Supersymmetry-generated complex optical potentials with real spectra

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT-symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PT symmetry is investigated.Comment: 6 pages, 4 figure

Universal Unitary Photonic Circuits by Interlacing Discrete Fractional Fourier Transform and Phase Modulation

We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$ unitary matrix into interlaced discrete fractional Fourier transforms and $N$-parameter diagonal phase shifts. We show that such a configuration can represent arbitrary unitary operators with $N+1$ phase layers. We discuss a gradient-based algorithm for finding the optimal phase parameters for implementing a given unitary matrix. By increasing the number of phase layers beyond the critical value of $N+1$, the optimization consistently converges faster as the system becomes over-determined. We propose an integrated photonic circuit realization of this architecture with coupled waveguide arrays and reconfigurable phase modulators. The proposed architecture can pave the way for developing novel families of programmable photonic circuits for optical classical and quantum information processing.Comment: Under review since January 15, 202

O papel da gestão urbana no desenvolvimento urbano sustentável no Irã

The present research studies the role of urban management in sustainable development in Iran. The present research is conducted in two theoretical and practical sections. In the theoretical part, the necessary information was collected using the library and documentation methodology and in the practical section, in a survey method, the necessary information was collected through interviews with experts and experts in urban development and development. By analyzing the content of these interviews, factors, variables (roles) have been identified. Then, using these variables, a questionnaire was designed and completed by some other experts. Creating ecological balance, creating aesthetic balance and creating a social balance is one of the main roles of councils and municians in Iran. Finally, the results of regression analysis showed that among the independent variables, the aesthetic equilibrium variable plays the most role in explaining sustainable urban development and ecological and social equilibrium in the next stages.La presente investigación estudia el papel de la gestión urbana en el desarrollo sostenible en Irán. La presente investigación se realiza en dos secciones teóricas y prácticas. En la parte teórica, se recopiló la información necesaria utilizando la metodología de la biblioteca y la documentación y en la sección práctica, en un método de encuesta, se recopiló la información necesaria a través de entrevistas con expertos y expertos en desarrollo y desarrollo urbano. Al analizar el contenido de estas entrevistas, se han identificado factores, variables (roles). Luego, usando estas variables, otros expertos diseñaron y completaron un cuestionario. Crear equilibrio ecológico, crear equilibrio estético y crear un equilibrio social es una de las funciones principales de los consejos y los municons en Irán. Finalmente, los resultados del análisis de regresión mostraron que entre las variables independientes, la variable de equilibrio estético juega el papel más importante para explicar el desarrollo urbano sostenible y el equilibrio ecológico y social en las siguientes etapas.A presente pesquisa estuda o papel da gestão urbana no desenvolvimento sustentável no Irã. A presente pesquisa é realizada em duas seções teóricas e práticas. Na parte teórica, as informações necessárias foram coletadas utilizando a metodologia de biblioteca e documentação e na seção prática, em um método de pesquisa, as informações necessárias foram coletadas através de entrevistas com especialistas e especialistas em desenvolvimento e desenvolvimento urbano. Ao analisar o conteúdo dessas entrevistas, fatores, variáveis (papéis) foram identificados. Então, usando essas variáveis, um questionário foi elaborado e concluído por alguns outros especialistas. Criar equilíbrio ecológico, criar equilíbrio estético e criar um equilíbrio social é um dos principais papéis dos conselhos e municipais no Irã. Finalmente, os resultados da análise de regressão mostraram que entre as variáveis independentes, a variável equilíbrio estético desempenha o maior papel na explicação do desenvolvimento urbano sustentável e do equilíbrio ecológico e social nos próximos estágios.&nbsp

Integrated Photonic Fractional Convolution Accelerator

An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices with equally-spaced eigenmode spectra and with different lengths that perform DFrDT operations of complementary orders sandwiching a modulator array. Numerical simulations show that smoothing and edge detection tasks are indeed performed even for noisy input signals

Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators

A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT-symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase transition point. The conclusions of our analysis are in agreement with experimental data.Comment: 9 pages, 8 figure