ABSTRACT
Thinking about the pumping and generated power of the longitudinally diode-pumped solid-state laser enhancement,
the question of an active material cooling should be solved. One of the possible solutions is the active
material cooling surface enlargement. Besides the cylindrical surface of the crystal, the laser rod front surfaces
could be cooled through undoped ends. The temperature gradient e ect in three various samples was investigated
in a computer experiment, and the di erences in generated output power were measured experimentally.
The samples were three Nd:YAG rods - one conventional, one with one undoped end, and one with two undoped
ends. The crystal samples were placed in sequence into a resonator 6 cm long and longitudinally diode-pumped.
The dependencies of the generated power on the absorbed pump power have shown that with the two undoped
ends the output power is more than twice as high as against the conventional Nd:YAG sample. The results
were explained by a computer experiment based on the heat transfer equation solution where the changes of
the temperature gradient were least for the Nd:YAG rod with two undoped ends.
Keywords: diode pumped solid state lasers, Nd:YAG, composite laser active medium
1. INTRODUCTION
Since the rst report on laser radiation by Maiman, many potential elds for its application have been investigated.
Various kinds of lasers have already become irreplaceable tools of modern technology, microelectronics,
metrology, holography, medicine, etc. For many of these elds, a more compact and even smaller laser system
with improved eciency could be very suitable.1 For that reason the diode pumped solid state lasers could
be the good compromise.2 As concern the pumping and generated power of longitudinally diode-pumped solidstate
laser enhancement, the question of active material cooling should be investigated. One possibility how to
decrease thermal e ects (such as thermal lensing and thermal stress-induced birefringence) and enhance the
laser system performance is to use advanced solid-state laser composite crystals.3 Using of the doped and the
undoped laser rod components enlarges the active material cooling surface and improves laser active media
thermal uniformity and heatsink.
This concept was experimentally con rmed using the diode end-pumped composite solid state laser. Three
types of crystals (the rst was a conventional Nd:YAG, the second a Nd:YAG crystal with one undoped end,
and the third a Nd:YAG crystal with two undoped ends) were tested in a resonator 6 cm long. The laser was
end-pumped by a 20 W bre coupled 808 nm laser diode. The output parameters and temperature of the
sample holder were measured. For better understanding of such system's thermal behavior, its mathematical
model was composed. This model was based on the numerical solution of the heat transfer equation using the
Finite Element Method and allowed to calculate the temperature eld, temperature gradient, and heat
ux
inside the laser crystal and in its nearest environment.
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2. EXPERIMENTAL COMPONENTS AND MATHEMATICAL MODEL
2.1. Active Nd:YAG material description
As the active material, three yttrium aluminum garnet rod samples doped with the neodymium ion (Nd-1 at. %)
were investigated in a physical and later in a computer experiment. The diameter of all the three samples was
equal to 5 mm. One of the samples was the conventional type Nd:YAG crystal 1 mm long (Fig. 1a). The second
sample was composed of a Nd:YAG crystal 1 mm long and an undoped yttrium aluminum garnet 3 mm long
(Fig. 1b). The third sample consisted of two undoped ends with a length of 3 mm each (Fig. 1c), and also of
an yttrium aluminum garnet 1 mm long doped with neodymium. The outer frontal part of all the samples had
antire
ection coatings for the wavelength of pumping and generated radiation.
Figure 1. Schematic of three investigated samples - (a) Nd:YAG crystal (0U), (b) Nd:YAG crystal with one undoped
part (1U), (c) Nd:YAG crystal with two undoped YAG parts (2U).
2.2. Nd:YAG diode pumped laser
2.2.1. Nd:YAG diode pumped laser construction
The pumping source used was a laser diode HLU20F400 (LIMO Laser Systems) with the maximum output
power 20 W at the end of the ber ( bre core diameter: 400 ¹m, numerical aperture: 0.22). The diode radiation
was focused into the active Nd:YAG crystal by two plan-convex lenses (L1, L2) with the focus length f = 50 mm.
The measured diameter of pumping beam focus inside the crystal was 390 mm. The resonator of the Nd:YAG
laser was formed by a planar dielectric mirror R1 with high transmissivity for the pumping radiation (RR1 <
1 %@808 nm) and high re
ectance for the generated radiation (RR1 = 100 %@1.06 ¹m), and by a concave
(r = 100 mm) dielectric mirror R2 serving as an output coupler (re
ectance for the generated wavelength
RR2 = 98 %@1.06 ¹m). The open resonator length was 60 mm (Fig. 2). Each active crystal was inserted into
the laser cavity to have the active (doped) part in the focus of the pumping beam.
Figure 2: Layout of diode pumped Nd:YAG laser.
2.2.2. Nd:YAG diode pumped laser model
The mathematical model for unstable di usion of heat in a body of some kind is a parabolic partial di erential
equation.4 The general di erential equation of heat conduction for a stationary, homogenous, isotropic solid
with heat generation within the body is where T is temperature distribution within the body, Q heat generation rate in the medium [W=m3], and t is
time; parameter k is thermal conductivity coecient of the material [W:m¡1:K¡1], ½ is density of the medium
[kg=m3], and Cp is the corresponding speci c heat [J:kg¡1:K¡1].
Figure 3. The layout of the crystal mount, its simpli ed model, cylindrical coordinates, and model geometry used
for calculations with speci ed boundary conditions. Subdomains: A - laser crystal (composite), B - cuprous ring, C -
high-re
ecting
at mirror, D - brass socket, E - duralumin kinematic mirror mount, F - air. Boundary conditions: (0) -
the Neumann homogenous boundary condition, (1), (2) and (3) - the Dirichlet boundary condition.
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laser crystal, cuprous ring, high-re
ecting
at mirror, brass socket, duralumin kinematic mirror mount, and air.
The laser crystal was placed inside the cuprous ring xed together with the high-re
ecting
at BK7-glass mirror
inside a brass socket. It was screwed in a duralumin kinematic mirror mount surrounded by air. The arrangement
is shown in Fig. 3a. The necessary physical properties of the materials used are presented in Table 1. For the
sake of simplicity, the geometry of the crystal mount was reduced so as to be axially symmetric (Fig. 3b). Thus
a cylindrical coordinate system could be used and the problem reduced from 3D to 2D. The nal 2D-geometry
used for calculations is shown in Fig. 3d. The heat conduction equations in the cylindrical coordinate system
(r; Á; z) shown in Fig. 3c thus become,
The di erential equation of heat conduction will have numerous solutions unless a set of boundary conditions
and an initial condition are prescribed. The initial condition speci es temperature distribution in the medium
at the origin of the time coordinate. In this case, the temperature of the system is 30 ±C at the time t = 0.
The boundary conditions specify the temperature or heat
ow at the boundaries of the region. The surrounding
temperature at the outer boundary is set to be 25 ±C. The cylinder axis r = 0 is not a boundary in the original
problem, but in this 2-D treatment it is. Thus it is assigned the arti cial boundary condition here - the Neumann
homogenous boundary condition, which demonstrates the axial symmetry of the temperature eld (Fig. 3d).
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The only heat source in this model is non-radiate transitions inside the doped part of the laser crystal. The
power transfer eciency from the pump to heat losses is given by
where ¸laser is the laser transition wavelength and ¸pump is the pump transition wavelength. When the Nd:YAG
is pumped by the 808 nm laser diode radiation, the heat losses reach at least 24 % of the absorbed power. If
the light intensity is I(r; z) and the active medium absorption coecient is ®, the local heat generation rate is
given by:
If the pump beam di raction inside the active medium is neglected, the pump beam pro le has a gaussian
of ve order shape, and the total pump power is Ppump, then the heat generation rate is given by:
To calculate the heat conduction di erential equations, the following values of parameters were used:
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3. EXPERIMENTAL RESULTS
3.1. Physical experiment
The characterization of this laser system was accomplished for all the three samples investigated 0U, 1U and 2U.
The dependence of the output power on the absorbed diode pumping power was measured with the Molectron
Laser Power Meter Max 500A (probe PM3 and PM10). The results measured are summarized in Fig. 4a. The
time development of laser output power was monitored also by the PIN photodiode HP 4207 and recorded
by the oscilloscope Tektronix TDS 3032. The active crystal starting temperature value was 30 ±C - being the
same for all the three measurements. The dependencies measured are displayed in Fig. 4b. The measured decay
of power at the beginning of measurements shows an instantaneous temperature increase and its sequential
stabilization. The maximum power was achieved for the sample with two undoped ends (Fig. 4a).
Figure 4. (a) The dependency of the diode pumped Nd:YAG laser output power on the power absorbed in active
material for three di erent types of the active material. (b) The diode pumped Nd:YAG laser output power long-term
time dependency for the constant absorbed power 1.5 W.
For better characterization of the laser system, the output beam space structure for all the three types of
the active medium arrangement was recorded by CCD camera ELECTRIM EDC - 1000HR. The results for the
Nd:YAG sample 0U and the sample with the two undoped ends 2U are plotted in Fig. 5.
Figure 5. Diode pumped Nd:YAG laser output radiation space structure (the Nd:YAG laser crystal 0U (a), the Nd:YAG
laser crystal with two undoped parts 2U (b) (horizontal axis 10 ¹m/div, vertical axis - normalized unit of intensity).
3.2. Computer experiment
The di erential equation of heat conduction (2) was solved using the Finite Element Method in the region
shown in Fig. 3d. The part of the the laser crystal and its heatsing rz-plane cat used for the data imaging
is shown in Fig. 6. The calculation was made for all the three crystals samples (the crystal 0U, 1U and 2U -
Fig. 1). Fig. 7 shows the calculated temperature eld and heat
ux inside the laser crystal and in its nearest
surrounding at the time t = 400 s.
Figure 6. Layout of diode pumped Nd:YAG crystal with a housing.
The data displayed in Fig. 7 correspond to marked rz-plane
4. DISCUSSION
From the experimental results it follows that for the same absorbed pumping power, the output power of the
laser whose active medium is composed of doped and undoped parts (described in detail above) is higher than
the output power for the system with the conventional active medium design. The di erences observed can be
explained by a more homogeneous distribution of the thermal eld into the doped part of the active material
and by its ecient cooling.
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Figure 7. The results summarization of the calculated temperature eld (a) and heat
ux (b) inside the laser crystal
and in its vicinity (the rz-plane cut) in time t = 400 s for the particular cases. 0U - conventional type of the active
Nd:YAG medium , 1U - Nd:YAG crystal with the one undoped end 1U), 2U - Nd:YAG crystal with two undoped ends -
see Fig. 1
For better understanding of the temperature distribution inside a laser material, a computer experiment
based on the numerical solution of the heat transfer equation was performed. This model gave the possibility
to calculate the temperature arrangement inside the laser crystal and for its nearest surrounding in the case
of continuous diode pumping. Good agreement was obtained when the calculated and measured values (in the
vicinity of the active crystal) were compared.
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It is the thermal gradient inside the active crystal that plays the most important role in the crystal's optical
characteristics. Its value a ects the refractive index and the thermal lens creation, and, therefore, the thermal
gradient mostly a ects the output beam parameters. From the mathematical model it follows that in case of
the active medium with two undoped ends in comparison with the conventional type of crystal, i.e. without
the undoped ends, the value of the thermal gradient is one half. From Fig. 7 it can be seen that if only the
conventional Nd:YAG crystal is placed in the laser resonator, the heat is dissipated through the cylindrical
surface of the active crystal only. From the computer model it follows that for this case the maximum crystal
temperature achieved in the pumping area center is 62 ±C (Fig. 7a-0U). In case of the crystal with one undoped
end placed in the input of the pumping radiation, the heat is removed from the center of the crystal more
e ectively (Fig. 7b-1U). The maximum temperature inside the crystal settles down to 54 ±C (Fig. 7a-1U). The
most e ective cooling is obtained for the crystal with two undoped ends. The heat added the pumping is
dissipated more uniformly (Fig. 7b-2U). For this case the maximum active medium center temperature reaches
52 ±C only (Fig. 7a-2U).
5. CONCLUSION
In the computer and physical experiments, three Nd:YAG rods sample designs (one conventional, one with
undoped end, and one with two undoped ends) intended for longitudinal diode pumping were investigated.
Both experiments have proved the positive in
uence of the Nd:YAG undoped ends on the output laser radiation
characteristics. The dependencies of the generated laser power on the absorbed pumping diode power have shown
that the output power for the active crystal with two undoped ends is more than twice as high in comparison
with the conventional Nd:YAG sample (i.e., sample without undoped ends). These results are in good agreement
with the computer results where the temperature gradient changes were the smallest for the Nd:YAG rod with
two undoped ends.
For the same level of the absorbed power (1.5 W - continuous pumping) for the case of the crystal with
two undoped ends, the laser output power was two times higher as compared with the conventional type of
crystal. This corresponds also to the computer experiment results. The computed temperature gradient inside
the crystal with two undoped ends is two times lower than this value calculated for the conventional crystal.
When these two cases were compared, the di erence of the maximal temperatures in the doped part of the
crystal was as high as 10 ±C. For the system in which the active medium with two undoped ends is used, the
temperature conditions in the active medium are more homogeneous.
Composite solid-state laser crystals are attractive for the possibility of improving thermal management
especially of high power diode-pumped lasers.
ACKNOWLEDGMENTS
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