By using monosubstituted 2,2'-bipyridine asymmetric ancillary ligands with different electron donor moieties and an arene ligand (p-cymene), we successfully designed and synthesized six Ru(II) compounds (RuBPY1-6) that belong to a piano-stool-type system. The NLO properties of the synthesized complexes have been studied in both solution and the solid state. The electronic spectra of these compounds show a broad feature with two absorption bands in the visible window (350-650 nm). RuBPY1-6 complexes exhibit NIR emission spectra in the solution state (at >720 nm), the maxima of which are bathochromically shifted in comparison to those of the concerned ligands. Interestingly, compounds RuBPY1-6 show NIR emission in their solid state too. Title compounds RuBPY1-6 have lifetimes in the range of 0.2 to 0.9 ns. An important feature of this work is the π-association of the p-cymene ligand to Ru(II) in the synthesized complexes; the π complex is formed by breaking the symmetry of p-cymene, found in the starting precursor (Ru2 dimer). This has been established by NMR spectral studies along with DFT calculations on the 1H NMR spectra. We could derive the molecular structure of the cationic part of this system by density functional theory (DFT), associated with 1H NMR spectral studies. The minimum energy structures for RuBPY1 and RuBPY2 have been optimized at DFT/B3LYP along with the LANL2DZ basis set for ruthenium atoms. These optimized structures are further considered to calculate the excited state properties using the TDDFT method. The electrochemical studies of the complexes, investigated in acetonitrile solution, show that this system is associated with a well-defined Ru(III)/Ru(II) reversible couple, rarely observed for a Ru(II) piano-stool-type compound, along with a feature of irreversible ligand oxidation. The absorption cross-section values, obtained from the two-photon absorption studies of title compounds RuBPY1-6, are worth reporting and lie in the range of 3-28 GM (in the femtosecond case).