Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers

In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schrödinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk, effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any modulation formats. Here, we demonstrate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods, such as orthogonal frequency division multiplexing and Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 4.5 dB, which is comparable to results achievable with multi-step per span digital back propagation.

Synthesis and characterization of triazolotriazines

The Dimroth rearrangement in ring-fused 1,2,4-triazoles has been reviewed in detail in Part I and the synthesis of all known triazolo-triazines is described in Part II. Experimental investigations concerned the establishinent of the skeletal arrangement of a variety of triazolotriazines formed by several synthetic routes. Interaction of 3-amino-5-hydrazino-12,4-triazole and benzilafforded 2-amino-6, 7-diphenyl-1, 2,4-triazolo[ 5, 1-c-]-1,2,4-triazine,whereas cyclization of 5,6-diphenyl-3-hydrazino-1,2,4-triazine withcyanogen bromide resulted in the isomeric 3-amino-6,7-diphenyl,-1,2,4-triazolo [4, 3-b]-1,2,4-triazine: both amines were deaminated with amyl nitrite in boiling tetrahydrofuran without rearrangement of the heterocyclic skeleton. 6,7-Diphenyl-1,2,4-triazolo[5,1-cJ-1,2.4-triazine, synthesized from 3-hydrazino-1,2,4-triazole and benzil, formed a covalent hydrate which could be detected spectroscopically in solution, and a covalemt methanolate and ethanolate which could be isolated. A new route to 3-amino-5-hydrazino-pyrazole is described and cyclization to 7-amino-3,4-diphenyl-pyrazolo[ 5,1-.c]-1,2,4-triazine was achieved with benzil. The diazonium nitrate of 3-amino-1,2,4-triazole coupled with ethyl cyanoacetate to yield a mixture of two geometrical isomers of ethyl 2-(2H-1,2,4-triazol-3-ylhydrazono) cyanoacetate.Recrystallization of the crude coupling mixture from aqueous ethanol gave a single hydra-zone which cyclized predominantly to ethyl 7-amino-1,2,4-triazolo[5,1-c]-1,2,4-triazine-6-carboxylate in acid conditions and 6-cyano-1,2,4-triazolo[ 5,1-c]-1,2,4~triazin-7(4H)-one under basic conditions. The nature of the cyclizing medium also controlled the cyclization of .the (pyrazol-ylhydrazono) cyanoacetate hut the corresponding (tetrazol- ylhydrazono) cyanoacetate gave only ethyl 7-aminotetrazolo[ 5,1-cJ-1,2,4- -triazine-6-carboxylate. 2-( 2H-1,2,4-Triazol-3-:ylhydrazono) malonitrile cyclized unambiguously to 7-amino-6-cyano-1,2,4-triazolo-[ 5,1-c]-1,2,4- triazine. Drastic hydrolysis of ethyl 2-(2H-1,2,4-triazol-3-yllhydrazono)-cyanoacetate, ethyl 7-amino-1, 2,4-triazolo[ 5,1-c]-1,2,4-triazine-6-carboxylate, 6-cyano-1,2,4-triazolo[ 5,1-c]-1,2,4-triazin-7{ 4H)-one and 7-amino-6- cyano-1,2,4-triazolo[5,1-c]-1,2,4-triazine gave a hydrate of 1,2,4-triazo1o[5,1-c ]-1,2,4-triazin-7(4H)-one. Mass spectral fragmentations of 7-aminoazolo-[5,1-c]-1,2,4-triazinesconfirm that the azole ring is more stable than the 1,2,4-triazine ring on electron impact.