Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

In a theoretical work by P.W. Anderson ¹, it was shown that in the presence of disorder in a quantum electronic system, the diffusion process stops and localized electronic states develop. Anderson localization is a wave phenomenon that can also occur for classical waves such as light. Since the theoretical prediction of Anderson localization in optics ^2,3, there have been many efforts to realize this phenomenon experimentally with electromagnetic waves ^4,5. However, it has been very difficult to achieve strong localization because the optical scattering cross sections are often too small due to the low refractive index contrast of most optical materials. In 1989, De Raedt et al. ⁶ showed that it is possible to observe the Anderson localization in a quasi-two-dimensional disordered optical system with low refractive index contrasts. They showed that if the disorder is confined to the transverse plane of a propagating wave in a longitudinally invariant medium, the beam can remain confined to a small region in the transverse direction due to strong transverse scattering. Transverse Anderson localization was first observed in two-dimensional waveguides that were created by using interference patterns in a photo-refractive crystal ⁷. Fused silica is the other medium that has been used for the observation of transverse Anderson localization ^8,9, where disordered waveguides are written using femtosecond pulses along the sample. The refractive index difference of disordered sites in the above mentioned systems are on the order of 10^-4 , so the localization radius is quite large. Additionally, the typical waveguides are usually not longer than several centimeters; therefore, they may not be practical for guided-wave applications. We point out that the observation of transverse Anderson localization in a one-dimensional disordered waveguide was reported earlier in Ref ¹⁰.

The optical fiber developed here has several advantages over the previous realizations of transverse Anderson localization for guided-wave applications ^11,12. First, the large refractive difference of 0.1 between the disorder sites of the fiber results in a small localized beam comparable to the beam radius of regular optical fibers. Second, the polymer disordered optical fiber can be made much longer than the disordered waveguides written externally into photorefractive crystals or fused silica. We were able to observe transverse Anderson localization in a 60-cm-long fiber ¹¹. Third, the polymer disordered optical fiber is flexible, making it practical for real world device-level applications that rely on the transport of light waves in fibers ¹³.

In order to fabricate the disordered optical fiber, 40,000 strands of PMMA and 40,000 strands of PS were randomly mixed, where each strand was 8 inches long and 250 μm in diameter. The randomly mixed strands were assembled into a square cross-section preform with a side-width of about 2.5 inches. The preform was then drawn to a square optical fiber with a side width of about 250 μm (Figure 1). In order to randomly mix the original fiber strands, we spread a layer of PMMA fiber strands on a large table, added a layer of PS fiber strands, and then randomly mixed them together. The procedure was repeated many times until a good random mixture was obtained.

We used a scanning electron microscope (SEM) to image the refractive index profile of the disordered polymer optical fiber. Regular cleaving techniques such as using a sharp heated blade cannot be used to prepare the fiber samples for the SEM imaging of the fiber end to map its refractive index profile, because the blade damages the morphology of the fiber end. Polishing the fiber has a similar detrimental impact on the quality of the fiber end. In order to prepare high-quality samples for the SEM imaging, we submerged each fiber in liquid nitrogen for several minutes and then broke the fiber; if done on enough fiber samples, this method results in a few good fiber pieces (around 15% success rate) with very high-quality and smooth end surfaces for the SEM imaging. We then used a 70% ethyl alcohol solution at 60 °C for about 3 min to dissolve the PMMA sites on the fiber end; longer exposure can disintegrate the entire fiber end. We then coated the samples with Au/Pd and placed them in the SEM chamber. The zoomed-in SEM image of the disordered polymer optical fiber is shown in Figure 2. The light gray sites are PS and the dark sites are PMMA. The total width of the image is 24 μm where the smallest features sizes in this image are ~0.9 μm, corresponding to the individual site sizes of the fiber strands, after the draw process.

In order to characterize the waveguide properties of the disordered optical fiber, we used a He-Ne laser at 633 nm wavelength. The He-Ne laser is coupled to a single mode SMF630hp optical fiber with a mode field diameter of about 4 μm, which is then butt-coupled to the disordered polymer optical fiber using a high-precision motorized stage. The output is then imaged on a CCD camera beam profiler using a 40X objective.

In the first set of experiments, we chose 20 different disordered fiber samples, each 5-cm long; the 5-cm length was chosen to match the propagation length in our numerical simulations. The numerical simulations of the disordered fiber are generally very time consuming, even on a high performance computing cluster with 1,100 elements. The full transverse Anderson localization for the wavelength of 633 nm happens only after about 2.5 cm of propagation ^11,12; therefore, we decided that the 5-cm length is sufficient for our purposes. Because of the stochastic nature of the Anderson localization, we needed to repeat both the experiments and the simulations for 100 realizations, in order to collect sufficient statistics to compare the experimental and numerical values of the average beam diameter. In practice, 100 different measurements are obtained by taking five spatially separated measurements on each of the 20 different disordered fiber samples.

It is fairly hard to prepare the disordered polymer optical fibers for measurements, compared with glass optical fibers. For example, one cannot use the advanced cleaving and polishing tools and techniques that are well-developed for standard silica-based fiber. A refined procedure for cleaving and polishing polymer optical fibers has been reported by Abdi et al. ¹⁴; we used their methods with some minor modifications to prepare our fiber samples. In order to cleave a polymer disordered optical fiber, a curved X-Acto blade is heated to 65 °C , and the fiber to 37 °C . The tip of the fiber is aligned on a cutting surface so that a clean, perpendicular cut can be made. The blade is placed on the side of the fiber, and quickly rolled across. The entire cleaving process should be done as fast as possible to ensure that the temperatures of the blade and fiber do not change considerably. After cleaving the fiber and inspecting it under an optical microscope, the fiber end is polished using standard fiber lapping sheets (0.3 μm Thorlabs LFG03P Aluminum Oxide Polishing Paper) to ensure that any minor imperfections are removed. To polish the fiber end, it is held in a pair of tweezers with the tweezers holding the fiber approximately 1.5 mm away from the end face being polished. The fiber is drawn over the paper in one-inch long figure-8-shaped paths, approximately eight times. Polishing the fiber results in smoother edges as inspected under the optical microscope. Moreover, polishing facilitates proper coupling to a localized spot in the fiber, which in turn reduces the attenuation both in the coupling and also in the initial propagation distance before the localized spot is formed.

We used a CCD camera beam profiler to image the output beam intensity. The near-field intensity profile was captured using a 40X objective. In order to find the boundaries of the fiber, we saturated the CCD by increasing the power of the incoming light from the SMF630hp fiber. After detecting the intensity profile of the localized beam with respect to the boundaries, we set the CCD beam profiler to the auto-exposure option. We used the image of the intensity profile in order to calculate the effective beam radius. In order to remove the effect of the ambient noise, we calibrated our image processing procedure to ensure that we obtain the expected beam diameter of the SMF630hp fiber. The average measured value of the beam radius and its variations around the average value agree well with the numerical simulations, as shown in Ref. ¹¹. The output beam profile in the polymer fiber clearly follows a change in the position of the incident beam as shown in Refs. ^11,12,13.

A comprehensive study of the impact of the design parameters such as the disorder site sizes and the incident wavelength on the beam radius of the localized beam was presented in Refs.^12,15.