Phase-conjugation (PC) can be realized using Four-Wave-Mixing (FWM) in photorefractive crystals. Two waves, a signal and a pump wave, interfere inside the medium and create a refractive index hologram. The phase conjugated wave is created by reading this hologram by a second pump wave.
Mutually pumped PC (MPPC) is a principle where two incident signal
waves get phase conjugated at the same time (Fig.1). The waves
do not need to be mutually coherent. Both waves build up their
fanning, an asymmetrical amplified scattered light. Every signal
wave interferes with its own fanning building a grating. This
grating is read by the fanning of the other signal wave, respectively.
Figure 1: Principal arrangement for MPPC
In order to read a refractive index hologram, the Bragg condition, that is very sharp in the case of thick gratings, has to be fulfilled. The fanning of both waves has the shape of a cone in space. It consists of light which propagates not only in one direction but in a whole angle range. This way, any part of a fanning cone always fulfills the Bragg condition to read the grating built by the other signal wave and its fanning, respectively. No additional pump waves are necessary, because the fanning of every wave acts as a pump wave.
Normally, the beam coupling and with that the beam fanning effect in BTO is too small to observe the MPPC. But, the recording of the holographic grating can be strongly enhanced by non-stationary methods, in our case by applying a square wave alternating electric field to the crystal.
We used fiber-like crystals of BTO where the dimension along the propagation direction is much longer then the other dimensions. These fiber-like photorefractive materials have some special properties compared to bulk materials.
They enable high interaction efficiency because of the large interaction length of the beams inside the crystal. Because of the small distance of the electrodes high electric fields can be applied using a moderate voltage of a few kV. Therefore, MPPC could be observed with our BTO samples.
Fig.2 shows the intensity distribution of one of the reflected waves if it is coupled out by a beam splitter and projected on a screen. A disadvantage of this method gets obvious. The intensity of the reflected signal builds a part of a ring structure, but, it should be concentrated in one certain point if we phase conjugate a simple laser beam. So, what happens seems not to be phase conjugation in the exact meaning.
The reason is the structure of the fanning in space, it builds
a cone. Therefore, there are additional gratings that are not
built by the interference of signal and fanning but by the interference
of different parts of the fanning with one another. This system
of gratings is read out by the fanning of the other wave that
has the shape of a cone too. This results in an output signal
that consists of waves that lie on the surface of a cone and therefore
build the intensity distribution shown in Fig.2.
Figure 2: Intensity distribution of a reflected
wave on the screen
MPPC could be shown in BaTiO3 too. The coupling in this medium is very anisotropic because of the very different coupling coefficents. By a self-organizing process, the additional gratings are suppressed and after a certain time the intensity is concentrated very near to the ideal point.
In BTO this is not the case. Therefore, the applicability of MPPC in BTO could be limited.
In order to study the quality of the MPPC, a Michelson interferometer as shown in Fig.3 was arranged. A BTO-crystal working as MPPC mirror is installed in one path.
For test purposes the phase correction property of phase conjugation was applied. A lens was used to simulate the phase disturbance.
Parallel fringes could be observed on the screen. Therefore, the
reflected wave is plane despite the inserted lens. This shows
that the phase disturbance is corrected if the plane signal wave
propagates twice through the disturbing lens. This, on the other
hand, means that the reflected wave is phase conjugated with respect
to the signal wave, at least in a certain area around the central
point on the screen. Reflectivities in the range of 30% could
be reached with MPPC in BTO.
Figure 3: Arrangement for the phase conjugation
test
It was tried to realize a SPPCM (self-pumped PCM) with our BTO sample. For this purpose, the part of the fanning of the signal wave that is reflected at the back face of the crystal is used as the reading pump wave of a FWM process (Fig.4). Because the reflected fanning has the same large angular range as the original fanning, one part of it always fulfills the Bragg condition with respect to the written grating.
The self-pumped phase conjugation (SPPC) could be shown for the
fiber-like BTO crystal. Because of the low reflectivity at the
back face and the absorption inside the crystal the reading pump
wave is much weaker then the signal wave. Therefore, the pc-reflectivity
in the used SPPCM configuration with BTO is small (in the range
of 1%). The SPPC shows the same strange intensity distribution
of the pc wave as the MPPC and it needs a longer onset time. The
small aperture of the crystals seems to be another limitation
of the phase conjugation in fiber-like crystals, because no strong
structured waves can be phase conjugated but only waves with nearly
plane wave fronts.
Figure 4: Principal arrangement for SPPCM
However, we showed the realizability of MPPC and SPPC in a fiber-like
BTO crystal. This is remarkable because these effects normally
only occur in media with very high coupling, like BaTiO3.
The advantage of using BTO is that the crystals are easier to
grow and because of that they are much cheaper. The reachable
reflectivities and the quality of phase conjugation are rather
low. Nevertheless, applications are thinkable.
Acknowledgment
This research has been partially supported by the
Deutsche Forschungsgemeinschaft (DFG) within the Innovationskolleg
"Optische Informationstechnik" and within the SFB225
and by the DAAD.
References