Propagation-invariant Fields Research Articles

Airy beam assisted NIR-II light-sheet microscopy

Near-infrared II (1000–1700 nm) three-dimensional (3D) microscopy addresses a significant improvement on the penetration depth for bioimaging, but is challenging in high z-direction spatial resolution, leading to imaging distortion in deep tissue bioimaging. Here, we developed Airy beam-assisted NIR-II light-sheet Microscope (NIR-II Airy LSM) to improve z-direction spatial resolution with large field of view (FOV) on thick biological specimens via self-healing properties of the propagation-invariant field. The axial resolution was measured to be consistently 3.5 µm across the whole FOV (∼ 600 µm), about 4 times higher than traditional Gaussian-beam based microscopy (∼ 15 µm). Besides, the NIR-II Airy LSM demonstrates 2–3 times higher signal background ratio (SBR) than NIR-I imaging, at the penetration depth of approximately 2.5 mm. The increased spatial resolution and SBR allows us to observe pathological conditions and progression of glomeruli and tubules of radiation induced kidney injury and discriminated integral damage degree of intestinal mucosal cells from intestinal tissue accurately via 3D volumetric multiplexed imaging. The improved NIR-II light-sheet microscopy exhibit complete 3D imaging capabilities of whole bio tissues without sacrificing axial resolution and avoid imaging distortion under deep tissue.

SU(2) Poincaré sphere: A generalized representation for multidimensional structured light

Structured light, as a general term for arbitrary states of amplitude, phase, and polarization in optical fields, is highly topical because of a myriad of applications it has fostered. A geometric description to graphically group classes of structured light has obvious benefits, with some notable advances in analogous Poincar\'e sphere (PS) mapping for both spin and orbital angular momentum (OAM), as well as ray-optical PS approaches for propagation-invariant fields, but all limited in dimensionality they can describe. Here we propose a generalized SU(2) PS for arbitrary dimensional structured light. The states on it represent extended families of beams with multidimensional ray-wave structures, accurately described by SU(2) symmetry groups. We outline how to construct this mapping theoretically, revealing insights into mode transformations involving OAM and geometric phase, and fully verify its efficacy experimentally. The generality of our approach is evident by the reduction to prior PS representations as special cases. We also demonstrate an extension of our approach to explain a more general high-dimensional vector beam. This construction naturally accounts for the salient topology of the classical PSs while bringing to more new degrees of freedom and dimensions for tailoring a larger variety of quantum-to-classical structured beams for a variety of applications.

Multi-photon attenuation-compensated light-sheet fluorescence microscopy

Attenuation of optical fields owing to scattering and absorption limits the penetration depth for imaging. Whilst aberration correction may be used, this is difficult to implement over a large field-of-view in heterogeneous tissue. Attenuation-compensation allows tailoring of the maximum lobe of a propagation-invariant light field and promises an increase in depth penetration for imaging. Here we show this promising approach may be implemented in multi-photon (two-photon) light-sheet fluorescence microscopy and, furthermore, can be achieved in a facile manner utilizing a graded neutral density filter, circumventing the need for complex beam shaping apparatus. A “gold standard” system utilizing a spatial light modulator for beam shaping is used to benchmark our implementation. The approach will open up enhanced depth penetration in light-sheet imaging to a wide range of end users.

Light-sheet microscopy with attenuation-compensated propagation-invariant beams.

Scattering and absorption limit the penetration of optical fields into tissue. We demonstrate a new approach for increased depth penetration in light-sheet microscopy: attenuation-compensation of the light field. This tailors an exponential intensity increase along the illuminating propagation-invariant field, enabling the redistribution of intensity strategically within a sample to maximize signal and minimize irradiation. A key attribute of this method is that only minimal knowledge of the specimen transmission properties is required. We numerically quantify the imaging capabilities of attenuation-compensated Airy and Bessel light sheets, showing that increased depth penetration is gained without compromising any other beam attributes. This powerful yet straightforward concept, combined with the self-healing properties of the propagation-invariant field, improves the contrast-to-noise ratio of light-sheet microscopy up to eightfold across the entire field of view in thick biological specimens. This improvement can significantly increase the imaging capabilities of light-sheet microscopy techniques using Airy, Bessel, and other propagation-invariant beam types, paving the way for widespread uptake by the biomedical community.

Spectrally partially coherent propagation-invariant fields

Polychromatic propagation-invariant fields (localized waves) with variable spectral coherence properties are considered. A bridge is provided between coherent propagation-invariant pulses, including Bessel pulses, X-waves and focus wave modes, and stationary polychromatic propagation-invariant fields using a difference-frequency spectral-correlation model. In the space-time domain, this assumption leads to a representation of a partially coherent field as a continuum of spectrally fully coherent, mutually independent pulses originating at different instants of time. The influence of partial spectral coherence on temporal coherence and pulse shape as well as intensity distribution and transverse spatial coherence is illustrated by considering fields with propagation-invariant Bessel-mode monochromatic components.

Space-time coherence of polychromatic propagation-invariant fields

Polychromatic stationary propagation-invariant fields with complete spatial coherence in the space-frequency domain are considered. In general, the field is shown to be spatially partially coherent in the space-time domain, apart from transversely achromatic fields with complete transverse coherence. Particular attention is paid to fields that possess the same cone angle at each frequency; these are stationary counterparts of pulsed conical fields known as X waves. It is shown that, for such fields, the radius of the space-time-domain transverse coherence area depends critically on the bandwidth of the power spectrum and can be comparable to the central-lobe radius of the monochromatic field component at the peak frequency of the spectrum.

Propagation-invariant fields of the third kind and their optical generation

Propagation-invariant fields of the third kind (PIFs-III) are defined on the basis of a modal theory proposed recently by the authors. We show the existence of specific PIFs-III termed light string and light capillary beams, which are characterized by the extremely sharply localized transverse intensity distribution propagating in free space without expansion. A technique for generating the PIFs-III is proposed and its capacity is demonstrated by experimental results for the optical synthesis of the light string and light capillary beams.

Propagation-invariant beams in uniaxial crystals

Propagation-invariant electromagnetic beams, propagating along the optical axis of a uniaxially anisotropic crystal, are investigated. The beams are a superposition of propagation-invariant ordinary and extraordinary fields, with different polarizations states and Bessel profiles. The analytical expression of the Poynting vector reveals an azimuthal transverse energy flow that becomes pure longitudinal, if the complex amplitudes of the ordinary and extraordinary fields are either in phase or in phase opposition.

General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields

A novel decomposition of the transversal part of the electric field vector of a general non-paraxial electromagnetic field is presented, which is an extension of the radial/aximuthal decomposition and is known as gammazeta decomposition. Purely gamma and zeta polarized fields are examined and the decomposition is applied to propagation-invariant, rotating, and self-imaging electromagnetic fields. An experimental example on the effect of state of polarization in the propagation characteristics of the field: its is shown that a simple modification of the polarization conditions of the angular spectrum converts a self-imaging field into a propagation-invariant field.

Two-element diffractive systems for generation of Bessel fields

We demonstrate experimentally a combination of two apodizing diffractive elements, which generate nearly propagation-invariant Bessel fields efficiently with almost uniform axial intensity distributions over the specified region recently introduced by two of the present authors. Strongly reduced intensity fluctuations near both ends of the propagation-invariant range are verified. Various design and alignment issues of the two-element systrem are addressed numerically.

Invariant propagation of uniform-intensity Schell-model fields

Propagation of partially coherent uniform-intensity Schell-model fields in a uniform dielectric medium is considered. It is first established that the spatial frequencies contained in such a field are non-correlated. Then it is shown that the distribution of the complex degree of spatial coherence associated with any such field is propagation invariant. An experimental set-up consisting of a diffractive beam-shaping element, a rotating diffuser, an aperture and a lens is suggested for the generation of transversely confined approximations of a large class of propagation-invariant Schell-model fields.

Coherent-mode representation of propagation-invariant fields

The general coherent-mode structure of a propagation-invariant field is found as the solution of the differential equation for propagation of the coherent modes of said field. It is shown that three kinds of the propagation-invariant fields exist. Examples of propagation-invariant fields of the three kinds are discussed.

Generation of vectorial propagation-invariant fields by polarization-grating axicons

An approach based on a combination of generalized polarization gratings and diffractive axicons is introduced for transforming an electromagnetic plane wave into a conical wave that exhibits the property of approximate propagation invariance. The method of stationary phase is used to show that our approach permits the generation of, e.g., radially and azimuthally polarized Bessel fields.

Propagation-invariant electromagnetic fields: theory and experiment

Abstract The vector concept of the propagation invariance is formulated to be applied to the stationary electromagnetic fields. The analysed exact solutions of the Maxwell equations are obtained on the basis of general propagation-invariant solutions of the scalar Helmholtz equation. A possible classification of the propagation-invariant fields based on quantities which appear in the complex Poynting theorem is proposed. The longitudinal periodicity of the electromagnetic field obtained due to the superposition of two Bessel beams is verified by a simple experiment.

Propagation-invariant electromagnetic fields: Theory and experiment

Abstract The vector concept of the propagation invariance is formulated to be applied to the stationary electromagnetic fields. The analysed exact solutions of the Maxwell equations are obtained on the basis of general propagation-invariant solutions of the scalar Helmholtz equation. A possible classification of the propagation-invariant fields based on quantities which appear in the complex Poynting theorem is proposed. The longitudinal periodicity of the electromagnetic field obtained due to the superposition of two Bessel beams is verified by a simple experiment.

Partially coherent propagation-invariant beams: Passage through paraxial optical systems.

The cross-spectral-density function characterizing a general propagation-invariant wave field satisfies the associated (planar) paraxial equation. Building on this result, we solve exactly the problem of the passage of such fields through arbitrary lossless optical systems characterized by their ABCD matrices. It is shown that the wave field remains shape invariant in all such systems, but that the property of strict propagation invariance is conserved only if the system is afocal.

Propagation invariance and self-imaging in variable-coherence optics

The concept of propagation invariance in partially coherent optics is introduced. Explicit expressions are given for the cross-spectral density and the angular correlation function (cross-angular spectrum) characterizing a class of fields that are propagation invariant in the sense that their correlation properties in the space-frequency domain are exactly the same in every transverse plane. The so-called diffraction-free beams are shown to be members of this new, wider class of wave fields, which itself is a subset of a generalized class of partially coherent self-imaging fields. The existence of partially coherent propagation-invariant fields with a sharp correlation peak is verified experimentally by considering radiation from a planar J0 Bessel-correlated source.