Phase modulation and far-field spatial patterns due to the transformational thermal-lens effect

Abstract

In earlier work we have reported a thermal-lens effect that is opposite in sign from and much stronger than the well-known effect in fluids and isotropic solids: Very near the transformation temperature in crystals undergoing structural phase transitions, certain indices of refraction have temperature derivatives that are large and positive (\ensuremath{\simeq}+${10}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}1}$), in contrast to the negative values of dn/dT that arise from thermal expansion in glasses or fluids. We evaluated the steady-state and time-dependent behavior of these effects in ${\mathrm{Ba}}_{2}$${\mathrm{NaNb}}_{5}$${\mathrm{O}}_{15}$ near ${\mathit{T}}_{\mathit{c}}$=850 K. In the present paper we extend these studies to examine the far-field spatial pattern produced by self-induced phase modulation. We also utilize the thermal-lens effect to investigate the critical behavior near the tricritical point of ${\mathrm{Ba}}_{2}$${\mathrm{NaNb}}_{5}$${\mathrm{O}}_{15}$, and the critical exponent \ensuremath{\beta} is obtained as ${\mathrm{\ensuremath{\beta}}}_{\mathit{c}}$=0.28\ifmmode\pm\else\textpm\fi{}0.01 and ${\mathrm{\ensuremath{\beta}}}_{\mathit{a}}$=0.31\ifmmode\pm\else\textpm\fi{}0.01.