu, Opt. Express 20, 3866 (2012).
[10] L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, Electron. Lett. 50, 309 (2014).
[11] C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, Appl. Phys. Lett. 91, 131122 (2007).
[12] J. S. Blakemore, J. Appl. Phys. 53, R123 (1982).
4 BIBLIOGRAPHY BIBLIOGRAPHY
[13] M. R¨osch, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 9, 42 (2015).
5 BIBLIOGRAPHY BIBLIOGRAPHY
6 Chapter 2
Spectral emission control of THz QCL with narrow-band THz pulses
Abstract
Control of the spectral emission from a THz QCL is achived by using a narrow- band phase seeding technique. Narrow-band THz seed pulses are generated in a periodically poled lithium niobate (PPLN) crystal. The frequency of narrow-band THz seed pulses are adjusted by choosing an appropriate poling period of the PPLN crystal. The spectral selectivity of a THz QCL is achieved by overlapping the narrow-band seed spectrum with the QCL spectrum. In order to achieve single mode selection, the spectral broadening of the narrowband THz source must be smaller than the longitudinal mode spacing of the cascade laser. The time dependent dynamics is studied as a function of cavity roundtrip time. This shows how the QCL spectrum is influenced when it is seeded outside the full width half maximum of the spectral gain.
7 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
There are several ways to generate narrow-band THz pulses [1]. One of these is to use photomixers. For this purpose two continuous wave laser beams with the same polarisation and frequencies ω1 and ω2 are spatially mixed together and are focused on a photoconductive material. The focused laser beams generate carriers in the photoconduction material which modulates the conductivity and hence the current with the frequency difference (ω1 − ω2). The oscillating current in the photomixer leads to the radiation of THz waves. However, this technique has performance lim- itations. The output power drops dramatically above 1 THz due to several reasons such as impedance mismatch of the Antenna and the Vacuum, carrier lifetimes and heating effects [2–4]. Another approach is to use a mid-infrared QCL for THz gen- eration. Due to the intra cavity mixing of two NIR transitions within the active region, which are energetically close to each other, the THz emission becomes pos- sible. This approach is rarely used, because of low THz power [5–7]. A further method is to make use of the system nonlinearities in order to generate THz pulses by difference frequency mixing. The problem of this technique is a low conversion efficiency (10−6 − 10−5)[8]. In this work coherent narrow-band THz pulses are generated by optical rectification. Optical rectification is a second order nonlinear effect. For this case a polarisation P can be expanded in a Taylor series. For the THz generation only a second term of the
nl 2 2 Taylor series play a role P2 = χ E . For a Laser pulse with a given frequency band- width, a difference frequency generation will occur between the frequencies that are present in the laser pulse because of the E2 factor. Also sum frequency generation is present, which is not responsible for the THz generation. Several materials can be used for this purpose such as: LiNbO3, ZnTe [8,9], GaP [10–12] and GaAs [13]. Out of all the above-mentioned materials, LiNbO3 has one of the highest electro-optic constants. Recently a conversion efficiency of 10−3 [14] was demonstrated by strong optical pumping. This is due to the large energy bandgap that hinders multi-photon absorption if the optical pump is strong enough to promote multi-photon absorption [15]. In this way the generated THz pulses experience less free carrier absorption as compared in materials such as ZnTe or GaAs. The THz emission from periodically poled lithium niobate (PPLN) crystal is used as a source for injection seeding ex-
8 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.1: THz generation principle in PPLN crystal. NIR pulse is propagating from left to right and generate a THz pulse, as shown here in a forward direction. The crystal consists of periodically poled domains with alternating sign of the second order nonlinearity (χ2). The poling period Λ consist of two domains with −χ2 and χ2. One poling period Λ generate one THz oscillation. periments on the THz QCL and is discussed elaborately in this chapter. In PPLN crystals, the poling is done in such a way that the second order nonlinear suscepti- bility changes its sign altrenatively as described schematically in Fig. 2.1. The main idea is to explore the velocity mismatch of the optical and the THz pulse [16]. The refractive index of the optical excitation pulse is nIR ≈ 2 and of the generated THz pulse nT Hz ≈ 5 [16]. If the duration of the optical pulse is τIR, then the temporal walk-off of the generated THz pulse is given by lw = cτIR/(nT Hz −nIR). This is valid if the THz pulse propagation is in the same direction (forward direction) as the exci- tation pulse. However, the THz pulses are also generated in the backward direction.
The temporal walk-off is then given by lb = cτIR/(nT Hz + nIR). If the domain wall thickness (Λ/2) is chosen in a such a way that Λ/2 = lw, then the number of THz cycles is given by L/(Λ), where L is the length of the PPLN crystal. The period of one THz cycle in forward direction is TT Hz,w = Λ(nT Hz − nIR)/c and in backward direction TT Hz,b = Λ(nT Hz +nIR)/c. The frequency of the forward and the backward propagating THz pulses can be adjusted by changing the domain length Λ/2 and temperature [17, 18]. The THz pulse shape generated from the PPLN crystal can be calculated using the wave equation. We assume an abrupt change of the second
9 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES order nonlinearity at the domain interface along the z direction (crystal length). If the polarization of the second order is taken as the source, the wave equation in frequency domain can be written as: (ω)ω2 ∆ + E (r, ω) = −µ ω2P (r, ω) (2.1) c2 T Hz 0 where ε(ω) is the dielectric constant and P, is the Fourier transformed optical ex- citation pulse. As a good approximation P can be described by a Gaussian pulse in time and hence in a frequency domain. Details on the solution of this equation can be found in [16] and for more complicated cases where the excitation pulse has a chirp in [19]. For a 1.2 mm long crystal and 30 µm wide domain, the calculated and the measured PPLN pulses for a 150 fs long excitation pulses are shown in [16] In Fig. 2.2 (a) there are 20 electric field oscillations, which correspond to 40 domains. Fig. 2.2 (b) shows the corresponding Fourier Transform of the Fig. 2.2 (a). The broadening of the spectra is due to the 20 oscillations of the electric field. From the theoretical point of view, the broadening can be reduced to zero (delta function) if the number of the oscillations (domain number) is infinite. However, the broadening of the PPLN pulse is not always limited by the crystal length; it might be limited by the absorption in the crystal as well. Figs. 2.2 (b) and (e) show the calculated THz pulse and the spectra with the absorption coefficient, g = 7.5
−3 −1 −1 ·10 THz (calculated to 8.4 cm for nT Hz = 5.2). Figs. 2.2 (c) and (f) show the measured data which are in a very good agreement with the calculated ones in Fig. 2.2 (b) and (e), respectively [16]. In addition to the forward and backward THz pulses that exist in PPLN crystal [20, 21], an angle dependent frequency emission (shown in Fig. 2.3), was studied in [22]. According to [22] the angle dependent PPLN emission frequency Ω can be calculated by using the following equation: c 1 Ω = (2.2) Λ |nIR − nT HzsinΦ| For a fixed domain period and refractive indices the PPLN emission frequency can be calculated from the above equation. The corresponding results [22] are shown in Fig. 2.4. Due to the introduced angle in the above equation, the forward and backward propagating PPLN pulses are special cases for 90◦ and -90◦. Not only the periodic oscillations but also more complicated waveforms can be generated with an
10 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.2: Simulated and measured THz waveforms and corresponding power spec-
trum. PPLN domain structure parameters are assumed as L=1.2 mm and ld=30 µm. (a) and (d): g=0.0 THz−1, (b) end (e): g= 7.5 10−3 THz−1. And (c) and (f): experimental results [16] . aperiodically poled lithium niobate and multiple beam excitations. These kinds of waveforms are beyond the scope of this thesis and are not discussed in this chapter. Interested readers can find these results in [23, 24] In order to detect time-resolved QCL emission, the QCL must be phase-locked to a master laser [25, 26]. For the current experiments, the QCL is phase-locked to a Ti:Sa laser with a repetition rate of 80 MHz. The emission of the Ti:Sa laser is centred at 800 nm with pulse duration of 80 fs. A sketch of the experimental setup is shown in Fig. 2.5 (a). The NIR beam is split into three beams. The first beam is used for electro-optic sampling. The second beam is focused on the fast photo-diode for RF pulse generation. The generated RF signal used to gain switch the THz QCL is shown in Fig. 2.5 (d). The
11 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.3: Sketch of the generated PPLN THz signal which is angle dependent [22].
Figure 2.4: Angle dependent frequency emission from PPLN crystal [22]. Backward and forward THz pulse generations are spatial cases for 90◦ and -90◦. third laser beam is used for the THz pulse generation. The THz source is placed at the focus of the first 90◦ off-axis parabolic mirror. As can be seen in Fig. 2.5 (a), the reflection geometry is chosen for the experiments where the generated THz beam in order to generate a backward propagating wave. At first the PPLN crystal is characterized, as shown in Fig. 2.5 (a), without the QCL. Both, first NIR laser beam and the generated THz radiation are focused via parabolic mirrors on the ZnTe crystal. The spectra corresponding to the PPLN crystal and the photocon- ductive antenna are plotted in Figs. 2.5 (b) and (c), respectively. Clearly it can be seen the spectrum of the photoconductive antenna is broad-band while that of
12 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
the PPLN crystal is a narrow-band spectrum. The inserts show the corresponding THz signal in time domain. While the E-field oscillation last for only 1 ps in time for the antenna that results in the broad-band signal, the E-field oscillations last for several ps for the PPLN crystals resulting in a narrow-band signal. The PPLN crystal used for the experiment is 5 mm long. The crystal contains different do- main width periodicities, which are horizontally aligned (see schematic in Fig. 2.5 (b)). Each 5 mm long PPLN row is 0.5 mm wide and is separated by 0.3 mm from the other rows as shown schematically in Fig. 2.6 (c). The PPLN crystal is then excited with an NIR pulse. By changing the position of the translation stage on which the PPLN crystal is mounted, different PPLN periodicities can be accessed and thus all possible narrow-band THz pulses from this crystal were investigated. The PPLN periodicity is varied from 18.50 µm to 20.90 µm in 30 µm steps. The generated narrow-band THz pulses and their spectra are shown in Fig. 2.6 (a). The frequencies of the narrow-band pulses span from 2.023 THz to 2.270 THz in steps of approximately 30 GHz. In order to decrease the absorption in the crystal, the PPLN is cooled down to 10 K. The broadening of the narrow-band THz pulses is nearly ∆ = 13 GHz and is limited by the absorption and not by the crystal length. The measured spectral line broadening can be converted to the absorption coefficient. Assuming that the recorded PPLN spectra can be fitted by a Lorentzian function, than the relation between line width ∆ν and the exponential decay constant γ in time domain are related by the fourie transformation and are given by: ∆ν = γ/2Π. From the Beers law, the absorption coefficient α and the line width ∆ν are related by: α = γnT Hz/c = 2Π∆ν = nT Hz/c. For the THz refractive index nT Hz = 5 at 2 THz, the corresponding absorption coefficient is α=13.7 cm−1 which is in a good agreement with the measurements reported in [28] for a congruent PPLN crystal with 1.3 % of MgO doping. The QCL used for the experiment is 3.25 mm long, 0.15-mm-wide and hence the longitudinal mode spacing is 13 GHz. The GaAs/AlGaAs laser has a bound-to- continuum design and is grown by molecular beam epitaxy. It is processed as a surface plasmon waveguide. The laser threshold current is 100 A/cm2 and the max- imum operating temperature is 70 K. The device is indium-bonded on a gold coated
13 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.5: (a) Schematic of the experimental setup. Red lines are 80 fs NIR- pulses with a center wavelength of 800 nm, an 80 MHz repetition rate, and an approximately 1 W of average power. Green lines are the THz beam generated by the NIR-pulses. The dotted line is the purge box which prevents water vapor absorption of the THz beam. Both broad-band and narrow-band THz seed pulses are generated in reflection geometry. The THz seeds are coupled in to and out of the facets of the THz QCL with 90◦ off-axis parabolic mirrors. An RF bias pulse, synchronized to the femtosecond laser repetition rate, drives the THz QCL above threshold. The THz fields are measured by an electro-optic sampling using a 2 mm thick ZnTe crystal. (b) The spectrum of the narrow-band THz seed pulse generated by optical rectification of the NIR pulses in the PPLN crystal. Insert: Electric field of the narrow-band seed versus time. (c) The spectrum of the broad-band THz seed pulse generated by an interdigitated photoconductive antenna. Insert: Electric field of the broad-band seed versus time. (d) Voltage trace of the RF bias pulse recorded by an optical sampling oscilloscope through a 50 Ohm load with an attenuation of 40 dB. From [27].
copper sub-mount for better heat sinking. For the injection seeding experiments, and hence for the spectral emission control, the QCL is placed in the setup (as shown in the schematic of Fig. 2.5 (a)) and is cooled to 20 K. The second 90◦ off-axis parabolic mirror couples the THz pulses to the left QCL facet while the
14 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.6: Generated PPLN waveforms. (a)-(b) generated PPLN waveforms and corresponding color-coded spectra in the backward direction. The insert in (b) shows the domain periodicity of the PPLN crystal which corresponds to the generated narrow-band THz pulse. The measurements were performed at 10 K (c) Sketch of the PPLN crystal use for the THz pulse generation. Each color-coded row generates one corresponding narrow-band spectrum. One PPLN row is 0.5 mm wide and is separated by 0.3 mm from row above and below. From [27]. third parabolic mirror collects the THz emission from the right QCL facet. For gain switching the QCL, which results in pulse amplification, the generated RF-pulse is applied to the QCL [29]. The resulting amplified pulses are sampled with a 2 mm thick ZnTe crystal. This is possible because the RF pulse and hence the QCL emis- sion are synchronized to the repetition rate of the Ti:Sa laser. To ensure that the 2W RF bias pulse is strong enough to gain switch the QCL, a DC voltage (voltage offset) is superimposed with the RF pulse and is applied to the QCL. The RF build up time is approximately 200 ps. The distortion of the RF pulse shape is due to nonlinearities in the RF amplifier. Fig. 2.7 a i) shows the seeded QCL emission
15 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.7: (a) THz waveforms emitted by the QCL for (i) a broad-band seed pulse from the interdigitated antenna, and for (ii)(iv) narrow-band seed pulses from the PPLN crystal with frequencies of 2.204, 2.240, and 2.270 THz, respectively. The zero time corresponds to the first transmission of the seed pulse through the QCL. The black dashed lines are the trace of the RF bias pulse shown in Fig. 2.5 (d). (b) Maxima of the QCL field amplitudes in Fig. 2.7 (a) at 246 ps, as a function of the applied antenna voltage (for the broad-band seed) and the optical excitation power on the PPLN crystal (for the narrow-band seeds). The applied antenna voltage and the optical excitation power are proportional to the seed amplitude. The femtosecond laser has a spot size of approximately 300 µm. From [27]. with a broad-band pulse origination from the photoconductive antenna. Recorded waveforms (ii)-(iv) in Fig. 2.7 (a) are seeded with narrow-band. In all recorded waveforms the shape of the envelope follows the RF pulse shape, which is plotted in the dashed line. One of the important aspects of the injection seeding experiments is that the recorded emission should originate mostly from the seeded emission and not from the amplified spontaneous emission. Since the QCL is synchronized to the Ti:Sa laser and the detection is realized with electro-optic sampling, only the seeded emission can be detected and not the spontaneous emission. This issue can be solved by taking the the QCL spectrum with an FTIR or by recording the satu- ration curves as shown in [30]. In this work the saturation curves were recorded for
16 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES a time delay of approximately 250 ps. The amplitude of the amplified THz pulses at 250 ps is plotted in Fig. 2.7 (b) as a function of the optical excitation power for each PPLN domain period.. It can be seen that the saturation is achieved above 600 mW of optical excitation power. For the case of the photo conductive antenna, the NIR power was fixed and the applied antenna voltage was varied. Above 3 V, the seeded QCL emission starts to saturate. This ensures that the spontaneous emis- sion is minimized and the recorded emission is dominated by the seeded emission. In order to verify that the QCL spectra can be modified by narrowband seeding, a the Fourier transform of the waveforms in Fig. 2.7 (a) is plotted in Fig. 2.8 (a). The black spectrum in Fig. 2.8 (a-i) is the QCL spectrum when seeded with the broad-band THz pulse. The spectrum consists of several modes. The main mode is centered at 2.223 THz. The longitudinal mode spacing is 13 GHz as expected from the cavity length. Fig. 2.8 (a) (ii-iv) shows the resulting QCL spectra and the su- perimposed narrow-band seed pulse (dashed lines). From Figs. 2.8 (a) (ii) it can be seen that only those modes are selected that are within the narrow-band THz pulse at 2.204 THz. This generated seed frequency corresponds to 19.1 µm PPLN crystal period. By switching to 18.8 µm PPLN crystal period, a seed frequency is shifted to 2.240 THz. The seed frequency difference for these two crystal periodicities is 36 GHz, which approximately correspond to two longitudinal QCL modes. This is also reflected in the seeded spectrum in Fig. 2.8 (a) (iii), where the selected mode is shifted by two longitudinal modes to higher frequencies in comparison to Fig. 2.8 (a) (ii). This concept indicates that by choosing a proper narrow-band seed pulse the QCL spectrum can be modified. This is not the case in Fig. 2.8 (iv). In order to understand why for a particular seed the QCL spectrum can not be modified, a QCL gain spectrum is measured from the single pass transmission with the broad-band THz Pulse. The resulting gain spectrum is shown in Fig. 2.8 (b). The black arrows in Fig. 2.8 (b) indicate the seed frequencies of the narrow-band THz pulses. We can clearly see that only the longitudinal modes that within the full width of half maxi- mum (FWHM) of the gain profile can be selected. The seed at 2.270 THz is outside the FWHM and hence this seed frequency cannot be used for spectral selectivity even though the seeded emission is saturated. The time-resolved dynamics of the
17 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.8: (a) Normalized spectral amplitude of the QCL when seeded by (i) the broadband THz pulse, and (ii)(iv) narrow band THz pulses. The corresponding normalized PPLN seed spectra are superimposed as dashed lines and is fifty times smaller as the QCL spectra. (b) Gain curve of the QCL measured from a single pass transmission with the broadband THz source. Arrows indicate the seed frequencies. From [27]. mode selection process are studied by performing Fourier transforms of the QCL emission for each round-trip. Fig. 2.9 (a) shows the spectrum of a narrow-band THz pulse, used to injection seed the QCL (Fig. 2.9 (b)), on a logarithmic scale. Fig. 2.9 (c) contains the same waveform as Fig. 2.7 (a-iv). The longitudinal modes of the QCL are not resolved due to the 77 ps window. The spectrum of the first round trip time (red spectrum) in Fig. 2.9 (d) shows the biggest spectral amplitude at the seed frequency and also some spectral components around the FWHM of the spectral QCL gain. This is due to the seed, which has also spectral components at these frequencies as shown in Fig. 2.9 (a). For the second and the third round trip
18 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.9: (a) Spectral amplitude of the 2.270 THz seed in Fig. 2.7 (b-iv) on a logarithmic scale. (b) Evolution of the QCL emission frequency as a function of the round-trip time for the 2.270 THz narrow-band seed. Each spectrum is obtained by applying a Fourier transform on each round-trip pulse within the waveform of Fig. 2.7 (a-iv). The rectangular window for each Fourier transform is 77 ps corresponding to the round-trip time in the QCL. Adapted from [27].
times the spectral components at the seed frequency becomes smaller in comparison to the spectral frequency at the QCL gain maximum (2.223 THz). For further round trip times the spectrum becomes narrow and is mainly dominated by the FWHM is the QCL gain spectrum. For comparison the FFT of the entire waveform (from 0 ps to 1ns) is shown in the bottom of Fig. 2.9 (d). As shown in the Fig. 2.6 (a) and (b) narrow-band THz pulses with other frequencies could also be generated. The mode selection was also performed with seeds at 2.174 THz (pink) and 2.138 (brown) (see Fig. 2.6 (a) and (b)). For these seed frequencies the saturation curves were recorded as well. The saturation curves for all the seed are shown in Fig. 2.10 (a). The seeds at 2.174 THz (pink) and 2.138 (brown) are not able to saturate the QCL
19 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES
Figure 2.10: (a) Saturation curves for seeds at 2.138 THz (brown-i), 2.174 THz (pink-ii), 2.204 THz (blue-iii), 2.240 THz (red-iv) and 2.270 THz (green-v). (b) Recorded QCL spectra and superimposed with the corresponding seed from (i) to (v) in dashed line. The spectral amplitude of the seed is 50 times smaller than the QCL spectra.
20 CHAPTER 2. SPECTRAL EMISSION CONTROL OF THZ QCL WITH NARROW-BAND THZ PULSES emission and hence the recorded QCL emission consists of amplified spontaneous emission and the seeded emission. These two cases can not be compared with the other seeded QCL spectra, because the amount of undetected spontaneous emission is unknown. This is different for spectra (iii), (iv) and (v) in Fig. 2.10 (b) because the saturation curves show that the spontaneous emission is negligible for optical excitation power above 600 mW. In conclusion, it was possible to generated narrow-band THz pulses by using PPLN crystal from 2.033 THz to 2.270 THz. It can be shown that the linewidth of the generated narrow-band THz pulses are limited by the material absorption in PPLN crystal. For 5 mm long crystal with an average PPLN crystal periodicity of 20 µm without absorption one have to expect 250 oscillations. At 2 THz 250 oscillations corresponds to 125 ps and hence to 8 GHz line width. The measured line width is almost twice bigger (13 GHz) and hence limited by the absorption of 13.7 cm−1 as calculated before. By seeding the QCL with a proper THz seed it is possible to select the longitudinal modes and hence to modify the spectral emission. Only mode selection within the FWHM of the spectral QCL gain is possible. When the seed spectra were outside the FHWM of the gain, the injection-seeded emission spectra of the QCL was shifted to the gain maximum. The advantage of this technique is that the QCL spectrum can be reversibly controlled without any QCL modification just by selecting the proper PPLN crystal period.
21 BIBLIOGRAPHY BIBLIOGRAPHY
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25 Chapter 3
Spectral emission control via broad-band double pulse injection seeding
Abstract
Spectral emission of a terahertz quantum cascade laser (THz QCL) is controlled by using a double pulse phase seeding technique. Two broad-band THz pulses, generated by a photo-conductive antenna, are delayed in time. This imprints a modulation on their combined spectrum. The modified spectrum is used to injection seed the THz QCL. Moreover by setting a proper time delay between the broad- band seed pulses, single mode emission is achieved. By applying a sliding Fourier transform to the recorded QCL emission, the mode selection dynamics are studied as a function of time.
26 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
In the last 20 years, the field of THz technology has rapidly developed. THz ra- diation is now used for imaging [1,2], metrology [3–5], spectroscopy and security [6] applications. Many of these applications such as chemical gas sensing [7], gas spectroscopy and many others require spectral control of the THz source. Since the development of THz QCLs in 2002 [8], a lot of effort has been made to have control over the emission spectrum of this compact and coherent THz source. One com- mon way of spectral emission control in the laser community is the use of gratings or mirrors. For this purpose, one of the laser facets is covered with antireflection coating. The laser emission can be coupled out and illuminates the grating. The grating reflects back into the cavity only those frequency on which the laser sup- posed to operate. Instead of the grating a mirror can be used. Changing the mirror position change the length of the cavity and hence the allowed longitudinal modes. The grating and the mirror technique can be combined. Using mirror for spectral emission control in THz QCLs was demonstrated in[9] and [10] by selecting and feeding back the preferential mode. Another successful demonstration of emission control was realized with second [11, 12] and third [13] order distributed feedback (DFB) lasers. These lasers show single mode emission with a narrow beam profile. The disadvantage is that this method is irreversible. Ones the ridge is modified to the grating, which reflects one particular frequency component back into the gain medium, it can not be reversed any more. Photonic crystals can also be used to control the spectral emission of THz QCLs [14–17]. However, the realization and the tunability of such devises are quite complicated. One of the practical approaches was demonstrated in [18], and [19] where for a special active region design, the QCL emission spectrum is tuned electrically. In this chapter the control of the spectral emission via broad-band THz pulses is demonstrated on a THz QCL. This technique works without making any modifications to the laser medium or the laser waveguide. In comparison to narrow-band injection seeding [20–22], mode selection is realized with two broad-band THz pulses, even though, the spectrum of each broad-band pulse is much broader than the laser spectrum and gain bandwidth of the THz QCL. The principle behind this technique is shown in Fig. 3.1. The spectrum of the first THz pulse can be described in the time domain with a function f(t), whic has a
27 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
R ∞ −iωt following form in frequency domain: F1(ω) = −∞ f(t)e dt By introducing a sec- ond THz pulse, which is delayed by τ and denoated by f(t − τ) with the spectrum
R ∞ −iωt F2(ω, τ) = −∞ f(t − τ)e dt, the combined spectrum is given by: Z ∞ F (ω, τ) = (f(t) + f(t − τ))e−iωtdt (3.1) −∞ The magnitude of the spectra of the two seeds has a following form:
−iωτ |F (ω, τ)| = |1 + e | · |F1(ω)| (3.2) | {z } Broadband Thus it can be said that the resulting spectral magnitude is a broadband spectrum of a single THz pulse, which is modulated with the factor √ |1 + e−iωτ | = 2 · p1 + cos(ωτ). The spectra of two simulated THz pulses which are separated by 2 ps are shown in Fig. 3.1 (a). Increasing the delay between the pulses to 26 ps, results in more rapid oscillations of the combined seed spectrum (see Fig. 3.1 (b)). The variation of the spectral amplitude with delay-time at a fixed frequency ω (lasing frequency of a THz QCL) is of particular interest. The spectral magnitude for a fixed frequency (ω=2 THz) and a varied time delay is shown in Fig. 3.1 (c). The period of the rapid spectral oscillations with delay- time corresponds to 1/ω. In the case of Fig. 3.1 (c), a delay of 250 fs modulates the spectral magnitude from maximum to minimum and indicates that changing thedelay-time can be used to control between the two broad-band THz pulses is a crucial parameter for mode selection. Fig. 3.2 illustrates the longitudinal mode selection in a THz QCL for a given QCL spectrum. Figs. 3.2 (a)-(d) shows the two identical THz pulses that are separated by a fixed time delay τ. In Figs. 3.2 (a)-(d), the spectra of the seed pulsess in Figs. 3.2 (a)-(d) and the corresponding emission spectrum are presented. The inserts show the zoomed-in region of the QCL emission and the combined seed spectrum. From the inserts in Figs. 3.2 (a)-(d) it can be seen which longitudinal modes for a given time delay are seeded or rather selected. Only those QCL modes are selected that have an overlap with the spectral seed magnitude, otherwise they are suppressed. The corresponding resulting selected QCL modes are shown in Figs. 3.2 (a)-(d). The sketch of experimental setup is shown in Fig. 3.3 (a). The beam from the Ti:Sa laser is split into three beams. The first beam is focused on a fast photo diode for RF-pulse generation. The second
28 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.1: Normalized spectral amplitude of two simulated THz pulses (insets) separated by (a) 2 ps and (b) 26 ps. As the time delay between the two pulses increases, the modulation in the spectrum becomes more pronounced. (c) The nor- malized spectral seed amplitude variation at 2 THz as a function of the time delay τ. From [23].
one is used for electro-optic sampling that passes through the electro-optic sampling delay-line and is focused onto a 2 mm thick ZnTe crystal. The third beam is coupled to the Michelson-Interferometer, where two NIR pulses are generated and can be delayed in time by varying the position of the mirror M2. Two NIR pulses from the Michelson interferometer are focused on a low temperature grown GaAs antenna (LT-GaAs). The LT-GaAs enables the generation of consecutive THz pulses with ps/sub-ps time delay. This is due to the fast recombination of the electrons and holes[24–31] in LT-GaAs. Without the LT-GaAs material the first NIR pulse would generate carriers that would screen the bias field. This would lead to small THz signal from the second NIR pulse. For the experiments the THz seed power is crucial and is necessary for the saturation measurements as already discussed in the previous chapter. In order to generate high power THz pulses, LT-GaAs layer was grown on top of a Bragg-mirror. As shown in [32], by designing a proper Bragg-mirror with the appropriate LT-GaAs thickness, the NIR absorption in a thin LT-GaAs layer can be increased in comparison to the bulk material. A large area interdigitated photoconductive antenna was processed [33, 34] on the grown LT-GaAs layer. The LT-GaAs photonconductive antenna is biased with high RF voltage pulses. More details on the antenna structure, fabrication, and the growth- sequence of the Bragg-mirror and LT-GaAs are given in Appendix. The QCL used for this experiment has a bound-to-continuum structure design and is processed
29 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.2: Principle of spectral emission control via broad-band double pulse injec- tion seeding. (a)-(d) normalized THz pulses separated by 2.5 ps, 21 ps, 37.5 ps and 46.5 ps time delay. (a)-(d) seed spectra (Fourier Transform of (a)-(d)) seen by the QCL and the QCL emission spectra. The inserts are the zoomed-in region of the resulting seed and the QCL emission spectra. (a)-(d) selected longitudinal modes of the QCL spectra by corresponding seed in a surface plasmon waveguide. The emission bandwidth is approximately 100 GHz and is peaked up at 2.14 THz (see Fig. 3.2 (c)) (growth sheet of this laser is attached in the Appendix).The generated THz pulses are focused via two 90 off-
30 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING axis parabolic mirrors on the facet of the THz QCL. The QCL is indium bonded on a gold-coated copper sub-mount for a better heat sinking. For measurements the QCL is cryogenically cooled to 15 K. The two THz pulses are coupled into the QCL facet. The QCL is biased with the RF pulse above the threshold just before the first THz seed arrives at the QCL facet in order to amplify the THz seed [35]. Ideally the first THz pulse enters the QCL cavity when the QCL is biased above the threshold (see Fig. 3.2 (b)). The second THz pulse arrives at the QCL facet on the rising edge of the RF-pulse. In order to minimize the spontaneous emission in the laser cavity, the seed must be strong enough to saturate the laser emission [36]. The QCL emission spectrum and the saturation curve (insert Fig. 3.2 (c)) are shown in Fig. 3.2. In this case the QCL is seeded with broadband pulses (single THz pulse). The arrow in the insert of Fig. 3.2 (c) indicates that the injected seed is strong enough to saturate the QCL emission and hence the spontaneous emission in the laser cavity is negligible. Measurements were first performed without the QCL in order to characterize the THz pulses. Figs. 3.4 (a), (c) show the recorded THz pulses in time domain, which are separated by 2 ps and 26 ps, respectively. The corresponding spectral magnitudes are shown in Figs. 3.2 (b), (d). As expected from the theoretical description above and calculations in Fig. 3.1 and Fig. 3.2 the resulting THz spectra look very similar. Fig. 3.4 (e) shows the recorded QCL emission with the first single pulse. To demonstrate the spectral mode selectivity the non-hatched region (150-300) ps is recorded when seeded with the second pulse and the corresponding FT is plotted for each delay between the two pulses (see Figs. 3.4 (f)-(g)). In Fig. 3.4 (f) the normalized spectral amplitude of the QCL emission is color-coded and plotted as a function of the frequency and the varied double pulse delay from 2 to 3.4 ps. A slice of a matrix plot at 2.14 THz (dashed black line) along the double pulse delay is plotted on the right side and shows that the normalized spectral amplitude varies from 0 to1 depending on the time delay. Two color-coded arrows (red and blue) indicate the double pulse delay time for which the inserts in Fig. 3.4 (f) are plotted. These are slices of the matrix plot when the QCL emission and hence the seed power is maximum and minimum. The pattern in Fig. 3.4 (f) repeats itself periodically as expected from Fig. 3.1 (c). For this double pulse delay
31 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.3: (a) Schematic of the experimental setup. Before being focused on the THz antenna, the laser beam (80 fs, 80 MHz) is divided into two beams by the beam splitter (BS). The time delay between the two generated THz pulses is induced by moving mirror M2. The QCL is gain-switched with an RF-pulse synchronized to the laser repetition rate. The injection seeded QCL emission is recorded by electro-optic sampling with a 2 mm thick ZnTe crystal. (b) Schematic of the RF pulse rising edge. At threshold, the QCL is injection seeded by a first broad-band THz pulse. At a later time, the second identical pulse is injected into the cavity to modulate the spectral amplitude of the first broad-band seed. (c) Seeded QCL emission spectrum induced by the first broad-band THz pulse. Inset: Saturation curve of the seeded emission as a function of the antenna bias for the single THz seed. Arrow: antenna bias used for the experiments. From [23].
(2 ps) mode selectivity is not possible because the spectral seed modulation for this time delay is not rapid enough to select or suppress some of the longitudinal modes. This is different in the case of the Fig. 3.4 (g). The double pulse delay is varied from 26 to 27.4 ps. The pattern in the matrix plot is periodic and has a period of approximately 0.24 ps. For a double pulse delay of 26.3 ps and 27 ps, the inserts show the slices of the matrix plot. For a delay of 26.3 ps the main lasing mode is suppressed and the side modes at 2.12 THz and 2.16 THz are selected. This is exactly the opposite case for the double pulse delay of 27 ps. Only the main mode is selected and the side modes are suppressed. In order to show that other possible spectral patterns can be selected, a scan of 500 ps of the QCL emission for 27 ps, 35 ps, and 35.25 ps double pulse delay time are recorded (see insert of Figs. 3.5 (a)-(c)). A Fourier transform (FT) is applied to these 500 ps long scans and the corresponding spectra are shown in Figs. 3.5 (a)-(c). A single mode emission is achieved for the
32 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.4: (a) Recorded E-field oscillations of two THz pulses separated by 2 ps and the corresponding Fourier transform (b). (c) Recorded E-field oscillations of the two THz pulses separated by 26 ps and the corresponding Fourier transform (d). (e) Selected time window of the QCL E-field for the contour plots (non-hatch region). (f) Contour plot of the normalized spectral emission of the QCL as a function of frequency and time delay between the two THz pulses around 2 ps delay. The spectral amplitude profile of the seeded QCL emission as a function of the time delay between the two THz pulses at 2.14 THz ia shown as indicated by blackdashed line on the contour plot. Inset: Spectra from the contour plot corresponding to low (blue arrow) and high (red arrow) seed modulation amplitude at 2.14 THz. (g) Contour plot of the normalized spectral emission of the QCL as a function of frequency and time delay between the two THz pulses around 26 ps delay. The amplitude profile of the seeded QCL emission as a function of the time delay between the two THz pulses at 2.14 THz is shown as indicated by black-dashed line on the contour plot. Inset: Spectra from the contour plot corresponding to low (see blue arrow) and high (see red arrow) seed modulation amplitude at 2.14 THz. The spectral resolution is 6 GHz. From [23].
33 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.5: QCL emission spectrum when seeded with two pulses with a delay of (a) 27 ps (b) 35 ps and (c) 35.25 ps. For a delay of 27 ps the emission spectrum is centered at 2.14 THz. When the delay between the two pulses is 35 ps the emission spectrum consists of two frequencies at 2.14 THz and 2.16 THz. While a delay of 35.25 ps between the two pulses results in the emission spectrum centred at 2.16 THz. Insets: Corresponding QCL E-Field oscillations. The spectral resolution is 2 GHz. From [23]. delay of 27 ps (Fig. 3.5 (a)) and suppressed for 35 ps (Fig. 3.5 (b)). For 35.25 ps the main mode and some sides mode are selected. It is important to point out that by using electro-optical sampling only the emission that is phase-locked to the laser is recorded. In order to verify that the recorded waveform and hence the QCL spectra only consists of the seeded emission and that the spontaneous emission of the laser is negligible, saturation curves are taken (see Fig. 3.6)[36]. These curves are taken by varying the voltage on the photoconductive antenna and hence the THz seed power. The black arrow in Fig. 3.6 indicates the operation regime for the experiments. For all spectra measured in Fig. 3.6 the QCL seeded emission could be saturated, which clearly indicates that the spontaneous emission in the laser cavity can be neglected. It is also of particular interest to study the time resolved dynamics of the double pulse injected THz QCL. In order to investigate the time resolved QCL dynamics a sliding FT is applied to the recorded QCL waveforms. Figs. 3.7 (a)-(c) show the recorded 500 ps long scan of the QCL emission (these are the same waveforms as in the inserts of Fig. 3.5). A rectangular window with a width of 110 ps is chosen, which corresponds to two round trips in the QCL cavity. Every 110 ps step, a rectangular FT window is applied to the waveform. The resulting spectrum and the corresponding rectangular FT windows are color-coded in Fig. 3.7. In all three cases
34 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.6: Saturation curves of the seeded QCL emission as a function of the antenna bias for the spectra described in Fig. 3.5. Arrow: Antenna bias for the recorded spectra in Fig. 3.5. From [23].
(Figs. 3.7 (a)-(c)) the first QCL spectrum is a broad spectrum. This indicates that the first THz pulse seeds all the longitudinal modes of the QCL and with time the spectral evolution becomes narrower because of the second THz pulse that induces a spectral seed modification. This spectral seed modification is amplified over time and hence results in a modified narrow spectrum. In conclusion, the selection of longitudinal modes is successfully demonstrated by broad-band injection of THz pulses. For a proper double pulse delay and for the given QCL gain spectrum, a single mode emission has also been achieved. By adjusting the double pulse delay, the QCL spectrum can be easily and at the same time reversibly modified. Also a time resolved mode selection has been investigated by applying a rectangular FT window to the recorded QCL waveforms. These studies support the supposition that: that the QCL experiences the combined THz seed spectrum of the two broad-band THz pulses.
35 CHAPTER 3. SPECTRAL EMISSION CONTROL VIA BROAD-BAND DOUBLE PULSE INJECTION SEEDING
Figure 3.7: Time-resolved spectral QCL dynamics when seeded with two pulses with a delay of (a) 27 ps (red curve), (b) 35 ps (green curve) and (c) 35.25 ps (blue curve) for a 500 ps scan length of the QCL emission. A 110 ps wide and color- coded rectangular sliding FT window is applied to all the recorded QCL waveforms of the corresponding double pulse delay. The rectangular FT windows and the corresponding color-coded spectra are shown in (a)-(c).
36 BIBLIOGRAPHY BIBLIOGRAPHY
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41 Chapter 4
Phase Seeding-Phase Probing technique for investigation of ultrafast time-resolved laser dynamics
Abstract
Ultrafast measurements are traditionally performed with pump-probe techniques. These techniques often require amplified laser pulses, which are technologically de- manding. In addition, the pulse duration of the pump and probe intrinsically limit the time resolution. In order to overcome these problems, a new spectroscopic tech- nique is presented, the Phase Seeding-Phase Probing (PSPP) technique, which offers femtosecond information on the spatial gain dynamics with weak pulses. More pre- cisely, a weak seed pulse is used to lock and amplify the seeded emission of a laser, while a phase-locked probe pulse is used to study time-resolved laser dynamics. Since the phase of the probe pulse is locked, it can be detected via electro-optic sampling, which provides time, frequency and phase information. The PSPP technique is demonstrated by studying the time-resolved gain dynamics of a THz Quantum Cas- cade Laser (QCL) on sub-ps time scales. Time-resolved gain modulation of the investigated QCL at multiple frequencies, a spectral gain shift and gain bleaching are observed. In order to explain the observed phenomena, a quantum-mechanical
42 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS two-level model is employed based on the density matrix formalism. As demon- strated on a THz QCL, the presented PSPP technique will provide new insights towards the future research and development of lasers.
43 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
One of the subjects of THz QCL research is the development of new measurements methods for THz metrology [1], spectroscopy [2] and real-time imaging [3] applica- tions. Recent progress in this area includes the capability to measure phase-resolved stimulated laser emission [4,5], which lead to the emergence of devices such as THz amplifiers [6]. The necessity of having a stable THz reference source for spectroscopy and metrology applications resulted in the development of broadband and octave spanning lasers, and hence the direct generation of frequency combs in the laser cavity [7]. Another approach to stabilize the THz QCL emission is to phase-lock it to a mode-locked laser [8] or to the free-space terahertz comb [1]. An alternative approach for a stable QCL source is to use active mode locking [9, 10]. In this method, the QCL is seeded with a THz pulse and a sinusoidal RF-modulation is applied to the QCL. All these techniques require knowledge of the QCL dynamics, especially active mode locking and the octave-spanning laser. An understanding of the laser dynamics is the key for improving and designing new laser structures. Until now there is a lack of measurement techniques that allows investigation of time- and frequency-resolved gain dynamics on fs and ps time scales. There are only a few experimental studies on time-resolved gain dynamics in THz QCLs [11–13]. In this work a new spectroscopic approach is reported to investigate the time-resolved gain dynamics of a THz QCL. In comparison to pump-probe techniques, the proposed method does not require strong pulses. Two weak THz pulses with an adjustable time delay are necessary to study the laser properties. The first THz pulse (seed pulse) is injected into the laser cavity. While entering the cavity, the laser is biased with an RF pulse. This results in the amplification of the seed pulse that produces a strong electric field in the cavity, which can be considered as a pump field. By varying the delay and recording the second THz pulse (probe pulse), access to the time-resolved dynamics is possible. Due to the phase sensitive nature of the mea- surements both time and spectral gain information can be extracted. The phase seeding-phase probing technique can be used for nonlinear and 2D spectroscopy on solid-state lasers as well. The above-mentioned technique is applied to a THz QCL and hence the gain dynamics on ps and fs time scales is studied. It has been ob- served that the gain of the laser recovers on the order of 20 ps, which is determined
44 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS by the THz pulse duration in the laser cavity. The duration of THz pulses in the laser cavity is mainly determined by the gain bandwidth of the investigated laser. Moreover, rapid spatial gain oscillations on fs time scales at multiple frequencies are observed, that reflect highly nonlinear laser behavior. Besides these, spectral holes and spectral emission shifts on fs time scales are also observed. To explain the physical origin of the observed phenomena a theoretical model based on the density matrix formalism is employed.
Phase Seeding-Phase Probing Technique
In order to study time-resolved gain dynamics of a THz QCL, two THz pulses with a fixed phase and adjustable time delay are required (see Fig. 1.1 (a)). Strong THz pulses are not mandatory and hence can be generated by illuminating a photocon- ductive antenna, ZnTe, GaAs or GaP crystals with fs laser pulses. In this work, the THz pulses are generated via an interdigitated photoconductive antenna [14] fabricated on GaAs. The first THz pulse is referred to as the seed pulse since it ini- tializes (or seeds) laser emission in the QCL cavity. While entering the laser cavity, the QCL is gain-switched with the RF pulse [6, 15, 16]. The seeded and amplified emission of the QCL is recorded by electro-optic sampling and shown in Fig. 1.1 (b) with the superimposed RF pulse. The corresponding QCL spectrum is obtained by applying a Fourier-Transform to the QCL electric field waveform, shown in the inset of Fig. 1.1 (b). It can be seen that the QCL emission spectra spans over 100 GHz and is peaked at 2.14 THz. The amplification of the small THz seed pulse results in the large electric field that reaches the maximum when the gain is clamped. In this way the seeded QCL emission can be separated into a linear- (from 0-330 ps) and a saturation-regime (for times greater than 330 ps). The THz QCL pulses are separated by a round trip time of 48 ps, which corresponds to the 2 mm long cavity. In order to investigate the QCL gain dynamics, a THz probe pulse with a fixed phase relation to the THz seed pulse (and hence to the seeded QCL emission) is injected into the laser cavity. By varying the seed-probe delay time and recording the probe transmission, the gain dynamics in the linear and the saturation regime can be studied. For example, the probe transmission for a seed-probe delay of 335
45 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
Figure 4.1: Measurement scheme: (a) Injection of the THz seed and THz probe pulse into the QCL cavity. The QCL is gain-switched with an RF pulse when the seed is entering the laser cavity. The probe transmission is recorded with electro-optic sampling. (b) RF pulse (black) and the seeded QCL electric field (green) are plotted vs. the electro-optical time delay (sampling time). The spectrum of the seeded QCL is shown in the inset. (c) By controlling the seed-probe delay the phase-locked THz probe pulse is injected into the QCL cavity. The probe transmission is recorded by electro-optical sampling for a seed-probe delay of 335 ps as indicated with the red arrows in (b). Recorded probe signal consist of the antenna signal (green) and the QCL amplification (red). The spectrum of the probe amplification is shown in the inset. ps is plotted in Fig 1.1 (c). The probe transmission waveform is composed of two sections, one from the antenna (green) and the other from the QCL amplification (red). By applying the FT to the amplified QCL signal (red curve of Fig. 1.1 (c)), a probe spectrum is extracted. This is shown in the inset of Fig 1.1 (c). The spectral
46 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS probe maximum (for a seed-probe delay of 335 ps) is at 2.14 THz, which matches with the spectral maximum of the QCL emission. The maximum of the spectral probe gain (marked with the blue dot in the inset of Fig. 1.1 (c)) will be used to study the time-resolved gain dynamics of the laser.
Time-resolved QCL gain dynamics
QCL emission and the probe are recorded by electro-optic sampling (see Fig. 1.1 (c)). The respective probe transmissions are recorded as a function of seed-probe delay. For each seed-probe delay, the spectral probe maximum is calculated from the FT and plotted as shown in Fig. 4.2 (a), blue curve. Oscillations of the spectral probe maximum as a function of seed-probe delay time are observed since the THz seed and probe pulse are phase-locked. The field of the seeded QCL emission is shown on the same time scale in Fig. 4.2 (a), green curve, for reference. In order to remove the oscillations, a digital filter with a corner frequency of 0.2 THz is applied. The resulting filtered curve is plotted in Fig. 4.2 (a) (black curve). The spectral probe envelope (black curve) shows the probe transmission at 2.14 THz. In Fig. 4.2 (a), it is observed that the gain decreases when a strong electric field is present in the laser cavity. As the QCL electric field decreases, the probe transmission recovers. On large time scales, this gain behavior is seen in the linear as well in the saturation regime. In Fig. 4.2 (b), the QCL electric field intensity (the square of electric field) (green curve) is plotted versus the sampling time, along with the envelope of the spectral probe transmission at 2.14 THz (black curve). The spectral gain at 2.14 THz decreases with increasing QCL electric field intensity and achieves a local minimum at 335 ps when the field intensity is maximal. With decreasing QCL electric field intensity, the gain recovers to a local maximum within approx- imately 20 ps. The envelope of the spectral probe transmission in Fig. 4.2 (b) is dominated by the shape of the laser electric field intensity. This is more pronounced around 360 ps where the envelope has a kink, which originates from the shape of the electric field. From the spectral probe envelope, which follows the seeded QCL electric field, it is possible to conclude that the relaxation gain dynamics must be much faster than 20 ps. The stated value can only be taken as an upper limit for
47 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS dynamical processes. As mentioned earlier, the gain grating dynamics which are manifested by the oscillations (blue curve Fig. 4.2 (a) ) of the probe spectral ampli- tude, can also be studied. In Fig. 4.2 (a), the seed-probe delay is varied from 95ps to 600 ps with a step size of 0.9 ps, that covers both the linear and the saturation regimes. Measurements are also performed with step sizes of 0.5 ps and 0.4 ps (not shown). These measurements result in an identical envelope curve, but have a dif- ferent spectral probe oscillation frequency. This indicates aliasing of the recorded spectral probe maximum. In order to remove the aliasing, a 6 ps scan, consisting of 150 recorded probe waveforms, is taken with a 40 fs time step. Fig. 4.2 (c) shows the zoomed-in region of the spectral probe oscillations of Fig. 4.2 (a) from 334 ps to 340 ps as a function of seed-probe delay time. Delaying the probe by 160 fs from 335.16 ps (point 1) to 335.32 ps (point 2) in Fig. 4.2 (c) results in a large difference of the spectral probe transmission. The insets (1) and (2) in Fig. 4.2 (c) show the recorded probe waveform for the spectral maximum at time 335.16 ps (inset (1)) and minimum at time 335.32 ps (inset (2)). The origin and the explanation of these rapid oscillations involve standing waves which form gain grating in the cavity and will be discussed further in the simulation sections. At this point, it is of interest to know how fast the maximum of the spectral probe transmission is modulated and hence the frequency components of the formed gain grating. In order to answer this question, an FT of the spectral probe oscillations in Fig. 4.2 (c) is performed and plotted in Fig. 4.2 (d). It is seen that the spectral gain is not only modulated by the laser intensity (at 4.28 THz) but also by the electric field (at 2.14 THz). In order to verify that 4.28 THz is not a lasing frequency, FTIR measurements are performed under the same measurement conditions without the seed and the probe. The resulting FTIR spectrum of the QCL is shown in the inset of Fig. 4.2 (d). FTIR measurements confirm that the QCL is lasing at approximately 2.14 THz and not at 4.28 THz. The FTIR resolution for the QCL spectrum (inset Fig. 4.2 (d)) is 33 GHz and hence the longitudinal modes are not resolve as in the insert of Fig. 1.1 (b). Frequencies higher than the lasing frequency in Fig. 4.2 (d) originate from the spectral probe modulation (spatial gain grating), which is explained in the discus- sion section. Until now, only the spectral probe component at 2.14 THz is analyzed
48 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
Figure 4.2: Gain trace: (a) The seeded QCL emission (green) as a function of electro-optical sampling delay (sampling time) and the spectral probe amplitude at 2.14 THz as a function of seed-probe delay. The seed-probe delay is varied from 95 ps to 600 ps with a step size of 0.9 ps. The black curve indicates the envelop of aliased spectral probe amplitude at 2.14 THz. (b) Electric field intensity (green curve) of the seeded QCL from 310 ps to 370 ps and the envelop of aliased spectral probe amplitude at 2.14 THz (black curve). (c) Zoomed section of the spectral probe amplification from 334 ps to 340 ps. The seed-probe time step size is 0.04 ps. The insets (red oscillations) (1) and (2) show the probe amplified waveform in the time domain of the corresponding spectral amplitude at 2.14 THz. (d) Spectrum of the spectral probe amplitude at 2.14 THz. The inset shows the FTIR spectrum of the RF-biased QCL without the seed and probe. and studied as a function of the seed-probe delay. Fig 4.3 (a) shows the spectral probe components at 2.12 THz (black curve) and 2.25 THz (red curve) as a function of the seed-probe delay. Both spectral probe components have a fixed phase shift of 125 with respect to each other and nearly the same period of 0.465 ps (2.14 THz). The relative maximum of the spectral probe transmission at 2.12 THz is bigger than that of 2.25 THz because the QCL spectrum is peaked at 2.14 THz as shown in Fig 1.1 (c). Three color-coded arrows (orange, grey, and purple) in Fig. 4.3 (a) indicate a fixed time for which the probe transmission is plotted in Fig. 4.3 (b), (c) and (d), respectively. These seed-probe delays are selected because the ratio of spectral
49 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
Figure 4.3: Spectral probe transmission: (a) Spectral probe transmission at 2.12 THz (black curve) and 2.25 THz (red curve) as a function of the seed-probe delay and are correspondingly color-coded in (e) with black/red dashed lines. Both spectral probe transmissions at 2.12 THz and 2.25 THz exhibit a phase shift to each other. (b), (c), (d) Spectral probe transmission for a fixed seed-probe delay. The seed- probe delays of the figures (b), (c) and (d) are color-coded and are indicated by the corresponding color-coded arrows in (a). In case of (b) with a seed-probe delay of 334.20 ps, the probe transmission is peaked at 2.12 THz where as the probe transmission at 2.25 THz is almost zero. For the case (c) with a seed-probe delay of 335.28 ps, both the spectral probe amplitudes (at 2.12 THz and 2.25 THz) are equal. In case of the figure (d) with a seed-probe delay of 336.72 ps, the main laser frequency is zero while the mode at 2.25 THz has a maximum spectral probe transmission. (e) Contour plot of the spectral probe transmission for the seed-probe delay varying from 334 ps to 337 ps. The spectral probe transmission is color-coded and has a periodic pattern that is separated by gain holes with a periodicity of 0.46 ps (2.1 THz).
50 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS probe transmission at 2.12 THz and 2.25 THz is maximum, equal or minimum, in Fig 4.3 (b), (c) and (d). In Fig. 4.3 (b), the seed-probe delay is 334.13 ps, where the probe transmission spectrum is mainly composed of a single frequency (2.12 THz). For a seed-probe delay of 335.70 ps (Fig. 4.3 (c)), the spectral probe components are distributed equally around 2.12 THz and 2.25 THz. In the case of Fig. 4.3 (d) (for a delay of 336.72 ps), the spectral probe transmission at 2.12 THz is nearly zero and the probe transmission is shifted to 2.25 THz. A spectral hole is clearly visible at 2.12 THz. In all spectra of Fig. 4.3 (b), (c) and (d) the background from the photoconductive antenna is the same. Fig. 4.3 (a) is a slice of Fig. 1.1 (e) along the seed-probe delay axis. This is indicated and correspondingly color-coded with dashed lines in Fig 4.3 (e). Fig. 4.3 (b), (c) and (d) are also slices of Fig. 4.3 (e) for fixed seed-probe delay as mentioned above. Fig. 4.3 (e) is a matrix plot and shows the spectral probe transmission from 1.8 THz to 3.5 THz as a function of the seed-probe delay. The spectral probe patterns have a periodicity of 2.12 THz, which is within the measurement resolution of the maximum probe frequency. The probe patterns are separated by spectral/spatial holes. It is also observed that the highest probe amplification at 2.14 THz starts to shift to higher frequencies, which is also periodic. This shift is marked with white arrows for the corresponding seed-probe delay.
Simulation: Two-level model
To investigate the observed gain oscillations on ps and fs time scales, simulations based on the density matrix formalism are performed. The simulation is based on a two level model where parameters such as lifetime and dephasing are considered for both the upper and the lower laser states. In Fig. 4.4 shows the simulation results for a 2 mm long laser cavity, as used in this experiment. More details on the theoretical part of the simulation are found in the methods section. Fig. 4.4 (a), (b) and (c) show the electric field in the cavity for particular times and Fig. 4.4 (a), (b) and (c) are the corresponding population inversions. The QCL cavity is surrounded by air, which is denoted by shaded areas in Fig. 4.4. As soon as the THz seed enters the cavity, the population inversion starts to increase. This is
51 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS comparable to the experiment in the sense that the population inversion is caused by the applied RF pulse. The rising time of the RF pulse, which is applied to the QCL and the build-up time of the population inversion in the cavity are not neces- sarily equal to each other. Fig. 4.4 (a) shows the injected THz pulse, 13 ps after entering the QCL cavity. Due to the 2 mm long cavity, the THz pulse is located in its middle. In Fig. 4.4 (a) within 13 ps, the population inversion builds up to 70% and has a small minimum of 0.02% at the position of the THz seed pulse. The small minimum in the population inversion is caused by the presence of the THz seed pulse. After several round-trips in the cavity, the electric field distribution and the corresponding population inversion are shown in Fig. 4.4 (b) and (b). Dur- ing 365 ps, the small injected-THz seed pulse is amplified and the resulting electric field is distributed along the whole QCL cavity. The distributed electric field in the cavity is a superposition of forward and backward propagating THz pulses, which originate from reflections at the laser facets. The electric field in the cavity mod- ulates the gain, which results in a population grating with a modulation depth of up to 50% (Fig. 4.4 (b) and (c)). The modulation frequency of the population grating corresponds to the frequency of the QCL intensity, as shown in the inset of Fig. 4.4 (b) and (c) where both the electric field and the population inversion are spatially superimposed. Fig. 4.4 (c) and (c) show the electric field and the popula- tion inversion in the cavity a half round-trip time later. The situation is symmetric to the previous case (Fig. 4.4 (b) and (b)). It can be seen that the envelope of the electric field and the population inversion are moving with time but the elec- tric field and the gain grating (population grating) are visualized as standing waves with fixed nodes in space. The gain grating is only present when the electric field is distributed along the entire cavity. In order to understand the influence of the injected THz probe (and hence the experimental data), the simulation is extended by adding a small THz probe pulse into the system. Fig 4.5 (a) shows the electric field (green curve) in the cavity, which originates from the amplified seed. The in- jected THz probe (blue curve) enters the cavity from the left facet. The induced probe population inversion (or rather the difference of the population inversion with and without the probe) is plotted in red. When propagating through the cavity, the
52 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
Figure 4.4: Electric field distribution and population grating: (a), (b) and (c) show the electric field distribution and (a), (b) and (c) the population inversion in the 2 mm long cavity, which is surrounded by air (indicated with the shaded regions). (a) Electric field distribution of the injected seed 13 ps after entering the cavity. (a) Population inversion in the cavity: During 13 ps, the population inversion increased up to 70% and has a minimum at the seed position (zoomed-in). (b) After several round trip times in the cavity, the seed is amplified and the electric field is distributed along the whole cavity. The electric field is a superposition of the forward and backward propagating waves resulting from the reflection at the cavity-air interface. (b) Population inversion in the cavity 365 ps after the seed injection: At this time the system reached the steady state regime. Because of the high field strength, the population inversion is modulated up to 50%. Due to the distribution of the electric field along the 2 mm cavity, the gain/population grating is present along the whole cavity. The inset shows superimposed electric field and the population inversion. The gain/population grating has a twice-higher frequency because it is modulated by the electric field intensity. (c)/(c) Electric field distribution and the population inversion, a half of the round trip time later compared to (b)/(b). The electric field and the population inversion are symmetric as compared to (b)/(b). Only the envelop of the electric field and the population inversion is moving with the group velocity, the nodes are fixed in space.
53 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS probe pulse experiences amplification. The probe amplification is manifested in the tails of the probe transmission. This is seen in Fig. 4.5 (b) and (c). For all times in the cavity, the probe-induced population inversion is approximately 2 % (at the probe position). In contrast to Fig. 4.5 (a), (b) and (c), the probe is delayed by 125 fs in Fig. 4.5 (d), (e) and (f). For these cases, the injected probe is plotted in black. For all times in the cavity, the black probe pulse induces a change in the population inversion, which is below 2 % (at the probe position). The differences in the induced population inversion (in Fig. 4.4 (a)-(c) and (d)-(f)) originate from the phase difference of the probes and the QCL electric field. By recording the probe transmission outside the QCL cavity (shown in Fig. 4.5 (g)), the difference in probe waveforms is visible from 5 to 20 ps of the recorded probe waveforms. To compare the transmitted probes, an FT is applied to the probe waveform portion that originates from the QCL amplification (marked in Fig. 4.5 (g) with the dashed rectangle). The spectrum of both probes is shown in the inset of Fig. 4.5 (g). The peak of spectral amplitude of the blue probe transmission is almost four times higher than that of the black one. The difference in the spectral amplitudes comes from the different injection times of the probe. The probe and the amplified THz seed are phase-locked. Depending on the phase relation between the QCL field in the cavity and the probe pulse, the electric fields interfere constructively or destructively. Even small changes in the phase introduced by the seed-probe delay become easily visible, because the probe amplification occurs along the whole QCL cavity. By fixing the spectral peak amplitude of the probe transmission and plotting it over the seed- probe delay (Fig. 4.5 (e)), time-resolved access to the QCL gain dynamics becomes possible. The modulation of the probe spectral amplitude, which is observed in the experiment (Fig. 4.2 (d)) can also be investigated with simulations. The spectral probe transmission at 2.14 THz for 6 ps window of the seed-probe delay with a 50 fs time step is simulated. An FT applied to the simulated probe transmission is shown in Fig. 4.5 (i). The experimental data (Fig. 4.2 (c)) and the simulation results (Fig. 4.5 (i)) reproduce the modulation of the spectral probe transmission at the lasing and the QCL intensity frequency, although the peak ratio in the simulation results is inverted as compared to the experimental results. Possible reasons for this
54 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
Figure 4.5: (a)-(f) QCL E-field in the cavity (green curve) in the saturation regime. Injected probe (blue/black curves) and the induced population inversion (red curves) with and without the probe. (a), (b) and (c) shows the probe propagation in the cavity and hence induce a population inversion of nearly 2 % for all times. In (d), (e) and (f) the probe is on the same position in the cavity like in (a), (b) and (c) but has a time delay which is introduced by seed-probe delay of 125 fs. The population inversion, induced by the black probe for all times is less than 2 %. (g) The probe transmission recorded outside the cavity. The inset shows the probe spectra of the amplified probe waveforms for the region marked with dotted rectangle. (h) Seeded QCL emission (green curve) recorded outside the QCL cavity and the peak of the spectral amplitude (red curve) as a function of a seed-probe delay. (i) FT of the spectral probe transmission at 2.14 THz.
55 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS discrepancy could be material dispersion and the electric field distribution in the cavity, which are not taken into account by the simulations. By comparing Fig. 4.5 (h) and Fig. 4.2 (a), it is seen that the simulated field is not as dispersive as the mea- sured field. Nonetheless, the frequencies at which the spectral probe modulations occur are identical for the simulations and measurements. Thus, the time-resolved QCL gain dynamics are in a good agreement with the measured data in Fig. 4.2 (a) and the FT of the spectral probe amplitude is explained in a qualitative manner.
Discussion:
The Phase Seeding-Phase Probing technique enables the time-resolved gain dynam- ics to be studied in solid-state lasers. The experimental results of the gain trace (Fig. 4.2) (where the spectral probe maximum is plotted as a function of internal QCL E-field) are modeled and are in good agreement with the theory presented in Fig. 4.5 (h). The rapid oscillations on fs time scales of the probe amplification originate from interference of the probe and the QCL electric field. In order to observe this effect, the phase of the QCL and the probe must be locked. Even small changes in the phase difference between the probe and the electric field are visible. While the probe propagates in the cavity, the probe waveform with a fixed phase difference is amplified. This is seen in Fig. 4.2 (c) where a few fs delay results in a large change of the spectral probe transmission. It is possible to observe this effect since the QCL is phase-locked and thus the existing gain-grating (population-grating) in the cavity can be calculated (shown in Fig. 4.4). The rapid spatial gain oscillations are modulated at two frequencies, corresponding to the lasing frequency (at 2.14 THz) and the intensity of the electric field (at 4.28 THz). Due to fast laser dynamics, it is not surprising that the gain follows the laser intensity. Such qualitative results are observed in the simulation only if the lifetime of the lower laser state is introduced. This indicates that the lifetime of the lower laser state plays an important role in the nonlinear gain dynamics. On time scales that are comparable with the round-trip time, the spectral gain has a minimum when the QCL electric field has its maximum (see Fig. 4.2 (b)). The spectral peak gain recovers within 20 ps. This is in a rough agreement with the experimental and simulation results observed by Freeman et
56 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
al. [11] of 12 ps and Green et al [12] of 50 ps, respectively. Not only the spectral probe maximum, but also the complete time-dependent probe and hence the gain spectrum is analyzed in this work. The time dependence of the gain spectrum re- veals phenomena such as gain bleaching and gain shifting on ultrafast time scales. Furthermore, the developed model, which includes the QCL electric-field and the probe field can be used for optimization and investigation of active mode locking where the gain recovery dynamics and the group velocity dispersion (GVD) are a few dominant mechanisms limiting the THz pulse shape. More generally, due to the phase-locked probe and electro-optical probe detection, this method can be used for nonlinear and 2D spectroscopy of solid-state lasers.
Methods:
Laser design
A 2 mm long molecular beam epitaxy grown THz QCL is used for the experiment. It is processed as a surface plasmon waveguide. The active region is based on GaAs/AlGaAs bound-to-continuum design and consists of a chirped periodic sup- perlattice. The laser emission is centered at 2.14 THz with a gain bandwidth of 100 GHz. The QCL is indium bonded on a gold-coated oxygen-free copper sub-mount to ensure effective heat sinking. For this experiments, the QCL is cryogenically cooled down to 10 K. Time domain Spectroscopy Setup: The time domain spectroscopy setup used in this work is described in previous chapter and in [15]. A laser beam generated by a Ti:Sapphire laser is splitted into three beams. One of the beams is used for electro-optic sampling. The remaining two beams are used for the THz generation. In comparison to [15], the two THz pulses are generated by NIR illu- mination of two photoconductive antennas that are processed on the same wafer die. This enables separate electrical modulation and hence a better signal-to-noise ratio. The duration of the NIR pulses is 80 fs long with a center wavelength of 790 nm. Four 90◦ off-axis parabolic mirrors are used for focusing and collecting the THz radiation. A 2 mm ZnTe crystal is used for electro-optical detection.
57 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
Two-level model: Simulation In order to study the time-resolved light-matter interaction, the density matrix approach was used [11, 17]. For this the Liouville von Neumann equation is solved, which describes how the density operators evolve in time: ∂ρ i = − [H, ρ] − Γ, (4.1) ∂t h¯ where ρ is the density operator, H is the system Hamiltonian, is the dephasing matrix and is the Planck constant. The Hamiltonian H, the dephasing matrix , and the density matrix ρ used for the simulation are given by: ρUU ρUL h¯ ωUL 2ΩE τ − T ρUU ρUL H = , Γ = U 2 , ρ = . 2 ρLU ρLL 2ΩE −ωUL − ρLU ρLL T2 τL
MULE Ω = ¯h where MUL is the dipole matrix element for the two level system. τU and τL are the life times of the upper and the lower laser state and T2 is the de- phasing time andhω ¯ UL is the energy difference between the upper and lower level
(ωUL = ωU − ωL). It is an open two level system. ρUU /ρLL is the population of the ∗ upper/lower laser state and ρUL = ρLU is the system dephasing. Eq. 4.1 is split into real and imaginary parts by applying the following transformations: ρ − ρ ρ ≡ a b LU 2 for the real part and ρ + ρ ρ ≡ a b UL 2 for the imaginary part. Using the above transformations, eq. (1) can be now rewritten in terms of the real components ρa and ρb and the population inversion w = ρUU − ρLL. The total population of the system is set equal to Nw where is N the number of electrons per unit volume in the upper and lower laser state. Note that this requires that ρUU + ρLL = 1. The resulting equations are listed below:
∂ρa ρa = ωULρb − ∂t T2 ∂ρb ρb = −ωULρa + 2ΩEw − ∂t T2 ∂ρUU ρUU = R − ΩEρb − ∂t τU ∂ρLL ρUU ρLL = ΩEρb + − ∂t τU τL
58 CHAPTER 4. PHASE SEEDING-PHASE PROBING TECHNIQUE FOR INVESTIGATION OF ULTRAFAST TIME-RESOLVED LASER DYNAMICS
R is the pumping rate and is set to R = ρUU for the steady state regime. In order τU to calculate the electric field in the entire cavity, the following Maxwell equations are solved:
∂H ∂E µ x = − z ∂t ∂y E ∂H ∂P (E , ρ) z = − x − z , ∂t ∂y ∂t where µ (permeability) and (permittivity) are position dependent material param- eters. H and E are the magnetic and electric field vectors, respectively. The electric
field interacts with the two level system via the Ez component. The polarization, P can be expressed in terms of the coherences of the density matrix components
(P = −NMUL(ρUL − ρLU ), see [11, 17]. The resulting coupled Maxwell and the density matrix equations are solved numerically. For calculating the electric field, the finite-difference time-domain method (FDTD) [18] is used, which has a leap-frog time stepping scheme. In the first time-step the magnetic field is calculated from the electric field values of the previous time-step. In the second time-step, the elec- tric field values are found from the previous magnetic field value and the current polarization. During this time step, the density matrix elements are also updated. The updates for both the electric field and density elements depend on each other in a nonlinear manner. This prevents the updates from being written in terms of their previous values and requires a predictor-corrector method [11].
Symbol Unit Description
τU 10 ps Lifetime of the upper state
τU 3 ps Lifetime of the lower state
MUL 6.2 nm [11] Dipole matrix element
ωUL 2.2 THz Laser transition frequency
T2 1 ps Dephasing
nGaAs 3.6 Refractive index of the active medium N 1.4 ·1020 cm−3 Number of electrons per unit volume
Table 4.1: Parameters used for the two level model
59 BIBLIOGRAPHY BIBLIOGRAPHY
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62 Chapter 5
Nonlinear spatial gain grating in THz Quantum Cascade Laser
Abstract
In this work, a method for the investigation of nonlinear gain dynamics in injection seeded THz quantum cascade laser (QCL) is reported. A THz seed pulse is used to injection seed a THz QCL, which is amplified in the laser cavity. After multiple round-trips in the cavity, the amplified pulse (pump-pulse) is probed with a sec- ond weak THz probe pulse. Due to the time-resolved measurement, the QCL gain dynamics can be studied in both the time and frequency domains as a function of the electric field strength. Complex spectral probe gain behavior is observed that is dependent on the electric field strength. This gain behavior is a manifestation of system non-linearities.
63 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
Recently it has been demonstrated that quantum cascade lasers (QCLs) are poten- tial candidates for frequency shifters in optical fiber networks [1–5]. Optical fiber networks are used for data transmission of communication signals over both short (on the order of centimeters) and long (intercontinental) distances. The main task of a frequency shifter is to shift the optical pulse to higher or to lower frequencies. This allows a greater optical bandwidth to be utilized and more information to be sent through the optical network. Frequency shifting of near infrared (NIR) pulses can be achieved in QCLs by using the nonlinearities in the active medium. The frequency of intraband NIR light is down or up converted by multiples of the THz lasing frequency. In experiments, resonant interband nonlinearities of the QCL are excited with a NIR laser and the lower NIR side-band (ωNIR-ωT Hz) are detected.
The upper side-band (ωNIR + ωT Hz) is almost absorbed in the laser. This effect is assigned to the second order susceptibility (χ2) and has a conversion efficiency of 0.13% [1]. In addition to second order nonlinearities, third order nonlinearities (χ3) were also observed in QCLs [2,6]. There are also conversion effects that are based on the intersub- band nonlinearities through intracavity difference-frequency [7–10] generation as well as the sum [11] of two NIR pulses. In order to observe second order intersubband nonlinearities, the inversion symmetry of the system must be broken [12]. This is automatically achieved in QCLs when a bias is applied. These non- linearities can be further enhanced by growing asymmetric quantum wells [13, 14], using coupled or uncoupled quantum wells, breaking the symmetry with quantum Stark effect [15] and hence having control over the nonlinearities . One way to study nonlinearities is to perform two dimensional spectroscopy (2D spectroscopy). Two dimensional spectroscopy utilizes pump-probe measurement techniques. In contrast to conventional pump-probe experiments, phase information is obtained. This al- lows Fourier transformations of the data into the frequency domain. Two Fourier transforms can be taken with respect to time scales associated with a pump and probe. This allows spectral information to be plotted as a contour function of two frequency axes. This is the approach chosen for this work. The terahertz time do- main system used in this work records the electric field of the pump and the probe as a function of time, which makes 2D spectroscopy possible.
64 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
In this Chapter, the gain dynamics of a THz QCL are studied as a function of the time delay between a seeded QCL field and a probe pulse delay. Over the round-trip time of the laser, the seeded QCL field varies as a function of time due to multi-mode effects. This allows the data to be investigated as a function of a THz field strength. Modulations at multiple frequencies (with respect to time-delay) of the probe trans- mission are observed and studied via 2D spectroscopy. These modulations of the spectral probe transmission are assigned to QCL intersubband nonlinearities. The experimental setup used for this experiment is similar to those described in previous chapters and is sketched in Fig. 5.1 (a). In order to investigate the laser dynamics as a function of the laser field intensity, the QCL is injection seeded with a broad-band THz pulse and probed with a second broad-band THz pulse. There are two main differences with the experiments in chapter 4. The first difference is that the range of delay times is larger than the round trip time. The second difference is that the QCL laser has a wider gain bandwidth (see for comparison insert of Fig. 1.1 (b) and Fig. 5.1 (b)). Because of this, the measured QCL field has significantly larger variations in the electric field. The amplified THz seeded pulse (which is considered as the pump in this experiment) is shown in Fig. 5.1 (b). The zero time of the recorded QCL waveform corresponds to the injection of the THz seed pulse into the left QCL facet. This time is denoted as the absolute time
tabs. The corresponding QCL electric field, shown in Fig. 5.1 (a), is a function of the absolute time EQCL(tabs). The peaks of the QCL emission waveform occur at multiples of the round-trip time. The amplitude of the peaks roughly follows the applied RF pulse shape, which is superimposed on the data in Fig. 5.1 (b) (black curve). The spectrum of the QCL waveform is shown in the insert of Fig. 5.1 (b) and is calculated by performing the Fourier transform:
Z tabs=750ps −iωabstabs |FQCL(ωabs)| = | EQCL(tabs)e dtabs|. tabs=0ps The spectral amplitude of the QCL field is peaked at 2.2 THz with a bandwidth of approximately 150 GHz. To probe the gain of the THz QCL, the second THz pulse is injected and the first pass through the cavity is recorded. The probe transmission
is recorded in the saturation regime of a QCL (from tabs=345 ps to tabs=435 ps). In this scanning region the intensity in the QCL cavity varies from the round-trip
65 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
Figure 5.1: (a) Experimental setup for injection seeding and gain probing of a THz QCL. The RF pulse is locked to the repetition rate of a Ti:Sa laser and is used for gain switching the QCL. (b) The injection seeded waveform is shown in green and the superimposed RF pulse shape in black (insert: FT of the QCL waveform). Red arrows in the RF pulse shape indicate the seed and the probe position. The red-dashed rectangle indicates the time period over which the probe transmission is recorded. (c) Spectrum of the probe transmission (insert: probe waveform in the time domain). The red-marked oscillations of the waveform correspond to the QCL gain spectrum and the green oscillations to the broad-band antenna spectrum.
66 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER maximum value to almost zero and then back to the next round-trip maximum. The experiment is performed by varying the seed-probe delay (tdelay) in steps of 0.05 ps
(∆ tdelay=0.05 ps) and recording the probe waveform for each step. These small time steps enable the observation of seed-probe frequency (ωdelay) modulations of up to
10 THz. The detection of the probe transmission (Eprobe(t)) and the QCL seeded emission (EQCL(t)) is realized with electro-optic sampling. The recorded electric field of the probe is denoted with two variables. These are the seed-probe delay
(tdelay) and the probe time (tprobe). The seed-probe delay (tdelay) refers to the time delay between the QCL E-field and the probe. The probe time (tprobe) is the time axis for the detection of the probe electric field. The insert in Fig. 5.1 (c) shows an example of a sampled probe waveform for a seed-probe delay of tdelay=350 ps. The spectrum of the probe transmission is shown in Fig. 5.1 (c) and is calculated as:
Z tprobe=13ps |Fprobe(tdelay = 350ps, ωprobe)| = | Eprobe(tdelay = 350ps, tprobe)· tprobe=6ps
−iωprobetprobe e dtprobe|
Only the red-marked oscillations (from tprobe=6 ps to tprobe=13 ps) in the insert correspond to the probe spectrum in Fig 5.1 (c). The green oscillations in Fig. 5.1 (c) originate from the broad-band antenna. These oscillations are not of interest, because they are not caused by the QCL amplification and hence these oscillations do not contain any information on the QCL dynamics. The QCL used for this experiment has a slightly larger gain bandwidth than the QCL from the previous chapter. This allows us to study the gain dynamics as a function of seed-probe delay tdelay (QCL intensity) for the following spectral probe components: ωprobe=2.09 THz,
ωprobe=2.17 THz, ωprobe=2.25 THz and ωprobe=2.33 THz (see Fig. 5.1 (c)). For every recorded probe waveform the above mentioned spectral probe components are plotted versus the seed-probe delay tdelay (Fig. 5.2 (b)-(e)). Fig 5.2 (a) shows the electric field of the THz QCL for the corresponding seed-probe delay times. There are two inserts in each Fig. 5.2 (b)-(e). These are the zoom- in regions from tdelay=350 to tdelay=352.5 ps and from tdelay=360 ps to tdelay=362.5 ps. From the zoomed-in windows it can be seen that each spectral probe component has a multi frequency modulation along the seed-probe delay axis tdelay. In order to investigate which modulation frequencies are present in each spectral probe components, a
67 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
Fourier transform of each spectral probe component is performed along the seed- probe delay time axis:
Z tdelay=435ps |Fprobe(ωdelay, ωprobe = 2.33 T Hz)| = | Eprobe(tdelay, ωprobe = 2.33 T Hz)· tdelay=345ps
−itdelayωdelay e dtdelay|,
Z tdelay=435ps |Fprobe(ωdelay, ωprobe = 2.25 T Hz)| = | Eprobe(tdelay, ωprobe = 2.25 T Hz)· tdelay=345ps
−itdelayωdelay e dtdelay|,
Z tdelay=435ps |Fprobe(ωdelay, ωprobe = 2.17 T Hz)| = | Eprobe(tdelay, ωprobe = 2.17 T Hz)· tdelay=345ps
−itdelayωdelay e dtdelay|,
Z tdelay=435ps |Fprobe(ωdelay, ωprobe = 2.09 T Hz)| = | Eprobe(tdelay, ωprobe = 2.09 T Hz)· tdelay=345ps
−itdelayωdelay e dtdelay|.
The Fourier transform of the spectral probe components are shown in Figs. 5.2 (b)-(e). The inserts in Figs. 5.2 (b)-(e) are the zoomed-in regions from 5 THz to 9 THz that show the presence of higher order frequency components. Each spectral probe component is mainly modulated at the 1st, 2nd and 3rd harmonics of the laser frequency. The spectral probe components at ωprobe=2.17 THz and ωprobe=2.25 THz also show a modulation around ωdelay=5.3 THz that is not a multiple of the main lasing frequency of the THz QCL. These spectral probe oscillations are observed in the injection seeded QCL for the first time. Till now these physical phenomena have not been reported in THz QCLs. The appearance of the spectral gain modulation at ωdelay=5.3 THz is quite unexpected and is still under investigation. It could be attributed to transitions within the intersubband energy levels that are coherently coupled to the laser transition. Also the origin of gain modulation of each spectral probe component is very intriguing. These phenomena are analyzed and discussed in this chapter. The 2nd harmonic can be understood as a manifestation of the spatial modulation of the spectral gain inside the laser cavity. This spatial modulation is
68 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
Figure 5.2: (a) A segment of the electric field waveform of Fig. 5.2 (b) from 0.345 ns to 0.435 ns over which the gain is probed. (b)-(e) Spectral probe component of the probe transmission at ωprobe=2.33 THz, ωprobe=2.25 THz, ωprobe=2,17 THz and ωprobe=2.09 THz, respectively. These spectral probe components of the probe transmission are shown in Fig. 5.2 (c). The inserts in (b)-(e) show the zoomed-in region of each spectral probe component from 350-352.5 ps and 360-362.5 ps. (b)-(e) To identify the frequency components that contains in (b)-(e) the FT of the (b)-(c) is performed. The inserts in (b)-(e) is the zoomed-in region from 5 to 9 THz. produced by the formation of standing waves in the laser cavity. Since the intensity of the standing waves, which is the square of the electric field, modulates the spectral gain, this modulation occurs at twice the laser frequency. Due to the existence of other nonlinearities in the system, the spectral gain modulation can also be present
69 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER at other multiple frequencies. If the observation in Figs. 5.2 (b)-(e) is a nonlinear effect, the modulation frequencies (1st, 2nd and 3rd harmonics) must depend on the electric field strength. In order to verify this hypothesis, a short-time Fourier trans- form (STFT) (short time Fourier transform) with a rectangular window function width of 5ps is applied to each spectral probe component. The window function is slided continuously over the full data range (from tdelay=345 ps to tdelay=435 ps). The data treatment of STFT can be written as: Z ∞ 0 0 |H(tdelay, ωdelay)| = | w(tdelay − tdelay) · |Fprobe(tdelay, ωprobe = const.)|· −∞ 0 −iωdelaytdelay 0 e dtdelay|,
0 w(tdelay −tdelay) is a rectangular window function which is slided along the seed-probe 0 delay axis tdelay along the function |Fprobe(tdelay, ωprobe = const.)| for a constant probe frequency ωprobe. In general the square of the resulting function |H(tdelay, ωdelay)| is a spectrogram. The general equation above is applied to Fig. 5.2 (b)-(e) and evaluated
st nd rd for the 1 , 2 and 3 harmonics (ωdelay=2.2 THz, ωdelay=4.4 THz and ωdelay=6.6 THz). The results of STFT are plotted in Figs. 5.3 (a)-(d) as a function of the seed- probe delay tdelay and hence as a function of QCL intensity for each spectral gain component. The intensity dependence of the spectral probe modulation for the 1st,
nd rd 2 and 3 harmonics are shown in Fig. 5.3 (a) for a frequency ωprobe=2.33 THz, Fig.
5.3 (b) ωprobe=2.25THz, Fig. 5.3 (c) ωprobe=2.17 THz and Fig. 5.3 (d) for ωprobe=2.09 THz of the spectral probe component. From now, the main focus will lie on the probe components at ωprobe=2.17 THz (Fig. 5.3 (c)) and ωprobe=2.25 THz (Fig. 1.3 (b)), because these are the probe components with the highest STFT amplitude. Fig. 5.3
(b) and Fig. 5.3 (c) shows completely different dynamic behavior from tdelay=345 ps to tdelay=435 ps, where the field intensity is maximum. Both spectral probe components are modulated with the 1st, 2nd and 3rd harmonics. In Fig. 5.3 (b) the amplitude of STFT for the fundamental frequency is recovering where as in Fig. 5.3 (c) it is saturating and achieves its minimum at the QCL peak intensity. After the peak intensity (after tdelay=350 ps), the STFT amplitude for the modulation of the fundamental laser frequency (Fig. 5.3 (b)) is decreasing while it is increasing in
Fig. 5.3 (c). This process is of opposite nature till tdelay=365 ps and for later time behaves similarly where the field intensity is not so high. The general behavior of the
70 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
STFT amplitude for the 2nd and 3rd harmonics are similar. The STFT amplitude for the 2nd and 3rd harmonics decreases in the presence of a strong electric field. An important observation is that the spectral STFT amplitude modulation ratio of the 1st and 2nd harmonics can be inverted in the presence of strong electric field (see
Fig. 5.3 (c) at tdelay=350 ps and Fig. 5.3 (b) at tdelay=360 ps). From the presented data in Fig. 5.3 (a)-(d) it can be seen that the STFT amplitude modulation is a complicated physical phenomenon. It is different for each spectral probe component and is additionally intensity dependent. Thus it becomes necessary to develop a model that can explain the observed results in order to gain deeper understanding of this physical behavior. One of the helpful ways to analyze the data, is to present it in a two dimensional contour plot as shown in Figs. 5.3 (e)-(f). This can be realized by performing a two dimensional Fourier transform of the recorded probe
waveform Eprobe(tdelay,tprobe) for Fig. 5.3 (e):
Z tdelay=390ps Z tprobe=13ps |Fprobe(ωprobe, ωdelay)| = | Eprobe(tdelay, tprobe)· tdelay=345ps tprobe=6ps
−i(ωdelaytdelay+ωprobetprobe) e dtprobedtdelay| and for Fig. 5.3 (f)
Z tdelay=435ps Z tprobe=13ps |Fprobe(ωprobe, ωdelay)| = | Eprobe(tdelay, tprobe)· tdelay=390ps tprobe=6ps
−i(ωdelaytdelay+ωprobetprobe) e dtprobedtdelay|
Figs. 5.3 (e)-(f) show a color-coded 2D spectral probe amplitude as a function of the spectral probe frequency ωprobe and seed-probe frequency ωdelay. Figs. 5.3 (e)/(f) are matrix plots of the data in Figs. 5.3 (b)-(e) from (tdelay=345 ps to tdelay=390 ps)/( tdelay=390 ps to tdelay=435 ps), respectively. In this representation it is much easier to recognize the modulation frequencies of each spectral probe component. The graphs above the contour plots in Figs. 5.3 (e)-(f) are the slices for a fixed spectral probe component of ωprobe=2.25 THz. Besides the frequency components which are not multiples of the laser frequency it can be clearly seen, that other components modulate the gain as well. However, the observation of such a complicated gain dynamics needs to be explained and understood in more details with theoretical models that are not developed yet. This is one of the possible directions to explore
71 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER and to understand deeper the gain dynamics of a THz QCL in the future.
Figure 5.3: (a)-(d) Sliding Fourier transform of the spectral probe component
ωprobe=2.33 THz, ωprobe=2.25 THz, ωprobe=2,17 THz and ωprobe=2.09 THz of Figs. 5.2 (b)-(e). The window function of the sliding Fourier transform is rectangular with
5 ps width. Only the time evaluation for the seed-probe frequencies of ωdelay=2.2
THz, ωdelay=4.4 THz and ωdelay=6.6 THz are plotted. (e)/(f) 2D plots of spec- tral probe amplitude as a function of the spectral probe frequency ωprobe and the seed-probe frequency ωdelay from (345 ps to 390 ps)/(390 ps to 435 ps) respectively.
72 CHAPTER 5. NONLINEAR SPATIAL GAIN GRATING IN THZ QUANTUM CASCADE LASER
73 BIBLIOGRAPHY BIBLIOGRAPHY
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[2] P. Cavali´e,J. Freeman, K. Maussang, E. Strupiechonski, G. Xu, R. Colombelli, L. Li, A. G. Davies, E. H. Linfield, J. Tignon, and S. S. Dhillon, Appl. Phys. Lett. 102, 221101 (2013).
[3] S. S. Dhillon, C. Sirtori, J. Alton, S. Barbieri, A. de Rossi, H. E. Beere, and D. A. Ritchie, Nat. Photonics 1, 411 (2007).
[4] S. Houver, P. Cavali´e,M. I. A. M. Renaudat St-Jean, C. Sirtori, L. H. Li, A. G. Davies, E. H. Linfield, T. A. S. Pereira, A. Lebreton, J. Tignon, and S. S. Dhillon, Opt. Express 23, 4012 (2015).
[5] C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
[6] J. Bai and D. S. Citrin, J. Appl. Phys. 106, 031101 (2009).
[7] N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, Phys. Rev. Lett. 90, 043902 (2003).
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[9] Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, Appl. Phys. Lett. 101, 251121 (2012).
[10] Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, Opt. Express 21, 968 (2013).
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[12] E. Rosencher and P. Bois, Phys. Rev. 44, 11315 (1991).
[13] M. Gurnick and T. DeTemple, IEEE J. Quantum Electron. 19, 791 (1983).
74 BIBLIOGRAPHY BIBLIOGRAPHY
[14] P. F. Yuh and K. L. Wang, J. Appl. Phys. 65, 4377 (1987).
[15] F. Capasso, C. Sirtori, and A. Y. Cho, IEEE J. Quantum Electron. 30, 1313 (1994).
75 BIBLIOGRAPHY BIBLIOGRAPHY
76 Chapter 6
Outlook
This chapter briefly discusses the ideas and possible realizations of future planned experiments. The concepts and the techniques developed in this thesis can be fur- ther extended for the investigation and a deeper understanding of different QCL structures such as LO-phonon and hybrid designs. Time-resolved investigations of broad-band QCLs, such as octave spanning THz QCLs, are also of great interest, because of their potential use for spectroscopy and metrology applications as well as an understanding of the complex gain dynamics in THz QCLs. The developed density matrix model is a flexible tool that can be extended to simulations of active mode locking and continuous-wave (CW) seeding experiments. With this model, the influence of different parameters on the QCL dynamics and the emission properties can be studied independently. Unfortunately it is not possible to independently vary laser parameters, such as individual life-times and dephasing time, in the ex- periments. Models based on two, three, and four or more laser energy states can be studied and compared with each other. The advantage of the model is that the electric field distribution can be calculated not only outside the cavity (which is measured in the experiments) but also inside the cavity as a function of space and time (which cannot be measured in the experiments). The model takes several ef- fects into account and can be extended to include other effects such as intersubband nonlinearities, material-, waveguide- and gain-dispersion. A THz time-domain sys- tem has been set up for performing 2D spectroscopy on THz QCL as well as CW injection seeding experiments. In 2D spectroscopy, two THz pulses will be injected
77 CHAPTER 6. OUTLOOK
into the QCL and the QCL emission will be recorded as a function of the double pulse delay in the saturation regime. The recorded data can be represented in a 2D plot (matrix plot) that is comprised of two frequency axes. For the CW modulation experiments, the QCL will be seeded with the narrow-band seed and the amplified QCL emission will be detected as a function of the injected seed frequency.
78 Appendices
79 Appendix A
Design strategy of the photoconductive antenna
80 APPENDIX A. DESIGN STRATEGY OF THE PHOTOCONDUCTIVE ANTENNA
One problem with semi-insulating photoconductive antennas is the difficulty of gen- erating consecutive THz pulses. For THz pulse generation, a NIR pulse creates electron hole pairs in GaAs substrate, which are accelerated in the external field. The acceleration of charges results in the emission of THz radiation. For the genera- tion of second THz pulse, which is separated by view picoseconds from the first THz pulse, it is necessary that charges (electron hole pairs) recombine before the second NIR pulse arrives. Otherwise the charges would screen the external bias field and these results in the small amplitude of second THz pulse. To overcome this difficulty a material with short lifetimes is required. This can be realized with low tempera- ture grown GaAs (LT-GaAs). It is also of interest to increase the THz pulse power. As described in Chapter 3, this is realized by growing a thin layer of LT-GaAs on top of the Bragg mirror. The number N of the Bragg pairs is important to prevent the NIR absorption in the GaAs substrate. The Bragg mirror should reflect the majority (99%) of the incoming laser light in order to prohibit absorption in the GaAs substrate. This prevents the generation of long-lived carriers in the substrate which would otherwise screen the bias field. In order to know the number of Bragg pairs for NIR transmission that is less than 1%, calculations are performed for the structure in Fig. A.1 and are shown in Fig. A.2. The Aluminum content x in the
Bragg mirror is chosen to be 31%, because the Al31Ga69As band gap is large enough to prevent interband absorption of the 800 nm NIR laser pulse. The duration of the NIR pulse is 100 fs and has 10 nm of bandwidth. From the results in Fig. A.1 it fol- lows that 30 Bragg pairs are necessary to have less than 1% absorption in the GaAs substrate. To generate THz pluses with higher power, it is necessary to increase the absorption in the LT-GaAs layer on top of the Bragg mirror. This achieved by constructive interference from reflections between the GaAs/air interface and GaAs/Bragg mirror interface. The absorption in the LT-GaAs layer depends on its optical thickness. Fig. A.3 shows the simulation results for the absorption in the LT-GaAs layer as a function of the optical thickness for N = 5, 10, 15, 20, 25 and 30 Bragg pairs. The absorption coefficient of GaAs at 800 nm is taken to be 1.4 · 104 cm−1 [1]. The simulations are performed with the CAMFR Software [2]. The results show oscillations in the absorption with varying optical thicknesses. This is due to
81 APPENDIX A. DESIGN STRATEGY OF THE PHOTOCONDUCTIVE ANTENNA the constructive and destructive interference in the LT-GaAs layer. Interestingly, nearly 100% absorption can be achieved for 30 Bragg pairs with an optical thickness of 1.75. This is not possible in the bulk GaAs, since the GaAs/air interface reflects nearly 30% of the incident power. The reflected power can be eliminated with the Bragg mirror since reflections from the Bragg interfere destructive with the reflec- tion the GaAs-air interface. For thickness above the absolute absorption maximum this effect breaks down and for very thick optical thicknesses the maximal achievable absorption approaches 70%. This is equal to the absorption in bulk GaAs material. The fabricated photoconductive antenna and the growth structure (growth sheet) are shown in Fig. A.4 and Fig. A.5, respectively.
Figure A.1: Bragg mirror on top of the semi-insulating GaAs substrate. The Bragg pair consists of an alternating sequence of materials (AlGaAs/AlAs) that have dif- ferent refractive indices. The aluminum concentration is chosen to be 31% in order to avoid interband absorption in AlGaAs. The thicknesses of the AlAs and AlGaAs layers are equal to the λ/4 of the excitation wavelength (indicated with red arrows).
82 BIBLIOGRAPHY BIBLIOGRAPHY
Figure A.2: Transmission as a function of wavelength for Bragg mirrors consisting
of N=5, 10, 15, 20, 25 and 30 pairs of AlAs/Al31Ga69As.
Bibliography
[1] J. S. Blakemore, J. Appl. Phys. 53, R123 (1982).
[2] P. Bienstman, Department of Information Technology (INTEC), Ghent Uni- versity, Ghent, Belgium. Available from: camfr. sourceforge. net.[Accessed 1 October 2006] (2006).
83 BIBLIOGRAPHY BIBLIOGRAPHY
Figure A.3: Light absorption at 800 nm as a function of the optical thickness of GaAs for Bragg mirrors consisting of N=5, 10, 15, 20, 25 and 30 pairs of AlAs/Al31Ga69As.
84 BIBLIOGRAPHY BIBLIOGRAPHY
Figure A.4: Fabricated interdigitated photoconductive antennas on top of the Bragg mirror and the LT-GaAs with a finger spacing of 5 µm.
85 BIBLIOGRAPHY BIBLIOGRAPHY
Sample: 14599 Material: GaAs
Orientation: (100)
Wafer: WV/23596/Un17
Rotation: 4
Pressure (Torr): 4.6 x 10-8
Date: 16.07.2014
File: 14599.csv
300K 77K 4.2K 1K µ [cm2 / Vs] dark n [cm-2]
µ [cm2 / Vs] illum n [cm-2]
Layer Loop T [°C] Dur. [s] Thickn. [nm] Cells (°C) GaAs 692.0 500.3 100 As-LF 390 °C AlAs Start: 30x 692.0 22.2 2 As-UF 700 °C
Al0.31Ga0.69As End 692.0 6.9 2 Al 1097 °C AlAs Start: 30x 692.0 739.8 66.6 Ga-LF 1010 °C
Al0.31Ga0.69As End 692.0 201.2 58.3 Ga-UF 800 °C GaAs 300.0 1357.9 271.4
Comment LT-GaAs Bragg-Mirror
T(pyro) = 630°C As: 67% pF: 7.9e-6 Torr
Degased by 700°C Tsub
Annealed at 600°C Tpyro
(Grown by S. Scholz)
Angewandte Festkörperphysik, Ruhr-Universität Bochum, Germany
Figure A.5: Growth sheet of the Bragg mirror and the LT-GaAs layer on top.
86 Appendix B
Electronics used for the injection seeding experiments
87 APPENDIX B. ELECTRONICS USED FOR THE INJECTION SEEDING EXPERIMENTS
The electronics used for the injection seeding experiments are shown in the block diagram of Fig. B.1. A photodiode with a fast response is used for the generation of high frequency (RF) electrical pulses. Every laser pulse generates one RF pulse. The generated RF pulse is sent to an RF amplifier and is then divided into two equal RF pulses. The first RF pulse is used for biasing the THz antenna, and the second one is used for biasing the QCL. The delay between these RF pulses is controlled with a programmable electronic delay in steps of 10 ps. The RF pulse that is sent to the THz antenna first passes through a digital attenuator and then the RF amplifier. The amplitude of the voltage pulses across the THz antenna is controlled by the digital attenuator. With the help of the electronic delay line, the incoming laser pulses and the RF pulses can be applied to the THz antenna at the same time for efficient generation of THz pulses. The second RF pulse is sent to the comparator. The incoming RF pulse is a trigger for the comparator. The comparator generates a square RF pulse with a constant amplitude and adjustable duration. The square RF pulse is amplified and superimposed with quasi-DC signal (of a few kHz). The quasi DC signal is generated from a function generator and is used as the input (Vinput) of the quasi DC amplifier LT1210. The LT1210 amplifier is a voltage amplifier which is able to drive up to 1.1 A of current in CW. The input voltage signal is amplified with a factor of 3.2 (1+22kΩ/10 kΩ) and is applied across the serial connection of the QCL and 1Ω resistor. The current of this amplifier comes from the power supply of the amplifier, not from the function generator. The series connection of 1 resistor and the QCL makes possible to measure directly the voltage across the
QCL. By monitoring the voltages V1Ω + VQCL and VQCL with the oscilloscope, the
QCL current (IQCL) can be calculated by subtracting V1Ω + VQCL from VQCL and diving by 1Ω. Superposition of a quasi-DC voltage and the RF pulses is necessary for the injection-seeding experiments, because the RF pulses are not strong enough to bias the QCL above the threshold by themselves.
88 APPENDIX B. ELECTRONICS USED FOR THE INJECTION SEEDING EXPERIMENTS
Figure B.1: Schematic of the electronics for the injection seeding experiments. Short RF pulses are generated by illumination of the fast photodiode with laser pulses. Generated RF pulse is divided in two RF pulses. One for driving the THz antenna and the second one is superimposed with the quasi DC signal for biasing the QCL.
89 Appendix C
THz Quantum Cascade Laser used for the experiments
90 APPENDIX C. THZ QUANTUM CASCADE LASER USED FOR THE EXPERIMENTS
The figure below shows the THz QCL laser used for the experiments in Chapter 5. Fig. C.1 (a)-(b) show the gold-coated oxygen-free sub mount and indium boded QCL on it. The QCL is electrically connected via bond-wires to the SMA connector. Fig. 1 (c) shows the facet into which the THz pulses are coupled. Fig. C.1 (d) is a zoomed-in view of the circled region of Fig. C.1 (c). The band diagram of the THz QCL is calculated and shown in Fig. C.2. The upper laser level (square of the wave function) is marked in red and the lower laser level in black. The energy difference of these two levels corresponds to the energy of the emitted photon. The growth sheet of this THz QCL is attached below (Fig. C.3)
Figure C.1: (a)-(b) Top-view of the THz QCL on a gold-coated sub mount that is electrically connected to the SMA connector. (c)-(d) Side-view of the THz QCL facet in to which the THz pulses generated from the antenna are coupled in.
91 APPENDIX C. THZ QUANTUM CASCADE LASER USED FOR THE EXPERIMENTS
Figure C.2: Energy band diagram of the THz QCL for an applied electric field of 1.9 kV/cm−1.
92 APPENDIX C. THZ QUANTUM CASCADE LASER USED FOR THE EXPERIMENTS
NAME: Original 2THz Sample: L960
Growth Step Composition Thickness (Angs) Doping (cm-3)
SI GaAs SUBSTRATE
1 GaAs (BUFFER) 2500.0 2 AlGaAs 3000.0 x = 50% 3 GaAs 6000.0 1.0E18 4 As INTERRUPT - (Si -> 1.3E16)
START SL STRUCTURE - REPEAT LOOP x 110
5 AlGaAs 50.00 x = 10% 6 GaAs 126.00 7 AlGaAs 44.00 x = 10% 8 GaAs 120.00 9 AlGaAs 32.00 x = 10% 10 GaAs 124.00 1.3E16 11 AlGaAs 30.00 x = 10% 12 GaAs 132.00 1.3E16 13 AlGaAs 24.00 x = 10% 14 GaAs 144.00 15 AlGaAs 24.00 x = 10% 16 GaAs 144.00 17 AlGaAs 10.00 x = 10% 18 GaAs 118.00 19 AlGaAs 10.00 x = 10% 20 GaAs 144.00
END SL STRUCTURE
21 AlGaAs 50.00 x = 10% 22 GaAs 126.00 23 AlGaAs 44.00 x = 10% 24 GaAs 120.00 25 AlGaAs 32.00 x = 10% 26 GaAs 124.00 1.3E16 27 AlGaAs 30.00 x = 10% 28 GaAs 200.00 (Si 1.3E16 -> 5.0E18) 29 GaAs 700.00 5.0E18
Figure C.3: Grow sheet of the THz QCL
93 Acknowledgement
I would like to take this opportunity to thank everyone who contributed, motivated, inspired and helped me during my PhD time.
I am very thankful to Dr. Nathan Jukam for giving me the opportunity to work in his group on interesting topics in the field of THz QCL spectroscopy, technology, metamaterials and strong coupling experiments. I enjoyed every moment with vari- ous scientific discussions and thank him for encouraging me to discuss new ideas and experiment any time and in a very extensive way. The created working atmosphere, which was great, inspired me to think about new versatile projects and motivated me the throughout this period. I am also thankful to him for sending me to the international conferences, research stays and of course for the collected knowledge and skills. I also thank Dr. Nathan Jukam and extend my gratitude to him for supervising me, giving valuable comments and suggestions. I would also like to thank Prof. Dr. Andreas Wieck for supervising me, giving advices, sharing the expertise in semiconductor physics and of course for introducing me into the working principles of Fourier transform spectroscopy, which is the com- plementary technique to the time domain spectroscopy. Additionally, I am thankful to him for allowing me to use the facilities and expertise of the chair (Lehrstuhl f¨urAngewandte Festk¨orperphysik), because without it the realization of this thesis would have been impossible. I was very happy to work together with Dr. Hanond Nong. I learned a lot from him, especially how to handle and work with laboratory equipments. Dr. Hanond Nong taught me everything from the beginning. From mounting and aligning a single mirror till setting up the complex experiments. He also taught me how to
94 align and optimize optical systems and to see Physics in the raw data. Thank you for teaching and transferring all these expertise to me. Special thanks goes to Dr. Shovon Pal. I really do not know what I could do without Dr. Shovon Pal. No one will believe me, but Dr. Pal can realize any complicated electrical circuit that is sketched on a piece of paper. More even, it is done within a few minutes, looks like a commercial product and works. He is not only great in electronics but also in mechanical design and engineering. No matter what, Dr. Pal will design it. I think it will be easy for him to set up a new lab. Such kind of hard and smart persons are required in every lab. I would also like to thank Dr. Pal for proofreading and correcting my thesis. I am also thankful to Negar Hekmat and Tobias Fobbe for bonding, cleaving and mounting the lasers as well as for a fruitful discussion on waveguide properties, waveguide design and simulations and lastly being nice colleagues at work. Last but not the least, I would like to thank all my family members, my parents and my brother for supporting me in all my endeavors. I am grateful to them for bestowing me with their blessings.
95 Curriculum Vitae
Personal data
First name: Sergej Last name: Markmann Date of birth: 5. November 1987 Birth place: Uman (Ukraine) Nationality: German
Education 01.12.2013 - Present Study at the Ruhr-Universität Bochum Department: Faculty of Physics and Astronomy Study focus: THz Quantum Cascade Lasers Degree: PhD
01.04.2012-30.09.2014 Study at the Ruhr-Universität Bochum aaaaaaaaaaa Department: Faculty of Electrical Engineering and Information Technology Study focus: High Frequency- and Optical Systems Degree: Master of Science
01.10.2011-30.09.2013 Study at the Ruhr-Universität Bochum Department: Faculty of Physics and Astronomy Study focus: Solid State Physics Degree: Master of Science
01.10.2008 - 30.09.2011 Study at the Ruhr-Universität Bochum Department: Faculty of Physics and Astronomy Degree: Bachelor of Science
96 School education
01.02.2001 - 21.06.2008 Heinrich-von-Kleist Gymnasium in Bochum Degree: Abitur 01.10.2005 - 30.09.2007 Participation in the pupil's university of the Ruhr aaaaaaaaaaaaaaaaaaaaaa University Bochum 02.02.2000 - 26.01.2001 German education class at Heinrich-von-Kleist a aaa Gymnasium in Bochum 01.09.1993 - 01.12.1999 High school in Uman, Ukraine Degree: 6 class
Awards 09.05.2016 3rd price on the ideas competition of „Gründer Campus aaaaaaaaaaaaaaaaaaaaaa Ruhr“ 2016
05.12.2014 First poster price on fifth international symposium on a aaaaaaaaaaaaaaaaaaaaaa Terahertz Nanoscience in Martinique (France).
01.04.2013-30.09.2014 RIM-scholarship for outstanding study at the faculty of Electrical Engineering and Information Technology from Blackberry company (Research In Motion) and government department NRW for Innovation, Science, Research and Technology. Duration: Complete Master degree program
01.10.2011-30.09.2012 Grant from the education fund of the Ruhr-University Bochum within the NRW/Germany scholarship program
01.10.2009 - 30.09.2010 Grant from the education fund of the Ruhr-University Bochum within the NRW Scholarship program
21.07.2008 Award of one-year free membership of the German
97 Physical Society in recognition of excellent performance a in advanced courses (Physics and Mathematics) at aaaaaaaaaaaaaaaaaaaaa Heinrich-von-Kleist Gymnasium in Bochum
Languages German Mother tongue Russian Mother tongue English Proficient Ukrainian Proficient French Elementary
98 Erkl¨arung
Hiermit versichere ich, dass ich meine Dissertation selbst¨andigund ohne unerlaubte fremde Hilfen angefertigt und verfasst habe, keine anderen als die angegebenen Hilfs- mittel und Hilfen benutzt wurden und die Dissertation in dieser order ¨ahnlicher Form noch bei keiner anderen Fakult¨atder Ruhr-Universit¨atBochum und bei keiner an- deren Hochschule eingereicht worden ist.
Bochum, den
Sergej Markmann
99