Abstract

Photonic-chip-based light illumination has recently found applications in optical microscopy and nanoscopy methodologies. The photonic chip removes the dependency on imaging objective lenses to generate the required illumination patterns for different microscopy methods. Until now, all the reported chip-based optical microscopy methods exploit the evanescent field present on top of a waveguide surface and are thus inherently limited to two-dimensional microscopy. Here, we perform systematic simulation studies to investigate different chip-based waveguide designs for static and dynamic shaping of light beams in the free-space. The simulation studies have been carefully designed considering the photo-lithography limitations and wavelength spectrum (405 nm to 660 nm) that is of interest in fluorescence based optical microscopy and nanoscopy. We first report the generation of a quasi-Bessel beam (QBB) using an on-chip axicon made at the end facet of a planar waveguide to mimic light sheet illumination. This is extended to the implementation of a counter propagating QBB for lattice light-sheet applications. The double axicon, a derivative of the axicon generates superimposed Bessel beams (SBB). Its waveguide-based implementation is proposed and analyzed. Finally, we investigate an optical phased array (OPA) approach to allow dynamic steering of the output light in the free-space. The aim of this study is to find suitable waveguide design parameters for free-space beam shaping operating in the visible spectrum opening possibilities for three-dimensional chip-based optical microscopy.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

2018 (1)

2017 (5)

2016 (1)

2015 (2)

I. Yahiatene, S. Hennig, M. Müller, and T. Huser, “Entropy-Based Super-Resolution Imaging (ESI): From Disorder to Fine Detail,” ACS Photonics 2(8), 1049–1056 (2015).
[Crossref]

R. A. A. G. Jonathan and P. Manigo, “Self-imaging, self-healing beams generated by photorefractive volume holography,” Opt. Eng. 54(10), 104113 (2015).
[Crossref]

2014 (2)

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref]

L. Li, W. M. Lee, X. Xie, W. Krolikowski, A. V. Rode, and J. Zhou, “Shaping self-imaging bottle beams with modified quasi-Bessel beams,” Opt. Lett. 39(8), 2278–2281 (2014).
[Crossref]

2013 (2)

P. Løvhaugen, B. S. Ahluwalia, T. R. Huser, and O. G. Hellesø, “Serial Raman spectroscopy of particles trapped on a waveguide,” Opt. Express 21(3), 2964–2970 (2013).
[Crossref]

G. S. Sokolovskii, V. V. Dyudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, V. Sibbet, and E. U. Rafailov, “Influence of the axicon characteristics and beam propagation parameter M2 on the formation of Bessel beams from semiconductor lasers,” Quantum Electron. 43(5), 423–427 (2013).
[Crossref]

2012 (1)

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref]

2011 (2)

2009 (2)

K. Van Acoleyen, W. Bogaerts, J. Jágerská, N. Le Thomas, R. Houdré, and R. Baets, “Off-chip beam steering with a one-dimensional optical phased array on silicon-on-insulator,” Opt. Lett. 34(9), 1477–1479 (2009).
[Crossref]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. 106(52), 22287–22292 (2009).
[Crossref]

2008 (3)

M. Heilemann, S. Van De Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem., Int. Ed. 47(33), 6172–6176 (2008).
[Crossref]

A. Hassanzadeh, M. Nitsche, S. Mittler, S. Armstrong, J. Dixon, and U. Langbein, “Waveguide evanescent field fluorescence microscopy: Thin film fluorescence intensities and its application in cell biology,” Appl. Phys. Lett. 92(23), 233503 (2008).
[Crossref]

O. Brzobohatý, T. Cižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16(17), 12688–12700 (2008).
[Crossref]

2007 (1)

X. C. Yuan, B. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. A: Pure Appl. Opt. 9(4), 329–334 (2007).
[Crossref]

2006 (6)

B. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, “Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids,” Opt. Lett. 31(7), 987–989 (2006).
[Crossref]

B. S. Ahluwalia, X. C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

H. M. Grandin, B. Städler, M. Textor, and J. Vörös, “Waveguide excitation fluorescence microscopy: A new tool for sensing and imaging the biointerface,” Biosens. Bioelectron. 21(8), 1476–1482 (2006).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM).,” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

2005 (1)

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon - the Most Important Optical Element,” Opt. Photonics News 16(4), 34–39 (2005).
[Crossref]

2004 (3)

B. S. Ahluwalia, X. C. Yuan, and S. H. Tao, “Generation of self-imaged optical bottle beams,” Opt. Commun. 238(1-3), 177–184 (2004).
[Crossref]

B. S. Ahluwalia, X.-C. Yuan, and S. H. Tao, “Transfer of ‘pure’ on-axis spin angular momentum to the absorptive particle using self-imaged bottle beam optical tweezers system,” Opt. Express 12(21), 5172–5177 (2004).
[Crossref]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

2003 (1)

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottle beams,” Opt. Commun. 225(4-6), 215–222 (2003).
[Crossref]

2000 (2)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref]

1998 (2)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[Crossref]

S. Chávez-Cerda, E. Tepichin, M. A. Meneses-Nava, G. Ramirez, and J. M. Hickmann, “Experimental observation of interfering Bessel beams,” Opt. Express 3(13), 524–529 (1998).
[Crossref]

1994 (1)

1993 (1)

A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc. 170(3), 229–236 (1993).
[Crossref]

1991 (1)

1987 (2)

J. Durnin, “Exact solutions for nondiffracting beams I The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

1954 (1)

1950 (1)

Agnarsson, B.

Ahluwalia, B. S.

Ø. I. Helle, D. A. Coucheron, J.-C. Tinguely, C. I. Øie, and B. S. Ahluwalia, “Nanoscopy on-a-chip: super-resolution imaging on the millimeter scale,” Opt. Express 27(5), 6700–6710 (2019).
[Crossref]

R. Diekmann, Ø. I. Helle, C. I. Øie, P. McCourt, T. R. Huser, M. Schüttpelz, and B. S. Ahluwalia, “Chip-based wide field-of-view nanoscopy,” Nat. Photonics 11(5), 322–328 (2017).
[Crossref]

J.-C. Tinguely, Ø. I. Helle, and B. S. Ahluwalia, “Silicon nitride waveguide platform for fluorescence microscopy of living cells,” Opt. Express 25(22), 27678–27690 (2017).
[Crossref]

P. Løvhaugen, B. S. Ahluwalia, T. R. Huser, and O. G. Hellesø, “Serial Raman spectroscopy of particles trapped on a waveguide,” Opt. Express 21(3), 2964–2970 (2013).
[Crossref]

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref]

B. S. Ahluwalia, P. Løvhaugen, and O. G. Hellesø, “Waveguide trapping of hollow glass spheres.,” Opt. Lett. 36(17), 3347–3349 (2011).
[Crossref]

X. C. Yuan, B. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. A: Pure Appl. Opt. 9(4), 329–334 (2007).
[Crossref]

B. S. Ahluwalia, X. C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

B. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, “Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids,” Opt. Lett. 31(7), 987–989 (2006).
[Crossref]

B. S. Ahluwalia, X.-C. Yuan, and S. H. Tao, “Transfer of ‘pure’ on-axis spin angular momentum to the absorptive particle using self-imaged bottle beam optical tweezers system,” Opt. Express 12(21), 5172–5177 (2004).
[Crossref]

B. S. Ahluwalia, X. C. Yuan, and S. H. Tao, “Generation of self-imaged optical bottle beams,” Opt. Commun. 238(1-3), 177–184 (2004).
[Crossref]

B. S. Ahluwalia and O. G. Hellesø, “Optical waveguide loop for planar trapping of blood cells and microspheres,” in Optical Trapping and Optical Micromanipulation X, vol. 8810 (2013), p. 88100T.

Ø. I. Helle, F. T. Dullo, M. Lahrberg, J.-C. Tinguely, and B. S. Ahluwalia, “Structured illumination microscopy using a photonic chip,” arXiv preprint arXiv:1903.05512 (2019).

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Armstrong, S.

A. Hassanzadeh, M. Nitsche, S. Mittler, S. Armstrong, J. Dixon, and U. Langbein, “Waveguide evanescent field fluorescence microscopy: Thin film fluorescence intensities and its application in cell biology,” Appl. Phys. Lett. 92(23), 233503 (2008).
[Crossref]

Arnfinnsdottir, N. B.

Baets, R.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM).,” Nat. Methods 3(10), 793–796 (2006).
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Supplementary Material (2)

NameDescription
» Visualization 1       Demonstration of the beam tilting capabilities of the OPA.
» Visualization 2       Demonstration of the beam steering capabilities of the OPA.

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Figures (16)

Fig. 1.
Fig. 1. A rib waveguide using a linear waveguide taper in order to maintain the fundamental mode. Panel (a) shows the general rib waveguide under consideration. Boundary modes (b)-(e) for a model at a vacuum wavelength of 660 nm with materials of refractive indices $1.46$ (Substrate, SiO$_2$), $2.12$ (Slab and Rib, Ta$_2$O$_5$), and $1.33$ (water on top). The slab and rib height are set to 200 nm and 50 nm respectively. In (b) the fundamental waveguide mode for a rib waveguide of 500 nm width is shown. It is the only guided mode, the first order mode (b) (mode with next lower effective refractive index) is not guided (propagates in the slab). For a rib waveguide with a rib width of 1.5 µm not only the fundamental mode (d), but also the first order mode (e) is guided in the waveguide. The boundary modes are presented as the norm of their electric field distribution in arbitrary units, color bar in (d).
Fig. 2.
Fig. 2. The chip-based axicon and its ability to form a 1D light sheet as part of 1D-QBB. In (a) a general design for an axicon using a planar waveguide and the beam shaping capability is shown. The top view in (b) shows the $xy$-plane where the 1D-QBB intensity profile is generated. Following [26], the DOF of the generated QBB profile can be approximated using the optical properties and geometry shown in (c) where only one half of the top view is presented. Describing the QBB as an interference pattern can be done using the sketch in (d), where the axicon is set of to the left for better visualization.
Fig. 3.
Fig. 3. The chip-based double axicon and its ability to form a light sheet as part of a SBB. In (a) a general design for a double axicon using a planar waveguide and the beam shaping capability is shown. In (b), as for the (single) axicon in Fig. 2(c), the necessary parameters to approximate the interaction length along the optical axis, where a SBB profile may be generated, is shown.
Fig. 4.
Fig. 4. Simulation results for an axicon with $R = 20$ µm at a vacuum wavelength of $\lambda _0 = 532$ nm, $n_{\textrm {i}} = 2.0559$, $n_{\textrm {o}} = 1.3371$. Shown are the values for the electric field norm squared in arbitrary units for (a) $\alpha = 6^{\circ }$, (b) $\alpha = {8}^{\circ }$, (c) $\alpha = 10^{\circ }$, (d) $\alpha = 12^{\circ }$, and (e) $\alpha = 15^{\circ }$.
Fig. 5.
Fig. 5. The central beam along the optical axis as simulated for an axicon with $R = 20$ µm at a vacuum wavelength of $\lambda _0 = 532$ nm, $n_{\textrm {i}} = 2.0559$, $n_{\textrm {o}} = 1.3371$ and varying axicon angles $\alpha$ using FEM is evaluated. (a) The intensity (here in terms of the electric field norm squared) along the direction of propagation is show for different angles. (b) Comparing the FWHM of the central beam at its maximum as given in the simulations is compared to is FWHM given by $\frac {\Delta r}{2}$.
Fig. 6.
Fig. 6. Simulation results for an axicon with (a) $R = 20$ µm and (b) $R = 40$ µm at a vacuum wavelength of $\lambda _0 = 532$ nm, $n_{\textrm {i}} = 2.0559$, $n_{\textrm {o}} = 1.3371$ at an axicon angle of $\alpha = 8^{\circ }$. Presented is the square of the electric field norm as an indicator of the light intensity. Panel (c) shows the intensity profiles along the central part of the output for the two axicon, both normalized to their maximum value. The FWHM at maximum intensity are 1.47 µm and 1.45 µm for the $R = 20$ µm and $R = 40$ µm axicons respectively. The geometrically expected FWHM is 1.31 µm for both cases.
Fig. 7.
Fig. 7. A photonic chip incorporating two axicons that generate two counter-propagating QBBs with an intensity modulation suitable for SIM. Introducing a phase shift $\Delta \Phi$ in one arm will shift the generated interference pattern along the $x$-axis. Depending on the axicon width a waveguide taper as shown in Fig. 1 may be required. Phase control is achieved by thermo-optic means as indicated in Fig. 1.
Fig. 8.
Fig. 8. Using a configuration as presented in Fig. 7, the simulated intensity distribution is shown for axicon angles (as defined in Fig. 2(c)) of $\alpha =$ 6°, 10° and 15° as presented in (a)(c) respectively. Data samples are taken from the highlighted rectangular regions and a sinusoidal function (see Eq. (7)) is fitted (red curve) to the data (blue dots) to extract the pattern period; an example is shown in (d) for the pattern in (c). The pattern periods are found to be 199 nm, 200 nm and 201 nm.
Fig. 9.
Fig. 9. The output of the on-chip double axicon as simulated in COMSOL on the left-hand side and the corresponding result as per Eq. (3) on the right-hand side. Displayed is the normalized intensity, cut off at 10 % to achieve a representation similar to what is shown in [40,43]. The axicon angles are set to be $\alpha _1 = 12^{\circ }$ and $\alpha _2 =$ 3° and 6° for (a) and (b) respectively. The axicon size is set to $R_1 = 20$ µm and $R_2 = R_1\frac {\alpha _2}{\alpha _1}$ to obtain a good overlap of the green and red region in Fig. 3(b).
Fig. 10.
Fig. 10. Beam shaping using an OPA. According to the Huygens principle (a) a set of point sources (red x) generates spherical wavefronts (dashed lines) that form a plane wave in the far field. The general concept is presented in (b), the waveguide is presented clinched the $x$-direction. Manipulating the phases $\phi _n$ and amplitudes $A_n$ in each arm ((c)), wavefronts similar to those generated by a (double) axicon are generated in order to obtain QBBs and SBBs. Depending on the amplitude and phase distribution over the antennas, a QBB ((d)) or a SBB ((e)) may be generated. A dynamic manipulation of $\phi _n$ and $A_n$ allows for dynamic beam shaping and steering. A spatially extended array may also allow for lateral beam shifting without alteration of the beam profile ((e)).
Fig. 11.
Fig. 11. The waveguide structure in the phased arrays. (a) The Ta$_2$O$_5$ on SiO$_2$ structure covert with water is shown. The slab height is 200 nm, the rib height and width are 50 nm and 500 nm respectively. Using a vacuum wavelength of 660 nm only the fundamental TE mode is guided. The distribution of the electric field norm is presented in (b) in arbitrary units.
Fig. 12.
Fig. 12. Given an OPA with 16 elements, the output has been simulated using (a) Eq. (8) and (b) FEM in COMSOL. The applied amplitude and phase distribution among the waveguides is shown in (c) and (d) respectively.
Fig. 13.
Fig. 13. Given an OPA with 32 elements, the output has been simulated using (a) Eq. (8) and (b) FEM in COMSOL. The applied amplitude and phase distribution among the waveguides is shown in (c) and (d) respectively.
Fig. 14.
Fig. 14. A similar setup as shown in Fig. 13 is used to demonstrate the tilting capabilities of the OPA. A linear phase gradient of $n\pi /2$ with the waveguide number $n$ is added to the original (red) phase distribution thus changing it to the blue distribution in (b). The SBB in (a) is thus tilted from its original optical axis (dashed red line) to an angled direction. See also Visualization 1.
Fig. 15.
Fig. 15. Manipulating the phase distribution of the OPA in order to shift the intensity minima (i, ii, iii, iv) of the SBB along the optical axis. The intensity distributions presented in (a) and (b) are generated with the phase distributions presented in (c) in blue and red respectively. See also Visualization 2.
Fig. 16.
Fig. 16. The profile of the axicon tip is expected to deviate from a perfectly sharp to a round shape due to fabrication limitations. In (a) the perfectly sharp and a rounded (hyperbolic) tip profile are shown. The resulting intensity profile of the qbbs are shown in (b).

Equations (9)

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E j ( ρ , x ) = J 0 ( k ρ j ρ ) exp [ i ( k x j x + ϕ j ) ] ,
I j ( ρ ) J 0 2 ( k ρ j ρ )
I ( ρ , x ) J 0 2 ( k ρ 1 ρ ) + J 0 2 ( k ρ 2 ρ ) + 2 J 0 ( k ρ 1 ρ ) J 0 ( k ρ 2 ρ ) × cos [ ( k x 1 k x 2 ) x + ϕ 1 ϕ 2 ] .
D O F = x max x min ,
N lobes = W Δ r .
d = λ 0 2 sin ( 90 θ ) n o .
f ( x ) = a 1 + a 2 cos ( 2 a 3 x π a 4 )
E ( r ) = n = 1 N = a n exp [ i ( 2 π r n r 2 λ ) + ϕ n ] .
x = a 2 + y 2 tan 2 ( τ / 2 ) ,