RTP CRYSTALS FOR ELECTRO-OPTIC Q-SWITCHING
M. Rotha, E. Samokaa, E. Mojaeva and M. Tseitlinb
a
Faculty of Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
b
Research Institute, The College of Judea and Samaria, Ariel 444837, Israel
Abstract.
The wavelength dependencies of half-wave voltages for both X- and Y-oriented
thermally compensated double-crystal RTP (RbTiOPO4) Q-switches have been
determined by a common polarized optics technique. The dispersion of the respective
electro-optic coefficients has been deduced from these results and compared with the
existing data. Variation of the extinction ratios of the crystals in different geometries
have been studied as a function of compositional gradients developing in the crystals
during growth, parallelism of the optical elements and the wavelength used. The
results show that the extinction ratio of such crystal is extremely sensitive to these
parameters.
1. Introduction
A new generation of oxide crystals is emerging for electro-optic Q-switching
[1], or for high pulse power laser operation. As opposed to the acousto-optic Qswitches, where the overall turn-off time is limited by the sound wave transit duration
(110-200 ns/mm) across the beam diameter, electro-optic devices offer a shorter than
10 ns response [2] needed for minimum loss in high-gain and high repetition rate solid
state lasers. Better than 200:1 extinction ratios allow the electro-optic crystals to
provide good hold-off, in contrast to about 40% single pass dynamic loss [3] with
acousto-optic devices hindering the use of the latter in high gain lasers. Convenient
electro-optic Q-switching can be achieved by amplitude or phase modulation in
crystals due to optical distortion induced by an external electric field, namely
employing the electro-optic effect [4]. Among the existing useful electro-optic
crystals, such as the traditional DKDP [3] and lithium niobate [5] and the newer BBO
[6] and langasite-structure [7] materials, the RTP (RbTiOPO4) crystal stands out in its
ability to achieve amplitude modulation at extremely high frequencies, or repetition
rates, of up to 1 MHz [8-10].
RTP belongs to the KTP(KTiOPO4)-family of ferroelectric optical crystals,
but embodies a number of advantages over KTP. It has larger electro-optic
coefficients and lower half-wave voltage [11], twice as high optical damage threshold
(ca. 1.8 GW/cm2 for 10 ns pulses at 1.064 mm), and crystals with as-grown electrical
resistivity > 1010 cm can be readily obtained. High resistivity RTP with proper
choice of the evaporated electrode materials is not electrochromic. Excellent thermal
stability in the 25-125°C temperature range has been reported for a couple of 11 mm
long properly matched RTP crystals (thermally compensated scheme [8]), and their
extinction ratio or the ratio of intensities of light passing through two polarizers with
their axes oriented parallel and perpendicular to the beam polarization plane, can be as
high as 800:1 [12]. However, the extinction ratio is closely related to the variation of
the birefringence, n, or to the crystal optical uniformity across the crystal aperture.
The latter depends directly on the compositional homogeneity of as-grown crystals.
We have reported recently [13] that RTP crystals grown from self-fluxes undergo the
ferroelectric phase transition in a relatively wide temperature range, from 770 to
202
800°C (Curie temperature, Tc), depending on the flux chemical composition in terms
of the [Rb]/[P] atomic ratio. The actual Tc values are defined by the rubidium
stoichiometry in the crystal, similarly to potassium stoichiometry in KTP [14], and
they serve as a good relative measure of the compositional variation in large RTP
crystals from the seed area to the periphery. Moreover, unlike KTP, nominally pure
RTP crystals exhibit different Tc values for different growth sectors, even when
solidified simultaneously. The questions of tolerance of the optical properties with
respect to the compositional variations and the geometry of RTP electro-optic
elements have to be elucidated.
In the present work, we analyze and determine experimentally some key
parameters important for the RTP operation as a thermally compensated doublecrystal electro-optic Q-switch, such as the half-wave voltage and effective electrooptic coefficients. Their dispersions for both X- and Y-cut crystal configurations are
explored in a broad spectral range. The main factors influencing the extinction ratio
are treated theoretically, and initial quantitative estimates with respect to the growthinduced optical nonuniformity are made. The influence of the optical element
parallelism on the extinction ratio of the double-crystal design is discussed as well.
2. RTP Pockels cell
Most common electro-optic Q-switching is based upon the rotation of
polarized light by the linear electro-optic, or Pockels, effect in crystals lacking a
center of symmetry, such as the ferroelectric RTP crystal. In the linear effect, the
applied electric field causes a change in optical anisotropy of a birefringent crystal
characterized by two orthogonal directions (fast and slow axes) with different indices
of refraction, nf and ns, inducing a phase retardation  = (2 l/)n, where n = nf – ns
is the birefringence, l is the crystal length and  is the wavelength of light. An
incident plane-polarized beam (at 45° to the slow and fast axes) will split into two
components traveling at different velocities and, upon traversing the crystal, will turn
into an elliptical, circular or linearly polarized beam depending on the field magnitude
[3]. The latter case corresponds to the more commonly employed 'half-wave' light
intensity retardation. Hereby, the crystal is placed between two crossed polarizers, and
in the 'light-pulse-on' configuration (no voltage applied) maximum light extinction is
achieved. With the half-voltage (V) on, a 90° rotation of the linear polarization is
caused at each pass of the beam through the crystal, and the light transmission given
by [2]
T  ( I o / I i )  sin 2 ( / 2)
(1)
is maximal if  (Io and Ii are the output and input light intensities respectively).
When the light beam is directed off the optical axes,  comprises also the natural
(static) birefringence of the crystal, which is very sensitive to temperature changes. In
order to achieve thermal stability of the Pockels cell operation, double-crystal
compensated designs have been suggested for the biaxial KTP crystal [15] holding
also for RTP.
203
(a)
(b)
-V
-V
Y
+V
+V
Z
X
+V
Z
45°
+V
Z
45°
X
-V
Z
Y
Y
-V
Light polarization
X
Light polarization
Fig. 1: Thermally compensated Q-switch designs for Y-cut (a) and X-cut pairs of RTP
crystals.
Figure 1 shows two configurations of Pockels cells utilizing double-crystal RTP
layouts for plain-polarized light, at 45° to the Z,X or Y,Z axes, propagating along the
Y- or X-direction respectively. For configuration (a), the phase retardation contributed
by each crystal is given by [16]
 3
l
nz rc1V ,


d
2
 3
l
2  
l (nx  nz )  nz rc1V ,


d
1  
2
l ( nz  nx ) 
(2)
where rc1 = r33 – (nx/nz)3r13 is the corresponding effective electro-optic coefficient, V
is the voltage across the electrodes (Z-direction) and d is the distance between
electrodes. If the refractive indices and dimensions of each of the crystals are
identical, the half-wave voltage can be derived by putting  = 1 + 2 =  :
   d 
V  
.
3 
 2rc1nz   l 
(3)
A similar relation can be given for a pair of X-cut RTP crystals, but rc1 must be
replaced by rc2 = r33 – (ny/nz)3r23. Apparently, thinner and longer crystals are needed
for reducing the half-wave voltage.
3. Experimental
RTP crystals were grown by the top-seeded solution growth (TSSG) method
with pulling on either X- or Y-oriented seeds from the R6 (Rb6P4O13) self-flux [13].
RTP solutions of desirable concentrations were prepared by reacting the Aldrich 3N
purity TiO2, Rb2CO3 and Merck (Suprapur) NH4H2PO4 and (NH4)2HPO4 in
appropriate proportions. The charges were loaded into 200 to 1000 ml Pt crucibles
and subjected to 24 hours soaking through homogenization aided by a Pt stirrer prior
to crystal growth. The crucibles were mounted in a custom-made resistance furnace
with a long hot zone allowing to obtain a quite uniform temperature distribution with
a gradient not exceeding 2°C in the solution. The pulling/rotation mechanisms and the
online temperature and weight control were realized using the “Ariel-1” crystal
growth system developed by Raicol Crystals Ltd. The seed rotation rates varied from
70 rpm to 20 rpm at different stages of growth. Variable pulling rates, from 0.02 to 1
mm/day were employed. Fine adjustment of the seeding temperature was achieved by
repeated seeding with the seed-solution contact control using a thermoelectric circuit.
The general temperature range for growth of RTP crystals from different self-fluxes
204
was 980-880°C, while the temperature lowering rates changed from 0.5 to 3°C/day.
As a result, RTP crystals of 506050 mm3 dimensions along the X, Y and Z axis and
weighing up to 450 g could be routinely obtained.
Both X- and Y-cut crystal elements with optically polished faces were prepared
for half-wave voltage measurements. Their typical dimensions were 4420 mm3, and
the relatively large aspect ratio ([r]/[l]  1/5) was chosen in order to reduce the
operating voltage. A custom made DC 5 kV power supply was used to apply variable
voltage to the titanium electrodes evaporated on the RTP crystal Z-surfaces. The
crystal was placed between crossed polarizers and irradiated with lasers of seven
different wavelengths, namely: 473 nm (LaserCompact LCS-DTL-166QA DPSS laser
doubled with a Raicol PPKTP elemnt), 532 nm (LaserCompact LCS-DTL-112QT
DPSS laser), 633 nm (He-Ne laser), 946 nm (LaserCompact LCS-DTL-166QA DPSS
laser), 1064 nm (LaserCompact LCS-DTL-112QT DPSS laser without a frequency
doubling element), 1572 nm (obtained by OPO with the LAGRAN LTI-245 flashlamp pumped Nd:YAG laser and a Raicol KTP noncritically phase-matched element)
and 2  (dedicated Tm:YAG DPSS laser [17]). Various Ophir Optronics power
meters were employed for measuring the transmitted light intensity. Voltage was
initially applied to the crystal to obtain complete light extinction. The polarizers were
then aligned in parallel for maximum transmission, and the voltage was further raised
until full extinction was achieved again. The difference between the two voltage
levels was adopted as the half-wave voltage value for a crystal with the specific
geometry used.
4. Results and Discussion
4.1 Half-wave voltage and electro-optic coefficients
One of the most significant operational parameters of the electro-optic Qswitch is the maximum voltage that has to be applied. Despite the voltage limitations
of power supplies and drivers used in the Q-switch system, lower voltage also reduces
the detrimental leakage currents across the crystal and electrochromism [15].
According to eq. (3), one way of decreasing V, at a given wavelength, is reducing the
aspect ratio (d/l), the other is employing a configuration with a larger effective
electro-optic coefficient. Both in KTP [16] and RTP [12], the reported rc1 values are
on the average 20% higher than those of rc2, implying that Y-cut RTP crystals are
advantageous in terms of lower half-wave voltages. We have performed a detailed
series of V measurements for both X- and Y-cut RTP crystals at seven different
wavelengths (see Experimental), recalculated the experimental values for d = l (cubic
crystal geometry), and the results are presented in Figure 2.
35
12000
8000
rc (pm/V)
Half-wave voltage (Volts)
40
X-direction
V  = 9.3512λ - 2009.8
l =d
16000
Y-direction
V  = 8.0169λ - 1902.9
l=d
4000
30
25
20
15
0
0
500
1000
1500
2000
2500
0
500
1000
1500
Wavelength (nm)
Wavelength (nm)
205
2000
2500
Fig. 3: Comparison of the -dispersion of rc1
(squares) and rc2 (triangles) effective electrooptic coefficients for Y- and X-cut RTP
crystals respectively.
Fig. 2: Wavelength dependencies of half-wave
voltages of X-cut (upper slope) and Y-cut
(lower slope) RTP crystals.
The results show that Y-cut crystals indeed exhibit lower half-wave voltages at
all wavelengths examined. Even at 2 , a 20 mm long RTP crystal may have a 6 mm
aperture with a still reasonable V value. Linear dependencies have been obtained for
both X- and Y-cut crystals, and the half-wave voltages can be easily calculated for any
wavelength from the slopes (see boxes of Figure 2). Although, from eq. (3), V is
proportional to , the linear dependences have not been expected a priori, in view of
the existing dispersions in the refractive indices and electro-optic coefficients [18]. In
fact, with the known -dispersion of the RTP refractive indices [19], the dispersion of
rc1 and rc2 can be now calculated from the data of Figure 2. The results are depicted in
Figure 3, and they represent the unclamped (constant stress) coefficients [18], rcT1 and
rcT2 , since the measurements have been performed under DC voltage. The overall rc
dispersion behavior is similar to KTP and other electro-optic crystals [18], but our
measurements have been performed in a slightly broader spectral range, showing that
in the near IR (above 1 ) the variation of electro-optic coefficients in RTP is
insignificant. The fact of rc2 being about 20% smaller than rc1 emphasizes again the
advantage of using Y-cut crystals, especially at longer wavelengths where the halfwave voltages are larger.
4.2 Extinction ratio
One important performance parameter for an electro-optic Q-switch is the
extinction ratio, ER, defined as the ratio of the transmission when the device is fully
open (parallel polarizers) to the transmission when the device is fully closed (crossed
polarizers), or


sin 2   
2
2 .
ER 
2 
sin
2
 
(4)
A high value of the extinction ratio is desirable because it determines the maximum
contrast (ratio of light intensities at crossed polarizers with and without V). In
practice there is always some light leakage, and the minimum transmission never
reaches zero. Yet, commercial Q-switches can have excellent extinction ratios in
excess of 1000, when the phase retardation is mainly due to the polarizing optics
rather than to the electro-optic crystal. An ideal crystal employed for broad beam
operation must have a high transverse optical uniformity. This can be largely achieved
with an X-cut RTP crystal, since when grown in the X-direction the latter develops a
large flat (100) facet [13], and the natural birefringence n = nz – ny  const across the
Pockels cell element face perpendicular to the light propagation direction. In reality,
some optical nonuniformity is still induced by the point and line defects as well as
thermomechanical stresses inherently present in crystals. However, the situation is
essentially changed when Y-cut RTP crystals have to be used for their larger rc1
values. The Y-face embodies material layers that crystallize at different times, and a
gradual variation of the transverse birefringence is expected due to compositional
changes [13]. We assume linear variations of the refractive indices across the crystal
206
aperture, in similarity with the experimental data on KTP [20]. The transverse phase
retardation for a beam propagating perpendicularly to the X-Z crystal plane is then
expressed by
2 l

(5)
 n  z  grad(n) ,

where n = nz – nx, while the gradient of the refractive indices along one of the two
axes is known to be negligible, based on our experimental observations, depending on
the crystal growth sector the sample is cut from. n at the center of the crystal can be
compensated to zero, either thermally or using a phase plate, so the normalized
transmission along the aperture d, for the crossed polarizers configuration (eq. (1))
can be calculated through the following integration:
1 0.5 d
 l

T
sin 2  z  grad(n) dz.

d 0.5 d


(6)
For the case of polarizers aligned in parallel, the argument under the sine function is
( +/2). After replacing the numerator and denominator in eq. (4) with the
appropriate integrals of the eq. (6) type, we obtain
ER = 12/2,
where  = [·l·d·grad(n)]/,
(7)
provided that  < 1 – condition always met for a few mm to cm sized crystals and
grad(n) ~ (1-2)105 cm1. Although the measured grad(n) in KTP [20] is of the
order of 104 cm1, we presume that smaller compositional changes in RTP
manifested by a more moderate variation of the Tc values [13,14] justifies the one
order of magnitude smaller assessment of the refractive index gradient. Figure 4
shows the extinction ratio as a function of the crystal length at four different values of
grad(n) for d = 5 mm and  = 1064 nm.
Extinction Ratio
2000
grad(Δn )=1.25*10^-5(cm^-1)
1500
grad(Δn)=1.5*10^-5(cm^-
1000
grad(Δn )=1.75*10^-5(cm^-1)
500
grad(Δn )=2.0*10^-5(cm^-1)
0
0.4
0.5
0.6
0.7
0.8
0.9
1
Length (cm)
Fig. 4: Extinction ratio dependence on crystal length at four different values of transverse
refractive index gradients for  = 1064 nm (d = 5 mm).
The sample curves of Figure 4 show that if the transverse gradient of refractive
indices is kept smaller than 2105 cm1, even a 10 mm long crystal (with an aperture
of 5 mm) yields a reasonably high extinction ratio of > 100:1. Shorter crystals are
obviously better in terms of the ER, but a trade-off between high ER and low V (see
Figure 2) has to be made. At longer wavelengths, say for the 2  Tm:YAG laser, the
extinction ratio is substantially higher, since it scales as the square of the wavelength.
207
Naturally, factors other than the gradient of refractive indices difference may
affect the extinction ratio. One of them is the lack of parallelism between the front and
rear faces of the crystal. If the angle between the faces is , for an optically uniform
crystal (n = const), the extinction ratio can be calculated using eq. (7) with
 = [·d·n·tan]/.
(8)
Adopting the typical commercial tolerance of  = 10 arc sec, n = nz – nx = 0.086 at
1064 nm for RTP and d = 5 mm, we calculate ER  3170. This is a large number, well
in excess of the ER values of Figure 4, implying that the practically achievable small
nonparallelism may degrade the extinction ratio of the RTP crystals only for
nonrealistically large apertures or at short wavelengths, although even near the RTP
cutoff wavelength of 400 nm the extinction ratio due to nonparallelism is ~ 500.
5. Summary
To summarize the above, a number of parameters important for Q-switching
operation of RTP electro-optic crystals have been evaluated. The half-wave voltages
of both X- and Y-cut RTP crystals have been determined experimentally in a wide
spectral range, from below 0.5 to 2 . Y-cut crystals require an about 20% lower halfwave voltage (applied in the Z-direction) at any wavelength, which makes the single
or double-crystal RTP Q-switch design with light propagating along the Y-direction of
great advantage. However, our numerical calculations show that the appreciably lower
transverse optical uniformity of Y-cut crystals limits their application to smaller
apertures of 4-5 mm, if extinction ratios in excess of > 100:1 are required at
reasonably low half-wave voltages. Our calculations also show that the practically
achievable high parallelism of the crystal front and rear surfaces excludes
nonparallelism as a tangible factor contributing to the phase retardation.
1.
2.
3.
4.
5.
6.
7.
8.
9.
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