Optical Fourier surfaces

Abstract

Gratings 1 and holograms 2 are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered 3 , 4 . Further advances could exploit Fourier optics 5 , which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal waves, each with a well-defined amplitude, spatial frequency, and phase. However, because fabrication techniques typically yield profiles with at most a few depth levels, complex ‘wavy’ surfaces cannot be obtained, limiting the straightforward mathematical design and implementation of sophisticated diffractive optics. Here we present a simple yet powerful approach to eliminate this design–fabrication mismatch by demonstrating optical surfaces that contain an arbitrary number of specified sinusoids. We combine thermal scanning-probe lithography 6 – 8 and templating 9 to create periodic and aperiodic surface patterns with continuous depth control and subwavelength spatial resolution. Multicomponent linear gratings allow precise manipulation of electromagnetic signals through Fourier-spectrum engineering 10 . Consequently, we overcome a previous limitation in photonics by creating an ultrathin grating that simultaneously couples red, green, and blue light at the same angle of incidence. More broadly, we analytically design and accurately replicate intricate twodimensional moiré patterns 11 , 12 , quasicrystals 13 , 14 , and holograms 15 , 16 , demonstrating a variety of previously impossible diffractive surfaces. Therefore, this approach can provide benefit for optical devices (biosensors 17 , lasers 18 , 19 , metasurfaces 4 , and modulators 20 ) and emerging topics in photonics (topological structures 21 , transformation optics 22 , and valleytronics 23 ).

Super-Resolution Photothermal Patterning in Conductive Polymers Enabled by Thermally Activated Solubility

“…The self-limiting behavior seen in the transparent solution model is noteworthy because it could enable relatively simple writing of repeating surface structures, e.g., for photonic structures. 32 In addition, this self-limiting behavior ensures that the remaining film is never exposed to excessively high temperatures, preventing, for example, unwanted phase transitions or chemical degradation. Lastly, comparing the transparent and absorbing solution cases, the strong selflimiting behavior seen in the transparent solution case should reduce exposure-dependent broadening, leading to narrower features.…”

Digital holographic microscopy for real-time observation of surface-relief grating formation on azobenzene-containing films

“…For surface patterning, the realtime feedback, once fully integrated into the pattern generation would enable fabrication of arbitrary 3D surface profiles. This is something that is either very difficult to do with conventional lithography tools, or a very slow process of writing and measuring the surface point by point with thermal scanning probe microscopy 48 .…”

Broadband Decoupling of Intensity and Polarization with Vectorial Fourier Metasurfaces

“…Among the different methods to address the electromagnetic field distribution in the farfield, optical metasurfaces [1][2][3][4][5][6][7][8][9][10][11][12] , artificial materials that consist of subwavelength structure arrays, are capable of tailoring the waveform of the electromagnetic waves with unpreceded level of precision. In particular, due to the versatility of this approach, it is possible to engineer both amplitude and polarization information at will.…”