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

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 ({}+10^-1 K^-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 Ba₂{NaNb}₅O₁₅ near Tc=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 Ba₂{NaNb}₅O₁₅, and the critical exponent {β} is obtained as βc=0.28±{}0.01 and βₐ=0.31±{}0.01.