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The performance of direct and unwrapped phase retrieval, which combines digital holography with the transport of intensity, is examined in detail in this paper. In this technique, digital holography is used to numerically reconstruct the intensities at different planes around the image plane, and phase retrieval is achieved by the transport of intensity. Digital holography with transport of intensity is examined for inline and off-axis geometries. The effect of twin images in the inline case is evaluated. Phase-shifting digital holography with transport of intensity is introduced. The performance of digital holography with transport of intensity is compared with traditional off-axis single- and dual-wavelength techniques, which employ standard phase unwrapping algorithms. Simulations and experiments are performed to determine and compare the accuracy of phase retrieval through a mean-squared-error figure of merit as well as the computational speeds of the various methods.

Second harmonic generation from Au-Al2O3 interfaces is analyzed to estimate the density of delocalized electrons occupying metal induced gap states (MIGS). Laser light of wavelength 810 nm is incident on an Au substrate and the second harmonic at 405 nm is monitored, where the area fraction of Al2O3 coverage on Au is precisely controlled via atomic layer deposition—from no coverage to full coverage. Extensive electromagnetic simulations are performed using a phenomenological model containing a dimensionless MIGS factor “α,” to represent the strength of the delocalized electrons in MIGS in attenuating the second harmonic signal. By fitting the model to experimental data, an α = 0.13 is obtained leading to a room temperature, areal density of delocalized electrons of (3.53 ± 0.4) × 1014 cm−2 for the Au-Al2O3 interface and representing a 44% occupancy of MIGS.

We report that the second and third harmonic signal reductions with insulator film surface coverage over a gold substrate gives a measure of the electron density in the spill out volume of the insulator, which is dubbed metal insulator gap states. For metal-insulator-metal (MIM) structures we observe enhancement saturation and quenching of the third harmonic efficiencies well above the efficiencies for metal-insulator (MI) samples. The measured optical harmonics of scattered light from MI and MIM systems are compared with detailed simulations of the nonlinear interactions including free electron spill out into the insulator, nonlocal and electron quantum tunneling effects. Gold coated substrates are covered with variable thin insulator film thicknesses using atomic layer deposition. Optical harmonics of light scattered from two insulator materials (ZnO and Al2O3) are measured in our experiments. Based on our simulations we conclude that the observed MIM signal enhancement effects are primarily due to nonlocal phenomena in an electron gas.We present additional, detailed information about our simulations and experiments in this supplement.

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