We present the use of the Douglas-Gunn Alternating Direction Implicit finite difference method for computationally efficient simulation of the electric field propagation through a wide variety of optical fiber geometries. The method can accommodate refractive index profiles of arbitrary shape and is implemented in a tool called BPM-Matlab. We validate BPM-Matlab by comparing it to published experimental, numerical, and theoretical data and to commercially available state-of-the-art software. It is user-friendly, fast, and is available open-source. BPM-Matlab has a broad scope of applications in modeling a variety of optical fibers for diverse fields such as imaging, communication, material processing, and remote sensing.
We derive analytical expressions for the length, thickness, and curvature of an Airy light sheet in terms of basic parameters of the cubic phase and the paraxially defined focusing optics that form the beam. The length and thickness are defined analogously to the Rayleigh range and beam waist of a Gaussian beam, hence providing a direct and quantitative comparison between the two beam types. The analytical results are confirmed via numerical Fresnel propagation simulations and discussed within the context of light-sheet microscopy, providing a comprehensive guide for the design of the illumination unit.
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-ofview 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 fluorescence microscopy (LSFM) has transformed the field of imaging in recent years, owing to its optical sectioning capabilities, resulting in fast, highly resolved images with significantly reduced photo-bleaching and photo-toxicity 1,2. Propagation-invariant light fields, such as Airy and Bessel beams, have been employed in LSFM not only because of their pseudo-nondiffracting properties which enables them to retain their transverse profile on propagation, but also due to their self-healing capabilities on interaction with obstacles during propagation 3-7. However, attenuation due to scattering and absorption results in an exponential decay of intensity of any given optical field as it penetrates deep into tissue and limits the penetration depth achievable for deep tissue imaging. Recently, the capability to shape the envelope profile of a light field arbitrarily 8-11 has been demonstrated to counteract the attenuation-induced exponential decrease in intensity, by tailoring an exponential rise in intensity along the direction of propagation 10. Building upon this, LSFM exploiting attenuation-compensated Airy beams in single-photon imaging has demonstrated improved image quality at depth in attenuating biological specimens without any increase in the peak intensity of the illuminating light-sheet 12. This is achieved by the selective delivery of additional intensity to greater depths within the attenuating medium, potentially minimizing photo-damage across the specimen. Our previous work utilized a spatial light modulator (SLM) for generation of attenuation-compensated Airy beams solely for single-photon imaging. While this approach offers excellent beam quality and has the flexibility to dynamically adjust the beam shape to optimally counteract the specimen attenuation, it adds cost and complexity to such a system, limiting the potential uptake of the method. In this work, we show that attenuation-compensation of propagation invariant Airy fields can be achieved for multi-photon (two-photon) LSFM, and can be implemented in an inexpensive and facile manner. This is achieved by exploiting readily-available graded neutral densi...
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 (twophoton) light-sheet fluorescence microscopy and, furthermore, 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.
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