Lithium niobate (LiNbO3) crystals have found extended use in electrooptics and photonics because of their desirable optical, piezoelectric, and photorefractive properties. Apart from various optical applications—such as optical modulators,1 optical filters,2 and holographic data storage3—they are also widely used in integrated optics for the preparation of planar waveguides.4 Among the techniques used for their fabrication, those that use light to induce holographic grating formation in LiNbO3 are generating significant interest for the design of dynamic interconnections in optical communications.5 Moreover, recent progress in the field of photonic crystal preparation adds a new dimension for the utilization of LiNbO3 crystals.
Conventional photonic-crystal-fiber fabrication is based on preform stacking methods in glass. Typically, a stack of glass tubes is constructed as a macroscopic “preform” with the required photonic-crystal structure. It is then fused together and drawn to fiber using a standard fiber drawing tower. This approach however, requires expensive advanced technology that represents a drawback for the development of novel waveguides. A solution is to use software to design and investigate the properties of novel structures, but this does not eliminate the requirement to compare the behavior of a model to that of a fabricated structure.
Our current research effort is focused on the efficient design of simple test structures. We design equipment for imaging refractive index distributions using LiNbO3:Fe, a relatively inexpensive material with good photorefractive properties. A promising feature of our approach is that the fabricated structures are erasable and can be re-used.
We investigate the photorefractive effect, i.e., the nonlinear optical effect observed in materials that respond to light by modifying their refractive index.6 It is well-known that the non-homogeneous illumination of a crystal results in the spatial redistribution of charge-carrying electrons, including those captured in traps or donor centers. This induces a space charge field in the crystal. In the regions where the field is strongest, the electro-optic effect changes the refractive index of the crystal. The result is a spatially-varying refractive index grating that occurs throughout the crystal. In principle, any refractive index inhomogeneity induced by light can be treated as a record of the space charge field.
Since LiNbO3 is anisotropic, we selected the crystal orientation with respect to the light gradient most likely to provide the best response during recording. In our experiments, we generated a grating using a two-beam interference method, so as to be able to use the grating in both transmission and reflection regimes. We started by recording a transmission grating and we measured the time dependence of the diffraction efficiency of the maxima resulting from the diffraction of the light illuminating the crystal from another light source. This provided the required grating information, such as the maximum amplitude of the refractive index modulation and its time dependence (see Figure 1).7
Figure 1. Time-dependence of the first-order diffraction efficiency in a transmission grating, showing measured (red) and fitted (blue) curves.
Using simplified coupled-mode theory, we also investigated the grating in the reflection regime. This allowed us to define conditions for the grating to behave as a filter (see Figure 2.). Our results prompted us to to change our approach for visible light applications, which required that the grating be formed using a standing wave with the spacing between two peaks being half of the wavelength of the original waves in the medium.
Figure 2. Calculated diffraction efficiency in a reflection grating.
Depending on the application, more complex optical fields can also be recorded. However, in the case of crystalline photorefractive materials, a limitation is introduced by the geometry of the field being recorded and by the photorefractive response of the crystal.
In principle, we are able to create various optical fields using one or more light beams. For example, we created optical fields using an argon laser beam to generate suitable amplitude and phase masks, as shown in Figure 3. Using an appropriate lens, we then projected the generated diffraction pattern onto the crystal. Recorded optical fields represent phase objects, which can be well observed by, for example, using a Mach-Zehnder interferometer.8
Figure 3. Optical fields to be recorded (a, b) and their interferograms after recording (c, d).
In conclusion, we used the LiNbO3: Fe crystal as a medium to design light-induced microstructures. Our work may provide a simple approach to test and image the refractive index properties of proposed novel photonic crystal structures.
This work was supported by the Slovak Science and Technology Assistance Agency under contract No. APVT-20-013504 and partially by the European Action COST 299 "FIDES - Optical fibres for new challenges facing the information society".
Norbert Tarjányi, Daniel Kácik, Gabriela Tarjányiová
Department of Physics
University of Zilina