Optical Materials 23 (2003) 235–241
www.elsevier.com/locate/optmat
Waveguides and waveguide arrays formed by incoherent
light in photorefractive materials
Zhigang Chen *, Hector Martin
Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132, USA
Abstract
We report on experimental observations of nonlinear optical waveguides and waveguide arrays formed by incoherent light in photorefractive materials. Such waveguides are made possible by creating partially spatially incoherent
solitons in a noninstantaneous self-focusing photorefractive medium. In addition to planar, Y-junction, and circular
waveguides, we report the first demonstration of pixel-like spatial solitons from partially incoherent light. An array of
as many as 56 56 soliton pixels is readily realized by launching a spatially modulated incoherent beam into the selffocusing photorefractive medium. These solitons are stable and robust, forming a steady-state two-dimensional
waveguide array in which optical coupling and control of local waveguide channels can be achieved. These experiments
bring about the possibility of controlling high-power laser beams with low-power incoherent light sources as well as the
possibility for optically inducing three-dimensional reconfigurable photonic lattices in a bulk medium.
Ó 2002 Elsevier Science B.V. All rights reserved.
Optical spatial solitons are considered to be
among the prime candidates for controlling light
by light. Since the demonstration of Kerr-type
spatial solitons and their ability to guide and
switch other beams [1,2], there has been an increasing interest in soliton-induced waveguides
and their applications. In particular, recent work
on self-trapping and light guiding in various 3D
saturable nonlinear materials [3] has opened up
several avenues for possible applications of spatial
solitons in optical interconnects, optical communications, and other areas. For instance, spatial
switching with quadratic solitons [4] and directional couplers based on photorefractive soliton-
*
Corresponding author.
E-mail address: [email protected] (Z. Chen).
induced waveguides [5] have been demonstrated,
and soliton-induced waveguides have even been
employed to achieve high efficiency frequency
conversion in nonlinear vð2Þ photorefractive media
[6]. In addition to one- or two-waveguide structures, which involve only a few solitons, spatial
soliton pixels and soliton-based waveguide arrays
have been proposed for applications in signal
processing and information technology [7]. Recently, pixel-like spatial solitons have been demonstrated in a semiconductor microcavity and in a
cavityless optical parameteric amplifier [8]. In all
those previous studies, spatial soliton arrays were
generated with coherent light waves.
For decades, solitons have been exclusively
considered to be coherent entities, and optical
solitons have been studied only with intense coherent light beams. Nature, however, is full of
0925-3467/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0925-3467(02)00295-1
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Z. Chen, H. Martin / Optical Materials 23 (2003) 235–241
incoherent radiation sources. Can incoherent light
also form a soliton and thus induce a waveguide?
This intriguing and challenging question has recently motivated several experiments [9,10] on selftrapping of incoherent light. By now, a series of
experimental and theoretical studies [9–12] has
clearly demonstrated that incoherent spatial solitons are indeed possible in slow-responding nonlinear media such as biased photorefractives. This
brings about the interesting possibility of using
low-power incoherent light beams to form solitons
that can guide and control other high-power coherent laser beams. This is simply because the
light-induced variation of the refractive index
associated with either bright or dark incoherent
solitons can form a waveguide structure in the selftrapped region, and a probe beam can be guided at
much higher power level as long as it has a less
photosensitive wavelength [13–15].
In this paper, we review our experimental
work on waveguides induced by incoherent dark
solitons. These induced waveguides allow optical
guidance of other beams that may be coherent or
incoherent. In addition, we report the first experimental observation of pixel-like two-dimensional
spatial soliton arrays from partially spatially incoherent light. Optical waveguide arrays are of
particular interest because of their potential applications as well as their collective behavior of
nonlinear wave propagation that exhibits many
intriguing phenomena found also in other nonlinear discrete systems. Yet, it has always been a
challenge to create or fabricate two-dimensional
waveguide arrays in bulk media. We create a 2D
waveguide array induced by as many as 56 56
pixel-like spatial solitons by launching a spatially
modulated incoherent beam into a self-focusing
photorefractive nonlinear crystal. These spatial
solitons are stable and robust, provided that the
coherence of the beam and the strength of nonlinearity are set at an appropriate value. If the
coherence is too high or the nonlinearity is too
strong, the beam tends to break up into disordered
patterns rather than ordered soliton structures.
Once the soliton pixels form in steady state, they
induce a two-dimensional waveguide array capable of guiding an intense probe beam of a longer
wavelength. Optical waveguiding and control of
nearby waveguide channels in the array are demonstrated in experiments. These soliton pixels may
find particular applications in image transmission
and information encoding, as there is no or only
weak correlation among the various pixels on the
soliton array due to the nature of incoherent light.
In our experiments, we first convert a coherent
beam from an argon ion laser (k ¼ 514 nm) into a
quasi-monochromatic spatially incoherent light
source by passing it through a rotating diffuser
[9,10]. The laser beam is focused by a lens onto the
diffuser, and the scattered light from the diffuser is
collected by another lens. The rotating diffuser
provides random phase fluctuations, thus turning
the beam into partially spatially incoherent. The
spatial degree of coherence of this beam is revealed
by the average size of the speckles borne on it. One
can actually trace the temporally varying speckles
with a fast camera, or, as we do here, monitor the
beam when the diffuser is stationary. We then
launch the speckled beam onto a phase or an amplitude mask, and redirect the reflected dark beam
onto the input face of a photorefractive crystal in a
way similar to that previously followed in generating coherent dark screening solitons [14,16]. The
photorefractive crystal used here is a 12-mm-long
SBN grown at Stanford using the Vertical Bridgeman method. We first generate a 1D incoherent
dark stripe from a phase mask (odd initial conditions) [14]. When the diffuser is stationary, what the
crystal ‘‘sees’’ is the speckled pattern shown in Fig.
1a. However, as the diffuser rotates at a time scale
much faster than the response time of the crystal,
the crystal ‘‘sees’’ a dark stripe superimposed on a
smooth intensity profile (Fig. 1b) rather than the
speckled pattern. This illustrates that our photorefractive crystal responds to the time-averaged
envelope and not to the instantaneous speckles. By
providing an appropriate bias field, we obtain selftrapping of the incoherent dark stripe. We then
launch a cylindrically focused probe beam from a
HeNe laser (k ¼ 633 nm) into the soliton to test its
waveguide properties. Fig. 2 shows typical experimental results. At input, the dark beam has a coherence length (estimated from the average speckle
size) of 15 lm. The incoherent dark soliton is 18
lm (FWHM) wide, generated at a bias field of 950
V/cm. In the absence of nonlinearity, the probe
Z. Chen, H. Martin / Optical Materials 23 (2003) 235–241
237
Fig. 1. Photographs of intensity patterns of a spatially incoherent dark beam (a) with diffuser stationary and (b) with diffuser rotating.
Fig. 2. Photographs showing guidance of a probe beam (bottom) by an incoherent dark soliton (top) initiated from a phase mask.
(a) Input, (b) output with linear diffraction, and (c) output with nonlinearity.
beam diffracts from 20 lm (Fig. 2a) to about 68 lm
(Fig. 2b) after linear propagation through the
crystal. Once the dark incoherent soliton has
formed, guidance of the probe beam is observed
(Fig. 2c). For this experiment, the incoherent soliton beam has an average intensity of 4.5 mW/cm2 ,
and the intensity of the probe beam reaches 50
mW/cm2 . At output, nearly 80% of the input power
(normalized to Fresnel reflections and crystal absorption) of the probe beam is guided into the
waveguide channel induced by the incoherent dark
soliton.
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Z. Chen, H. Martin / Optical Materials 23 (2003) 235–241
In addition to using a phase mask, we can also
generate a dark stripe from an amplitude mask.
Such an amplitude mask can be a simple mirror
crossed by a fine wire, which provides the ‘‘even’’
input conditions necessary to excite Y-junction
dark solitons. Y-splitting of dark incoherent solitons was first predicted in Ref. [12] and recently
observed in experiments of Ref. [17]. We have
shown that such a dark incoherent Y-junction
soliton also induces a Y-splitting waveguide that
can be used to guide other beams [19]. Interestingly enough, as the coherence of the dark beam
decreases, the grayness of the soliton pair increases, but the spacing of the two incoherent gray
solitons at the crystal output face remains the same
as discussed in Ref. [17]. Recalling that a 2D incoherent dark soliton also induces a ‘‘fiber-like’’
waveguide channel similar to that of a coherent
vortex soliton, we have also tested the guiding
properties of such index structures using a helicoidal phase mask [18,19]. Although we employed a
quasi-monochromatic spatially incoherent light
source, our experiments suggest that spatial solitons formed from ‘‘fully’’ (temporally and spatially) incoherent light sources (e.g., incoherent
white light) can also induce waveguides capable of
guiding other coherent and incoherent beams.
Next, we demonstrate spatial soliton pixels
from incoherent light. Again, a partially spatially
incoherent light beam is generated by converting
an argon ion laser beam (k ¼ 488 nm) into a quasimonochromatic light source with a rotating diffuser. A biased photorefractive crystal (SBN:60;
5 5 20 mm3 ) is used to provide a self-focusing
noninstantaneous nonlinearity, as the rotating diffuser creates random phase fluctuations on a time
scale much faster than the response time of the
crystal. This noninstantaneous nonlinearity is essential for modulation instability, solitons, and
pattern formation of incoherent waves [20–22]. To
generate a grid-like intensity pattern, we use an
amplitude mask to modulate the uniform extraordinarily polarized incoherent beam after the
diffuser. The mask is then imaged onto the input
face of the crystal. A broad and uniform ordinarily
polarized beam from the same laser is used as dark
illumination to fine-tune the nonlinearity. A DC
field is applied along the crystalline c-axis, which is
oriented perpendicular to the propagation direction of all beams in the crystal. In addition, a
Gaussian beam from the same argon laser is used
as a control beam when it propagates in parallel
with the incoherent soliton-array beam, and a
red beam from a HeNe laser is used as a probe
beam to test the waveguides induced by the soliton
pixels.
Typical experimental results of spatial soliton
pixels are shown in Fig. 3. At the input to the
crystal, the transverse pattern of the incoherent
beam consists of 32 32 Gaussian-like intensity
pixels, with a 30-lm FWHM diameter of each
pixel and a 70-lm peak-to-peak separation between pixels. Due to magnification in imaging to
the CCD camera, only part of the beam (7 8
pixels) is recorded as shown in Fig. 3a. Without
the bias field, individual intensity spots diffract
dramatically as expected from incoherent light. As
the whole beam propagates through the 20-mm
long crystal, diffraction washes out the fine structures in the beam, leaving a fairly uniform intensity pattern at the crystal output (Fig. 3b). When
an electric field of 2400 V/cm is applied across the
crystal, the incoherent beam breaks up at the
output of the crystal due to induced modulation
instability [20]. After transient evolution, the input
intensity pattern is restored in steady state, forming an array of spatial soliton pixels as shown in
Fig. 3c and d. The size of each soliton pixel and the
separation between pixels are about the same as at
the input, as all solitons propagate in parallel
through the crystal. For the experiment shown in
Fig. 3, the spatial coherence of the beam is fixed at
20 lm, smaller than the size of each pixel. The
intensity ratio between the soliton beam and the
ordinarily polarized background beam is set at 4.
Under these conditions, the induced modulation
instability experiences a maximum growth rate at a
spatial frequency related to the input perturbation
period [20], and eventually leads to steady-state
soliton pixels of incoherent light. Formation of
such soliton pixels is a combined outcome of diffraction, modulation instability, and nonlinearity
experienced by the incoherent beam.
Once the spatial soliton pixels are formed, it is
possible to use a probe beam to test the waveguide
arrays induced by the solitons. To do so, we
Z. Chen, H. Martin / Optical Materials 23 (2003) 235–241
239
Fig. 3. Spatial soliton pixels of partially incoherent light. Shown are intensity patterns from (a) input, (b) output with linear diffraction,
and (c) output with nonlinearity. (d) Is the 3D-intensity plot of (c).
launch in parallel with the soliton beam an extraordinarily polarized beam from a HeNe laser
(k ¼ 633 nm) into the crystal. When the probe
beam is tightly focused at the input (Fig. 4a), it
diffracts rapidly to a very broad beam after 20-mm
of linear propagation (Fig. 4b). However, after we
turn on the nonlinearity and create the incoherent
soliton pixels, the probe is guided very well into
one of the channels at which it was initially aimed
(Fig. 4c). When the probe is a broad beam (quasiplane wave) at the input, it breaks up and fits into
the waveguide array at the output as expected
(Fig. 4d). It is worth mentioning that the waveguide array, although created from incoherent
light, can be used to guide an intense coherent
laser beam at longer wavelengths without being
damaged, and such soliton-induced waveguides
can even be fixed in the crystal permanently [23].
Should these soliton pixels and waveguide arrays be employed for applications in information
technology, it would be desirable to be able to
manipulate individual pixels, and to switch energy
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Z. Chen, H. Martin / Optical Materials 23 (2003) 235–241
Fig. 4. Waveguide arrays tested by (a–c) a focused beam and (d) a broad beam. Shown are (a) input, (b) diffraction, (c) guidance of the
focused beam into a soliton channel, and (d) guidance of a broad beam into all waveguide channels.
from one pixel into another. Towards this aim, we
have demonstrated the coupling between soliton
pixels by introducing another control beam from
the argon laser launched in the middle of four
pixels. Since the soliton pixels are partially spatially incoherent, the interaction between them and
the control beam is mutually incoherent interaction, which causes them to attract each other.
When the control beam is turned on, all four
nearby solitons are dragged towards the central
control beam. Such a scheme of coupling between
adjacent waveguide channels by a control beam
can be used for optical switching as proposed
previously [24]. When the control beam is turned
off, the array of soliton pixels restores in a new
steady state.
In addition to the above experiments, we have
performed a series of other experiments at different
degrees of spatial coherence, different strengths of
nonlinearity, as well as different pixel spacing at
the crystal input, all of which control the growth
rate of the induced incoherent modulation instability [25,26]. Photonic lattices of as many as
56 56 waveguide channels with a much smaller
spacing have also been created. Currently, we are
working on generation of 3D soliton-induced nonlinear waveguide arrays and interaction of a single
soliton with a light-induced photonic lattice. Such
interaction may lead to observation of a host of
new phenomena such as incoherent 2D discrete
solitons and optical polarons. Details will be reported elsewhere.
In summary, we have demonstrated waveguides
formed by incoherent solitons, and for the first
time, we have observed spatial soliton pixels and
waveguide arrays from partially spatially incoherent light. Apart from applications in optical control, optical switching, and information technology,
these soliton waveguide arrays open the door for
study of many fascinating behavior of light in optically induced real-time photonic lattices.
Acknowledgements
This research was supported by the Research
Corporation and a subaward from Army Research
Office. We appreciate assistance from M. Segev, G.
Salamo, D.N. Christodoulides and R. Feigelson.
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