Owing to the high frequency of its electromagnetic waves, light is an excellent carrier for signals. Since lasers were discovered and became available, there have been huge advances in optical waveguides and fibers for optical signal transmission as well as manipulation. Guiding optical signals does, in fact, avoid free-space diffraction and maintain a smooth transverse profile (the guided ‘mode’) while keeping the intensity nearly constant at levels dictated by the input excitation, the transverse cross-section of the guide, and the propagation losses. Together with guided-wave optics, nonlinear optics has come a long way since the first frequency-doubling experiment by P. Franken and coworkers in 1961.1 Among its fascinating achievements, progress in spatial optical solitons has been striking, with required powers steadily reducing in specific media and fascinating phenomena demonstrated.
In Kerr-like materials, where the intensity of light can increase the refractive index, spatial solitons (or solitary waves) are spatially nonspreading beams (the normal modes) trapping themselves in the waveguide they induce as a result of the balance between self-focusing and diffraction.2 Such soliton waveguides can support the guided-wave propagation of weaker colaunched signals, making the elementary constituents of integrated-optics circuits in which the signal-carrying channels are created and laid out in space by light itself. Soliton waveguides in two transverse dimensions are stable when the nonlinear response saturates with excitation and/or produces nonlocal changes in index, i.e., with transverse distribution wider than the beam waist.
Nematicons are optical spatial solitons in nematic liquid crystals (NLCs),3 organic fluids with properties encompassing birefringence, extended spectral transparency, reorientational nonlinear and electro-optic responses with saturation, and nonlocality.4 In the nematic phase, NLCs consist of elongated molecules aligned along a macroscopic optic axis, with refractive index larger for fields along it than orthogonally. When a beam goes through NLCs and its electric field is polarized in the (extraordinary) plane of the wavevector and the optic axis, it induces local dipoles in the organic molecules and these, in turn, tend to align to the field vector: see Figure 1(a). This reorients the optic axis and thereby increases the refractive index to yield a self-focusing response with saturable (the angle can only reach π/2) and nonlocal (due to the elastic forces between molecules in the fluid) character. Originally reported at milliwatt power levels, nematicons have been proven to be stable and robust, able to survive interactions with other solitary or free propagating beams, as well as localized defects or dielectric interfaces.3 Figure 1(b and c) shows photos of a diffracting beam compared with a nematicon in ‘E7,’ a standard NLC: the nematicon maintains its transverse shape and intensity for long (but finite, due to scattering) propagation distances, while it can also confine—otherwise diffracting: see Figure 1(d)—copropagating copolarized signals of different wavelengths: see Figure 1(e).
Figure 1. (a) The reorientation mechanism: as the field E becomes more intense, the optic axis ^ ntends to rotate locally toward E, thereby increasing the refractive index for extraordinary waves. zis the direction of beam propagation. (b) Linear evolution of a beam at 514nm undergoing diffraction. (c) A nematicon at 514nm, excited with a power of 2mW. (d) Output (z=2mm) cross-section of a probe colaunched at 632.8nm with the diffracting beam in (b). (e) Output transverse profile of a probe colaunched and copolarized at 632.8nm with the nematicon in (c). The probe was launched with a power of 100μW.
Nematicons and the associated waveguides can be bent, and so readdressed, by the presence of dielectric perturbations. We have explored several different approaches. For example, one or more external beams may modify the refractive index along the soliton path: see Figure 2(a).5,6 Another example is when the nematicon crosses a dielectric interface and undergoes refraction or total internal reflection: see Figure 2(b).7,8 It may also propagate in the presence of a voltage-tuned orientation that alters the beam walk-off, i.e., the direction of its power flow as compared with its wavevector.9Finally, it may interact with other nematicons nearby: see Figure 2(c).10, 11 We have successfully employed dual-frequency NLCs to change the walk-off from positive to negative angles by acting on the frequency of the applied voltage.12 We also demonstrated angular steering over angles as large as 55° for nematicons impinging a voltage-defined/adjusted interface.13
Figure 2. (a) Nematicon redirection via the refractive perturbation induced by an external beam orthogonal to the planar cell. Depending on the beam shape and location, the nematicon trajectory is bent in various directions and amounts. (b) Nematicon going through a voltage-defined dielectric interface in nematic liquid crystal (NLC): refraction (middle panel) and total internal reflection (bottom) can be obtained by independently varying the bias voltages in the two regions (top). (c) Interaction between two nematicons. (Top) Two 1.7mW nematicons launched with a 2°relative angle become parallel due to mutual attraction. (Bottom) When power is raised to 4.3mW each, the two nematicons cross and interleave, effectively making an X-waveguide junction.
The ability to control the nematicon trajectory with external voltage(s) and light beams means that we can also engineer simple guided-wave devices.14 See Figure 3(a) for an example of a logic gate, Figure 3(b) for a spatial router, and Figure 4 for controllable X- and Y-junctions.
Figure 3. (a) Example of logic gate XNOR with a nematicon and two external beams (green circles) as binary inputs. y0 indicates the ‘true’ output location. (b) Example of three-bit 1×8 all-optical router: the output location of the nematicon (y - y0) is controlled by three external beams with different shapes and location (top), redirecting the solitary waveguide and its signal according to their binary state (bottom).
Figure 4. (a) Two nematicons launched in parallel and noninteracting (initial separation exceeding nonlocality). (b) An X-junction and (c) a Y-junction formed by the nematicons in (a) but interacting via the perturbation induced by an external beam (green profile) between them, respectively. (d) Transverse profiles corresponding to (a) and (b) at z=1 .5mm. (e) Transverse profiles corresponding to (a) and (c) at z=1 .5mm.
Finally, nematicons can change their path based on their (input) power, as walk-off is tuned with reorientation itself.15 In the presence of specific dye-dopants enhancing the nonlinear response,16 nematicons were reported to change their direction of propagation by over 39° for powers between 180 and 400μW: see Figure 5.17
Figure 5. Nematicon power-dependent self-routing in a guest-host. Using a dye-doped NLC, a nematicon is generated at powers as low as 180μW and gets steered by 39° as its power increases up to 400μW. The photo sequence shows a red signal (produced by luminescence of the dye) guided by the nematicon excited at 442nm.
In conclusion, optical spatial solitons in soft matter, specifically NLCs, open new perspectives in all-optical signal routing, with voltage- and light-induced reorientation allowing the realization of reconfigurable and versatile guided-wave interconnects and circuits. We are now working on reducing thermal fluctuations and response times in order to develop simple circuits and demonstrate practical information processing capabilities.
Nonlinear Optics and Optoelectronics Lab (NooEL)
Roma Tre University
Gaetano Assanto is professor of optoelectronics and head of NooEL.
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