Active sorting of orbital angular momentum states of light with a cascaded tunable resonator

The orbital angular momentum (OAM) of light has been shown to be useful in diverse fields ranging from astronomy and optical trapping to optical communications and data storage. However, one of the primary impediments preventing such applications from widespread adoption is the lack of a straightforward and dynamic method to sort incident OAM states without altering the states. Here, we report a technique that can dynamically filter individual OAM states and preserve the incident OAM states for subsequent processing. Although the working principle of this technique is based on resonance, the device operation is not limited to a particular wavelength. OAM states with different wavelengths can resonate in the resonator without any additional modulation other than changing the length of the cavity. Consequently, we are able to demonstrate a reconfigurable OAM sorter that is constructed by cascading such optical resonators. This approach does not require specially designed components and is readily amenable to integration into potential applications.

Toward broadband, dynamic structuring of a complex plasmonic field

The ability to tailor a coherent surface plasmon polariton (SPP) field is an important step toward many new opportunities for a broad range of nanophotonic applications. Previously, both scanning a converging SPP spot and designing SPP profiles using an ensemble of spots have been demonstrated. SPPs, however, are normally excited by intense, coherent light sources, that is, lasers. Hence, interference between adjacent spots is inevitable and will affect the overall SPP field distributions. We report a reconfigurable and wavelength-independent platform for generating a tailored two-dimensional (2D) SPP field distribution by considering the coherent field as a whole rather than as individual spots. With this new approach, the inherent constraints in a 2D coherent field distribution are revealed. Our design approach works not only for SPP waves but also for other 2D wave systems such as surface acoustic waves.

Continuously Tunable, Polarization Controlled, Colour Palette Produced from Nanoscale Plasmonic Pixels

Colour filters based on nano-apertures in thin metallic films have been widely studied due to their extraordinary optical transmission and small size. These properties make them prime candidates for use in high-resolution colour displays and high accuracy bio-sensors. The inclusion of polarization sensitive plasmonic features in such devices allow additional control over the electromagnetic field distribution, critical for investigations of polarization induced phenomena. Here we demonstrate that cross-shaped nano-apertures can be used for polarization controlled color tuning in the visible range and apply fundamental theoretical models to interpret key features of the transmitted spectrum. Full color transmission was achieved by fine-tuning the periodicity of the apertures, whilst keeping the geometry of individual apertures constant. We demonstrate this effect for both transverse electric and magnetic fields. Furthermore we have been able to demonstrate the same polarization sensitivity even for nano-size, sub-wavelength sets of arrays, which is paramount for ultra-high resolution compact colour displays.

On-chip photonic Fourier transform with surface plasmon polaritons

The Fourier transform (FT), a cornerstone of optical processing, enables rapid evaluation of fundamental mathematical operations, such as derivatives and integrals. Conventionally, a converging lens performs an optical FT in free space when light passes through it. The speed of the transformation is limited by the thickness and the focal length of the lens. By using the wave nature of surface plasmon polaritons (SPPs), here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 μm, resulting in an increase of speed by four to five orders of magnitude. The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components. The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.

Broadband chirality-coded meta-aperture for photon-spin resolving

The behaviour of light transmitted through an individual subwavelength aperture becomes counterintuitive in the presence of surrounding ‘decoration', a phenomenon known as the extraordinary optical transmission. Despite being polarization-sensitive, such an individual nano-aperture, however, often cannot differentiate between the two distinct spin-states of photons because of the loss of photon information on light-aperture interaction. This creates a ‘blind-spot' for the aperture with respect to the helicity of chiral light. Here we report the development of a subwavelength aperture embedded with metasurfaces dubbed a ‘meta-aperture', which breaks this spin degeneracy. By exploiting the phase-shaping capabilities of metasurfaces, we are able to create specific meta-apertures in which the pair of circularly polarized light spin-states produces opposite transmission spectra over a broad spectral range. The concept incorporating metasurfaces with nano-apertures provides a venue for exploring new physics on spin-aperture interaction and potentially has a broad range of applications in spin-optoelectronics and chiral sensing.

Nano-apertures cannot distinguish between distinct spin-states of photons because of information loss upon light-aperture interaction. Here, Du et al. report a subwavelength aperture integrated with metasurfaces which breaks spin degeneracy and produces opposite transmission spectra over a broad spectral range.

Mode-matching metasurfaces: coherent reconstruction and multiplexing of surface waves

Metasurfaces are promising two-dimensional metamaterials that are engineered to provide unique properties or functionalities absent in naturally occurring homogeneous surfaces. Here, we report a type of metasurface for tailored reconstruction of surface plasmon waves from light. The design is based on an array of slit antennas arranged in a way that it matches the complex field distribution of the desired surface plasmon wave. The approach is generic so that one can readily create more intricate designs that selectively generate different surface plasmon waves through simple variation of the wavelength or the polarization state of incident light. The ultra-thin metasurface demonstrated in this paper provides a versatile interface between the conventional free-space optics and a two-dimensional platform such as surface plasmonics.

Temporal reshaping of two-dimensional pulses

An analytic study of complete cylindrical focusing of pulses in two dimensions is presented, and compared with the analogous three-dimensional case of focusing over a complete sphere. Such behavior is relevant for understanding the limiting performance of ultrafast, planar photonic and plasmonic devices. A particular spectral distribution is assumed that contains finite energy. Separate ingoing and outgoing pulsed waves are considered, along with the combination that would be generated in free space by an ingoing wave. It is shown that for the two dimensional case, in order to produce a temporally symmetrical pulse at the focus, an asymmetric pulse must be launched. A symmetrical outgoing pulse is generated from a source with asymmetric time behavior, or an anti-symmetric input pulse. These results are very different from the corresponding three-dimensional case, and imply fundamental limitations on the performance of ultrafast, tightly focused, two-dimensional devices.

Calculation of the volumetric diffracted field with a three-dimensional convolution: the three-dimensional angular spectrum method

The first Rayleigh-Sommerfeld diffraction formula is treated in an exact form as a three-dimensional (3D) convolution in the spatial domain. Therefore, a 3D Fourier transform can be employed to convert the 3D diffracted electromagnetic field to the reciprocal space without approximations, which we call the 3D angular spectrum (3D-AS) method. It is also demonstrated that if evanescent waves are neglected, the 3D-AS method can be readily implemented numerically, with the results in good agreement with theoretical predictions.

Rayleigh-Sommerfeld diffraction formula in k space

An angular spectrum representation in three dimensions is used to develop three-dimensional Fourier forms of the first and second Rayleigh-Sommerfeld diffraction formulae and the Kirchhoff diffraction formula. For forward-propagating waves, these reduce to three-dimensional Fourier representations for diffraction in the forward half-space.

Reconstruction in interferometric synthetic aperture microscopy: comparison with optical coherence tomography and digital holographic microscopy

It is shown that the spatial frequencies recorded in interferometric synthetic aperture microscopy do not correspond to exact backscattering [as they do in unistatic synthetic aperture radar (SAR)] and that the reconstruction process based on SAR is therefore based on an approximation. The spatial frequency response is developed based on the three-dimensional coherent transfer function approach and compared with that in optical coherence tomography and digital holographic microscopy.

Realistic 3D coherent transfer function inverse filtering of complex fields

We present a novel technique for three-dimensional (3D) image processing of complex fields. It consists in inverting the coherent image formation by filtering the complex spectrum with a realistic 3D coherent transfer function (CTF) of a high-NA digital holographic microscope. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of a scattering object field. Experimental reconstructions in phase and amplitude are presented under non-design imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample or illumination rotation.

Quantitative phase restoration by direct inversion using the optical transfer function

Quantitative phase recovery of phase objects is achieved by a direct inversion using the defocused weak object transfer function. The presented method is noniterative and is based on partially coherent principles. It also takes into account the optical properties of the system and gives the phase of the object directly. The proposed method is especially suitable for application to weak phase objects, such as live and unstained biological samples but, surprisingly, has also been shown to work with comparatively strong phase objects.

Direct calculation of a three-dimensional diffracted field

We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens-Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.

Phase from chromatic aberrations

We show that phase objects may be computed accurately from a single color image in a brightfield microscope, with no hardware modification. Our technique uses the chromatic aberration that is inherent to every lens-based imaging system as a phase contrast mechanism. This leads to a simple and inexpensive way of achieving single-shot quantitative phase recovery by a modified Transport of Intensity Equation (TIE) solution, allowing real-time phase imaging in a traditional microscope.

Transport-of-intensity approach to differential interference contrast (TI-DIC) microscopy for quantitative phase imaging

Differential interference contrast (DIC) microscopy is an inherently qualitative phase-imaging technique. What is obtained is an image with mixed phase-gradient and amplitude information rather than a true linear mapping of actual optical path length (OPL) differences. Here we investigate an approach that combines the transport-of-intensity equation (TIE) with DIC microscopy, thus improving direct visual observation. There is little hardware modification and the computation is noniterative. Numerically solving for the propagation of light in a series of through-focus DIC images allows linear phase information in a single slice to be completely determined and restored from DIC intensity values.

Image formation in holographic tomography: high-aperture imaging conditions

Three-dimensional (3D) imaging by holographic tomography can be performed for a fixed detector through rotation of either the object or the illumination beam. We have previously presented a paraxial treatment to distinguish between these two approaches using transfer function analysis. In particular, the cutoff of the transfer function when rotating the illumination about one axis was calculated analytically using one-dimensional Fourier integration of the defocused transfer function. However, high numerical aperture objectives are usually used in experimental arrangements, and the previous paraxial model is not accurate in this case. Hence, in this analysis, we utilize 3D analytical geometry to derive the imaging behavior for holographic tomography under high-aperture conditions. As expected, the cutoff of the new transfer function leads to a similar peanut shape, but we found that there was no line singularity as was previously observed in the paraxial case. We also present the theory of coherent transfer function for holographic tomography under object rotation while the detector is kept stationary. The derived coherent transfer functions offer quantitative insights into the image formation of a diffractive tomography system.

Image formation in holographic tomography

Tomography has been applied to holographic imaging systems recently to improve the 3D imaging performance. However, there are two distinct ways to achieve this: either by rotation of the object or by rotation of the illumination beam. We provide a transfer function analysis to distinguish between these two techniques and to predict the 3D imaging performance in holographic tomography when diffraction effects are considered. The results show that the configuration of rotating the illumination beam in one direction while fixing the sample leads to different 3D imaging performance as compared to the configuration of rotating the sample. The spatial frequency cutoff is nonisotropic in the case of rotating the illumination, and a curved line of singularity is observed. Rotating of the sample, on the contrary, has more symmetry in spatial frequency coverage but has a single point of singularity. The 3D transfer function derived can be used for 3D image reconstruction.