The mechanisms of excitation energy transfer are studied using systems consisting of blue light emitting novel thiophene substituted 1,3,4-oxadiazole derivatives as donors and green light emitting laser dye coumarin-334 (C-334) as an acceptor in ethanol and poly(methyl methacrylate) [PMMA] media from steady-state and time-resolved methods. Experimental observations like bimolecular quenching constant (k(q)) greater than translation diffusion rate parameter (k(d)), critical transfer distance (R-0) greater than diffusion length (D-l), donor-acceptor interaction strength (alpha) greater than donor-donor interaction strength (beta) and biexponential decay of the donor in the presence of the acceptor confirms that the overall energy transfer from donor to acceptor is due to Forster resonance energy transfer (FRET). Furthermore, enhancement of energy transfer efficiency and fluorescence intensity in polymer media suggests that these donor-acceptor doped PMMA matrixes may have potential applications such as luminescent solar concentrator (LSC), energy transfer dye lasers (ETDL) and chemical sensors.