Terahertz generation with tilted-pulse-front technique

Terahertz generation with tilted-pulse-front technique

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Author: Lu Wang

Supervisor: Koustuban Ravi, Dr. Xiaojun Wu

September 9, 2015

Abstract

This report discusses the generation of THz pulses with tilted-pulse-front technique. Experimentswith LiNbO3 crystal using pump wavelength of 1030nm and 800nm are discussed separately. Asimulation of the non-linear crystal GaP(Gallium Phosphate) on existing 1D MATLAB code isdeveloped.Keywords: THz, GaP, LiNbO3, tilt-pulse-front

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Lu Wang CONTENTS

Contents1 One dimensional simulation using MATLAB 3

1.1 Introduction to tilted-pulse-front . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Simulation with optical pump of 1030nm . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Effective length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Experiment with LiNb03 crystal 92.1 Experiment Setup for 800nm pump, non-bonded structure . . . . . . . . . . . . . . . . . 9

2.1.1 Optical pump output spectrum detection . . . . . . . . . . . . . . . . . . . . . . 92.1.2 THz signal detection with 800nm pump . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Experiment Setup with 1030nm pump, bonded structure at room temperature . . . . . 112.2.1 Optical pump output spectrum detection . . . . . . . . . . . . . . . . . . . . . . 12

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Lu Wang 1 ONE DIMENSIONAL SIMULATION USING MATLAB

1 One dimensional simulation using MATLAB

1.1 Introduction to tilted-pulse-front

THz enables the time-resolved spectrum measurements in physics, chemistry and biology.3 In addition,THz is amenable to non-invasive detection and charged particle acceleration.4;6 As a result, the genera-tion of high intensity, short pulse THz radiation has been of great interest. The principle of generationof the THz field is based on difference frequency generation or optical rectification (OR) in a nonlin-ear crystal. Femtosecond pulses are generally selected to be the pump.8 In our experiment, pump ofwavelengths of 0.8µm and 1.03µm are discussed separately. Tilted-pulse-front method is used to obtainphase matched THz in the form of a plane wave.2;8 Neglecting the depletion of the optical pump, theTHz field is given as,5

ETHz / Zsinc✓4kZ2

◆�

(2)Ipump. (1)

Here Z is the effective length, 4k is the phase mismatch, �(2) is the second order electric susceptibility.It can be seen from equation (1) that ETHz reaches a maximum when 4k = 0, which is the famousphase-matching condition.

Figure 1: (a) Sketch of difference frequency generation. (b) Tilted pulse front illustration.

As shown in figure (1) (part (a)), the phase matching condition can be written as,

~

k(⌦+ !)� ~

k(!)� ~

k(⌦) = 0��~k(⌦)�� cos � =

��~k(⌦+ !)

�� cos(✓/2)��~k(!)

�� cos(✓/2)��~k(⌦)

�� cos � ⇡��~k(⌦+ !)

��~k(!)

��

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As a result,

nTHz cos(�)⌦

c

⇡��~k(!)

��+d

��~k��

d!

0 |! ⌦��~k(!)

��

cos(�)nTHz ⇡ c

vgp(!)

cos(�) ⇡ ngp(!)

nTHz, (2)

where c is the speed of light, � is the phase matching angle, ~k is the wave vector, vgp(!) is the groupvelocity of the pump at frequency ! and ngp(w) is the corresponding refractive index. nTHz is therefractive index of THz at frequency ⌦. One can also think in another way as illustrated in figure (1)(part (b)). If the newly generated THz is in phase with the previous generated THz, then tvTHz cos(�) =

tvgp(!), where t represents time. This also leads to equation (2).

1.2 Simulation with optical pump of 1030nm

GaP and LiNbO3 have large band gaps compared with the energy of 1030nm optical pump. Therefore,the multiple photon absorption rate is relatively low for the pump, making these crystals ideal candidatesfor THz generation. It is worth to know that equation (2) is valid only when nTHz > ngp(!). This issimilar to the Cerenkov phase-matching condition.10. Study of the GaP is developed from an existing1D MATLAB code for LiNbO3.

Table 1: Properties of materials2;11

Crystal �

(2)[pm/V] n2 [10

�19m

2/W ] nTHz ngp �pump [nm] PM angle

GaP 2*21.7 20 3.34 3.30 1030 8

�

LiNbO3 2*152.4 0.91 - - 1030 62.26

�

The refractive index and absorption coefficients of THz simply follow the Lorentz model.9 To usethe numerical method, the fitting of the Lorentz model at resonance is necessary to avoid blowing upof the data.

Figure 2: The Lorentz model we used is valid within the range from 0 to 10 THz. As a result, theabsorption fitting function is chosen to have high absorption after 10 THz to avoid any unwanted signal.

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More detailed phase matched and non-phase matched situations are illustrated in the figure (3)

(a) (b)

(c) Contour plot of (a) (d) Contour plot of (b)

(e) ETHz at different positions (f) ETHz at different positions

Figure 3: (a), (c), (e) corrsponds non phase matched ETHz amplitude.(b), (d), (f) reprensent phasematched ETHz amplitude. Pump fluence is 500 J/m

2. It is easy to see that in the phase matchedcondition, ETHz adds up in phase and forms a smooth shape with only one maximum value.

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For the phase matched condition, figure(4) and (5) shows the conversion efficiency as a function ofeffective length Z.

Figure 4: One can see that within 1mm, the effect of n2 (self phase modulation) to the conversionefficiency ⌘ is negligible. With the increase of effective length, n2 reduces ⌘ significantly.

Figure 5: The efficiency of GaP takes a much longer distance to saturate. It is due to the absorption ofTHz in GaP is very low. Legend represents the pump fluence in the unite of J/m2.

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Figure 6: The absorption coefficient /alpha of LiNbO3 for THz is nearly a hundred times bigger thanthat of GaP within 1 THz region.

1.3 Effective length

The B integral is a way to evaluate the magnitude of the effective length.1;7

B =

Z2⇡

�

In2dz

B ⇡ 2⇡

�

n2IL

L ⇡ B

2⇡� n2I

,

where n2 is nonlinear refractive index, � is the center wavelength of the pump (1030nm) and I isthe intensity of the IR pump. Meanwhile, I = PumpFluency/⌧ , where ⌧ is the FWHM of the pulseduration of the pump. It is easy to see that high intensities lead to shorter effective lengths, but highintensity also leads to stronger THz generation. Consequently, the overall peak efficiency is difficult tobe determined.

The order of magnitude of the effective length according to the B integral is around 10

�4 m, which isfar smaller than the distance where the efficiency reaches the maximum. We expect to see the efficiencydecrease caused by pump break up when the effective length is beyond this scale, but for some reason,the efficiency keeps growing in the simulation.

There are some other mechanisms that need to be taken into consideration in order to derive areasonable effective length, such as self focusing, absorption of the optical pump, etc.

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Figure 7: Relation of efficiency to pump fluence and pulse duration. At short pulse duration regime, theefficiency doesn’t does not considerably depend on the fluence. At longer pulse duration, the efficiencyis sensitive to the fluence in the low fluence regime and saturates for high fluences

1.4 Conclusion

Assumptions

(1). The simulation is based on zero depletion of the pump, i.e. the simulation assumes that there isno absorption of the pump in the GaP crystal.

(2). The refractive indexes and absorption coefficients are calculated by the Lorentz model. This maynot be very comparable to the reality.

Results

(1). The influence of SPM (self phase modulation) on the phase matching angle is within the range of1

�.

(2). SPM reduces the efficiency.

(3). In the range between 0.3 ps and 1 ps, shorter pulse duration leads to larger conversion efficiency.

(4). The biggest efficiency (0.25%) of THz generation is found at 0.3 ps 900J/m2 in the range [0.3 ps,1 ps], [100J/m2, 900J/m2].

Future developments

(1). Examine the temperature dependence of the refractive index and absorption of THz.

(2). Take self focusing into consideration.

(3). Develop a more realistic way of calculating effective length.

(4). Extend the code to 2D or even 3D.

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Lu Wang 2 EXPERIMENT WITH LINB03 CRYSTAL

2 Experiment with LiNb03 crystal

2.1 Experiment Setup for 800nm pump, non-bonded structure

Figure 8: 800 nm pump sketch of the experiment.

2.1.1 Optical pump output spectrum detection

(a) Conversion efficiency VS pump energy (b) Output spectrum of the optical pump

Figure 9: Optical pump output spectrum and conversion efficiency at room temperature.

The efficiency ⌘ is calculated by

⌘ =

~!THz ⇤N~!IR

(3)

where !THz is the frequency of the generated THz, wIR is the optical pump frequency and N is thecascading number. N is calculated by the spectrum shift.

N =

!IR � !IRshift

!THz(4)

where the !IRshift is calculated by the center of mass method based on the spectrum in figure (9,(b)).Setting the amplitude of each data point of the spectrum to be yi, the corresponding wavelength to be

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xi, one can find that the center wavelength of the shifted spectrum is

�IRshift =

Pi yixiPi yi

. (5)

Consequently, substituting equation (4) and (5) to equation (3), it can be seen that

!IRshift =2⇡c

�IRshift(6)

⌘ =

!IR�!IRshift

!IR. (7)

In equation (7), ⌘ represents the internal efficiency which is at the condition when the absorption andthe collection loss of the THz haven’t been considered.

2.1.2 THz signal detection with 800nm pump

The detection of THz is is based on e-0 sampling.

Figure 10: EO sampling result with 800 nm pump. It can be seen that lower temperature leads tohigher field strength and higher central THz frequency.

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2.2 Experiment Setup with 1030nm pump, bonded structure at room tem-

perature

(a) Crystal (b) Setup sketch

(c) Experiment setup

Figure 11: (a) is 3 different types of bonded structure. We have tested the two that have square wafer.(b) is a sketch of experiment element in the bracket of (c). For the square wafers, the small crystal isbonded with 1 m wafer and the large crystal is bonded with 3 mm wafer.

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2.2.1 Optical pump output spectrum detection

(a) 1 mm efficiency (b) 1 mm spectrum

(c) 3 mm efficiency (d) 3 mm spectrum

Figure 12: Optical pump output spectrum

The above efficiency ⌘ is also calculated by equation (7). However, the highest signal measured on theoscilloscope for 1 mm and 3 mm bonded structures are 0.5⇤10�3mJ and 2⇤10�3mJ separately. With thecondition that the optical pump is 4mJ the final external efficiency ⌘e is 0.0125% and 0.05% separately.The fact that ⌘e is much smaller than ⌘ suggests that there is a big absorption loss and collection lossin the experiment. However, the ⌘e of 3 mm structure is 4 times the value of ⌘e of the 1 mm structure,which is consistent with the trend of ⌘.

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Lu Wang REFERENCES

References[1] Encyclopedia, RP P.: B Integral. https://www.rp-photonics.com/b_integral.html, . –

[Online; accessed 27-August-20015]

[2] Hebling, János ; Yeh, Ka-Lo ; Hoffmann, Matthias C. ; Bartal, Balázs ; Nelson, Keith A.:Generation of high-power terahertz pulses by tilted-pulse-front excitation and their applicationpossibilities. In: JOSA B 25 (2008), Nr. 7, S. B6–B19

[3] Hebling, János ; Yeh, Ka-Lo ; Hoffmann, Matthias C. ; Nelson, Keith u. a.: High-power THzgeneration, THz nonlinear optics, and THz nonlinear spectroscopy. In: Selected Topics in QuantumElectronics, IEEE Journal of 14 (2008), Nr. 2, S. 345–353

[4] Huang, W R. ; Nanni, Emilio A. ; Ravi, Koustuban ; Hong, Kyung-Han ; Wong, Liang J. ;Keathley, Phillip D. ; Fallahi, A ; Zapata, Luis ; Kärtner, Franz X.: A terahertz-drivenelectron gun. In: arXiv preprint arXiv:1409.8668 (2014)

[5] John, Tisch: Nonlinear optics/Laser Technology. Summary of lecture notes. University Lecture,2010

[6] Pawar, Ashish Y. ; Sonawane, Deepak D. ; Erande, Kiran B. ; Derle, Deelip V.: Terahertztechnology and its applications. In: Drug Invention Today 5 (2013), Nr. 2, S. 157–163

[7] Perry, M D. ; Ditmire, T ; Stuart, BC: Self-phase modulation in chirped-pulse amplification.In: Optics letters 19 (1994), Nr. 24, S. 2149–2151

[8] Ravi, Koustuban ; Huang, Wenqian R. ; Carbajo, Sergio ; Nanni, Emilio A. ; Schimpf,Damian N. ; Ippen, Erich P. ; Kärtner, Franz X.: Theory of terahertz generation by opticalrectification using tilted-pulse-fronts. In: Optics express 23 (2015), Nr. 4, S. 5253–5276

[9] Sara, Casalbuoni ; Holger, Schlarb ; Bernhard, Schmidt ; Peter, Schmüser ; Bernd, Steffen ;Axel, Winter: Numerical Studies on the Electro-Optic Sampling of Relativistic Electron Bunches/ DESY. 2005 (2005-01). – TESLA Report

[10] Suizu, Koji ; Kawase, Kodo ; Shibuya, Takayuki: Cherenkov Phase Matched MonochromaticTunable Terahertz Wave Generation. INTECH Open Access Publisher, 2010

[11] Vodopyanov, Konstantin L.: Optical THz-wave generation with periodically-inverted GaAs. In:Laser & Photonics Reviews 2 (2008), Nr. 1-2, S. 11–25

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https://www.rp-photonics.com/b_integral.html

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Terahertz generation with tilted-pulse-front technique