Characterization and optimization of mode-locking of a high-power Yb:YAG thin-disk laser

(1)

Characterization and optimization of mode-locking of a

high-power Yb:YAG thin-disk laser

Dissertation

zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften

an der Universit¨ at Konstanz Fachbereich Physik

vorgelegt von Farina Sch¨ attiger

Tag der m¨ undlichen Pr¨ ufung: 18.12.2014 1. Referent: Prof. Dr. T. Dekorsy

2. Referent: apl. Prof. Dr. Johannes Boneberg

(2)

(3)

List of publications

Parts of this PhD thesis are already published in the following journal papers or con- ference proceedings, one still with my maiden name Farina K¨onig.

• F. Sch¨attiger, O. Ristow, and T. Dekorsy, Spektroskopie koh¨arenter akustischer Phononen in Halbleiter-Bragg-Spiegeln, 4. Optik-Kolloquium, Leipzig, Septem- ber 4, 2014

• F. Sch¨attiger, O. Ristow, M. Hettich, and T. Dekorsy,Coherent Acoustic Phonons in Semiconductor Bragg Mirrors, CE-1.2, CLEO Europe, Munich, May 12-16, 2013

• R. Fleischhaker, N. Krauß, F. Sch¨attiger, and T. Dekorsy, Consistent characterization of semiconductor saturable absorber mirrors with single-pulse and pump- probe spectroscopy, Optics Express 21(6), p. 6764 (2013)

• F. Sch¨attiger, D. Bauer, J. Demsar, T. Dekorsy, J. Kleinbauer, D.H. Sutter, J. Puustinen, and M. Guina, Characterization of InGaAs and InGaAsN semiconductor saturable absorber mirrors for high-power mode-locked thin-disk lasers, Applied Physics B 106(3), p.605 (2012)

• F. Sch¨attiger, D. Bauer, D.H. Sutter, J. Puustinen, M. Guina, and T. Dekorsy, Characterization of InGaAs and InGaAsN saturable absorber mirrors for high power mode locked sub-ps thin-disk lasers, CE-1.2, CLEO Europe, Munich, May 22-26, 2011

• D. Bauer, P. Wagenblast, F. Sch¨attiger, J. Kleinbauer, D. Sutter, A. Killi, and T. Dekorsy,Energies above 30µJ and average power beyond 100 W directly from a mode-locked thin-disk oscillator, CWP2, CLEO USA, Baltimore, May 1-6, 2011

• D. Bauer, F. Sch¨attiger, J. Kleinbauer, D. Sutter, A. Killi, and T. Dekorsy, En- ergies above 30µJ and average power beyond 100 W directly from a mode-locked thin-disk oscillator, ATuC2, Advanced Solid State Photonics, Istanbul, February 13-16, 2011

• J. Zhang, F. K¨onig, J. Neuhaus, D. Bauer, T. Dekorsy, and Y. Chen, Dielectric coatings for optimized low-loss saturable absorbers for high-power ultrafast laser, Chinese Optics Letters 7(9), p. 819 (2009)

(6)

(7)

List of figures

2.1 Pulse shaping due to self phase modulation and negative group velocity

dispersion when propagating through transparent media . . . 7

2.2 Laser modes in a laser resonator . . . 9

2.3 Operating modes of a laser: cw, cw mode-locking, Q-switched mode- locking . . . 10

2.4 Pulse shaping mechanisms for passive mode-locking . . . 12

2.5 Schematic of a nonlinear mirror consisting of a nonlinear crystal and a dichroic output coupling mirror . . . 15

3.1 Typical layer structure of a SESAM . . . 18

3.2 Typical static reflectivity spectrum of a SESAM . . . 19

3.3 Typical nonlinear reflectivity curve of a SESAM . . . 21

3.4 Carrier dynamics in a semiconductor after optical excitation . . . 24

3.5 Band gap energy versus lattice constant for different semiconductor material systems . . . 26

3.6 Reflectivity transients of SESAMs with InGaAs and InGaAsN quantum wells, annealed at different temperatures . . . 28

4.1 Processes of a FTIR measurement: From interferogram to spectrum . . 34

4.2 Schematic of the beam path in the FTIR-spectrometer . . . 35

4.3 Setups for single pulse spectroscopy (SPS) and pump-probe spectroscopy (PPS) . . . 36

4.4 Photo diode signal at SPS setup and example for nonlinear reflectivity curve experimentally measured with SPS . . . 41

4.5 Steps how to extract nonlinear reflectivity cuves based on PPS data . . 43

4.6 Typical reflectivity transients of a SESAM for low and high fluences measured with PPS . . . 44

4.7 ASOPS transient and extracted oscillations . . . 47

5.1 Microscope picture and experimental results of damaged SESAM . . . 51

5.2 Design idea for a SESAM suppressing Q-switching . . . 53

5.3 Band gap energy of In0.153Ga0.847As versus temperature . . . 54

5.4 Static reflectivity of heated SAM-T1 . . . 55

5.5 Left: Temperature dependent band gap energy of In0.5Ga0.5As. Right: Absorption spectra of In_0.2Ga_0.8As/GaAs-QWs for different temperatures 57 5.6 Nonlinear reflectivity spectrum of heated SAM-T1, absolute values . . . 58

(8)

5.7 Selected characteristic parameters of heated SAM-T1, temperature de-

pendent . . . 59

5.8 Normalized reflectivity transients of SAM-T1 for different SESAM temperatures. . . 60

5.9 Static reflectivity of heated SAM-T2 . . . 61

5.10 Nonlinear reflectivity spectrum of heated SAM-T2, absolute values . . . 62

5.11 Selected characterizing parameters of heated SAM-T2, temperature dependent . . . 63

5.12 Normalized reflectivity transients of SAM-T2 for different SESAM temperatures. . . 64

5.13 Principle of laser cooling . . . 65

5.14 Calculated band diagram of an InGaAs double QW . . . 66

6.1 Phonon dispersion of a diatomic chain . . . 71

6.2 Calculated dispersion relation of acoustic phonons in bulk material and superlattice . . . 73

6.3 Coherent acoustic phonon measurement of a semiconductor Bragg mirror 76 6.4 Calculated dispersion relation of a Bragg mirror and Fourier transform of coherent acoustic phonon measurements of Bragg mirrors annealed at different temperatures . . . 78

6.5 Static reflectivity spectra of different annealed semiconductor Bragg mirrors, measured data . . . 79

6.6 Static reflectivity spectra of different annealed semiconductor Bragg mirrors, measured and calculated data . . . 80

7.1 Schematic of the thin-disk laser concept . . . 87

7.2 Schematic of the SESAM mode-locked Yb:YAG thin-disk laser resonator 91 7.3 Specifications of SESAM mode-locked thin-disk laser with 22 AMC passes: Output power and opt. efficiency vs. pump power, spectral width and pulse duration vs. output power . . . 93

7.4 Specifications of SESAM mode-locked thin-disk laser with 22 AMC passes: Intensity autocorrelation of 0.87 ps pulse and corresponding laser spectrum . . . 94

7.5 Long-term stability measurement over 1000 minutes: Output power log and monitoring of beam position . . . 95

7.6 Long-term stability: Pulse shape on the oscilloscope over 1000 minutes 96 7.7 Long-term stability: Output power log over 45 days . . . 97

7.8 SHG output of a single pass through a LBO crystal . . . 98

7.9 Setup for extracavity three wave mixing . . . 99

7.10 Three wave mixing: Output power of fundamental and second harmonic light after two passes through a nonlinear crystal . . . 100

7.11 Schematic of the Yb:YAG thin-disk resonator with intracavity SHG . . 101

(9)

List of figures

7.12 Specifications of SESAM mode-locked thin-disk laser with reduced output power due to other pump diode with 22 AMC passes: Output power and opt. efficiency vs. pump power, pulse duration vs. output power . 102 7.13 Specifications of NLM assisted SESAM mode-locked Yb:YAG thin-disk

laser: Output power vs. pump power, pulse duration vs. output power for different numbers of AMC passes . . . 106 7.14 Specification of SESAM mode-locked thin-disk laser with different OC

rates and different numbers of AMC passes: Pulse lengths vs. output power . . . 108

(10)

(11)

List of abbreviations

Al aluminum

AC autocorrelation AMC active multipass cell AR anti reflective

As arsenic

ASOPS asynchronous optical sampling AMC active multipass cell

BBO beta bariumborat

Cr chromium

cw continuous wave

DFG difference frequency generation

Er erbium

F₂ parameter for roll-over F_sat saturation fluence FCA free carrier absorption FFT fast Fourier transform

fs femtosecond

FTIR Fourier transform infrared FWHM full width at half maximum

He helium

HR high reflective HWP half wave plate

Ga gallium

GDD group delay dispersion

GTI Gires-Tournois interferometer GVD group velocity dispersion LBO lithium bariumborat LO longitudinal optical i.a. inter alia

i.e. id est

In indium

MBE molecular beam epitaxy

MIXSEL mode-locked integrated external-cavity surface-emitting laser

Mo molybdenum

MOCVD metal-organic chemical vapor deposition MQW multiple quantum wells

N nitride

(12)

Nd neodymium

Ne neon

NIR near infrared NLC nonlinear crystal NLM nonlinear mirror

ns nanosecond

OC output coupling PL photo luminescence

ps picosecond

PPS pump-probe spectroscopy

QW quantum well

QWP quarter wave plate R_lin linear reflectivity

R_ns nonsaturable reflectivity

∆ R change in reflectivity

∆ R₀ change in reflectivity at zero time delay

∆ R_mod modulation depth

∆ R_eff effective modulation depth

∆ R_ns nonsaturable losses RTA rapid thermal annealing SAM saturable absorber mirror

SESAM semiconductor saturable absorber mirror SHG second harmonic generation

Si silicon

SPM self phase modulation SPS single pulse spectroscopy τ_fast relaxation time constant τ_slow recombination time constant TBP time-bandwidth product TFP thin film polarizor TPA two photon absorption

VCSEL vertical-cavity surface-emitting laser

VECSEL vertical-external-cavity surface-emitting laser YAG yttrium aluminum garnet

Yb ytterbium

XUV extreme ultraviolet

(13)

1 Introduction

“Ultra-short pulse lasers for industrial mass production - manufacturing with light flashes” [Deu14], this cooperation project of Robert Bosch GmbH, Friedrich-Schiller University of Jena, Fraunhofer IOF, and TRUMPF Laser GmbH was presented with the Federal German Presidents Award for Innovation in Science and Technology in the year 2013. This prize underlines that manufacturing with lasers, especially with pulsed lasers, is an “outstanding innovation in the area of technology, engineering, and natural science” [Deu14] as it is written down in the prize’s statutes.

Industrial production, micromachining, medical diagnostics and therapy, and high-tech natural science is not imaginable without the use of pulsed lasers. Thus, the following two aspects are the essential basis for further developments in the field of pulsed lasers and their applications: Innovations to increase the variety of lasers’ output characteristics and innovations to optimize the pulse generation.

Speaking about the first aspect, the development and enhancement of the thin-disk concept [Gie94, Gie07] for diode-pumped solid-state lasers allowed for high output power combined with high beam quality, since this laser design exhibits good thermal management and remarkable power scaling capability. Thus, thin-disk lasers, especially mode-locked thin-disk lasers, set many records in the last years. The shortest pulses of a thin-disk laser, 62 fs, could be realized with Yb:CaGdAlO₄ as thin-disk material [Die13]. The highest pulse energies obtained directly from a laser resonator operating in ambient air were achieved from Bauer et al. with an Yb:YAG thin-disk laser with multipass geometry [Neu08a]. Pulse energies as high as 41µJ were emitted [Bau12b].

In vacuum, this value could even be doubled and energies as high as 80µJ were possible [Sar14]. In terms of output power the highest value of a mode-locked thin-disk laser is 275 W and was achieved in vacuum atmosphere [Sar12a]. The highest output power of the Yb:YAG thin-disk laser presented in this thesis is 44 W, resulting in pulse energies as high as 13µJ. Thus, this laser is ranked in the middle in terms of output parameters, but it wins with its outstanding long-term stability. Output characteristics and pulse generation were stable over a time period of several months without any realignment.

All these abovementioned results were realized with lasers mode-locked with a semiconductor saturable absorber mirror (SESAM) [Kel96]. However, the highest output power of a thin-disk resonator operating in air, 230 W, was achieved with a Kerr-lens mode-locked oscillator [Bro14].

All these milestone results show that improving laser output characteristics and finding appropriate mode-locking mechanisms go hand in hand. Thus, apart from pushing the limits in laser development, a great deal of work goes in innovations in the field of mode-locking mechanisms and their optimization.

(14)

A common mode-locking method is based on saturable absorbers and was invented with bleachable dye solutions in 1966 [DeM66]. However, with this technique only Q- switched mode-locking of a laser was possible, whereas stable continuous wave mode- locking of lasers could be realized for the first time with semiconductor based saturable absorbers [Kel92a].

Since its first realization more than twenty years ago, nowadays semiconductor saturable absorber mirrors, SESAMs [Bro95, Kel96], are the most common mode-locking devices in thin-disk lasers. Therefore, they are subjects of research as well as subjects of advancement, and further development: On the one hand the application of an ad- ditional voltage on the SESAM structure allows for the electrical control of SESAM parameters [Iso07, Zol09, Liu10], on the other hand increasing the output power of mode-locked lasers raises the requirements for SESAMs in terms of damage threshold [Sar12b]. Thus, the challenge of heat dissipation and damage prevention is a key issue in today’s SESAM development and therefore this thesis presents new design concepts for SESAMs dealing with these challenges. Nevertheless, degradation and heating de- formation of SESAMs [Sch12b] are still limiting aspects and push the development of alternatives. Examples include alternatives to saturable semiconductor quantum wells, such as saturable semiconductor quantum dots [Gue97, Raf04] or saturable absorbers based on graphene [Set04, Sun10, Ciz13].

A complete different mode-locking mechanism is Kerr-lens mode-locking and was adopted to thin-disk lasers for the first time in 2011 by Proninet al. [Pro11]. Another option for mode-locking consists of a nonlinear mirror and was firstly developed by Stankov et al. and is therefore called Stankov mode-locking [Sta88a]. So far, Stankov mode-locking was implemented into different laser geometries [Tho12, Ale14, Che14]

but not yet into thin-disk lasers. However, in this thesis first experiments towards the realization of a Stankov mode-locked Yb:YAG thin-disk laser are presented.

This thesis is structured as follows. In Chapter 2 the main aspects of laser pulse formation are given. Important effects such as self phase modulation, group velocity dispersion, and second harmonic generation are introduced as well as the principle, challenges, and techniques of mode-locking.

Chapter 3 deals with semiconductor saturable absorber mirrors (SESAMs). In this Chapter the most important features of such a device are introduced. At the end of the third Chapter a special focus is set on the requirements of a SESAM for mode- locking lasers and different growth and post-growth techniques to meet them.

In Chapter 4 all experimental methods for the SESAM characterization used during this PhD study are presented. For all these methods the experimental setups as well as the steps of data analysis and data interpretation are given.

These introductory chapters are followed by experimental results. Chapter 5 presents the consequences of laser damage on SESAMs as well as new design concepts as reme- dies. One design idea is based on the temperature dependence of the band gap energy of semiconductor materials, the other idea is based on quantum engineering, a technique that is already common for examples in quantum cascade lasers but not yet embedded in SESAM technology.

(15)

An important part of SESAMs and different semiconductor laser devices are Bragg mirrors. The consequences of post-growth annealing on these mirrors are analyzed in Chapter 6. The focus was set on any changes in the layer structure and in optical properties. The structural analysis was done with optical spectroscopy of coherent acoustic phonons theoretically embedded by means of the Rytov model [Jus89], which is a new metrological technique for long-periodic superlattices. The basic principles of the generation of coherent acoustic phonons and their detection is given at the beginning of Chapter 6.

In Chapter 7 all experimental results obtained with the high-power mode-locked Yb:YAG thin-disk laser based on the multipass geometry concept are summarized.

As an introduction the basic principles of thin-disk lasers [Gie94] and the active multipass cell [Neu08b] are given. Two kinds of mode-locking techniques could be realized:

Pure SESAM mode-locking and SESAM mode-locking assisted by a nonlinear mirror.

For both resonator designs the output characteristics of the laser are shown.

A final summary and outlook is given at the end of this thesis in Chapter 8. A summary in German can be found in Chapter 9.

(16)

(17)

2 Generation of ultrashort laser pulses

Today’s science and industrial manufacturing processes are often based on ultrashort laser pulses. Thus, the precise and reproducible generation of such laser pulses is a demanding requirement in science and manufacturing. For the emission of pulse trains instead of continuous wave laser emission the principle of mode-locking is responsible.

Thus, mode-locking in general and different methods for mode-locking are explained in Section 2.3 of this Chapter. The Yb:YAG thin-disk laser presented in this thesis is passively mode-locked with a slow absorber. This kind of mode-locking is described in Section 2.3.2.

Since the pulse formation is additionally based on effects such as self phase modulation (SPM) and group delay dispersion (GDD), Section 2.1 gives a short introduction in the mathematical description of a laser pulse including SPM and GDD. Nonlinear optical effects such as second harmonic generation and difference frequency generation are the basis of so called Stankov mode-locking. Thus, they are explained in Section 2.2.

2.1 Mathematical description of laser pulses

A laser pulse is a propagating electromagnetic wave packet and can be written as E(t, z) =E₀·E(t)˜ ·exp[i(k₀z−ω₀t)], (2.1) whereE₀ is the amplitude, ω₀ is the central angular frequency, andk₀ the central wave vector. Depending on the envelope function ˜E(t) one discriminates between

• a Gaussian beam with ˜E(t)∝exp[−1.385(t/τ_P)²] and

• a sech² beam with ˜E(t)∝sech²[1.763(t/τ_P)], with τ_P as the pulse length [Die06].

A laser pulse is built up by the constructive interference of waves with different frequencies. Thus, the frequency spectrum of a pulse can be calculated by Fourier transform of its time evolution function [Rul03]. Thus, the broader the spectrum the shorter the possible pulse. However, the minimum pulse duration for a given frequency spectrum and pulse shape is limited by the time-bandwidth product (TBP) K, which is calculated by the product of the pulse duration ∆τ_Pand the spectral width ∆ν_P of a pulse:

∆τ_P∆ν_P≥K

Typically for both values full width at half-maximum (FWHM) is taken [Rul03]. For a Gaussian beamK=0.441, for a sech²-beam K=0.315 [Die06].

The inequality in the time-bandwidth product holds for chirped pulses, respectively

(18)

pulses with frequency modulation. If the time-bandwidth product of a laser pulse is close to K, this indicates that the pulse is unchirped and that its duration is close to the bandwidth limit [Die06]. Hence, the time-bandwidth product is a quality indicator of the pulse.

If a light pulse propagates through a medium two different speed values have to be discriminated: The phase velocity is the speed of every single wave front within the wave packet, whereas the group velocity describes the speed of the envelope.

The group velocity v_G is defined as the derivative of the dispersion relation ω for a given central wave vectork₀ [Sal07]

vG= dω dk k0

. (2.2)

In transparent media optical properties such as the refractive index are frequency dependent. Hence, light pulses of different frequencies exhibit different group velocities.

This dependence leads to a term called group velocity dispersion (GVD) that is defined as [Rul03]

GVD = ∂

∂ω 1

v_G = ∂²k

∂ω² with (2.3)

[GVD] = s²

m. (2.4)

A direct consequence of GVD is a distortion of the pulse envelope. Depending on the sign of the GVD shorter wavelengths, respectively longer wavelengths, of a pulse propagate faster, respectively slower. If the group velocity increases with increasing wavelength, this is called positive (normal) GVD, whereas a reduction of the group velocity with increasing wavelength is referred to as negative (anomalous) dispersion [Rul03]. The upper part of Fig. 2.1 illustrates the effect of negative GVD.

Normal dispersive media exhibit a positive GVD, which leads to a temporal broadening of the pulse when propagating through the medium [Rul03]. Thus, for laser pulses with a stable pulse shape positive, respectively negative, group velocity dispersion has to be counterbalanced by the introduction of GVD with the opposite sign. Since most of the media, such as ordinary optical glasses, are normal dispersive media with positive GVD, several optical devices with a negative group velocity dispersion have been designed, such as prism or grating pairs and dispersive mirrors. All these devices have in common a frequency dependent optical pathlength [Rul03]. Longer wavelengths of the pulse spectrum have to propagate a longer way than the waves with shorter wavelengths.

This results in a negative group velocity dispersion and balances positive GVD.

For dispersive mirrors or laser resonators it is more convenient to use a term called group delay dispersion (GDD) per pass/round trip in units of fs² instead of GVD, which is defined as the group delay dispersion per unit length.

Apart from GVD another nonlinear effect called self phase modulation (SPM) is crucial for the generation of stable mode-locked laser pulses. Basis of SPM is the so called

(19)

2.1 Mathematical description of laser pulses

negative group velocity dispersion

self phase modulation

r

b b

r time

time

Figure 2.1: Pulse shaping due to negative group velocity dispersion and self phase modulation when the pulse is propagating through transparent media. The nonlinear effects shift the red (r) and blue (b) part of the pulse spectra in time. The figure is adopted from [Sal07].

Kerr-effect. This effect describes the intensity dependence of the refractive indexnof a material: n(I, t) =n1+n2I(t), wheren1is the linear refractive index,n2is the nonlinear refractive index, and I(t) is the time dependent intensity of the electromagnetic wave [Sal07]. Thus, due to the temporal intensity distribution a light pulse experiences different values as refractive index.

By substitutingk₀(t) =ω₀n(I, t)/c into Eq. (2.1) the phase Φ(t, z) = k₀z−ω₀t can be rewritten:

Φ(t, z) = ω₀

n(I, t)z c −t

(2.5)

= ω₀

[n₁+n₂I(t)]z

c −t

. (2.6)

The time dependent behavior of the so called instantaneous frequency ω(t) is given by the negative derivative of Eq. (2.6) [Sal07]:

ω(t) = −∂Φ(t, z)

∂t (2.7)

= ω₀− ω₀n₂z c

∂I(t)

∂t =ω₀+ ∆ω_SPM. (2.8)

∆ω_SPMrepresents the frequency shift caused by SPM with respect to the central angular frequencyω₀

∆ωSPM(t) =−ω₀n₂z c

∂I(t)

∂t . (2.9)

(20)

According to Eq. (2.8) at the rising edge of a pulse with ∂I/∂t > 0 lower frequencies are generated, at the falling edge with ∂I/∂t < 0 higher frequencies are generated.

Such a frequency modulated pulse is denoted as a chirped pulse [Die06, Sal07].

Based on the above given formulas and explanations it is obvious that the pulse shaping effects of self phase modulation and negative group velocity dispersion are of opposite signs. Fig. 2.1 illustrate the frequency modulations due to negative GVD and SPM. It is apparent that due to SPM the shorter wavelengths of a pulse spectrum are ’at the front’ of the pulse, whereas negative GVD results in a frequency modulation where the shorter wavelengths are at the ’rear’ part of the pulse. Consequently, negative GVD compensates for SPM and allows for the generation of a pulse whose spectral and temporal shape remains constant. Such a pulse-like stationary wave is called soliton and can be described mathematically as a squared hyperbolic secant, sech² [Sal07].

2.2 Nonlinear optical effects

During the work of this PhD thesis first experiments of a Stankov mode-locked [Sta88a]

thin-disk laser were realized. An introduction into this mode-locking technique is given in Section 2.3.4, first experimental results are presented in Section 7.4.

Since this mode-locking technique is based on two nonlinear optical effects, second harmonic generation (SHG) and difference frequency generation (DFG), both effects will be discussed shortly in this section.

Pulsed lasers allow for field intensities in the range of MW/cm². The interaction of such high field intensities with a medium leads to nonlinear effects within the medium.

For small field strengths E there is a linear relation between E and the polarization P of the medium: P ∝ E. However, P can be written as a power series in the field strengthE~

P~(t) = h

χ⁽¹⁾E(t) +~ χ⁽²⁾E~²(t) +χ⁽³⁾E~³(t) +...i

(2.10)

= P~⁽¹⁾+P~⁽²⁾+P~⁽³⁾+... (2.11) with as the free space permittivity and χ⁽ⁿ⁾ being the n-th order nonlinear optical susceptibility [Koe06, Boy08]. Since the nonlinear optical susceptibilities decrease strongly for increasing n, nonlinear optical effects only occur for very high electric field strengths in media exhibiting nonlinear susceptibilities [Koe06].

In materials with non-vanishing χ⁽²⁾ second harmonic generation (SHG) is possible.

With E(t) =~ E~₀e^−iωt +E~₀e^iωt being the electric field of the incident electromagnetic wave the 2nd-order polarisation P~⁽²⁾ ∝ E~² consists of a contribution at frequency ω and additionally at the doubled frequency 2ω leading to the generation of a scattered radiation at twice the frequency of the fundamental [Boy08]. This process is called second harmonic generation (SHG).

(21)

2.3 Basics of mode-locking

õ äõ I(õ)

õ0

õ Äõ

Gain

Losses

{

allowed modes

Figure 2.2: Longitudinal modes in a resonator. The gain bandwidth ∆ν of the active medium and the losses within the resonator determine the allowed laser modes that are centered aroundν0and exhibit a spacing ofδν.

Figure is adopted from [Sal91].

In general, the conversion efficiency into second harmonic is very weak. Hence, for strong SHG output the second harmonic waves generated at every point of the nonlinear medium must interfere constructively. This requirement is met when the fundamental and the second harmonic wave remain in phase, i.e. are phase matched, when traveling through the medium. That condition is fulfilled when the refractive indexes of both waves are identical, respectively nω =n2ω [Koe06]. Since in dispersive media generally n_ω 6=n_2ω, one way to realize identical refractive indexes is the use of birefringent crystals. These crystals exhibit different refractive indexes depending on the polarization of the electromagnetic wave. Since the fundamental and the second harmonic wave are orthogonally polarized, the refractive indexes of both can be identical by an appropriate choice of the incident angle in respect to the crystal axis and an appropriate cutting of the birefringent crystal. More details about phase matching can be found in [Koe06].

Another 2nd-order nonlinear optical effect is three wave mixing: Two electromagnetic waves of frequencies ω₁ and ω₂ hit the nonlinear medium and generate a wave at fre- quencyω₃ fulfilling momentum and energy conservation. The generation of a wave at frequency ω₃ = ω₂+ω₁ with ω₃ > ω₁, ω₂ is called sum frequency generation, whereas difference frequency generation is referred for the generation of a wave with frequency ω₃ = ω₁ −ω₂ with ω₁ > ω₂, ω₃ [Boy08]. Consequently, SHG is a special case of sum frequency generation with ω₁ =ω₂ =ω. By means of three wave mixing it is possible to reconvert second harmonic light into fundamental light again. For all these processes the same phase matching conditions as already mentioned for SHG have to be fulfilled.

2.3 Basics of mode-locking

In a laser resonator different longitudinal laser modes can exist. Due to the cavity length L all longitudinal modes with frequency ν, respectively wavelength λ = c/ν with c being the speed of light, have to fulfill the condition of nλ/2 = nc/(2ν) = L withn= 1,2,3, ...resulting in an infinite number of possible modes spaced by the axial mode intervalδν =c/(2L) [Koe06]. However, the number of the longitudinal modes of a laser is restricted by the spectral bandwidth ∆ν of the gain medium and the losses of the resonator. This leads to a defined number of modes centered around the atomic resonance frequencyν₀ of the gain medium [Sal07], as it is illustrated in Fig. 2.2.

(22)

Porwe

(a) Time

Power

(c) Time

Power

(b) Time

Figure 2.3: Different operating modes of a laser. (a) Continuous wave (cw) laser output, (b) cw mode-locking, (c) Q-switched mode-locking. This figure is adopted from [Kel96].

Depending on the phase relationship of the different laser modes one distinguishes between a free-running laser and a pulsed laser. In the free-running laser the modes oscillate without a fixed phase relationship resulting in a continuous wave (cw) laser output. Just for a very short time scale, given by the coherence time (∆ν)⁻¹, some modes oscillate in phase [Fre95]. Hence, as it is shown in Fig. 2.3(a), the temporal output of a cw laser is a time-averaged statistical mean value. In the frequency domain the laser light exists of a large number of modes spaced by δν and oscillating with a randomly distributed phase [Koe06].

If the modes of the laser oscillate in phase the temporal output of the laser is well defined. For each round trip with round trip timeT_R the laser emits a pulse, resulting in a pulse train with a repetition rate of 1/T_R =c/(2L) [Koe06]. As it is shown in Fig.

2.3(b), cw mode-locking is referred to a pulse train where all pulses exhibit the same amplitude and intensity.

If the amplitudes of the pulse train are modulated by pulse envelopes in the microsec- ond regime (see Fig. 2.3(c)) this is called Q-switched mode-locking [Kel99]. Q-switched mode-locking originates from the following effect: Higher pulse energies bleach the saturable absorber stronger, so that the intracavity losses for higher pulses are reduced.

Therefore, at the beginning the increased pulse energies even grow exponentially. This in turn leads to a stronger saturation of the gain until it is fully saturated and decreases again [H¨on99, Kel99]. This instability of the pulse dynamics is the basis of Q-switching instabilities.

As mentioned above, in general, the modes do not oscillate in phase or with a fixed phase relationship. Hence, for a constant phase relationship the modes have to be cou- pled and locked together. This leads to constructive interference of all modes resulting in a laser pulse.

The minimum pulse durationτ_P is determined by the Fourier transform of its spectral profile. Hence, the pulse duration is inversely proportional to its spectral bandwidth

∆ν_P: τ_P ≈ ∆ν⁻¹ [Sal07]. The shortest pulse duration for a specific laser medium can be achieved when all modes within the spectral bandwidth of the gain medium ∆ν oscillate in phase and ∆ν_P equals ∆ν. Such a pulse is called transform limited and its pulse duration only depends on the spectral bandwidth of the laser medium leading to a time-bandwidth product of τ_P∆ν_P =τ_P∆ν =K [Fre95].

(23)

2.3.1 Different mode-locking techniques

Mode-locking can experimentally be achieved by the incorporation of a loss modulator into the laser cavity. One discriminates active and passive mode-locking techniques.

The laser built during this PhD thesis is passively mode-locked with a semiconductor saturable absorber mirror (SESAM). Since SESAM mode-locking belongs to passive mode-locking methods, this technique will be explained in more detail compared to active mode-locking.

If the loss/gain of the laser cavity is externally modulated this technique is called active mode-locking. An active mode-locking device is controlled by an external signal and modulates the loss periodically. If the periodicity of the loss modulator is matched to the cavity round trip time adjacent laser modes transfer energy and are locked together [Fre95]. Examples for active mode-locking devices are acousto-optic modulators and electro-optic modulators. For active mode-locking an essential and at the same time limiting requirement is a modulator with an operation frequency in the MHz and GHz range, corresponding to common cavity round trip times.

In passive mode-locking the pulse itself modulates the loss in the resonator by interaction with an intracavity element. No external modulation is required [Fre95].

The basic principle of passive mode-locking is the following: The intracavity element introduces an intensity dependent loss mechanism, so that higher intensities experience less loss than lower intensities. Hence, oscillations can only occur when due to mode-locking intense pulses are built up [Sal07].

Common devices for passive mode-locking are Kerr-lenses, saturable absorbers, and nonlinear mirrors.

Kerr-lens mode-locked lasers consist of a nonlinear medium with an intensity dependent refractive index combined with an intracavity aperture. Due to the Kerr-effect higher laser intensities are stronger focused than lower intensities. If the aperture is placed in that way that just more strongly focused light can pass it, it represents an intensity dependent loss mechanism leading to passive mode-locking [Sal07].

Apart from Kerr-lens mode-locking saturable absorbers are also used for passive mode- locking. Therefore, different design concepts can be found: Saturable absorbers based on carbon nanotubes [Set04, Sun10] as well as saturable absorbers based on quantum dots [Gue97, Raf04] and semiconductor saturable absorber mirrors (SESAMs) [Kel96].

A short introduction in mode-locking with slow absorbers is given in Section 2.3.2 of this Chapter, whereas Chapter 3 focuses on various aspects of SESAMs in general.

Another device for passive mode-locking is the nonlinear mirror, a combination of a nonlinear crystal and a dichroic output coupling (OC) mirror. This method is based on the intensity dependent conversion efficiency of second harmonic generation within the nonlinear crystal. Due to the reflectivity specification of the dichroic OC mirror (R<100 % for fundamental, R=100 % for second harmonic light) the loss decreases for increasing light intensity. This technique is explained in more detail in Section 2.3.4.

(24)

gain loss

(a) (b) (c)

Figure 2.4: Different pulse shaping mechanisms for passive mode-locking with a fast absorber (a), a slow absorber in combination with a saturable gain (b), and with a slow absorber and soliton generation (c). Figure taken from [K¨ar95].

2.3.2 Passive mode-locking with slow absorbers

As already mentioned saturable absorbers can be used as passive mode-locking devices.

As explained in more detail in Section 3.3 due to band filling the absorption of the absorber decreases with increasing light intensity [Fre95]. Thus, intense pulses exhibit lower losses than a low intensity background. This leads to mode-locking.

Based on the recovery time of the absorber one distinguishes between a fast and a slow absorber. Theoretical and experimental basics of different mode-locking techniques with those absorbers are published in [Kär95, Kär96, Kär98].

The recovery time of a fast absorber is in the range of the pulse duration. Hence, the very short net gain window follows the pulse profile resulting in a pulse whose duration is limited by the absorber recovery time, as it is shown in Fig. 2.4(a). The use of a Kerr-lens is an example for a fast absorber.

In contrast, the recovery time of a slow absorber is much longer than the pulse duration. Mode-locking with a slow absorber is either based on a loss modulation in addition with a gain modulation (see Fig. 2.4(b)) or on the generation of a soliton (see Fig.2.4(c)) [K¨ar95, K¨ar96]. The pulse shaping in the former technique is comparable to the mode-locking technique with a fast absorber, since the pulse is formed by a short net gain window [Kel99].

For soliton mode-locking there is just a slowly recovering loss modulation without gain modulation. Hence, the net gain window remains open and the pulse is formed by self phase modulation and negative group delay dispersion, two nonlinear effects which are explained in Section 2.1. These two effects lead to the generation of a soliton. Conse- quently, this mode-locking technique is called soliton mode-locking.

In this case the slow absorber just stabilizes the pulse against the growth of cw background and Q-switching instabilities [K¨ar98].

(25)

Since GDD and SPM are just counterbalanced for the soliton pulse, low-intensity continuum background experiences less SPM and is spread in time in response to GDD.

Due to the slow absorber recovery time the continuum still undergoes a loss modulation that is still strong enough to clean the background and stabilize the soliton pulse [K¨ar98, Kel99].

Experimental results of a SESAM mode-locked high-power Yb:YAG thin-disk laser are presented in detail in Chapter 7.3.

2.3.3 Stability requirements of soliton mode-locked pulses

For stable soliton-like pulses some requirements on the laser cavity and on the SESAM parameters are necessary and will be discussed in this section. Techniques to influence the SESAM parameters will be given in Section 3.4. Special requirements for SESAMs in high-power lasers are summarized in Section 3.5.

As it was described in Section 2.3.2 mode-locking occurs when statistical fluctuations in cw mode experience lower losses than the cw background, since the intensity peak saturates the absorber stronger than low-intensity background. Hence, the slope of the nonlinear reflectivity curve of the SESAM dR/dI determines the mode-locking build- up time. The relation is inverse so that a steeper slope, respectively lower saturation fluence, leads to a faster build-up time [Kel99].

In soliton mode-locking the pulse shaping is done by SPM and negative GDD. Hence, the absorber just stabilizes the pulse against the growth of cw background and Q- switching.

Since the pulse shaping is independent of the absorber response time, with the help of soliton mode-locking pulses much shorter than the recovery time of the absorber can be generated. For example, even with SESAMs exhibiting recovery times in the range of hundreds of fs up to hundreds of ps a pulse duration<100 fs could be achieved [Sar12b, Die13].

Consequently, an analytical estimation of the pulse durationτP of a soliton is independent of any SESAM parameter and only depends on group delay dispersion|GDD|per cavity round trip, the SPM coefficient γ_SPM per cavity round trip, and the intracavity pulse energy E_P,int [Pas01]

τ_P≈1.76 2|GDD|

|γSPM|EP,int

. (2.12)

This soliton theorem is limited to laser cavities with small output coupling (OC) rates and has to be modified for higher OC rates as it is realized for the Yb:YAG thin-disk laser presented in this thesis [Neu08b]:

τP≈1.762|GDD|ln(1−OC)

|γ_SPM|E_P,ext (2.13)

with E_P,ext as the external pulse energy.

Both formulas (2.12) and (2.13) have in common that soliton-like pulses show an inverse relation between the pulse energy, respectively laser output power, and the pulse

(26)

duration. Thus, with increasing output power the pulse duration is decreased. Such a behavior can be seen in the output characteristics of the SESAM mode-locked Yb:YAG thin-disk laser presented in Section 7.3.

Apart from the balance between SPM and GDD, stability against Q-switching and double pulsing is another crucial condition for stable cw mode-locking. For cw mode- locking the energy of every single pulse has to be constant. Hence, a fluctuation of the pulse energy, i.e. due to relaxation oscillations, must be suppressed. Following the explanation in [H¨on99] a growth of the pulse energy results in a stronger absorber bleaching leading to an exponential increase of the energy. Nevertheless, apart from the absorber also the gain shows a saturable behavior. Hence, the exponential increase of the pulse energy leads to a stronger bleaching of the absorber but on the other hand to a saturation of the gain medium. For stable cw mode-locking the gain saturation has to be strong enough to suppress the exponential growth of the pulse energy.

Thus, it exists a critical pulse energy E_c,P in this way that the laser is stable against Q-switching for laser pulses with energy E_P exceeding E_c,P [H¨on99]:

E_P> E_c,P with (2.14)

E_c,P = (E_sat,LE_sat,A∆R_mod)^1/2 (2.15)

where E_sat,L, respectively E_sat,A is the saturation energy of the laser (L) and the absorber (A), respectively, and ∆R_mod the modulation depth of the absorber. The saturation energy E_sat is calculated by the product of the saturation fluence F_sat of the laser/absorber with the effective laser mode A_eff inside the gain medium, respectively on the absorber: E_sat,i=F_sat,iA_eff,i withi∈ {A, L}[H¨on99]. This approximation is valid for passive mode-locking with slow absorbers.

According to Eq. (2.15) for a given pulse energy the laser is stable against Q-switching when the modulation depth ∆R_mod and the saturation fluences are small. However, for high-power lasers the saturation fluence of the absorber should be high (see Section 3.5), hence a small modulation depth is required.

On the other hand for fixed SESAM and laser parameters the laser exhibits Q-switching instabilities for small pulse energies, for example during the power-up process. Hence, with increasing pulse energy the laser becomes stable against Q-switching and enters the cw mode-locking regime. Nevertheless, there is an upper limit for the pulse energy.

First, increasing the pulse energy leads to double or even multiple pulsing. Double pulsing occurs when a splitting into two pulses with half the energy is energetically favored.

If the pulse energy is too high SPM and negative GDD do not balance each other and SPM becomes dominant resulting in a shorter pulse duration and consequently higher peak intensities. Due to bleaching high-intensity pulses experience reduced loss in the SESAM. However, a shorter pulse duration results from a broader frequency spectrum.

Due to the limited bandwidth of the gain medium a limit for the frequency spectrum of the pulse is given. That yields a lower limit for pulse duration. Consequently, the break up into two pulses with lower energy and longer pulse duration, respectively smaller spectral bandwidth, is favorable. Secondly, the damage threshold of the absorber and other optical components sets the upper limit for pulse energies.

(27)

NLC Ö_SHG=ð/2

Ö_DFG=-ð/2

Dichroic OC R(2ù)=100 % R(ù)<100 %

d ù

ù

2ù

{

ù

Figure 2.5: Schematic of a nonlinear mirror consisting of a nonlinear crystal (NLC) and a dichroic output coupler. In the first pass through the crystal the fundamental is partially converted into second harmonic (SHG) whereas during the second pass through the crystal the second harmonic light is reconverted into fundamental light by difference frequency generation (DFG). For second harmonic generation the phase between the fundamental and the second harmonic is ΦSHG=π/2, for effective DFG the phase must be Φ_DFG = −π/2. By adjusting the free pathlength through air between the two crystal passes, D_free = 2d, a phase shift of π can be introduced due to the dispersion in air. For better visibility the two passes through the crystal are drawn separately.

Furthermore, Q-switching tendencies are more likely for lasers with a longer life time of the upper laser level compared to short living upper laser levels [Bro95]. Additionally, the slow time constant of the saturable absorber influences the mode-locking stability, too. The faster the slow time constant the more stable is the laser against Q-switching [Kel99]. Besides, a faster relaxation time of the absorber makes the laser more stable against double pulsing, since a faster absorber recovery time shortens the time window when the absorber is bleached. Thus, for a shorter recovery time a second pulse experiences more loss. This effect suppresses double pulsing.

2.3.4 Passive mode-locking with a nonlinear mirror

As already mentioned in Section 2.3.1 the basic principle of mode-locking is the incorporation of an intensity dependent loss mechanism. Apart from the Kerr-lens and the SESAM also a nonlinear mirror can be used for mode-locking.

Stankov et al. introduced a mode-locking technique based on intracavity frequency mixing in a nonlinear crystal [Sta88b]. This method is known as Stankov mode-locking or as mode-locking with a nonlinear mirror.

In Fig. 2.5 a schematic of the mode-locking device is shown. The fundamental laser light passes a nonlinear crystal and is partially converted into second harmonic light (see Section 2.2 for a short introduction to nonlinear optical effects). A dichroic mirror that is HR coated for second harmonic light and only partially reflecting the funda-

(28)

mental wave is used as an output coupling mirror of the laser cavity. The reflected second harmonic light passes the nonlinear crystal a second time and is reconverted into fundamental light by means of difference frequency generation (DFG) (see again Section 2.2 for a short introduction to nonlinear optical effects). Since SHG is stronger for higher intensities and since second harmonic light is completely reflected whereas fundamental light is only partially reflected, the reflectivity of this device for the fundamental increases for increasing incident light. Such a behavior leads to mode-locking.

A crucial parameter for an effective reverse conversion during the second pass through the crystal is the relative phase between the fundamental and the second harmonic.

After the first pass through the crystal the phase relation is Φ_SHG = +^π₂ whereas for effective reconversion the phase relation has to be Φ_DFG = −^π₂. Thus, in between the two passes through the crystal a phase shift of ∆Φ =π is necessary [Sta88a].

The simplest method to introduce a phase shift is to use the dispersion in air. Since the refractive indexes of air for the fundamental and the second harmonic differ, a pre- defined phase shift can be introduced by an appropriate choice of the free pathlength through air between the two crystal passes, respectively by varying the distance d in Fig. 2.5 between the crystal and the dichroic OC mirror.

Apart from Stankov et al. a group at the Imperial College in London realized lasers mode-locked by a nonlinear mirror. Thomaset al. presented the first bounce geometry lasers mode-locked with a nonlinear mirror [Tho10] and increased the output power of a mode-locked Nd-doped mixed vanadate oscillator up 16.8 W [Tho12]. This record in output power of a mixed vanadate laser was just recently be broken by Aleksandrov et al. who reported 20 W output power of a Nd:YVO₄ laser mode-locked with a nonlinear mirror [Ale14]. The first realization of a Stankov mode-locked laser at 2µm was recently published by Chenget al. [Che14].

First steps towards the realization of a Stankov mode-locked thin-disk laser are presented in Chapter 7.4.

(29)

3 Semiconductor saturable absorber mirrors

A semiconductor saturable absorber mirror (SESAM) is a device with an intensity dependent reflectivity. It consists of a quantum well absorber which is integrated in an antiresonant Fabry-P´erot structure [Bro95]. Due to Pauli-blocking the absorber bleaches for high light intensities and the reflectivity of the SESAM increases, respectively. Due to this nonlinear reflectivity the SESAM creates an intensity dependent loss within a laser cavity and can therefore – according to the theory given in Section 2.3 – be used for mode-locking.

A lot of SESAM development and research is done at the ETH Zurich in the group of Prof. U. Keller. The basic principles of SESAMs were mainly explained by U.

Keller in [Bro95, Kel96]. A detailed review about the SESAM principle, different SESAM designs, and SESAM requirements for mode-locking lasers is given in [Kel99].

Special requirements for SESAM used in high-power lasers and the technical imple- mentations by design issues and dielectric coatings can be found in [Sar12b]. The working group of Prof. M. Guina at the Technical University of Tampere is specialized on different material systems, growth, and annealing techniques of saturable absorbers [Hak05, Gui07, Pak08, Hak08, Puu10, Paa14].

The layer structure of a SESAM is given at the beginning of this Chapter followed by sections about its optical properties. Different methods to tailor the SESAM properties are given in Section 3.4. At the end of this Chapter SESAM requirements for high-power thin-disk lasers are listed.

Experimental methods for the characterization of SESAMs and new SESAM design concepts are focused in separate Chapters of this thesis.

3.1 Layer structure of a SESAM

A SESAM is a semiconductor layer structure where a quantum well absorber is sandwiched between a bottom Bragg mirror and a top mirror, as it can be seen in Fig.

3.1. The quantum well absorbers are positioned in the so called active layer. For an optimum absorption the absorbers are located at the maximum of the standing wave inside the structure [Sp¨u05]. The material of the quantum well must be absorbing for the laser wavelength. Thus, for laser wavelengths in the near infrared InGaAs is widely used as quantum well absorber. The top mirror of a SESAM is in the simplest form the

(30)

Refractive index 4 3 2 1

top mirror

ë/4 z

AlAs AlAs

GaAs GaAs GaAs

QW

GaAs-

substrate bottom Bragg mirror:

25 x AlAs/GaAs

active layer

Figure 3.1: Typical quarter wave (λ/4) layer structure of a SESAM. The active layer with the quantum well absorbers is sandwiched between a bottom Bragg mirror and a top mirror. In the zoom the refractive indexes of the alternating materials is plotted.

For a laser wavelength of 1030 nm the Bragg mirror typically consists of 20-30 pairs of GaAs/AlAs layers.

(31)

3.1 Layer structure of a SESAM

980 1000 1020 1040 1060 1080 1100 1120 1140

0 10 20 30 40 50 60 70 80 90 100

Wavelength (nm)

Reflectivity (%)

Figure 3.2: Typical static reflectivity spectrum of a SESAM. The reflectivity is mainly determined by the reflectivity of the Bragg mirror and exhibits a region of nearby 100 % reflectivity, called the stopband, and oscillations below and above the stopband. These oscillations are based on destructive and constructive multilayer interference. The dip within the stopband at approximately 1090 nm results from excitonic absorption of the quantum well of the SESAM.

GaAs/air interface. Due to the difference in refractive index this mirror has a reflectivity of about 30 %. By dielectric coatings the reflectivity of the SESAM, respectively the field intensity within the SESAM, can be changed. Thus, important parameters such as the modulation depth or the saturation fluence can be influenced. A detailed analysis of coated SESAMs is given in [Sp¨u05] and [Sar12b] and is summarized in Sec- tion 3.4. The laser wavelength the SESAM is made for determines its layer structure.

The Bragg mirror is made of a sequence of alternating materials leading to a mirror with a reflectivity close to 100 %. For a laser wavelength of 1030 nm the Bragg mirror is typically made of 20-30 pairs of GaAs/AlAs.

(32)

3.2 Optical properties of a SESAM

3.2.1 Static reflectivity

The static reflectivity of a SESAM is mainly determined by the static reflectivity of the Bragg mirror. The Bragg mirror consists of a material with a high refractive index n_H and a material with low refractive index n_L. Typical materials for semiconductor Bragg mirrors for near infrared are AlAs/GaAs layer systems.

The reflectivity of the Bragg mirror is based on multilayer interference. Due to the difference of the refractive indexes of the Bragg mirror materials the incoming electromagnetic wave is partially transmitted and partially reflected on each interface. The reflected waves interfere constructively for a quarter wave layer structure where the single layers have a thickness of d = λ(4n)⁻¹, where n is the refractive index of the layer material and λ the laser wavelength [Dem04]. Hence, by means of multilayer interference the Bragg mirror is a device with a reflectivity close to 100 % for appropriate wavelengths. The wavelength range where the waves are best reflected is called stopband. The reflectivity of the stopband increases with the amount of layers build- ing the Bragg mirror. Increasing the ratio n_H/n_L of the refractive indexes leads to a broadening of the stopband [She95b]. A formalism to calculate the reflectivity spectra of a multilayer system can be found in [Bor86, She95b]. A formalism based on transfer matrix method is briefly introduced in Section 4.4.2.

Fig. 3.2 shows a typical static reflectivity spectrum of a SESAM. The spectrum clearly exhibits the stopband in the region of 1000-1100 nm. The dip within the stopband at approximately 1090 nm results from excitonic absorption of the quantum well. The oscillations outside the stopband region are due to multilayer interference.

3.2.2 Nonlinear reflectivity

As already mentioned the reflectivity of a SESAM depends on the incoming light intensity. Due to the absorber the reflectivity is lower for small intensities and increases with increasing intensity due to the absorber’s bleaching. This leads to a nonlinear reflectivity curve as it is plotted in Fig. 3.3. Based on this curve crucial parameters for SESAM characterization are stressed and will be explained in the following. The labels of the characterizing parameters are taken from [Hai04].

In Fig. 3.3 the reflectivity of a SESAM versus incoming fluence is plotted where fluence F_P = E_P/A is the pulse energy E_P per area A. When nonlinear effects such as two-photon absorption and free-carrier absorption are neglected the reflectivity increases and saturates at a given value (blue curve in Fig. 3.3). Taking into account nonlinear effects at high fluences (see Section 3.3.2) the reflectivity exhibits a roll-over and decreases again, as the red curve in Fig. 3.3 shows it [Hai04].

The maximum change of reflectivity is called modulation depth ∆R_mod and is determined by the difference between the linear reflectivity of a nonsaturated SESAM R_lin and a fully saturated SESAMR_ns: ∆R_mod =R_ns−R_lin.

(33)

3.2 Optical properties of a SESAM

10⁰ 10¹ 10² 10³ 10⁴

95 96 97 98 99 100

Reflectivity (%)

Fluence (µJ/cm²)

∆ R

∆ R eff mod

∆ R R ns

ns

Rlin

Fsat

Figure 3.3: Typical nonlinear reflectivity curves of a SESAM. The important characterizing parameters are explained in detail in the text. The blue curve is calculated according to Eq. (3.1). In the calculation of the red curve nonlinear effects such as two photon absorption and free carrier absorption are taken into account leading to the roll-over at high fluence values. This curve is calculated according to Eq. (3.2).

Both calculations are based on the following input parameters: R_lin=95.9 %,R_ns=99.0

%,F_sat=50 µJ/cm², andF₂=500 000µJ/cm² for the red curve.

(34)

However, due to the roll-over the maximum reflectivity decreases leading to a reduced modulation depth, which we call effective modulation depth ∆R_eff which is given by the difference of the maximum reflectivity and the linear reflectivity:

∆R_eff=Maximum(Reflectivity)−R_lin=Maximum(R(F_P)−R_lin)=Maximum(∆R).

∆R_ns are the nonsaturable losses and are determined by ∆R_ns = 100%−R_ns.

Reasons for nonsaturable losses are scattering losses at defect states and the surface of the SESAM, losses due to two-photon absorption and free-carrier absorption, and the reflectivity of the Bragg mirror that is just close to 100 % [Kel99].

The saturation fluenceF_sat characterizes the beginning of the saturation of the absorption. F_sat is the fluence value where the reflectivity reaches approximately 1/e≈ 37%

of the modulation depth: R(F_sat) =R_lin+ 1/e·∆R_mod. Hence, the saturation fluence characterizes the steepness of the nonlinear reflectivity curve.

The measure of the reduction of the reflectivity for high fluence values due to nonlinear effects is the roll-over parameter F₂. Analogous to F_sat the parameter F₂ corresponds to a fluence value, in particular a reflectivity curve with a strong roll-over has a small F₂-parameter, whereas a large F₂-parameter indicates that the roll-over occurs at high fluence values.

As it is published in [Hai04] the nonlinear reflectivity curve of a SESAM is based on these parameters and can be calculated according to

R(F_P) =R_ns ln

h

1 +Rlin/Rns

exp(FP/Fsat)−1 i

FP/Fsat

(3.1) with F_P as the pulse fluence.

In Equation (3.1) nonlinear effects are not taken into account. However, since in a laser cavity fluence values of a hundredµJ/cm²or even mJ/cm² can be reached, these fluence values are high enough to induce effects of induced absorption within the SESAM (see Section 3.3.2) that reduce the reflectivity. Hence, Equation (3.1) has to be modified and the reflectivity is given in [Hai04]:

R(F_P) =R_ns lnh

1 +R_lin/R_ns

exp(F_P/F_sat)−1i

F_P/F_sat exp(−F_P/F₂). (3.2) The reflectivity curves in Fig. 3.3 are based on Equations (3.1) and (3.2).

The roll-over parameter F₂ is a crucial parameter of SESAMs for high-power lasers, since it describes the reduction of the modulation depth. This has a negative impact for high-power lasers where the SESAM should exhibit the full modulation depth even at very high fluence values. Therefore, a large F₂-parameter is required. Different methods to influenceF₂ and other SESAM parameters will be stressed in Section 3.4.

(35)

3.3 Elementary processes in a SESAM

The intensity dependent reflectivity of a SESAM results from the saturation of the electronic transitions within the quantum well absorber. If an electron from the valence band absorbs incoming light with a photon energy exceeding the band gap energy the electron is excited into the conduction band. Due to the fact that the density of states in the conduction band of semiconductors is smaller than the density of states in the valence band, for high fluence values all states are occupied [Yu03]. Hence, due to band filling and Pauli’s exclusion principle the absorber bleaches and the photons are reflected by the Bragg mirror. This leads to an increase of the reflectivity with increasing light intensity. One distinguishes between single-photon absorption and induced absorption, two effects which will be discussed separately in the next sections.

3.3.1 Single photon absorption

If a SESAM is excited by a laser pulse with photon energy exceeding the band gap energy of the quantum well the absorption process is followed by different regimes of carrier distribution and carrier dynamics. The following regimes are taken from [Sha99]

and are explained in the following paragraph. Fig. 3.4 shows a schematic representa- tion of the carrier distribution and carrier dynamics.

The excitation energy of the photon exceeds the band gap energy so that the electron is excited in states above the band minimum, as it is shown in transition (1) in Fig. 3.4.

In SESAMs resonant excitation is avoided to prevent excitonic absorption close to the band gap energy. The carrier distribution directly after excitation is called coherent regime, since there is a fixed phase relation between the excited states and the exciting electromagnetic wave. Due to electron-phonon scattering and electron-electron scattering this regime is destroyed and the so called nonthermal regime follows. This regime is specified by the temperatures of the carrier distributions which exceed the lattice temperature. The excited electron-hole pairs thermalize mainly via carrier-carrier scattering, corresponding to transition (3) in Fig. 3.4, which leads to the hot carrier regime. The hot carriers lose their energy mainly via phonon interaction and relax in the band minimum, as it is shown in process (3) in Fig. 3.4. All carriers and phonons within the semiconductor are now thermally balanced.

The relaxation process is followed by the recombination process, where defect states function as recombination centers, as it is shown in transition Fig. 3.4 (4). The electron-hole pairs recombine nonradiative. The final regime after the relaxation is called isothermal regime.

These carrier dynamics determine the transient reflectivity in pump-probe measurements of SESAMs. For low fluence values and an exciting fs-pulse the transients exhibits a biexponential decay: The first decay with a fast time constant in the fs- regime correspond to the thermalization and relaxation process of the excited electrons, whereas the slow time constant correspond to the recombination process [Kel99]. As it is described in Section 3.4, the slow time constant is determined by the amount of defect states and can vary from a few ps up to ns depending on growth parameters.

(36)

VB CB

(1) (2)

(3)

(4)

E_gap D

(III) (I)

(II)

k E

Figure 3.4: Carrier dynamics in a semiconductor after optical excitation with photon energy exceeding the band gap energy: E_photon > E_gap. (1) Excitation of the electron from the valence band (VB) into the conduction band (CB) by photon absorption.

The carrier distribution is given by the energy spectrum of the exciting field (I). (2) Thermalization of the nonthermal regime into the hot electron regime by means of electron scattering. (3) Relaxation of the hot electrons into the conduction band minimum via phonon scattering. The carrier distribution is given in (II). (4) Electron-hole recombination via defect states (D). (III) shows the carrier distribution of the holes.

The figure is adopted from [Sei03], the carrier dynamics are taken from [Sha99].

Characterization and optimization of mode-locking of a high-power Yb:YAG thin-disk laser