Abstract

Precise direct-write lithography of 3D waveguides or diffractive structures within the volume of a photosensitive material is hindered by the lack of metrology that can yield predictive models for the micron-scale refractive index profile in response to a range of exposure conditions. We apply the transport of intensity equation in conjunction with confocal reflection microscopy to capture the complete spatial frequency spectrum of isolated 10 μm-scale gradient-refractive index structures written by single-photon direct-write laser lithography. The model material, a high-performance two-component photopolymer, is found to be linear, integrating, and described by a single master dose response function. The sharp saturation of this function is used to demonstrate nearly binary, flat-topped waveguide profiles in response to a Gaussian focus.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (1)

R. Malallah, H. Li, D. Kelly, J. Healy, and J. Sheridan, “A review of hologram storage and self-written waveguides formation in photopolymer media,” Polymers (Basel) 9(8), 337 (2017).
[Crossref]

2016 (3)

L. Vittadello, A. Zaltron, N. Argiolas, M. Bazzan, N. Rossetto, and R. Signorini, “Photorefractive direct laser writing,” J. Phys. D Appl. Phys. 49(12), 125103 (2016).
[Crossref]

B. A. Kowalski and R. R. McLeod, “Design concepts for diffusive holographic photopolymers,” J. Polym. Sci. Part B Polym. Phys. 54, 1021–1035 (2016).

A. Zanutta, E. Orselli, T. Fäcke, and A. Bianco, “Photopolymeric films with highly tunable refractive index modulation for high precision diffractive optics,” Opt. Mater. Express 6(1), 252 (2016).
[Crossref]

2015 (2)

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Multi-filter transport of intensity equation solver with equalized noise sensitivity,” Opt. Express 23(18), 23092–23107 (2015).
[Crossref] [PubMed]

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Solution to the Boundary problem for Fourier and Multigrid transport equation of intensity based solvers,” Photonics Lett. Pol. 7(1), 2–4 (2015).
[Crossref]

2014 (7)

R. Woods, S. Feldbacher, D. Zidar, G. Langer, V. Satzinger, V. Schmidt, N. Pucher, R. Liska, and W. Kern, “3D optical waveguides produced by two photon photopolymerisation of a flexible silanol terminated polysiloxane containing acrylate functional groups,” Opt. Mater. Express 4(3), 486 (2014).
[Crossref]

R. Woods, S. Feldbacher, D. Zidar, G. Langer, V. Satzinger, V. Schmidt, N. Pucher, R. Liska, and W. Kern, “3D optical waveguides produced by two photon photopolymerisation of a flexible silanol terminated polysiloxane containing acrylate functional groups,” Opt. Mater. Express 4(3), 486 (2014).
[Crossref]

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of Intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22(9), 10661–10674 (2014).
[Crossref] [PubMed]

B. A. Kowalski, A. C. Urness, M.-E. Baylor, M. C. Cole, W. L. Wilson, and R. R. McLeod, “Quantitative modeling of the reaction/diffusion kinetics of two-chemistry diffusive photopolymers,” Opt. Mater. Express 4(8), 1668 (2014).
[Crossref]

H. Li, Y. Qi, and J. T. Sheridan, “Three-dimensional extended nonlocal photopolymerization driven diffusion model Part I Absorption,” J. Opt. Soc. Am. B 31(11), 2638 (2014).
[Crossref]

H. Li, Y. Qi, and J. T. Sheridan, “Three-dimensional extended nonlocal photopolymerization driven diffusion model Part II Photopolymerization and model development,” J. Opt. Soc. Am. B 31(11), 2648 (2014).
[Crossref]

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Optimum plane selection for transport-of-intensity-equation-based solvers,” Appl. Opt. 53(30), 7050–7058 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (4)

C. Ye, K. T. Kamysiak, A. C. Sullivan, and R. R. McLeod, “Mode profile imaging and loss measurement for uniform and tapered single-mode 3D waveguides in diffusive photopolymer,” Opt. Express 20(6), 6575–6583 (2012).
[Crossref] [PubMed]

S. Bichler, S. Feldbacher, R. Woods, V. Satzinger, V. Schmidt, G. Jakopic, G. Langer, and W. Kern, “Functional flexible organic-inorganic hybrid polymer for two photon patterning of optical waveguides,” Opt. Mater. 34(5), 772–780 (2012).
[Crossref]

J. Guo, M. R. Gleeson, and J. T. Sheridan, “A review of the optimisation of photopolymer materials for holographic data storage,” Phys. Res. Int. 2012, 1–16 (2012).
[Crossref]

H. Arimoto, W. Watanabe, K. Masaki, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285(24), 4911–4917 (2012).
[Crossref]

2011 (2)

M. S. Dinleyici and C. Sümer, “Characterization and estimation of refractive index profile of laser-written photopolymer optical waveguides,” Opt. Commun. 284(21), 5067–5071 (2011).
[Crossref]

T. F. Scott, C. J. Kloxin, D. L. Forman, R. R. McLeod, C. N. Bowman, C. Eggeling, S. W. Hell, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, C. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, “Principles of voxel refinement in optical direct write lithography,” J. Mater. Chem. 21(37), 14150 (2011).
[Crossref]

2010 (2)

2008 (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

2007 (3)

2006 (1)

A. K. O’Brien and C. N. Bowman, “Impact of Oxygen on Photopolymerization Kinetics and Polymer Structure,” Macromolecules 39(7), 2501–2506 (2006).
[Crossref]

2005 (4)

2004 (3)

V. Apostolopoulos, L. Laversenne, T. Colomb, C. Depeursinge, R. P. Salathé, M. Pollnau, R. Osellame, G. Cerullo, and P. Laporta, “Femtosecond-irradiation-induced refractive-index changes and channel waveguiding in bulk Ti3+:Sapphire,” Appl. Phys. Lett. 85(7), 1122–1124 (2004).
[Crossref]

C. J. R. Sheppard, “Defocused transfer function for a partially coherent microscope and application to phase retrieval,” J. Opt. Soc. Am. A 21(5), 828–831 (2004).
[Crossref] [PubMed]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

2003 (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[Crossref]

2002 (1)

H.-B. Sun, T. Tanaka, and S. Kawata, “Three-dimensional focal spots related to two-photon excitation,” Appl. Phys. Lett. 80(20), 3673–3675 (2002).
[Crossref]

2001 (1)

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[Crossref]

1999 (1)

1998 (1)

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4(5), 840–848 (1998).
[Crossref]

1997 (2)

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997).
[Crossref]

T. Gureyev and K. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[Crossref]

1996 (4)

1995 (1)

1989 (1)

B. L. Booth, “Low loss channel waveguides in polymers,” J. Lightwave Technol. 7(10), 1445–1453 (1989).
[Crossref]

1985 (1)

C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet- and laser-induced polymerizations,” Macromolecules 18(6), 1241–1244 (1985).
[Crossref]

1984 (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[Crossref]

1983 (1)

1981 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

1965 (1)

W. Heller, “Remarks on Refractive Index Mixture Rules,” J. Phys. Chem. 69(4), 1123–1129 (1965).
[Crossref]

Aiello, L.

Allen, L. J.

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[Crossref]

Ams, M.

Andraud, C.

S. Klein, A. Barsella, H. Leblond, H. Bulou, A. Fort, C. Andraud, G. Lemercier, J. C. Mulatier, and K. Dorkenoo, “One-step waveguide and optical circuit writing in photopolymerizable materials processed by two-photon absorption,” Appl. Phys. Lett. 86(21), 211118 (2005).
[Crossref]

Apostolopoulos, V.

V. Apostolopoulos, L. Laversenne, T. Colomb, C. Depeursinge, R. P. Salathé, M. Pollnau, R. Osellame, G. Cerullo, and P. Laporta, “Femtosecond-irradiation-induced refractive-index changes and channel waveguiding in bulk Ti3+:Sapphire,” Appl. Phys. Lett. 85(7), 1122–1124 (2004).
[Crossref]

Argiolas, N.

L. Vittadello, A. Zaltron, N. Argiolas, M. Bazzan, N. Rossetto, and R. Signorini, “Photorefractive direct laser writing,” J. Phys. D Appl. Phys. 49(12), 125103 (2016).
[Crossref]

Arimoto, H.

H. Arimoto, W. Watanabe, K. Masaki, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285(24), 4911–4917 (2012).
[Crossref]

Barbastathis, G.

Barsella, A.

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Figures (10)

Fig. 1
Fig. 1 (a) Transmission microscope used to image the phase object. (b) Example of an ideal CTF for the transmission microscope configuration used in all of the following experiments, operating under coherent illumination with a 0.3 NA in a material with a refractive index of 1.5. (c-d) Measurement geometry for imaging perpendicular and parallel-write waveguides respectively. (e-f) 2D image of the normalized refractive index distribution seen by the instrument. The insets show the cross-sections along the respective lines. (g-h) Overlap of the object’s Fourier transform with the CTF (line) of the ideal imaging system from (b). The Fourier transform amplitude shown has been scaled by taking the square root and then normalizing the amplitude in order to show the structure more clearly. (i-j) The resulting reconstructed object using only the Fourier components that overlap with the CTF of the imaging system. The insets compare the ideal cross-sections seen by the microscope along the respective lines with the actual object cross-sections (black squares).

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Fig. 2
Fig. 2 The confocal reflection microscope (660 nm path) is used to position and measure the sample thickness, while the co-aligned 405 nm laser is used to expose the photopolymer and create phase structures (inset shows an example differential interference phase contrast microscopy image). The 660 nm laser is a 100 mW Coherent OBIS LX diode laser, and the 405 nm laser is a Power Technology Incorporated IQu2A105/8983 105 mW laser.

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Fig. 3
Fig. 3 (a-c) Example brightfield images required for solving the TIE, including two symmetrically defocused images (a,c) and one in-focus image (b). (d) The 2D reconstructed Δn using the images from (a-c) along with representative (e) cross-sections taken along the x- and y-axes.

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Fig. 4
Fig. 4 (a) Differential interference contrast microscopy image of a subset of the measured phase structures. (b-e) The peak Δn response for the model two-component photopolymer over a range of different exposure intensities, exposure times, and monomer loadings as measured by TIE-based quantitative phase imaging in conjunction with confocal reflection microscopy. (b) The Δn vs. exposure time for 10 wt% monomer loading. (c) The Δn vs. exposure time for 30 wt% monomer loading. (d) The Δn vs. exposure dose for 10 wt% writing monomer. (e) The Δn vs. exposure dose for 30 wt% writing monomer. Each symbol corresponds to 3 isolated exposures, each of which has been measured by the method described in the text. Error bars show the total spread of the three measurements.

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Fig. 5
Fig. 5 (a-b) The Δn response and FWHM for a series of phase structures that are exposed up to 4 times immediately after the initial exposure. For low doses below the saturation limit, the Δn continues to increase until the final saturation Δn is reached. Continued growth of the structure terminates due to consumption of all local monomer. (c-d) The Δn response and FWHM for the same structures plotted against the total exposure dose.

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Fig. 6
Fig. 6 (a) The phenomenological fit to Δn data acquired at different doses. (b) Cross-sections of the normalized exposure profile, the expected Δn predicted using the curve from (a), and the measured Δn using the TIE/confocal reflection system. (c) The measured vs. the predicted FWHM for a cross section along the y-axis. (d) The measured vs. the predicted FWHM for a cross-section along the x-axis.

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Fig. 7
Fig. 7 The shape of 3D phase structures written into a material using either two-photon polymerization or a thresholded single-photon polymerization response can be measured using the ascending scan method. The focus of the exposure beam is shifted by an amount Δz between each exposure until the substrate no longer truncates the resulting phase structure. Phase imaging can then be used to measure the differential optical path length between adjacent structures. Because these thin phase slices are assumed to be uniform in z, the spatial frequency content of each slice falls entirely within the CTF of the imaging system. Therefore, measuring each of the differential slices in the 3D structure allows one to reconstruct the entire voxel.

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Fig. 8
Fig. 8 The reconstructed Δn vs. defocus distance used in the TIE reconstruction algorithm. As the defocus distance increases beyond 3 µm, the TIE algorithm suffers from error due to discarded higher-order terms.

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Fig. 9
Fig. 9 (a) Brightfield microscope image showing the region of the microlens array used to test the TIE algorithm. (b) Reconstructed thickness profile of the boxed region in (a). The blue line shows the cross-section used in (c). (c) Cross section of a single microlens obtained through the TIE algorithm and atomic force microscopy. The radius of curvature agrees with the manufacturer quoted value of 42 µm.

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Fig. 10
Fig. 10 Plot showing the photoinitator concentration vs. exposure time for different exposure intensities. The time required to reach saturation of Δn is plotted as circles. Saturation is reached well before a significant fraction of photoinitiator is consumed.

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Equations (3)

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- 2π λ 0 ∂I( r ⊥ ,z ) ∂z | z=0 = ∇ r ⊥ [ I( r ⊥ ,z=0 ) ∇ r ⊥ Φ( r ⊥ ,z=0 ) ]
Φ( r ⊥ ,z )=− F −1 [ F( ∇ r ⊥ I −1 ( r ⊥ ,z=0 ) ∇ r ⊥ Ψ( r ⊥ ,z ) ) 4 π 2 ( f x 2 + f y 2 ) ]
Ψ( r ⊥ ,z )= F −1 [ F( k 0 ∂I ∂z ) 4 π 2 ( f x 2 + f y 2 ) ]

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