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Resonant field enhancement in optical cavities is provided over only narrow linewidths and for specific spatial modes. Consequently, spectrally restrictive planar Fabry-P{\'e}rot cavities have not contributed to date to white-light imaging, which necessitates a highly multimoded broadband field to satisfy the resonance condition. Here we show that introducing judicious angular-dispersion circumvents the fundamental trade-off between cavity linewidth and finesse in a Fabry-P{\'e}rot cavity by exciting a 130-nm-bandwidth achromatic resonance across the visible spectrum, which far exceeds the finesse-limited linewidth (0.5~nm), and even exceeds the free spectral range (45~nm). This omni-resonant configuration enables broadband color-imaging over a 100-nm-bandwidth in the visible with minimal spherical and chromatic aberrations. We demonstrate omni-resonant imaging using coherent and incoherent light, and spatially extended and localized fields comprising stationary and moving objects. This work paves the way to harnessing broadband resonant enhancements for spatially structured fields, as needed for example in solar windows.

When an optical pulse is focused into a multimode waveguide or fiber, the energy is divided among the available guided modes. Consequently, the initially localized intensity spreads transversely, the spatial profile undergoes rapid variations with axial propagation, and the pulse disperses temporally. Space-time (ST) supermodes are pulsed guided field configurations that propagate invariantly in multimode waveguides by assigning each mode to a prescribed wavelength. ST supermodes can be thus viewed as spectrally discrete, guided-wave counterpart of the recently demonstrated propagation-invariant ST wave packets in free space. The group velocity of an ST supermode is tunable independently -- in principle -- of the waveguide structure, group-velocity dispersion is eliminated or dramatically curtailed, and the time-averaged intensity profile is axially invariant along the waveguide in absence of mode-coupling. We establish here a theoretical framework for studying ST supermodes in planar waveguides. Modal engineering allows sculpting this axially invariant transverse intensity profile from an on-axis peak or dip (dark beam), to a multi-peak or flat distribution. Moreover, ST supermodes can be synthesized using spectrally incoherent light, thus paving the way to potential applications in optical beam delivery for lighting applications.

Omni-resonance refers to the broadening of the spectral transmission through a planar cavity, not by changing the cavity structure, but by judiciously preconditioning the incident optical field. As such, broadband imaging can be performed through such a cavity with all the wavelengths simultaneously resonating. We examine here the spatial resolution of omni-resonant imaging and find that the spectral linewidth of the cavity resonance determines the spatial resolution. Surprisingly, the spatial resolution improves at longer wavelengths because of the negative angular dispersion intrinsic to Fabry-Perot resonances, in contrast to conventional diffraction-limited optical imaging systems where the spatial resolution improves at shorter wavelengths. These results are important for applications ranging from transparent solar windows to nonlinear resonant image processing.

When an optical pulse is spatially localized in a highly multimoded waveguide, its energy is typically distributed among a multiplicity of modes, thus giving rise to a speckled transverse spatial profile that undergoes erratic changes with propagation. It has been suggested theoretically that pulsed multimode fields in which each wavelength is locked to an individual mode at a prescribed axial wave number will propagate invariantly along the waveguide at a tunable group velocity. In this conception, an initially localized field remains localized along the waveguide. Here, we provide proof-of-principle experimental confirmation for the existence of this new class of pulsed guided fields, which we denote space-time supermodes, and verify their propagation invariance in a planar waveguide. By superposing up to 21 modes, each assigned to a prescribed wavelength, we construct space-time supermodes in a 170-micron-thick planar glass waveguide with group indices extending from 1 to 2. The initial transverse width of the field is 6 microns, and the waveguide length is 9.1 mm, which is 257x the associated Rayleigh range. A variety of axially invariant transverse spatial profiles are produced by judicious selection of the modes contributing to the ST supermode, including single-peak and multi-peak fields, dark fields (containing a spatial dip), and even flat uniform intensity profiles.

The structure of an optical waveguide determines the characteristics of its guided modes, such as their spatial profile and group index. General features are shared by modes regardless of the waveguiding structure; for example, modal dispersion is inevitable in multimode waveguides, every mode experiences group-velocity dispersion, and higher-order modes are usually slower than their lower-order counterparts. We show here that such trends can be fundamentally altered -- altogether severing the link between modal order and group index hybrid and eliminating dispersion -- by exploiting hybrid guided space-time modes in a planar multimode waveguide. Such modes are confined in one-dimension by the waveguide and in the other by the spatio-temporal spectral structure of the field itself. Direct measurements of the modal group delays confirm that the group index for low-loss, dispersion-free, hybrid space-time modes can be each tuned away from the group index of the conventional mode of same order, and that the transverse size of these hybrid modes can be varied independently of the modal order and group index. These findings are verified in a few-mode planar waveguide consisting of a 25.5-mm-long, 4-$\mu$m-thick silica film deposited on a MgF$_2$ substrate.