Near-field transmission matrix microscopy for mapping high-order eigenmodes of subwavelength nanostructures

As nanoscale photonic devices are densely integrated, multiple near-field optical eigenmodes take part in their functionalization. Inevitably, these eigenmodes are highly multiplexed in their spectra and superposed in their spatial distributions, making it extremely difficult for conventional near-field scanning optical microscopy (NSOM) to address individual eigenmodes. Here, we develop a near-field transmission matrix microscopy for mapping the high-order eigenmodes of nanostructures, which are invisible with conventional NSOM. At an excitation wavelength where multiple modes are superposed, we measure the near-field amplitude and phase maps for various far-field illumination angles, from which we construct a fully phase-referenced far- to near-field transmission matrix. By performing the singular value decomposition, we extract orthogonal near-field eigenmodes such as anti-symmetric mode and quadruple mode of multiple nano-slits whose gap size (50 nm) is smaller than the probe aperture (150 nm). Analytic model and numerical mode analysis validated the experimentally observed modes. Nanoscale integrated photonic devices have complicated combinations of optical eigenmodes. Here, the authors develop a far- to near-field transmission matrix microscopy that enables measuring higher-order modes of nanostructures beyond the capabilities of conventional near-field microscopy.