The "Achilles heels" of optical beams in imaging (and other) applications are attenuation, obscuration, scattering, and diffraction, limiting the penetration depth of applicability due to distortion, attenuation and/or widening of the optical beam.

Nondiffracting beams are partially resilient to almost all of them, but still are strongly affected by attenuation. Such shaped optical beams have rapidly grown in recent years from abstract curiosities to taking a major role in imaging. These beams appear to defy diffraction and in light sheet fluorescence microscopy can lead to increases in resolution and field-of-view.

We have proposed and demonstrated diffractive light delivery control by using compensating beams for in fluorescence imaging, based on modified non-diffractive beams, keeping the light peak intensity under safe levels for reduce photo-toxicity while keeping an uniform generated signal.

Nondiffracting beams are a family of optical beams able to propagate with some degree of resilience to diffraction. Airy beams and Bessel beams are probably the most well known and studied nondiffracting beams.

Ideally, they are able to propagate without being affected by diffraction at all, where the intensity distribution remains undistorted during the propagation. Moreover, diffraction-free beams are robust to partial obscurations and scattering due to the self healing effect.

Although an ideal nondiffracting beams would require infinite energy, finite energy approximations has been successfully proven to remain these properties in a finite localised 3D volume of the propagating beam.

Compensating beams are a generalisation of "classic" nondiffracting beams to media with attenuation, where the beam can ideally propagate without any modification in its intensity profile in diffractive media with losses, by diffractive light delivery control designed to increase the peak intensity at the same rate as the intensity attenuation introduced by media losses.

This is obviously an ideal effect, since it would imply that the beam is able to "create energy" to overcome media losses. But here also we can have finite approaches to compensating nondiffracting beams which keep the properties of the ideal concept in a finite localize volume,as it was proposed and demonstrated in [Preciado2014] using compensating Airy beams.

In the temporal domain, optical pulses suffer a similar widening effect in temporal domain due to dispersion, where basically every (temporal) frequency component propagate at a different speed. Because of the similarity of the equations that rule both diffraction in spatial optics, and optical dispersion in temporal domain, we can speak of "space-time" duality [Kolner94], and temporal optics, where concepts such as temporal imaging, or temporal lenses (temporal counterpart of spatial lenses), can be applied.

Concretely, we also can find the counterpart of nondiffracting beams in temporal optics, called nondispersive pulses, although in this case there is not a diversity of nondiffracting beams as in the spatial optics counterparts, but Airy function is the only solution for one dimension (time).

In this context, the concept of compensating nondispersive pulse in [Preciado2012] was originally proposed and demonstrated in an modified Airy-based pulses, which was called Airy "rocket" pulses, performing dispersive ligth delivery control. Similarly, we can engineer the light delivery to match the media losses, keeping the intensity peak uniform along the propagation path.

Very recently, compensating nondiffracting beams has been demonstrated in light sheet microscopy [Nilk2018] for light delivery control designed to keep the peak intensity in low photo-toxicity levels, while maximising the light delivery at depth for better contrast (see Figure below).

References

[Preciado2014] MA Preciado*, K Dholakia, M Mazilu, "Generation of attenuation-compensating Airy beams", Optics letters 39 (16), 4950-4953 (2014)

[Preciado2012] MA Preciado*, K Sugden "Proposal and design of Airy-based rocket pulses for invariant propagation in lossy dispersive media" Optics letters 37 (23), 4970-4972 (2012)

[Nylk2018] J Nylk, K McCluskey, M A Preciado, M Mazilu, F J Gunn-Moore, S Aggarwal, J A Tello, D EK Ferrier, K Dholakia "Light-sheet microscopy with attenuation-compensated propagation-invariant beams" Science Advances 06 Apr 2018: Vol. 4, no. 4, eaar4817 https://doi.org/10.1126/sciadv.aar4817

[Kolner94] Kolner, Brian H. "Space-time duality and the theory of temporal imaging." IEEE Journal of Quantum Electronics 30.8 (1994): 1951-1963.