Journal of Modern Physics, 2013, 4, 23-28
doi:10.4236/jmp.2013.45B005 Published Online May 2013 (
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
Received 2013
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
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
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-
Copyright © 2013 SciRes. JMP
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-
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.
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,
 
, (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
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
Rf PRf
. (4)
For the linear case of Rfi dependence on power Pp it
eq ()=i
. (5)
Copyright © 2013 SciRes. JMP
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. 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
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.
Copyright © 2013 SciRes. JMP
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 =
4.2. Crystal Equivalent Temperature Kinetics
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
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:
. (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.
Copyright © 2013 SciRes. JMP
here m is crystal mass, c is specific heat capacity, S is
crystal surface area. Optical absorption coefficient is cal-
culated as follows
() T
. (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-
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)
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
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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