  The measurement of in-plane birefringence ($\Delta{n}$) of ultrathin film is
challenging due to a significant deviation of physical properties of materials
in ultrathin regime as compared to that in bulk state. Surface plasmon
resonance (SPR) phenomenon can be employed to measure change in refractive
index of ultrathin film at a very high resolution. This article discusses
simulation of SPR phenomenon in Kretschmann configuration for the measurement
of $\Delta{n}$ in organic thin film exhibiting nematic-like ordering on the two
dimensional gold surface. The distribution of plasmonic field on the gold
surface was found to be anisotropic. This suggested that the coupling plasmonic
field with that of organic thin film exhibiting nematic-like ordering on the
gold surface will be non-isotropic. Therefore, a non-zero difference in
resonance angle (RA) was obtained from SPR measurement performed along the
optic-axis (OA) and orthogonal to OA of the in-plane nematic ordering
($\Delta\theta$). A calibration surface showing the variation of
($\Delta\theta$) as a function of $\Delta{n}$ and thickness of thin organic
film consisting of shape anisotropic tilted molecules exhibiting nematic-like
ordering on gold surface was obtained. This calibration surface was employed
for the measurement of $\Delta{n}$ of single layer of Langmuir-Blodgett films
of cadmium stearate (CdSA) and 4'-octyl-4-biphenylcarbonitrile (8CB) deposited
on SPR chips. The thickness of the LB films was estimated using X-ray
reflectivity measurement and $\Delta\theta$ was measured using a home built SPR
instrument. The $\Delta{n}$ values were found to be 0.012 and 0.022 for
ultrathin films of CdSA and 8CB molecules, respectively.
