Photons propagating in Laguerre-Gaussian modes have characteristic orbital angular momenta, which are fundamental optical degrees of freedom. The orbital angular momentum of light has potential application in high capacity optical communication and even in quantum information processing. In this work, we experimentally construct a ring cavity with 4 lenses and 4 mirrors that is completely degenerate for LaguerreGaussian modes. By measuring the transmitted peaks and patterns of different modes, the ring cavity is shown to supporting more than 31 Laguerre-Gaussian modes. The constructed degenerate cavity opens a new way for using the unlimited resource of available angular momentum states simultaneously. The Laguerre-Gaussian (LG) modes are solutions for beam profiles with circularly symmetric. They are written in cylindrical coordinates using Laguerre polynomials and shown to obtained well-defined orbital angular momentum (OAM) [1]. The phase fronts of light beams in OAM eigenstates rotate, clockwise for positive OAM values, anti-clockwise for negative values, which could result in some unique features. The synthetic dimension with the values of OAM defined as the dimensional basis is recognized as a unique asset in many studies, including high-capacity optical communication [2,3], versatile optical tweezers [4], quantum information and quantum foundation [5][6][7]. It has been recently demonstrated quantum entanglement involving angular momenta as high as hundreds [6,8]. The manipulation and measurement of OAM states can be reached with high precision [5,[9][10][11], which leads to new applications of OAM states, such as detecting of a spinning object and lateral motion [12,13].Although, in principle, there are infinite synthetic degrees of freedom for OAM states, how to construct some functional devices by manipulating them in the synthetic dimension become a subject to be developed. Recently, a new kind of photonics simulator based on energy-degenerated optical cavities has been theoretically presented, which can support a large number of OAM modes [14]. By taking advantage of such kind of optical cavity, one can simulate photonics topological matters, as well as construct all-optical devices by manipulating in photonic synthetic dimension [15,16]. All such potentially novel applications are ascribed to set up a kind of degenerate optical cavity, which can support plenty of energy-degenerated OAM modes.Here, we present an experimental framework using numbers of OAM states in an optical cavity simultaneously, which is referred to a degenerate cavity. Different from previous works with OAM in cavities [17,18], we precisely measure the transmitted peaks and beam profles of different modes in the cavity, which is shown to supporting more than 31 LG modes. Moreover, the constructed cavity is in principle completely degenerate, which can be used to generate lasers and entangled photon sources with high dimensional LG modes [19][20][21][22] and other related fields [23][24][25].The theoretical framework of a degenera...
A type of fiber-based orbital angular momentum (OAM) modulator is designed according to transformation relation between OAM beam and optical fiber vector mode, together with mode-coupling theory, which is based on the combination of multimode fiber structure and chirally-coupled-cores structure. Instead of applying external force or grating etching to the fiber in the system, chirally-coupled-cores fiber can realize the modulation of any optical OAM by using single fiber at 1550 nm. Therefore, the test system is relatively simple. From the equation <inline-formula><tex-math id="M1000">\begin{document}${\rm{OAM}}_{ \pm l,n}^{ \pm \sigma } = {\rm{HE}}_{l + 1,n}^{{\rm{even}}} \pm {\rm{i}} \times {\rm{HE}}_{l + 1,n}^{{\rm{odd}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182036_M1000.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182036_M1000.png"/></alternatives></inline-formula>, it can be seen that the OAM mode generated by long period chirally-coupled-cores fiber depends on the higher-order modes supported by the central fiber core. Therefore, the generation and modulation of any order OAM beam can be realized by changing the diameter of the central fiber core in theory. Through theoretical analysis and numerical simulation, the effects of different structure parameters on OAM modes are analyzed, including mode purity, mode transmission loss and effective refractive index. By keeping the propagation constants of the center core and side cores unchanged, the number of side cores has no effect on mode purity nor effective refractive index, but which is not for mode transmission loss. The loss of mode transmission increases with the increase of the number of side cores. However, it does not mean that the less number of side cores is a better case, in that the fiber symmetry and processing technology should also be considered. And the pitch calculated by the formula of phase matching condition can change in value within a certain numerical range without strongly affecting the mode purity and mode transmission loss. Pitch has a great influence on the effective refractive index of modes, therefore the pitch can be under control to change the difference in effective refractive index between OAM modes and reduce crosstalk between disparate modes. The distance between the center core and side cores of fiber has little effect on mode purity, great effect on mode transmission loss, but no effect on effective refractive index. Theoretically, the mode purity and mode transmission loss perform better with the distance between two kinds of cores increasing. But it will be limited by the fiber integration level.
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