Optical second harmonic signature of phase coexistence in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>ferroelectric</mml:mtext><mml:mo>|</mml:mo><mml:mtext>dielectric</mml:mtext></mml:math> heterostructures

An exotic coexistence of polar states is known to occur in $\text{ferroelectric}|\text{dielectric} {\mathrm{PbTiO}}_{3}|{\mathrm{SrTiO}}_{3}$ ($\mathrm{PTO}|\mathrm{STO}$) heterostructures. In the PTO layers with a thickness 10--20 unit cells, in-plane-polarized regions order alongside so-called vortex phase whirl-like arrangement electric dipoles. We investigate optical signature these phases noninvasively using second harmonic generation (SHG) on $\mathrm{PTO}|\mathrm{STO}$-based identify down single $\mathrm{PTO}|\mathrm{STO}$ bilayer. By comparing SHG yield dependence number layers, we further find that interlayer coupling plays an important role setting final polarization state. Our nonlinear experiments demonstrate potential this noninvasive approach for identification and understanding complex noncollinear ordering dipole moments oxide heterostructures lays groundwork their operando investigation.