We propose a novel high-efficiency no-moving-parts Laguerre-Gauss (LG) spectrometer using two variable focus lenses and a variable sized pinhole that overcomes the limitations of the classical, projective, phase flattening technique for measuring the Laguerre-Gauss (LG) spectrum of light beams. Simulation results show that the coupling losses are virtually zero and the only losses are ring losses which are mode-dependent but beam waist-independent. Hence, the detection efficiency for all modes is simultaneously the maximum possible irrespective of the beam waist of the LG modes chosen for the decomposition. The losses can also be easily pre-calibrated to remove the efficiency bias amongst different modes. [4][5][6] as well as the OAM spectrum of light beams [7][8][9]. The measurement of LG spectrum of an unknown beam, though, remains tricky and direct methods such as projective phase-flattening [10] and then coupling into a single mode fiber (SMF) have their limitations [11]. In this paper, we address some of the limitations of the projective phase-flattening approach using electronically controlled variable focus lenses. Such variable focus lenses have been used in a number of applications [12].The projective phase-flattening approach works by projecting an unknown, incoming beam onto a conjugate Laguerre-Gaussian (LG) mode using a phase spatial light modulator (SLM). A Fourier lens is then used to take the Fourier transform of the resultant field at the phase SLM in the focal plane of the lens. This Fouriertransformed field is then coupled into a single-mode-fiber (SMF). If the input beam contains that particular mode, then the helical phase of the input beam is completely canceled and the Fourier-transformed field has a central bright spot similar to a Gaussian with a ringed intensity pattern around it. The central bright spot can then couple into an SMF as the SMF supports only the T EM 00 mode which is also similar to a Gaussian. The process is repeated for different modes to determine the complete LG spectrum.The limitations of this approach are highlighted in Ref. [11]. Firstly, the detection efficiency into the SMF varies from mode to mode and also with the selected value of beam waist w 0 of the LG mode (see Ref [11], Fig. 2). The maximum possible detection efficiency for all the different possible modes is not obtained for one particular value of w 0 , which implies that all modes cannot opti- * mumtaz.sheikh@lums.edu.pk mally couple into the SMF simultaneously. Moreover, for a particular value of w 0 , the detection efficiency decreases with mode order thus limiting the bandwidth of the measured OAM spectrum. Ideally, the choice of w 0 should be such that it gives high enough detection efficiencies for all modes. Secondly, the radial decomposition of the beam depends upon the value of the beam waist w 0 chosen for the modes. Optimal choice of the beam waist is the one that gives the minimum number of radial modes. However, that cannot be known a priori for an unknown incoming beam. Finally, since the...
We present an experimental demonstration of a Laguerre-Gauss (LG) spectrum measurement technique using variable focus lenses that is able to measure the strengths of all modes present in an unknown, incoming light beam with the highest possible efficiency. The experiment modifies the classical projective, phase flattening technique by including a variable sized pinhole and a two electronic lens variable imaging system that is tuned for each mode to give the highest possible detection efficiency irrespective of the beam waist of LG mode chosen for the projection/decomposition. The modified experiment preserves the orthogonality between the modes with only a 4 % cross-talk so that superposition states may also be detected efficiently. Our experiment results show efficient detection of OAM vortex beams with topological charge, l, values ranging from 0 to 4 with various different beam waists chosen for the decomposition.
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