Validity of classical Lorentz reciprocity theorem under nonclassical electromagnetic boundary condition for mesoscale metallic nanostructures

The optical response of mesoscale metallic nanostructures (MMNSs) with extreme nanoscale feature sizes is largely affected by the nonclassical quantum effects, which can be comprehensively described by the nonclassical electromagnetic boundary conditions (NEBC) formulated via Feibelman <i>d</i>-parameters. In classical electrodynamics, the classical Lorentz reciprocity theorem (CLRT) is of fundamental importance with extensive applications. In this work, we establish the nonclassical Lorentz reciprocity theorem (NLRT) under the NEBC, where the two non-perturbative <i>d</i>-parameters are considered in a rigorous manner. By comparing the NLRT with the CLRT under the classical electromagnetic boundary condition (CEBC), we derive the specific conditions under which the CLRT remains valid within the NEBC framework, and confirm their effectiveness by numerical examples. Our findings pave the way for directly extending the wide applications of the CLRT from classical electromagnetism to nonclassical regimes, and provide a theoretical justification for the rationality of the NEBC in describing the nonclassical effects without violating the CLRT.