Generating Bessel beams with broad depth-of-field by using phase-only acoustic holograms

[EN] We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.This work was supported by the Spanish Ministry of Economy and Innovation (MINECO) through Project TEC2016-80976-R. NJ and SJ acknowledge financial support from Generalitat Valenciana through grants APOSTD/2017/042, ACIF/2017/045 and GV/2018/11. FC acknowledges financial support from Agencia Valenciana de la Innovacio through grant INNCON00/18/9 and European Regional Development Fund (IDIFEDER/2018/022).Jiménez-Gambín, S.; Jimenez, N.; Benlloch Baviera, JM.; Camarena Femenia, F. (2019). Generating Bessel beams with broad depth-of-field by using phase-only acoustic holograms. Scientific Reports. 9:1-13. https://doi.org/10.1038/s41598-019-56369-zS1139Durnin, J. Exact solutions for nondiffracting beams. i. the scalar theory. J. Opt. Soc. Am. A 4, 651 (1987).Durnin, J., Miceli, J. Jr & Eberly, J. Diffraction-free beams. Physical review letters 58, 1499 (1987).Chu, X. Analytical study on the self-healing property of Bessel beam. Eur. Phys. J. D 66, 259 (2012).McLeod, E., Hopkins, A. B. & Arnold, C. B. Multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens. Opt. Lett. 31, 3155 (2006).Li, Z., Alici, K. B., Caglayan, H. & Ozbay, E. Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture. Phys. Rev. Lett. 102, 143901 (2009).Fahrbach, F. & Rohrbach, A. Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media. Nat. Commun. 3, 632 (2011).Lu, J.-y, Zou, H. & Greenleaf, J. F. Biomedical ultrasound beam forming. Ultrasound in medicine & biology 20, 403–428 (1994).Marston, P. L. Scattering of a Bessel beam by a sphere. J. Acous. Soc. Am. 121, 753 (2007).Marston, P. L. Scattering of a Bessel beam by a sphere: Ii. helicoidal case and spherical shell example. The Journal of the Acoustical Society of America 124, 2905–2910 (2008).Lu, J. & Greenleaf, F. Ultrasonic nondiffracting transducer for medical imaging. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 37, 438 (1990).Lu, J.-Y. & Greenleaf, J. F. Pulse-echo imaging using a nondiffracting beam transducer. Ultrasound in medicine & biology 17, 265–281 (1991).Lu, J.-y, Song, T.-K., Kinnick, R. R. & Greenleaf, J. F. In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams. IEEE transactions on medical imaging 12, 819–829 (1993).Lu, J.-y, Xu, X.-L., Zou, H. & Greenleaf, J. F. Application of Bessel beam for doppler velocity estimation. IEEE transactions on ultrasonics, ferroelectrics, and frequency control 42, 649–662 (1995).Nabavizadeh, A., Greenleaf, J. F., Fatemi, M. & Urban, M. W. Optimized shear wave generation using hybrid beamforming methods. Ultrasound in medicine & biology 40, 188–199 (2014).Marston, P. L. Axial radiation force of a Bessel beam on a sphere and direction reversal of the force. The Journal of the Acoustical Society of America 120, 3518–3524 (2006).Marston, P. L. Negative axial radiation forces on solid spheres and shells in a Bessel beam. The Journal of the Acoustical Society of America 122, 3162–3165 (2007).Marston, P. L. Radiation force of a helicoidal Bessel beam on a sphere. The Journal of the Acoustical Society of America 125, 3539–3547 (2009).Thomas, J.-L. & Marchiano, R. Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices. Physical review letters 91, 244302 (2003).Volke-Sepúlveda, K., Santillán, A. O. & Boullosa, R. R. Transfer of angular momentum to matter from acoustical vortices in free space. Phys. Rev. Lett. 100, 024302 (2008).Zhang, L. & Marston, P. L. Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres. Physical Review E 84, 035601 (2011).Courtney, C. R. et al. Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields. Applied Physics Letters 102, 123508 (2013).Hong, Z., Zhang, J. & Drinkwater, B. W. Observation of orbital angular momentum transfer from Bessel-shaped acoustic vortices to diphasic liquid-microparticle mixtures. Phys. Rev. Lett. 114, 214301 (2015).Baresch, D., Thomas, J.-L. &Marchiano, R. Observation of a single-beam gradient force acoustical trap for elastic particles: Acoustical tweezers. Phys. Rev. Lett. 116 (2016).Marzo, A., Caleap, M. & Drinkwater, B. W. Acoustic virtual vortices with tunable orbital angular momentum for trapping of mie particles. Phys. Rev. Lett. 120, 044301 (2018).Li, Y. et al. Acoustic radiation torque of an acoustic-vortex spanner exerted on axisymmetric objects. Applied Physics Letters 112, 254101 (2018).Riaud, A., Baudoin, M., Thomas, J.-L. & Matar, O. B. Cyclones and attractive streaming generated by acoustical vortices. Physical Review E 90, 013008 (2014).Shi, C., Dubois, M., Wang, Y. & Zhang, X. High-speed acoustic communication by multiplexing orbital angular momentum. Proceedings of the National Academy of Sciences 114, 7250–7253 (2017).Jiang, X., Liang, B., Cheng, J.-C. & Qiu, C.-W. Twisted acoustics: metasurface-enabled multiplexing and demultiplexing. Advanced Materials 30, 1800257 (2018).Hsu, D., Margetan, F. & Thompson, D. O. Bessel beam ultrasonic transducer: fabrication method and experimental results. Appl. Phys. Lett. 55, 2066 (1989).Campbell, J. A. & Soloway, S. Generation of a nondiffracting beam with frequency-independent beamwidth. The Journal of the Acoustical Society of America 88, 2467–2477 (1990).Masuyama, H., Yokoyama, T., Nagai, K. & Mizutani, K. Generation of Bessel beam from equiamplitude-driven annular transducer array consisting of a few elements. Jpn. J. Appl. Phys. 38, 3080 (1999).Fjield, T., Fan, X. & Hynynen, K. A parametric study of the concentric-ring transducer design for mri guided ultrasound surgery. J. Acoust. Soc. Am. 100, 1220 (1996).Chillara, V. K., Pantea, C. & Sinha, D. N. Low-frequency ultrasonic Bessel-like collimated beam generation from radial modes of piezoelectric transducers. Applied Physics Letters 110, 064101 (2017).Burckhardt, C., Hoffmann, H. & Grandchamp, P.-A. Ultrasound axicon: A device for focusing over a large depth. The Journal of the Acoustical Society of America 54, 1628–1630 (1973).Foster, F., Patterson, M., Arditi, M. & Hunt, J. The conical scanner: a two transducer ultrasound scatter imaging technique. Ultrasonic imaging 3, 62–82 (1981).McLeod, J. H. The axicon: A new type of optical element. J. Opt. Soc. Am. 44, 592 (1954).Arlt, J. & Dholakia, K. Generation of high-order Bessel beams by use of an axicon. Optics Communications 177, 297–301 (2000).Golub, I. Fresnel axicon. Optics letters 31, 1890–1892 (2006).Lirette, R. & Mobley, J. Broadband wave packet dynamics of minimally diffractive ultrasonic fields from axicon and stepped fraxicon lenses. The Journal of the Acoustical Society of America 146, 103–108 (2019).Jiménez, N. et al. Acoustic Bessel-like beam formation by an axisymmetric grating. Europhys. Lett. 106, 24005 (2014).Xu, Z., Xu, W., Qian, M., Cheng, Q. & Liu, X. A flat acoustic lens to generate a Bessel-like beam. Ultrasonics 80, 66–71 (2017).Li, Y., Liang, B., Gu, Z.-M., Zou, X.-Y. & Cheng, J.-C. Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces. Scientific Reports 3, 2546 (2013).Nye, J. & Berry, M. Dislocations in wave trains. Proc. R. Soc. London, Ser. A 336, 165–190 (1974).Jiménez, N. et al. Formation of high-order acoustic Bessel beams by spiral diffraction gratings. Physical Review E 94, 053004 (2016).Wang, T. et al. Particle manipulation with acoustic vortex beam induced by a brass plate with spiral shape structure. Applied Physics Letters 109, 123506 (2016).Jia, Y.-R., Wei, Q., Wu, D.-J., Xu, Z. & Liu, X.-J. Generation of fractional acoustic vortex with a discrete archimedean spiral structure plate. Applied Physics Letters 112, 173501 (2018).Jiménez, N., Romero-Garca, V., Garca-Raffi, L. M., Camarena, F. & Staliunas, K. Sharp acoustic vortex focusing by fresnel-spiral zone plates. Applied Physics Letters 112, 204101 (2018).Baudoin, M. et al. Folding a focalized acoustical vortex on a flat holographic transducer: miniaturized selective acoustical tweezers. Science advances 5, eaav1967 (2019).Muelas-Hurtado, R. D., Ealo, J. L., Pazos-Ospina, J. F. & Volke-Sepúlveda, K. Acoustic analysis of a broadband spiral source for the simultaneous generation of multiple Bessel vortices in air. The Journal of the Acoustical Society of America 144, 3252–3261 (2018).Muelas-Hurtado, R. D., Ealo, J. L., Pazos-Ospina, J. F. & Volke-Sepúlveda, K. Generation of multiple vortex beam by means of active diffraction gratings. Applied Physics Letters 112, 084101 (2018).Wunenburger, R., Lozano, J. I. V. & Brasselet, E. Acoustic orbital angular momentum transfer to matter by chiral scattering. New Journal of Physics 17, 103022 (2015).Terzi, M., Tsysar, S., Yuldashev, P., Karzova, M. & Sapozhnikov, O. Generation of a vortex ultrasonic beam with a phase plate with an angular dependence of the thickness. Moscow University Physics Bulletin 72, 61–67 (2017).Hefner, B. T. & Marston, P. L. An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems. Jour. Acous. Soc. Am. 106, 3313–3316 (1999).Ealo, J. L., Prieto, J. C. & Seco, F. Airborne ultrasonic vortex generation using flexible ferroelectrets. IEEE transactions on ultrasonics, ferroelectrics, and frequency control 58, 1651–1657 (2011).Naify, C. J. et al. Generation of topologically diverse acoustic vortex beams using a compact metamaterial aperture. Applied Physics Letters 108, 223503 (2016).Ye, L. et al. Making sound vortices by metasurfaces. AIP Advances 6, 085007 (2016).Jiang, X., Li, Y., Liang, B., Cheng, J.-C. & Zhang, L. Convert acoustic resonances to orbital angular momentum. Physical review letters 117, 034301 (2016).Esfahlani, H., Lissek, H. & Mosig, J. R. Generation of acoustic helical wavefronts using metasurfaces. Physical Review B 95, 024312 (2017).Jiménez-Gambn, S., Jiménez, N., Benlloch, J. M. & Camarena, F. Holograms to focus arbitrary ultrasonic fields through the skull. Physical Review Applied 12, 014016 (2019).Maimbourg, G., Houdouin, A., Deffieux, T., Tanter, M. & Aubry, J.-F. 3d-printed adaptive acoustic lens as a disruptive technology for transcranial ultrasound therapy using single-element transducers. Physics in Medicine & Biology 63, 025026 (2018).Ferri, M. et al. On the evaluation of the suitability of the materials used to 3d print holographic acoustic lenses to correct transcranial focused ultrasound aberrations. Polymers 11, 1521 (2019).Melde, K., Mark, A. G., Qiu, T. & Fischer, P. Holograms for acoustics. Nature 537, 518 (2016).Brown, M. D., Cox, B. T. & Treeby, B. E. Design of multi-frequency acoustic kinoforms. Applied Physics Letters 111, 244101 (2017).Brown, M., Nikitichev, D., Treeby, B. & Cox, B. Generating arbitrary ultrasound fields with tailored optoacoustic surface profiles. Applied Physics Letters 110, 094102 (2017).Zhu, Y. et al. Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase. Nature communications 9, 1632 (2018).Brown, M. D. Phase and amplitude modulation with acoustic holograms. Applied Physics Letters 115, 053701 (2019).Jiménez, N., Romero-Garca, V., Pagneux, V. & Groby, J.-P. Quasiperfect absorption by subwavelength acoustic panels in transmission using accumulation of resonances due to slow sound. Physical Review B 95, 014205 (2017).Tsang, P. W. M. & Poon, T.-C. Novel method for converting digital fresnel hologram to phase-only hologram based on bidirectional error diffusion. Optics Express 21, 23680–23686 (2013).Soret, J. Ueber die durch kreisgitter erzeugten diffractionsphänomene. Annalen der Physik 232, 99–113 (1875).Turunen, J., Vasara, A. & Friberg, A. T. Holographic generation of diffraction-free beams. Applied Optics 27, 3959–3962 (1988).Vasara, A., Turunen, J. & Friberg, A. T. Realization of general nondiffracting beams with computer-generated holograms. JOSA A 6, 1748–1754 (1989).Cunningham, K. B. & Hamilton, M. F. Bessel beams of finite amplitude in absorbing fluids. J. Acous. Soc. Am. 108, 519 (2000).Ding, D. & Y. Lu, J. Higher-order harmonics of limited diffraction Bessel beams. J. Acous. Soc. Am. 107, 1212 (2000).Skeldon, K., Wilson, C., Edgar, M. & Padgett, M. An acoustic spanner and its associated rotational Doppler shift. New J. Phys. 10, 013018 (2008).Wu, J. Acoustical tweezers. J. Acoust. Soc. Am. 89, 2140–2143 (1991).Zhang, L. & Marston, P. L. Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects. Physical Review E 84, 065601 (2011).Yoon, C., Kang, B. J., Lee, C., Kim, H. H. & Shung, K. K. Multi-particle trapping and manipulation by a high-frequency array transducer. Appl. Phys. Lett. 105, 214103 (2014).Marzo, A. et al. Holographic acoustic elements for manipulation of levitated objects. Nat. Commun. 6 (2015).Blackstock, D. T. Fundamentals of physical acoustics (John Wiley & Sons, 2000).Treeby, B. E. & Cox, B. Modeling power law absorption and dispersion for acoustic propagation using the fractional laplacian. The Journal of the Acoustical Society of America 127, 2741–2748 (2010).Treeby, B. E., Jaros, J., Rendell, A. P. & Cox, B. Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method. The Journal of the Acoustical Society of America 131, 4324–4336 (2012).Jiménez, N. et al. Time-domain simulation of ultrasound propagation in a tissue-like medium based on the resolution of the nonlinear acoustic constitutive relations. Acta Acustica united with Acustica 102, 876–892 (2016)

Characterization of micro-invasive trabecular bypass stents by ex vivo perfusion and computational flow modeling

Kendall S Hunter,1 Todd Fjield,2 Hal Heitzmann,2 Robin Shandas,1 Malik Y Kahook3 1Department of Bioengineering, University of Colorado Denver, Aurora, CO, USA; 2Glaukos Corporation, Laguna Hills, CA, USA; 3University of Colorado Hospital Eye Center, Aurora, CO, USA Abstract: Micro-invasive glaucoma surgery with the Glaukos iStent® or iStent inject® (Glaukos Corporation, Laguna Hills, CA, USA) is intended to create a bypass through the trabecular meshwork to Schlemm's canal to improve aqueous outflow through the natural physiologic pathway. While the iStent devices have been evaluated in ex vivo anterior segment models, they have not previously been evaluated in whole eye perfusion models nor characterized by computational fluid dynamics. Intraocular pressure (IOP) reduction with the iStent was evaluated in an ex vivo whole human eye perfusion model. Numerical modeling, including computational fluid dynamics, was used to evaluate the flow through the stents over physiologically relevant boundary conditions. In the ex vivo model, a single iStent reduced IOP by 6.0 mmHg from baseline, and addition of a second iStent further lowered IOP by 2.9 mmHg, for a total IOP reduction of 8.9 mmHg. Computational modeling showed that simulated flow through the iStent or iStent inject is smooth and laminar at physiological flow rates. Each stent was computed to have a negligible flow resistance consistent with an expected significant decrease in IOP. The present perfusion results agree with prior clinical and laboratory studies to show that both iStent and iStent inject therapies are potentially titratable, providing clinicians with the opportunity to achieve lower target IOPs by implanting additional stents. Keywords: glaucoma, iStent, trabecular bypass, intraocular pressure, ab-interno, CF