We experimentally observed the unusually fast response of the two-wave mixing process in fiber-like [1,2] BTO-crystals on a transient change of the applied electric field [3,4,5]. Pulses of the amplification of the signal wave with a buildup time of less than 1ms and a width of 1ms are obtained after applying a rising or decreasing front of the external electric field to the crystal. The dependence of this effect on several parameters is studied experimentally.
The experimental arrangement for our investigations is shown in
Fig.1.
Figure 1: Experimental arrangement
Two waves (signal and pump wave) interact inside a fiber-like BTO crystal with an applied changing voltage. The time to change the voltage was usually 1.5ms. The angle between the two beams is J. The intensity ratio IP/IS between pump wave and signal wave was about 270, and the total incident intensity was I0=1W/cm2 . The electric field is parallel to the holographic grating vector.
Fig.2 shows both the temporal course of the intensity of the signal beam with and without pump beam and the course of the voltage. One can see from curve "coupling" that there is a peak of light intensity just in the moment when the applied voltage changes. Here energy is transferred from the pump beam into the signal beam.
If the pump beam is off, then a little decrease of the intensity of the signal beam appears at the moment of voltage change, because more energy is transferred into the fanned light.
For the rise time of the peaks we found values down to less than 1ms with a width in the range of 1ms.
Figure 2: Temporal course
of the intensity of the transmitted signal beam. Intensity of
the signal beam 0.86 mW/mm2 and of the pump beam 12.9
mW/mm2. J=7°.
Sample size: 8.1´3.84´1.85
mm3. Beam diameter 1.2 mm.
To our knowledge, such a fast TWM response has not been observed with the given intensities. Typical values for the response time in TWM for the used intensity in BTO lie in the region of a few 100ms. This fast response may expand the field of applications of photorefractive crystals.
Fig.3 shows the dependence of the peak value on the applied electric field with the total intensity as a parameter.
Figure 3: Dependence of the TWM peak value on
the applied field and the intensity
A maximum peak value is found for a field between 3 and 3.5 kV/mm for intensities I>600mW/cm2. For lower intensities the dependence of the peak value on the field strength is much smaller.
As our measurements show, the raise time tr
decreases with increasing intensity and applied electric field
(Fig.4). The raise time for the peak shows the same dependence
tr ~
1/I0 as the TWM photorefractive response
time, that is described by the well known Kukhtarev equations
[Kukhtarev, FE22,1979].
Figure 4: Influence of the intensity on the rise time.
I=1ÞI=20mW/beam,
BTO-J:1´7´20
mm
As one can see from Fig.5 that the rise time decreases with increasing
applied electric field. This is opposite to the case of TWM with
a static electric field.
Figure 5: Influence of the E-field strength on
the rise time
Furthermore, the gain that can be reached in the peak is very
strong influenced by the entry position into the crystal of the
two beams. Fig.6 shows the result of a measurement where the
entry position was shifted across the front face of the crystal.
Figure 6: Influence of the entry position
At the edge positions where the entry occurs closer to the side
faces the gain is higher, and it decreases in direction to a more
central entry of the interacting beams. This can by explained
by the formation of so called photorefractive surface waves. By
the interaction of an incident beam with its own fanning that
is reflected at the side surfaces a grating is build that reflects
light back to these surfaces. This way, the energy is more and
more concentrated in a layer near the side faces. Therefore, the
influence of the entry position can be attributed to the influence
of the intensity.
Figure 6: Photorefractive surface waves
In conclusion, we have demonstrated the appearance of an effective transient two-wave mixing in fiber-like BTO crystals after applying a rising or decreasing slope of the external electric field to the crystal. This process is characterized by an unusual low response time of less than one millisecond (down to 0.3 ms) while the crystal is illuminated by two beams with 10 mW/mm2 (pump beam) and
0.6 mW/mm2 (signal beam) intensity, respectively,
at l=633nm and with an applied voltage
of 3 kV.
Acknowledgment
This research has been partially supported by the
Deutsche Forschungsgemeinschaft (DFG) within the Innovationskolleg
"Optische Informationstechnik" and within the SFB 225
and by the DAAD.
References
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[4] E. Raita, A.A. Kamshilin, V.V. Prokofiev, and T. Jaaskelainen, Appl. Phys. Lett. 70, 1641 (1997)
[5] S.I. Stepanov and M.P. Petrov, Opt. Commun. 53, 292 (1985)