## High numerical aperture hybrid optics for two-photon polymerization |

Optics Express, Vol. 20, Issue 7, pp. 7994-8005 (2012)

http://dx.doi.org/10.1364/OE.20.007994

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### Abstract

We report on an immersion hybrid optics specially designed for focusing ultrashort laser pulses into a polymer for direct laser writing via two-photon polymerization. The hybrid optics allows for well-corrected focusing over a large working distance range of 577 *μ*m with a numerical aperture (NA) of 1.33 and low internal dispersion. We combine the concepts of an aplanatic solid immersion lens (ASIL) for achieving a high NA with a diffractive optical element (DOE) for correction of aberrations. To demonstrate the improvements for volume structuring of the polymer, we compare the achievable structure sizes of our optics with a commercially available oil-immersion objective (100x, NA=1.4).

© 2012 OSA

## 1. Introduction

1. S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. **22**, 132–134 (1997). [CrossRef] [PubMed]

6. I. Staude, G. von Freymann, S. Essig, K. Busch, and M. Wegener, “Waveguides in three-dimensional photonic-bandgap materials by direct laser writing and silicon double inversion,” Opt. Lett. **36**, 67–69 (2011). [CrossRef] [PubMed]

7. M. J. Booth and T. Wilson, “Refractive-index-mismatch induced aberrations in single-photon and two-photon microscopy and the use of aberration correction,” J. Biomed. Opt. **6**, 266–272 (2001). [CrossRef] [PubMed]

8. M. J. Nasse and J. C. Woehl, “Realistic modeling of the illumination point spread function in confocal scanning optical microscopy,” J. Opt. Soc. Am. A **27**, 295–302 (2010). [CrossRef]

*μ*m and causes low internal dispersion.

## 2. Design and simulations

9. U. Fuchs, U. D. Zeitner, and A. Tünnermann, “Hybrid optics for focusing ultrashort laser pulses,” Opt. Lett. **31**, 1516–1518 (2006). [CrossRef] [PubMed]

10. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. **57**, 2615–2616 (1990). [CrossRef]

12. S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. **78**, 4071–4073 (2001). [CrossRef]

13. M. Lang, E. Aspnes, and T. D. Milster, “Geometrical analysis of third-order aberrations for a solid immersion lens,” Opt. Express **16**, 20008–20028 (2008). [CrossRef] [PubMed]

*n*

^{2}, due to the additional refraction at the surface of the ASIL [14

14. S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. **97**, 053105 (2005). [CrossRef]

^{®}(Micro Resist Technology GmbH, Germany).

_{515nm}= 1.568, almost exactly coinciding with n

_{515nm}= 1.569 of the polymer. For the substrate, we use standard microscope coverslips (thickness 170

*μ*m, n

_{515nm}= 1.528). With the focus located on the interface between coverslip and polymer, the thickness of the immersion fluid has to be 577

*μ*m according to Eq. (1), so that no additional aberrations are introduced. The thickness of the immersion fluid is simultaneously the working distance of the hybrid optics.

*i*is the number of polynomial coefficients in the series,

*A*is the coefficient on the 2

_{i}*i*power of

^{th}*ρ*, which is the normalized radial aperture coordinate. To ensure an achromatization over the complete spectrum of the laser pulses, the phase function was optimized for 515 ± 5 nm. The calculated coefficients are given in Table 1. The phase function was quantized by 2

*π*for the central wavelength of 515 nm, the resulting phase profile was continuously structured by means of gray tone laserlithography into a photo resist, and subsequently replicated into polymer onto a glass substrate (Borofloat, thickness 1.1 mm).

*λ*for the central wavelength of 515 nm. These are mainly spherical aberration caused by the refractive-index-mismatch between coverslip and the remaining parts of the ASIL. The wavefront errors for 510 nm and 520 nm are significant larger with up to 3

*λ*. When the DOE is applied for correction, the aberrations can be corrected down to 0.05

*λ*for the complete spectrum of the laser pulses.

*λ*= 515 nm. The PSF describes the intensity distribution in the focal region of a microscope objective illuminated with a collimated beam. We used the software program PSF Lab [16] for calculating the PSFs of both objectives. This program applies vector diffraction theory to calculate the PSF of microscope objectives, thereby correctly reproducing the optical setup including refractive index and thickness of immersion fluid, coverslip, and sample. The analytic equations applied for calculation of the PSF are given in appendix A and are described in more detail in Ref. [8

8. M. J. Nasse and J. C. Woehl, “Realistic modeling of the illumination point spread function in confocal scanning optical microscopy,” J. Opt. Soc. Am. A **27**, 295–302 (2010). [CrossRef]

*μ*m (n

_{515nm}= 1.528), with use of a standard immersion oil (n

_{515nm}= 1.52). The hybrid optics was modeled with NA = 1.33, the same thickness and refractive index of the coverslip, but with the polymer as immersion liquid (n

_{515nm}= 1.569). Figure 3 shows cross-sections of the resulting PSFs in the focal plane for different z-positions of the focus. The intensities are individually normalized for each objective to the peak intensity for the focus position located on the substrate surface (z = 0

*μ*m). The peak intensity of the microscope objective decreases with increasing z-positions of the focus inside the polymer, caused by the refractive-index-mismatch-induced spherical aberration. At z = 170

*μ*m, a typical working distance of immersion oil microscope objectives, the peak intensity has dropped to 14 % compared to the aberration-free case at z = 0

*μ*m. Owing to the correction for the spherical aberration of the hybrid optics and in combination with the homogeneous immersion, the PSF of the hybrid optics remains constant for all z-positions of the focus over the complete working distance range.

*τ*

_{0}denotes the transform limited pulse duration and

*z*the propagation length in the medium. The GVD can be calculated from the medium’s dispersion relation according to [17]: where

*k*is the wave vector,

*ω*the frequency,

*λ*

_{0}the central wavelength, and

*n*the wavelength dependent refractive index of the medium. The product of GVD and propagation length z in Eq. (3) is called the group delay dispersion (GDD). Since our optics consists of merely three optical elements, the introduced GDD is significant smaller than for microscope objectives of comparable NA. We calculated the total GDD from the dispersion curves of the optical materials and the corresponding propagation lengths to 842 fs

^{2}, whereas the GDD of the microscope objectives is in the range of 2000 fs

^{2}. Figure 4 shows the pulse duration after the optics in dependence of the initial pulse duration for both objectives. The low introduced GDD of the hybrid optics and the consequently reduced pulse broadening is significant for pulse durations shorter than 100 fs.

## 3. Experimental characterization

*μ*m and usage of the immersion oil Immersol

^{®}(n

*= 1.518, Zeiss MicroImaging GmbH, Germany). The entrance pupil diameter of the microscope objective is 4.1 mm. For our experiments, we used a frequency-doubled Yb:YAG oscillator (t-Pulse 500, Amplitude Systemes, France) at 515 nm, with a fundamental laser wavelength of 1030 nm, a pulse duration of 400 fs, and a repetition rate of 10 MHz. The laser power was adjusted with a polarization beam splitter in combination with a half-wave plate. An acousto-optic modulator (AOM) was applied as shutter. The laser beam was expanded to a diameter of d = 15 mm with a telescope, to illuminate the entire entrance pupil diameter d = 12.5 mm of the hybrid optics. The average laser powers were measured with a photodiode in front of the objectives. The coverslip with the polymer located on its backside was mounted on a three-axis positioning system (ALS 130–150, Aerotech GmbH, Germany), in order to enable three-dimensional structuring of the polymer. We used the polymer ORMOCORE*

_{e}^{®}with 3 wt. % of the photoinitiator IRGACURE

^{®}369 (Ciba AG, Switzerland).

*μ*m high walls onto the substrate. These walls acted as suspension for lines, structured in different writing depths with constant process parameters (laser power and writing speed). The linewidths were measured from SEM pictures. Figure 6 shows the linewidth in dependence of the writing depth for focusing with the microscope objective (a) and hybrid optics (b). The width of the lines written with the microscope objective becomes smaller with increasing writing depth. As illustrated in Fig. 3, the writing depth dependent spherical aberration lead to a drop of the peak intensity in the focal plane and consequently to smaller volumes of polymerization giving smaller linewidths. The increase of the linewidth up to a writing depth of 10

*μ*m for the series at 1.5 mW in Fig. 6(a) is caused by the aberration induced broadening of the intensity distribution, before the drop of the intensity becomes dominant, resulting in decreasing linewidths. In contrast, when the hybrid optics is applied for focusing into the polymer, the linewidth remains constant for different writing depths. Due to the correction of the writing depth dependent aberrations, the hybrid optics should theoretically allow for homogeneous structuring with constant writing parameters over the complete working distance range of 577

*μ*m.

## 4. Conclusion

*μ*m. The improvements for volume structuring of the polymer were experimentally verified in comparison to an oil-immersion microscope objective. The flexible design can be easily adapted to polymers with different refractive index, by adjusting the optical function of the DOE.

## Appendix A

8. M. J. Nasse and J. C. Woehl, “Realistic modeling of the illumination point spread function in confocal scanning optical microscopy,” J. Opt. Soc. Am. A **27**, 295–302 (2010). [CrossRef]

*λ*passes through a Babinet-Soleil compensator and is focused by a microscope objective into the sample after traversing three media of different refractive index (immersion medium,

_{ill}*n*

_{1}; coverslip,

*n*

_{2}; sample medium,

*n*

_{3}). The design values that were used by the manufacturer for the correction of the objective are denoted by an asterisk. The origin of the right-handed coordinate system is placed in the corrected Gaussian focus, which is the geometrical focus in the presence of stratified media as given by the design case. In this coordinate system, the zenith is denoted by

*θ*(0 ≤

*θ*≤

*π*), the azimuth by

*ϕ*(0 ≤

*ϕ*< 2

*π*), and the z axis points in the direction of propagation of the incident light.

*h*

_{1}and

*h*

_{2}are the coordinates (with increasing values toward the objective) of the interfaces of the coverslip (thickness

*t*=

*h*

_{1}–

*h*

_{2}) relative to the corrected Gaussian focus. Electric field vectors are represented with a lowercase

**e**, electric strength vectors with an

**E**, and 3 × 3 tensor matrices in bold and underlined (e.g.

**P**).

*k*= 2

_{j}*πn*

_{j}/λ_{ill}for the different media (

*k*

_{0}in vacuo). The half-angle

*α*, subtended by the objective lens, is obtained from the NA and the actual refractive indices. The expression Ψ =

*h*

_{2}

*n*

_{3}cos

*θ*

_{3}–

*h*

_{1}

*n*

_{1}cos

*θ*

_{1}is the initial aberration function, in which the angles

*θ*

_{1}and

*θ*

_{3}are linked by applying Snell’s law across the plane-parallel coverslip interfaces:

*n*

_{1}sin

*θ*

_{1}=

*n*

_{2}sin

*θ*

_{2}=

*n*

_{3}sin

*θ*

_{3}. The term

^{*}corresponds to the two-media case (

^{*}in the design case, allows for the simulation of objectives corrected for use with a certain coverslip and immersion fluid.

**E**

_{3}in the third medium is calculated assuming a plane wave with linear polarization along the

*x*axis:

**E**

_{0}= (1, 0, 0), which traverses a Babinet-Soleil compensator (BS

_{ill}). The Babinet-Soleil compensator allows to turn the axis of linearly polarized light or to convert

**E**

_{0}into circularly or elliptically polarized light. The electric strength vector in the immersion medium is consequently given by The apodization function for the illumination, allows the incorporation of a Gaussian intensity profile characterized by the filling parameter

*β*, where

_{G}*α*

^{*}is the half-angle subtended by the objective in the design case (

*j*in

**P**

_{(j)}ranges from 1 to 3, referring to the corresponding media. The matrix

**BS**

_{ill}describes the Babinet-Soleil compensator in the illumination path, defined by the components The orientation and retardation angles of the Babinet-Soleil compensator are denoted by

*ϕ*

_{BS,ill}and

*δ*

_{ill}, respectively.

*T*of all three media for the illumination light are where the index “pol” stands for either s-polarized (⊥) or p-polarized light (||),

*β*=

*k*

_{0}

*n*

_{2}|

*h*

_{2}–

*h*

_{1}| cos

*θ*

_{2}, and

*i*toward medium

*j*, are written as a function of the ratios

*a*=

_{ij}*n*/

_{j}*n*and

_{i}*b*= cos

_{ij}*θ*/cos

_{j}*θ*. The index “ill” indicates, all parameters appearing in Eq. (12) are those at the illumination wavelength

_{i}*λ*

_{ill}.

*ϕ*in Eq. (5) can be evaluated to This finally leads to the following set of analytic equations:

## Acknowledgments

## References and links

1. | S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. |

2. | S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature |

3. | M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. |

4. | A. Ovsianikov, A. Ostendorf, and B. N. Chichkov, “Three-dimensional photofabrication with
femtosecond lasers for applications in photonics and
biomedicine,” Appl. Surf. Sci. |

5. | I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. |

6. | I. Staude, G. von Freymann, S. Essig, K. Busch, and M. Wegener, “Waveguides in three-dimensional photonic-bandgap materials by direct laser writing and silicon double inversion,” Opt. Lett. |

7. | M. J. Booth and T. Wilson, “Refractive-index-mismatch induced aberrations in single-photon and two-photon microscopy and the use of aberration correction,” J. Biomed. Opt. |

8. | M. J. Nasse and J. C. Woehl, “Realistic modeling of the illumination point spread function in confocal scanning optical microscopy,” J. Opt. Soc. Am. A |

9. | U. Fuchs, U. D. Zeitner, and A. Tünnermann, “Hybrid optics for focusing ultrashort laser pulses,” Opt. Lett. |

10. | S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. |

11. | I. Ichimura, S. Hayashi, and G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. |

12. | S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. |

13. | M. Lang, E. Aspnes, and T. D. Milster, “Geometrical analysis of third-order aberrations for a solid immersion lens,” Opt. Express |

14. | S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. |

15. | “Zemax optical design programm,” ZEMAX Development Center Corporation USA. |

16. | ”PSF Lab” available at onemolecule.chem.uwm.edu/index.php/software. |

17. | J.-C. Diels and W. Rudolph, |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(220.3620) Optical design and fabrication : Lens system design

(220.4000) Optical design and fabrication : Microstructure fabrication

(320.5540) Ultrafast optics : Pulse shaping

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: December 2, 2011

Revised Manuscript: January 19, 2012

Manuscript Accepted: February 29, 2012

Published: March 22, 2012

**Citation**

Frank Burmeister, Uwe D. Zeitner, Stefan Nolte, and Andreas Tünnermann, "High numerical aperture hybrid optics for two-photon polymerization," Opt. Express **20**, 7994-8005 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7994

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### References

- S. Maruo, O. Nakamura, S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22, 132–134 (1997). [CrossRef] [PubMed]
- S. Kawata, H. B. Sun, T. Tanaka, K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001). [CrossRef] [PubMed]
- M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004). [CrossRef] [PubMed]
- A. Ovsianikov, A. Ostendorf, B. N. Chichkov, “Three-dimensional photofabrication with femtosecond lasers for applications in photonics and biomedicine,” Appl. Surf. Sci. 253, 6599–6602 (2007). [CrossRef]
- I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. 35, 1094–1096 (2010). [CrossRef] [PubMed]
- I. Staude, G. von Freymann, S. Essig, K. Busch, M. Wegener, “Waveguides in three-dimensional photonic-bandgap materials by direct laser writing and silicon double inversion,” Opt. Lett. 36, 67–69 (2011). [CrossRef] [PubMed]
- M. J. Booth, T. Wilson, “Refractive-index-mismatch induced aberrations in single-photon and two-photon microscopy and the use of aberration correction,” J. Biomed. Opt. 6, 266–272 (2001). [CrossRef] [PubMed]
- M. J. Nasse, J. C. Woehl, “Realistic modeling of the illumination point spread function in confocal scanning optical microscopy,” J. Opt. Soc. Am. A 27, 295–302 (2010). [CrossRef]
- U. Fuchs, U. D. Zeitner, A. Tünnermann, “Hybrid optics for focusing ultrashort laser pulses,” Opt. Lett. 31, 1516–1518 (2006). [CrossRef] [PubMed]
- S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990). [CrossRef]
- I. Ichimura, S. Hayashi, G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. 36, 4339–4348 (1997). [CrossRef] [PubMed]
- S. B. Ippolito, B. B. Goldberg, M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001). [CrossRef]
- M. Lang, E. Aspnes, T. D. Milster, “Geometrical analysis of third-order aberrations for a solid immersion lens,” Opt. Express 16, 20008–20028 (2008). [CrossRef] [PubMed]
- S. B. Ippolito, B. B. Goldberg, M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. 97, 053105 (2005). [CrossRef]
- “Zemax optical design programm,” ZEMAX Development Center Corporation USA.
- ”PSF Lab” available at onemolecule.chem.uwm.edu/index.php/software.
- J.-C. Diels, W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, 2006).

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