Thermal lensing measurements of Ti: Sapphire crystal

1

Thermal lensing measurements of Ti: Sapphire crystal pumped at 80 MHz

picosecond pulses by Shack-Hartmann wavefront sensor

Mukhtar Hussain a, , Tayyab Imran b, Adam Borzsonyi c, d

a GoLP, Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa,

Av. Rovisco Pais, 1049-001 Lisbon, Portugal b Department of Physics & Astronomy, College of Science, King Saud University, 11541, Riyadh,

Saudi Arabia c ELI-HU Non-Profit Ltd., Dugonics tér 13, Szeged, Hungary d Department of Optics and Quantum Electronics, University of Szeged, P.O. Box 406, H-6701

Szeged, Hungary

ABSTRACT

The thermal lensing effects in the lasing crystal appear to be dominant when the pump laser

focused on the lasing crystal which causes the local heating effect. The spatial refractive index

variations observed if the crystal has non-uniform temperature distribution. In the present study,

the demonstration of thermal lensing effect of Brewster-cut Ti: Sapphire crystal carried out when

pumped by 25 ps pulses at 80 MHz repetition rate with 532 nm central wavelength, while the

average pump power controlled by the attenuator. The thermal lensing effects measured first at the

~293 K temperature and later at ~40 K by using the cryogenic cooling system. The thermal lensing

variations at different average pump power were calculated and measured by using the HASO4

Shack-Hartmann wavefront sensor.

Keywords: Thermal lens, Cryogenic cooling, Ti: Sapphire crystal, Shack-Hartmann wavefront

sensor

1. Introduction

The thermal effects in the solid-state lasing materials have been under considerations more than a

couple of decades [1-3]. In the case of the lasing materials, one of the most problematic phenomena

is the thermal lensing which is caused by the pump beam transverse intensity profile [4-5]. If the

temperature in the crystal is non-uniform, it leads to spatial refractive index variations [6].

Consequently, thermal lens is formed. The high average pump power in amplifiers induced the

thermal effect in amplifying crystal which leads to the distortion of wavefronts of output pulses of

amplifying medium which reduces the focusing stability of laser spot which ultimately decreases

the efficiency of the amplifier. The impact of lensing gets progressively worse at higher repetition

rates when the average pump power is varied as the heat load per unit area increases. The

parameters of the laser significantly affected due to thermal lens effect which results in the

Corresponding author, E-mail address: [email protected]

mailto:[email protected]

2

wavefront distortion [7]. Usually, the improvement in the laser focusing intensity and correction

of wavefront distortion is carried out by employing the adaptive optics [8-11].

The temperature variations in the Ti: Sapphire crystal, the heat distributions and the heat

dissipation of absorbed pulse energy have been simulated [12]. The thermal lens properties and

heat distributions steady-state solutions have analyzed tediously [13]. The thermal lens effect

results in the mismatch of modes between the lasing material surface and wave-front of the beam

which enhanced the amplified spontaneous emission (ASE) and consequently the temporal

contrast drops [14]. Many groups have put effort to reduce the optical absorption in sapphire to

minimize the thermal lensing [15-17]. The reduction in the thermal lensing effect and thermal

distortion in the Ti: Sapphire based laser system carried by employing the water cooling [18-20],

Peltier coolers [21-23] and cryogenic cooler techniques [24-27]. The essential reduction in the

CEP noise because of the thermal instability can be forecasted by the enhancement of thermal

conductivity of Ti: Sapphire crystal at cryogenic cooling [24]. The suppression of thermal lens

effect in the Ti: Sapphire amplifier has been demonstrated [28] by employing the different focal

length lens.

For the experiment to perform, it is essentially required to characterize and optimize the spectral

and temporal evolution of thermal lensing compensated laser systems. Particularly, when the

lasing crystal pumped at a higher repetition rate and higher average pump power, the effect of

thermal lens and wavefront distortion is more significant. This effect needs to investigate and

compensate particularly when high repetition rate amplifier intended to build. In future, we

intended to build a Ti: Sapphire based booster amplifier pumped at a high repetition rate (80 MHz)

at the cryogenic cooling system. Therefore, we put the crystal in a similar condition of amplifier

except end mirrors to measure the thermal lensing at single pass and its effects by varying the high

repetition rate average pump power.

In this study, the thermal lensing effect at 293 K and cryogenic cooled Brewster-cut Ti: Sapphire

crystal which pumped at 80 MHz, 25 ps pulse duration, the central wavelength at 532 nm versus

the average pump power which is controlled by attenuator measured by the HASO4 Shack-

Hartmann wavefront sensor. We measured the focal length of the thermal lens, the wavefront of

pulses, Strehl ratio, beam divergence, Sagittal and Tangential focal length variation and M2 versus

the 80 MHz average pump power.

2. Theoretical calculation of thermal lensing

The focal length based on Gaussian beam approximation of the thermal lens inside the amplifying

crystal expressed as [29]

𝑓 =2𝑘𝜋𝑟2

(𝑑𝑛 𝑑𝑇⁄ )𝐸𝑣=

2𝑘

(𝑑𝑛 𝑑𝑇⁄ )𝐹𝑣 1

where 𝑘 is the thermal conductivity of the crystal, r is the pump radius at Rayleigh length, 𝑑𝑛 𝑑𝑇⁄

is the change in refractive index with temperature, E is the pump energy which converted into heat

and 𝑣 is the repetition rate of the pump and F=E/ (𝜋𝑟2) is the pump fluence. The heating effect of

the crystal can be compensated by cooling the crystal, such as water flow, installing the Peltier

3

cooler or cryogenic cooling system. Cooling of the crystal through water flow is insufficient for

high average power, therefore the cryogenic cooling system or Peltier cooler have been given

preference. The cryogenic cooling can be achieved with a cryogen such as liquid nitrogen or

helium, ideally circulating through channels in a cooling finger and attached to the laser crystal

which must refill from time to time or recycled in a closed loop. Furthermore, to avoid

condensation, the amplifier crystal must operate in a vacuum chamber.

The thermal lensing can be measured in three different ways: first, Measuring the changes in the

radius of curvature with a Shack-Hartmannn wavefront sensor. Second, measuring the beam size

change either with a high dynamic range CCD camera or using a combination of an iris aperture

and a photodiode and a third method is the expansion of the beam into cavity eigenmodes [30].

In this study, thermal lensing effect will be measured by employing the HASO4 Shack-Hartmann

wavefront sensor. The HASO4 wavefront sensor has the absolute accuracy of λ/100 root mean

square (RMS), measures the intensity and phase of beam independently or simultaneously and

renders the information related to the geometric parameters and the cause of perturbations as beam

propagated. The data acquired from HASO4 wavefront sensor can permit to understand the

evolution of beam over space and time, providing the information of beam’s aberrations and causes

of aberrations.

3. Experimental method of thermal lensing measurements

The two commercial laser systems used to study thermal lensing in Ti:Sapphire crystal (Fig. 1). A

first laser system having 532 nm central wavelength, 35 W nominal average power, working at 80

MHz repetition rate with 25 ps pulse duration from Photonics Industries (PS-532-35) used as a

pump. Second laser system (VENTEON power) used as a seed, working at 80 MHz repetition rate,

<8 fs pulse duration with 800 nm central wavelength of pulse energy >7 nJ. The Ti: Sapphire

crystal is a Brewster-cut of 6 mm diameter, 4 mm path length having 5.31/cm absorption at 532

nm. The output pulses from the pumped Ti: Sapphire crystal directed to the charged coupled

devices (CCD) camera and wavefront analyzer (HASO4) by using beam splitter to measure the

beam profile and wavefront distortion. The neutral density filters installed before the CCD and

HASO4 to avoid the optical damage the sensor.

The schematic of the beam alignment of high repetition rate (80 MHz) pumped Ti: Sapphire

crystal, and thermal lensing measuring setup shown in Fig. 1. The Shack-Hartmann wavefront

sensor method is adapted to measure the thermal lensing of Ti: Sapphire crystal. Initially, we

observed and measured the wavefront distortion at room temperature (293 K) and later at 40 K of

Ti: Sapphire crystal pumped by 80 MHz pulses as a function of average pump power. The

wavefront measurement carried out by using HASO4 (Imagine optic) wavefront sensor. Finally,

the thermal lensing analyzed from the wavefront measurements.

4

Fig. 1 Schematic of thermal lensing measurements of Ti: Sapphire crystal

4. Results and Discussions

The thermal lens variation versus average pump power at high repetition rate at various

temperature is calculated according to the equation 1. At 40 K, the thermal conductivity k= 3000

W/ (𝑚. 𝐾), at 77 K, for the Ti: Sapphire the 𝑘 = 980 𝑊/(𝑚. 𝐾) and 𝑑𝑛 𝑑𝑇⁄ = 1.8 × 10−6/𝐾 at

the pump fluence 3 J/cm2; ) and at the 20° C i.e. ~293 K, the thermal conductivity is ~35.4

W/(𝑚. 𝐾)and 𝑑𝑛 𝑑𝑇⁄ = 1.28 10−5/𝐾 [16-17, 31, 32].

The thermal lensing calculation versus average pump power at 80 MHz repetition rate at different

temperature (40 K, 77 K, 293 K) shown in Fig. 2. Which is calculated from the equation (1) by

considering the beam radius of 400 µm and neglecting the transmittance power, one must consider

it in high repetition amplifier. The thermal lensing effect is more significant at room temperature

and has a minor impact at low temperature that ascribed to the cooling system which compensate

the thermal lensing effects.

5

Fig. 2 Thermal lens focal length variation at 80 MHz versus average pump power at 40 K, 77 K

and 293 K

4.1. Measurements of thermal lensing at 293 K

The thermal lens variation along pump power is measured at 293 K up to the maximum power of

3 W at 80 MHz repetition rate as shown in Fig. 3(a). The focal length of the thermal lens decreases

with the increase of pump power from 1.7 m to 1.0 m which induces the heating, aberration,

wavefront distortion. The spatial distribution of energy in laser focal point obtained by measuring

the point spread function (PSF) which obtained by combining the phase and intensity measurement

on the sensor surface via the propagation of electromagnetic field.

The Strehl ratio which describes the quality of the image also obtained from the point spread

function (PSF). The Strehl ratio allows us to compare the actual maximum intensity on the focal

plane to a perfect intensity free of aberrations which fall from 0.966 to 0.333 at a pump power of

3 W as shown in Fig. 3(b). The Strehl ratio decreased with the increase of pumping power

indicating the spatial loss of energy in laser focal plane.

0.5 1.0 1.5 2.0 2.5 3.0

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Fo

ca

l le

ng

th (

m)

Average pump power (W)

0.5 1.0 1.5 2.0 2.5 3.0

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Str

eh

l ra

tio


(a) (b)

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0.5 1.0 1.5 2.0 2.5 3.0

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

Div

. (m

rad

)


0.5 1.0 1.5 2.0 2.5 3.0

0.25

0.30

0.35

0.40

0.45

RM

S (

um

)


0.5 1.0 1.5 2.0 2.5 3.0

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

PV

(u

m)


0.5 1.0 1.5 2.0 2.5 3.0

0.40

0.45

0.50

0.55

0.60

0.65

W0(m

m)


W0

W

Fig. 3 Variation of various parameters at different pumping power at Laboratory temperature (a)

Focal length(b) Strehl ratio (c)Beam divergence (d) Root mean square (RMS) wavefront aberration

(e) Peak to valley (PV) wavefront aberration and (f) Central beam waist (W0), Beam waist (W)

variations

Due to thermal lens effect and aberration, the beam diverges. The divergence of the beam varied

from 0.82 mrad to 1.18 mrad (Fig. 3(c)). The measurements showed the root mean square (RMS)

wavefront aberration and beam divergence increased by the increase of average pumping power

along with central beam waist, as shown in Fig. 3(c & d), respectively. The variation of the peak

to valley (PV) wavefront aberration and beam waist vindicates the observance of wavefront

distortion and fluctuations which attributable to thermal lensing effect in the crystal, Fig. 3(e & f),

respectively.

(c) (d)

(e) (f)

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Fig. 4 (a) Reference Wavefront , (b) Wavefront at 3 W average pump power

The wavefront of the oscillator (VENTEON) and pumped Ti: Sapphire crystal measured by Shack-

Hartmann wavefront sensor HASO4 (Imagine optic). The wavefront signal of the oscillator

(reference wavefront) and Ti: Sapphire crystal when a pump at 3 W is shown in Fig. 4(a & b),

respectively. The wavefront of the pumped Ti: Sapphire crystal indicates the distortion of the

wavefront which is due to the thermal lensing effect. Furthermore, the M2 parameters obtained

from the propagation length of the electromagnetic field in the different surface plane and

reconstructing the envelope of propagation which renders the beam waist position, quality and

beams divergence of the pulse. The M2 value escalated from 1.44 to 2.91 at 3 W average pump

power at 80 MHz which shows a minor beam profile distortion as shown in Fig. 4(b).

4.2. Measurements of thermal lensing at the cryogenic cooling

After measuring the thermal lensing effect in Ti: Sapphire crystal at low average power, the

cryogenic cooling system is employed to measure the thermal lensing effects at high average pump

power. The temperature in the cryogenic cooler adjusted to 40 K and the pump pulses focused into

Ti: Sapphire crystal as shown in Fig. 1. The focal length, beam divergence, propagation length,

Strehl ratio, PV wavefront aberration, RMS wavefront aberration, beam waist variation, sagittal

and tangential focal length variation of Brewster-cut Ti: sapphire crystal versus the average pump

power at 80 MHz measured by employing HASO4 Shack-Hartmann wavefront sensor at 40 K.

(a) (b)

8

0 2 4 6 8 10 12 14 16 18

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8F

oca

l L

en

gth

(m

)


0 2 4 6 8 10 12 14 16 18

0

2

4

6

8

10

12

14

16

18

M2


0 2 4 6 8 10 12 14 16 18 20

0.0

0.2

0.4

0.6

0.8

1.0

Str

eh

l ra

tio


0 2 4 6 8 10 12 14 16 18

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Div

. (m

rad

)


0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

20

25

30

PV

(u

m)


0 2 4 6 8 10 12 14 16 18 20

0

1

2

3

4

5

RM

S (

um

)


(a) (b)

(c) (d)

(e) (f)

9

0 2 4 6 8 10 12 14 16 18

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

W0(m

m)


0 2 4 6 8 10 12 14 16 18

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

W (

mm

)


Fig. 5 Variation of various parameters at different pump power at cryogenic cooling:(a) Focal

length, (b) M 2, (c) Strehl ratio (d)Beam divergence, (e) Root mean square (RMS) wavefront

aberration, (f) Peak to valley (PV) wavefront aberration, (g) Central beam waist (W0) and (h)Beam

waist W variations

The focal length of thermal lens variation versus the average pump power is measured at a

cryogenic cooling temperature up to the average power of 18.57 W at 80 MHz as shown in Fig.

5(a). The focal length of the thermal lens decreases with the increase of average pump power from

1.72 m to 1.06 m while the M2 value of the beam after Ti: Sapphire crystal increased from 1.39 to

16.62, Fig. 5(b). Due to the focusing of the pulses in the cryogenically cooled crystal, the Strehl

ratio falls from 0.96 to 0.017 while the beam divergence increased from 0.755 mrad to 3.18 mrad

as shown in Fig. 5(c & d).

Furthermore, the peak to valley (PV) wavefront aberration and root mean square (RMS) wavefront

aberration increased from 0.835 µm to 28.35 µm and 0.268 µm to 4.78 µm respectively. Which

witnesses the higher wavefront aberration the at the average power of 16 W due to the thermal

lensing effects as shown in Fig. 5(e & f). The variation of the beam waist at the focal point and

beam propagation at (1/e2) shown in Fig. 5(g & h), respectively. The wavefront distortion of laser

pulses happened due to the refractive index distribution in the lasing crystal along with the

distribution of temperature because of optical absorption. The wave-front distortion which is

measured by the HASO4 sensor at the average pump power of ~18 W is shown in Fig. 6. The

wavefront is highly distorted with enormous aberration having RMS and PV aberration of 4.769

µm and 28.668 µm, respectively. This indicates, the chances of optical damage of the crystal

increased, and energy extraction efficiency reduced enormously at high average pump power, high

repetition rate (80 MHz) even at cryogenic cooling (40 K).

(g) (h)

10

Fig. 6 Wavefront measurement at average pump power of 18 W

The variation of the sagittal and tangential focal length along the pump power at cryogenic cooling

(Fig. 7). The sagittal wavefront distortion of the pulses induced by the thermal lensing which

depends upon the absorption coefficient, thermal conductivity, and change in refractive index

variation with temperature of Ti:Sapphire crystal. The sagittal focal length falls by increasing the

average pump power which caused the enhancement of the thermal conductivity while the

tangential focal length varies slightly which attributable to the uneven cooling of crystal i.e. being

more cooled along the tangential direction than along sagittal one. The different gradient of sagittal

and tangential focal length of the wavefront is the clear signature of the thermal lens effects and

aberration in the crystal.

0 2 4 6 8 10 12 14 16 18 20

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Th

erm

al le

ns fo

ca

l le

ng

th (

m)


Sagittal focal length

Tangential focal length

Fig. 7 Sagittal and Tangential focal length variation with the average pump power

The effect of the thermal lens and aberration can be suppressed by cooling mechanics [18-27],

adaptive optics [8-11], beam expander before the amplifier, specific expanding ratio and

introducing beam divergence in injected pulses [28] or introducing the thermal eigenmode [30].

11

Our investigations show that only the cryogenic cooling is not sufficient to overcome thermal

lensing effect at high repetition rate pumped Ti: Sapphire crystal. Therefore, we will adopt the

cryogenic cooling mechanism and adaptive optics to compensate the thermal lensing effect in the

high repetition rate booster amplifier.

5. Conclusion

In the present study, the thermal lensing effects in Ti:Sapphire crystal seeded by 800 nm center

wavelength and pumped 532 nm central wavelength working at 80 MHz repetition rate as a

function of average pump power is calculated and measured at the ~293 K and later at 40 K by

using the cryogenic cooling system. The wavefront distortion at different average pump power

measured by using the HASO4 Shack-Hartmann wavefront pumped at a high repetition rate. The

investigation related to the beam quality, beam divergence, propagation length, Strehl ratio, PV

and RMS wavefront aberration, sagittal, and tangential focal length variation versus the average

pump power shows that the additional adaptive optics is essential along with the cooling

mechanism to suppress the thermal effects and to correct the wavefront aberration.

Acknowledgements

The authors would like to acknowledge the funding from ELI-ALPS with project number of

GINOP-2.3.6-15-2015-00001. The authors are thankful for Prof. Karoly Osvay at ELI-ALPS and

the people of the TeWaTi femtosecond laboratory at the Department of Optics and Quantum

Electronics of University of Szeged for facilitating the experiments.

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Thermal lensing measurements of Ti: Sapphire crystal