How to Reliably Determine the Complex Refractive Index (RI) of Graphene by Using Two Independent Measurement Constraints

Reliable determination of the complex refractive index (RI) of graphene inherently requires two independent measurement realizations for two independent unknowns of the real (n(G)) and imaginary (k(G)) components, i.e., RI = n(G) + i k(G). Thus, any single set of measurement realization provides only one constraint that is insufficient to uniquely determine the complex RI of graphene. Tandem uses of two independent measurement techniques, namely the surface plasmon resonance (SPR) angle detection and the attenuated total reflection (ATR) intensity measurement, allow for the unique determination of the complex RI of CVD-synthesized graphene. The presently measured graphene RI is determined to be 2.65 + 1.27i for the E-field oscillating parallel to graphene at 634 nm wavelength, with variations for different numbers of L (1, 3 and 5) remaining within +/- 3%. Thus, our demonstration results for the specified wavelength serve as an impetus to suggest the need for two independent measurement techniques in determining both the real and imaginary RI values for graphene. Additional efforts have been made to characterize graphene layers using the density function theory (DFT): this calculation provides RIG = 2.71 +/- 1.41i.