The number of eigenmodes in an optical fibre depends on the wavelength of the excitation laser beam as well as on the exact geometry and refractive index profile of the fibre. The latter is often proprietary information and, when available, is only specified to within manufacturing tolerances. We here present a method for obtaining the number of fibre modes, as well as their shape, which requires no knowledge about the fibre, save a very approximate core radius. The method is based on the singular value decomposition (SVD) of a set of speckle patterns, measured at the output end of the fiber, which is then expanded onto a set of orthonormal basis functions. We present two possible approaches for the field expansion, where the first approach uses a generic orthonormal basis, such as Laguerre–Gaussian or Zernike functions, and the second one is a basis-free approach where the set of speckled patterns themselves form the basis. Using a set of simulated speckles patterns, we observed that the correct number of fibre modes can be obtained through the SVD decomposition, even at high levels of additive random noise. With a slight extension, using speckle patterns obtained at multiple excitation wavelengths (or equivalently, for different lengths of the same fiber) the method can also retrieve the shape of the actual fibre modes, by forming an appropriate linear combination of SVD modes.
Advanced wavefront-shaping methods can be used to transform a simple multimode fiber into an ultra-thin laser scanning microscope. Here, we extend this technique to label-free non-linear microscopy with chemical contrast using coherent anti-Stokes Raman scattering (CARS) through a multimode fiber endoscope, which opens up new avenues for instant and in-situ diagnosis of potentially malignant tissue. We use a commercial, 125 μm diameter, 0.29 NA, GRIN fiber as the endoscopic probe. Wavefront shaping on a spatial light modulator is used to create a focus, where the 1-2 ps long pump and Stokes pulses are overlapped in time, which is scanned behind the fiber facet across the sample. The chemical selectivity is demonstrated by imaging 2 μm polystyrene and 2.5 μm PMMA beads with per pixel integration time as low as 1 ms for epi-detection. Epi-detection through the fiber is possible despite the fact that the CARS signal is emitted mainly in the forward direction, away from the fiber facet. Detecting the back-scattered signal from the underlying tissue, requires a large detector aperture to be efficient. By detecting through both the core and the cladding of the fiber, we obtain sufficient detection efficiency.
Multimode fiber imaging using transmission matrix (TM) is a promising way of deep inspection of living objects. These techniques, however, face a problem of obtaining the transmission matrix using phase-shifting interferometry with external reference beam, which requires additional instrumentation and increases space requirements of the experiment. We suggest a method employing input mode represented by a focal spot at the proximal end of the fiber as an internal reference wave. Due to speckle nature of the output, it is necessary to cover blind spots in the transmission matrix arising from the lack of interference signal by several measurements with different input modes used as a reference. The effect of optimized selection of internal references will be analyzed and compared with the external reference approach.
When using multimode fibers as high-resolution endoscopes, advanced adaptive optics is needed to overcome the modal dispersion which scrambles the image. Additionally, for non-linear imaging methods, all the wavelengths of a femtosecond laser pulse must be simultaneously focused at the sample plane, with appropriate dispersion compensation, that might vary across the sample area. We investigate the bandwidth of the focused spot for a graded index fiber used as a point scanning imaging device. We demonstrate that with proper compensation for the dispersion of the spatial light modulator this can be <45 nm. We also measure the spectral phase at the sample plane, and demonstrate that this does not vary substantially with spot position.
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