Transmission Matrix Measurement of Multimode Optical Fibers by Mode-Selective Excitation Using One Spatial Light Modulator  
[PERSON]  
1 Technische Universitat Dresden, Laboratory of Measurement and Sensor System Technique, Helmholtzstrasse 18, 01069 Dresden, Germany; [EMAIL_ADDRESS] (H.R. ); nekatrios.koukourakis@tu-dresden. a multi-mode device. The level of secrecy is measured by the uncertainty of an eavesdropper about a sent message [9]. For these contexts, the TM describes the amplitude and phase relations between the spatial and polarization modes of the complete fiber's mode domain. Several groups have already presented approaches to obtain access to the TM of disordered media like MMFs. In [10], the first measurement of a TM has been published, where the light propagation through a random scattering sample was investigated. By using a phase-only spatial light modulator (SLM), Hadamard patterns, whose elements are either \(+1\) or \(-1\) in amplitude, were chosen as the input basis for the illumination of the sample. The light that propagated through the sample was interferometrically measured using phase-shifting holography (PSH), which produces a measurement effort of at least \(4N\) (\(N\) = number of controlled segments). The presented work paved the way for various studies based on a TM observation. However, the explained procedure was developed for a sample having generalised scattering properties, but in terms of MMF applications, there are more practical ways to acquire the TM. Aiming to use the MMF as a flexible image transmission system, for example, as an ultra-thin endoscope, the TM is used to reconstruct a desired image at one end of the fiber [11; 12]. For this reason, focal spots scanning the input fiber facet of the MMF are generated with an SLM. The output signal is again measured using PSH. The mode-based TM is then generated by determining a conversion matrix that transfers the focal spot domain to the fiber's mode domain. Concerning information-technical approaches in this case, it is more accurate to relinquish the approximation step of determining a conversion matrix and to directly excite the modes in the MMF to observe the coupling process. In [7; 13], the supported MMF modes are sequentially excited by using an SLM. Additionally, another SLM is applied at the fiber output in order to decompose the MMF output signal into the mode domain. A correlation filter method is used, where the efficiency of diffracted light off the SLM surface into a power meter is proportional to the correlation of the fiber output with a desired mode. Consequently, the TM entries are obtained individually and the measurement effort is \(N^{2}\). Likewise, the presented technique in [14] to obtain the TM distinguishes a holographic setup at the fiber output. They measure the pure intensity distributions at the MMF output and use a computational algorithm to determine the individual TM entries. However, optimization approaches like the introduced _complex semi-definite programming_ have a major flaw concerning the computational effort in the case of measuring TMs with a large number of modes. In this paper, an optical setup is developed to acquire the fiber's TM by using an SLM at the fiber input to sequentially excite every mode that the waveguide supports. The light's phase and amplitude is directly shaped using proper combinations of neighbored SLM pixels forming a superpixel. Since the selective mode excitation is challenging to align, a thorough instruction of the presented setup is given. The light field that propagated through the MMF is analyzed using a novel approach. The MMF output is recorded with digital holography (DH) and the amplitude and phase of the captured signal are reconstructed numerically with the _angular spectrum_ method obtaining the complex light field distribution. The measured field distribution is used to determine the individual TM entries by decomposing it into the fiber's mode domain.