Acousto-Resonance Spectroscopy of Nonlinear-Optical Crystals in Process of Laser Frequency Conversion

doi:10.4236/jmp.2013.45B005

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Journal of Modern Physics, 2013, 4, 23-28

doi:10.4236/jmp.2013.45B005 Published Online May 2013 (http://www.scirp.org/journal/jmp)

Acousto-Resonance Spectroscopy of Nonlinear-Optical

Crystals in Process of Laser Frequency Conversion

O. A. Ryabushkin1,2 , A. V. Konyashkin1,2 , D. V. Myasnikov1,2, V. A. Tyrtyshnyy2,

O. I. Vershinin1,2, A. I. Baranov1,2

1Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudnyy, Russia

2NTO “IRE-Polus”, Vvedensky Sq.1, Fryazino, Russia

Email: [email protected]

Received 2013

ABSTRACT

Dependence of the periodically poled nonlinear-optical lithium niobate (PPLN) crystal temperature on laser power in

the course of laser frequency conversion was measured using piezoelectric resonance. Crystal’s temperature tuning

curves are precisely measured using concept of the equivalent temperature. Both optical absorption and heat transfer

coefficients of the crystal are measured employing kinetics of the crystal equivalent temperature.

Keywords: Piezoelectric Resonance; Nonlinear-Optical Crystals; Second Harmonic Generation; Equivalent

Temperature

1. Introduction

Nonlinear-optical crystals are widely used in various

nonlinear-optical processes [1-6]. Due to optical absorp-

tion any interaction of the laser radiation with crystals

results in its heating. In high-power laser applications

optical absorption can cause crystal structural defects

formation and even its destruction [7,8].

It is well known that efficient nonlinear frequency

conversion occurs when phase matching condition is

fulfilled for wavelengths involved [1]. Here the crystal

temperature control plays crucial role because tempera-

ture deviation from the optimum point results in effi-

ciency decreasing. Pump power increase leads to crystal

overheating and phase matching violation. In Second

Harmonic Generation (SHG) experiments optimum tem-

perature is usually determined by adjusting the thermostat

temperature while monitoring the output second harmonic

power.

It is well known that most crystals applied in nonlinear

optics possess piezoelectric properties. External radiof-

requency electric field excites acoustical vibrations in

such crystals due to indirect piezoelectric effect. When

external electric field frequency coincides with one of the

crystal internal acoustical mode frequency the piezoelec-

tric resonance is excited.

Strongly temperature-sensitive piezoelectric resonance

frequency is a powerful tool for research of nonlinear-

optical crystals interaction with laser radiation. It was

demonstrated that such important properties as ionic

conductivity [9,10] and optical absorption [11-13] can be

precisely measured using crystal piezoelectric resonances.

Novel method based on the piezoelectric resonance

spectroscopy technique was proposed for the accurate

temperature determination of nonlinear-optical crystal

interacting with laser radiation [12,13].

It was demonstrated that for the extremely wide range

of laser power values the internal crystal temperature can

be directly determined by measuring its piezoelectric

resonance frequency shift [12,13]. Thus measured tem-

perature is called crystal equivalent temperature θeq. In

this paper we present results of the periodically poled

nonlinear-optical lithium niobate (PPLN) crystals tempera-

ture measurement in the course of the second harmonic

generation of the CW single-mode ytterbium-doped fiber

laser radiation.

2. Experiment

2.1. Crystal Samples

Two specimens of PPLN crystals were used in the experi-

ment. Both are rectangular parallelepipeds with dimen-

sions 1  2.6  4.9 mm3 (PPLN1) and 1 × 3 × 10 mm3

(PPLN2) respectively. Crystals are poled along z-axis (1

mm) and quasi-phase-matched for SHG of the 1064 nm

wavelength. Crystal’s input and output facets are

anti-reflective coated for both 532 nm and 1064 nm.

2.2. Experimental Setup

Simplified block-scheme of the experimental setup for the

nonlinear-optical crystal’s electrical impedance measure-

O. A. RYABUSHKIN ET AL.

ments during interaction with laser radiation is shown in

Figure 1. Crystal sample is placed in unclamped manner

onto silica fibers between two strip metallic electrodes

that form the capacitor. Voltage of the frequency f from

the radiofrequency (RF) generator is applied to the ca-

pacitor that is connected in series with the load resistor R

= 50 Ohm. Capacitor with crystal in it is placed inside

the thermostat. Temperature stabilization is better than

50 mK. Crystal response to the applied electric field is

analyzed by measuring spectra of the voltage amplitude

|UR| and phase φ on the load resistor via lock-in amplifier.

These signals are proportional to the amplitude and phase

of the electrical current flowing through the crystal. Thus

crystal electrical admittance can be calculated. At the

certain frequency Rf piezoelectric resonance between the

external electric field and one of the crystal internal vi-

bration modes can be observed.

CW laser source is polarized single-mode ytterbium-

doped fiber laser. Operating wavelength is λ1 = 1064 nm,

spectral line width is 0.1 nm, output power is up to 25 W.

Beam quality factor М2 is 1.05. Laser polarization degree

is 20 dB. Laser beam is focused inside the crystal. Beam

waist is 30 µm. Beam splitter is used for separating pump

λ1 = 532 nm and orthogonally polarized second harmonic

λ2 = 532 nm radiation.

Temperature calibration of the piezoelectric resonance

frequencies should be performed prior to the investiga-

tion of the crystal interaction with laser radiation. Figure

2 shows dependencies of the UR voltage phase φ on fre-

quency f measured near PPLN1 piezoelectric resonance

for two temperatures. Piezoelectric resonance frequency

Rfi at each temperature corresponds to the phase mini-

mum.

3. Crystal Equivalent Temperature

When crystal is uniformly heated its resonance frequency

Rfi linearly depends on crystal temperature θcr with the

piezoelectric thermal coefficient prt

of the particular

i-th vibration mode [12,13]:

Figure 1. Block scheme of the experimental setup for meas-

uring piezoelectric resonances of the nonlinear-optical

crystal during its interaction with laser radiation.

Figure 2. Frequency dependencies of the UR voltage phase

measured near PPLN1 piezoelectric resonances for two

crystal temperatures.



()=()+

prt

icr icr

RfRf K











. (1)

here θ0 is initial crystal temperature.

When crystal is nonuniformly heated by laser radiation

its temperature distribution can be obtained by solving

heat conduction equation using appropriate boundary

condition at the crystal-air interface. In assumption of

weak optical absorption and crystal convective air cool-

ing it can be written as follows



in out

θ() ,0,

θθθ.

Ixy





















 





, (2)

here κcr and κa are thermal conductivities of the crystal

and air respectively; I(x,y) is radiation intensity distribu-

tion; α(λ) is optical absorption coefficient, which is

wavelength dependent; θin and θout are temperatures at the

interface of crystal and air respectively; n is the normal

vector to the interface; hT is the heat transfer coefficient.

It was demonstrated earlier that piezoelectric reso-

nance frequencies dependence on laser power Pp can be

characterized by piezoelectric resonance optical coeffi-

cients pro

[12,13].

Then temperature of the laser heated crystal can be

precisely determined using notion of crystal equivalent

temperature. Crystal equivalent temperature is expressed

as follows

eq0 eq

() ()







 . (3)

Here θ0 is crystal temperature at Pp = 0 and Δθeq (Pp) is

crystal equivalent heating temperature determined directly

from the i-th piezoelectric resonance frequency shift

() (0)

()=

ip i

pprt

Rf PRf





. (4)

For the linear case of Rfi dependence on power Pp it

equals

eq ()=i

pro

prt





. (5)

O. A. RYABUSHKIN ET AL. 25

Here β is piezoelectric resonance optothermal coeffi-

cient. Value of β depends on crystal optical absorption

α(λ), polarization of laser radiation and heat exchange

conditions. However, in case of nonlinear-optical fre-

quency conversion crystal is heated nonlinearly. Still its

temperature can be determined using relations (3) and

(4).

4. Experimental Results

4.1. Stationary Measurements of Crystal

Equivalent Temperature

Piezoelectric resonance thermal coefficients were meas-

ured using eq. (1) for two resonances observed in PPLN1

and PPLN2 crystals. Parameters of the piezoelectric reso-

nances selected for detailed investigation are listed in

Table 1.

Crystal equivalent temperature θeq was measured for

each pump laser power Pp value after reaching stationary

temperature state of the crystal with surrounding air.

Thermostat temperature was fixed at 20℃. It was observed

that when laser polarization is perpendicular to the crystal

poling axis no second harmonic is generated and crystal

equivalent temperature linearly depends on pump power

for both crystals. In case laser polarization ep is parallel

to the crystal poling axis second harmonic can be efficiently

generated when crystal is at phase matching temperature.

Results of crystal’s equivalent temperature measurement

for the case of pump power subsequent increase from 0

to its maximum are presented in Figure 3.

Table 1. Crystal piezoelectric resonances.

Piezoelectric resonance parameters

Crystal

Rf at θ0=297 K, kHz prt

, Hz/K

PPLN1 2023.4 –179

PPLN2 2006.6 –150

Figure 3. Dependencies of the equivalent temperature on

laser power measured for PPLN1 and PPLN2 crystals.

As it can be seen for low Pp values both PPLN1 and

PPLN2 are linearly heated with coefficients β1 = 1.7 K/W

and β2 = 1.3 K/W respectively. Above certain power

value (Pp = 13.4 W for PPLN1, Pp = 15.6 W for PPLN2)

abrupt temperature rise occurs because crystal tempera-

ture approaches to the corresponding phase matching

temperature. These points are unstable because small

increase of Pp leads to rapid rise of both second harmonic

power Psh and crystal temperature (see Figure 4). PPLN1

crystal stationary temperature point at Pp =13.5 W is

slightly less than its phase matching temperature θpm.

PPLN2 has higher value of θpm. So that here break point

is observed at higher Pp value. Second harmonic power

rose from Psh = 50 mW at Pp = 15.6 W reaching 750 mW

and resulted in stationary Psh = 150 mW at Pp=16.6 W. It

means that PPLN2 temperature overcame the phase

matching temperature. Further power increase results in

moderate θeq rise. If now after reaching its maximum

pump power is subsequently decreased then the tem-

perature break point occurs at lower Pp value.

Experimental results of θeq and Psh dependence on Pp

measured for PPLN2 when Pp is lowered are presented in

Figures 5 and 6. Here crystal temperature is once again

approaches to the phase matching temperature at Pp = 12

W (Figure 5). At the next point Pp = 11.4 W PPLN2

Figure 4. Dependencies of the second harmonic power on

the pump power measured for PPLN1 and PPLN2.

Figure 5. Dependencies of PPLN2 equivalent temperature

on pump power measured for Pp increase to maximum and

subsequent decrease to zero.

O. A. RYABUSHKIN ET AL.

crystal temperature is considerably lower than phase

matching temperature. Second harmonic power nonline-

arly rose from Psh = 70 mW at Pp = 25 W to Psh = 350

mW at Pp = 12 W and then fell to Psh = 10 mW at Pp =

11.4 W (see Figure 6).

True temperature tuning curves of the PPLN crystals

can be also precisely measured using concept of equiva-

lent temperature. In this case thermostat temperature

should be tuned when pump power is fixed. Results ob-

tained for PPLN1 crystal are presented in Figure 7. PPLN1

phase matching temperature decreases with power:

dθpm/dPp = – 0.11 K/W. Crystal temperature acceptance

bandwidth is almost the same for these Pp values: Δθpm =

6℃.

4.2. Crystal Equivalent Temperature Kinetics

Measurements

Conventional method for the precise determination of

optical absorption coefficients of nonlinear-optical crys-

tals is laser calorimetry [14]. It is based on measurements

of the heating kinetics of air near the crystal surface dur-

ing and after laser irradiation. Both optical absorption α

Figure 6. Dependencies for ep|| Zcr of the second harmonic

power on the pump laser power measured for Pp increase to

maximum and subsequent decrease to zero.

Figure 7. Temperature tuning curves measured for PPLN1

at different pump powers.

and heat transfer hT coefficients are then calculated by

solving nonstationary heat conduction equation taking

into account boundary conditions. To the present day

there are no simple direct methods for the precise crystal

temperature measurement during interaction with laser

radiation.

Novel modification of calorimetry technique that we

propose is to use concept of the crystal equivalent tem-

perature for measuring temperature kinetics of the laser

heated crystal. Crystal equivalent temperature kinetics is

directly measured using resonance frequency shift ΔRf

dependence on time t when the laser power is switched

on. Here we use the same experimental setup. As it is

shown in Figure 8 the RF generator frequency f is changed

stepwise (step Δf) and phase response (φ) minimum that

corresponds to Rf at moment ti is measured in each Δt

interval. Characteristic Rf kinetics time constant τ is ob-

tained using fitting function

()()() exp()()

RftRftRf PtRf P





 

 . (6)

Here Rf (Pp) corresponds to the temperature stationary

point for the given power Pp. Obviously crystal equiva-

lent temperature kinetics τ value is identical to that of Rf

kinetics. Then heat transfer coefficient is obtained:

Tmc



. (7)

Figure 8. Experiment of Rf kinetics measurement: time

dependence of Rf (corresponds to φ minimum) is measured

via stepwise change of the generator frequency f.

O. A. RYABUSHKIN ET AL. 27

here m is crystal mass, c is specific heat capacity, S is

crystal surface area. Optical absorption coefficient is cal-

culated as follows

() T

LhS







. (8)

here L is crystal length. Equivalent tempearature kinetics

measured for PPLN1 crystal for Pp = 5.6 W is shown in

Figure 9. Values of hT and α(λ)L obtained for PPLN1

crystal (L = 4.9 mm) are summarized in Table 2.

5. Discussion and Conclusions

Novel powerful method of acousto-resonant spectroscopy

employing concept of crystal equivalent temperature was

applied for precise PPLN temperature measurement dur-

ing nonlinear-optical interaction with laser radiation.

Hysteresis of PPLN temperature and optical bistability

of second harmonic power in respect to pump power

were observed in the course of second harmonic genera-

tion.

Temperature tuning curves of nonlinear-optical crystals

can be precisely measured using concept of the equiva-

lent temperature. Rate of phase matching temperature

decrease with pump power measured for PPLN crystal

dθpm/dPp = –0.11 K/W is of the same order as that ob-

tained for MgO:sPPLT crystal (dθpm/dPp = – 0.14 K/W)

[4].

Crystal equivalent temperature kinetics during its in-

teraction with laser radiation is employed for the accurate

measurement of both crystal optical absorption and heat

transfer coefficients.

Our experiments reveal that temperature control of crys-

tals interacting with laser radiation via acoustic resonance

Figure 9. Kinetics of piezoelectric resonance frequency Rf

measured for laser heating of PPLN1 crystal.

Table 2. Results of laser heated PPLN temperature kinetics.

Table Column Head

Crystal

τ, s hT, W/m2K α(λ)L

PPLN1 22.2 43 2.9×10–3

techniques is restricted only by laser powers that lead to

crystal optical damage.

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