Abstract

We demonstrated the fabrication of a phase shaper for generating a ‘doughnut mode’ laser beam using a thin, circular polymer film on a substrate. The fabrication method is based on a combination of spin-coating and drop-casting. The alignment procedure to get ideal ‘doughnut modes’ is described. The intensity distribution at the focus is analyzed with single molecule spectroscopy.

© 2006 Optical Society of America

1. Introduction

Recently, spatially phase modulated laser beams find applications in the various field, such as stimulated emission depletion (STED) fluorescence microscopy [1], laser manipulation [2, 3], quantum communication [4], and so on. Especially, in the field of the microscopy, “doughnut modes” which contain a three dimensional, sharp zero-intensity hole attract attention since it is indispensable for STED microscopy using reversible saturable optical fluorophore transitions (RESOLFT) [5]. STED microscopy has the potential to overcome the diffraction limit of optical microscope [1].

In order to realize “doughnut modes”, several methods have been applied, amongst them the use of a circular pattern of vapor deposited MgF2 [1], of liquid crystal thin films [6], of polymer films patterned with electron beam [7] and the use of liquid crystal phase modulators[8]. All the phase modulation devices mentioned before require the use of complex machinery or complex techniques for their fabrication. In this paper, we describe the fabrication of a phase shaper using a polymer film on a substrate, by using a combination of spin-coating and drop-casting. Spin-coating and drop-casting are very easy and low-cost techniques. We show that with the proposed method phase shapers for a broad range of wavelengths can be easily made, just by varying the thickness of the circular polymer thin film.

2. Theory

In order to make doughnut mode with a sharp three-dimensional intensity hole, we follow in part the approach proposed by S. Hell and coworkers [1] while developing for STED microscopy. They coat a circular MgF2 vapor deposited film on a substrate, however, in our case, the circular film of retardation material comprises a polymer film. The phase retardation is determined by the refractive index of the polymer and its thickness. The retardation generated by the polymer film is as follows,

Δϕ=2πdλ0(npolymernair)

Here, Δϕ, λ0, d, npolymer, nair, are the phase retardation, the wavelength in the vacuum, the thickness of the polymer, the refractive index of polymer and the refractive index of air, respectively. The thickness of the polymer film d should be adjusted so that Δϕ becomes π.

The diameter of the circular phase retardation material is also an important parameter, since perfect destructive interference at the focal point is indispensable to get the “zero” intensity hole of the ‘doughnut’. If we assume the laser beam to be a plane wave, in order to make the zero-intensity hole at the centre of the beam, the diameter of the circle should be 1/√2 of the diameter of the laser beam. The amplitude distribution of a focused beam can be represented by the following expression [9],

U(P)=2πia2Aλf2ei(fa)2u01J0(vρ)e12iuρ2ρdρ

Here, a, A/f, ρ are the radius of aperture, the amplitude at the aperture and the normalized distance from the origin in the aperture plane, respectively. And u, v are expressed as follows [9],

u=2πλ(af)2z,v=2πλ(af)r=2πλafx2+y2

As we can see from Eq. (2), the electric field at the focal point is proportional to the area of the aperture. Therefore, the electric field of the laser beam passing through the phase shaper E can be represented as superposition of two components (Fig. 1.).

 

Fig. 1. Electric field of the laser beam passing through the phase shaper. (a0: radius of the laser beam, a1: radius of circular thin film).

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The first component E0 is the electric field of the incident laser beam, and the other component E1 is the π phase shifted electric field which has two times the amplitude of the non-shifted field. The intensity distribution |E|2 of the phase shaped laser beam at the focus is shown in Fig. 2.

 

Fig. 2. Simulated intensity distribution at the focus (a) in x-y plane, (b) in x-z plane (λ=633 nm, f=2.3 mm, a0=3 mm (incident laser beam radius), a1=2.12 mm (phase shifted field)). The intensity value is normalized to that of the non-apodized beam at the focus.

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Note that Eq. (2) represents the electromagnetic field near the focus in the scalar approximation, i.e. for rather low NA, but the high NA case is not much different [9].

3. Experiment and discussion

The strategy to make a circular thin polymer film pattern is as illustrated in Fig. 3. First, we spin coat one polymer, and this layer will be used to generate the phase retardation. Then, we place a droplet of another polymer on top, creating a circular protection layer. After that, we do wet-etching with a solvent, removing the non protected hydrophobic polymer film. The exact procedure is as follows. Glass cover slips are used as a substrate. They are carefully cleaned by consecutively applying acetone, a sodium hydro oxide solution and milli-Q water. After cleaning, the surface of the glass cover slip is modified to be hydrophobic by applying a silane coupling agent ((3-Aminopropyl)trimethoxysilane) solution in ethanol. This step is done to avoid detaching of the polymer film from the substrate during wet etching. Actually any hydrophobic polymer can be used in order to generate the required phase shift. We used two different hydrophobic polymers to demonstrate the general character of the method. Poly-methylmethacrylate (PMMA) and polystyrene (PS) were selected since they are known to have excellent film forming properties. 1–10 wt% solutions of the selected polymer in toluene or chloroform are spin coated on the substrate. The thickness of the polymer film was controlled by changing the concentration of polymer solution and the rotation speed of spin coating.

As hydrophilic polymer, polyvinyl alcohol dissolved in water was used. The PVA film forms the protection layer or mask for the spatial pattern of hydrophobic polymer film that one wants to generate. The size and the circular shape of the mask critically depend on the size of the droplet of the PVA solution placed on the hydrophobic polymer. Note that, due to dewetting, the droplet of aqueous polymer solution will keep its initial shape when placed on the hydrophobic retardation layer [10]. After drying overnight, the drop forms became a circle protection pattern. Then, the hydrophobic polymer in unprotected areas is removed using chloroform. The cover slip is dried with Ar gas. Next, the polyvinyl alcohol protection layer was removed by milli-Q water, and dried with Ar gas.

 

Fig. 3. Scheme of phase shaper fabrication.

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The spatial phase modulator was analyzed using an interferometer. A Mach-Zehnder type interferometer was used since it allows [9] direct observation of the phase shift of the wave front. The fabricated phase shaper was placed on an optical mount, and placed at the center of the laser beam in one arm of the interferometer. The phase shift introduced by different phase shapers made with different concentrations of PMMA solution is shown in Fig. 4. The phase shift by the phase shaper clearly depends on the concentration of the PMMA solutions, therefore, a phase shaper for any wavelength can be fabricated just by controlling the PMMA concentration in solution. A phase shaper for 633 nm was prepared and the interferogram of the polymer film phase shaper taken by a CCD camera is shown in Fig. 5.

 

Fig. 4. Phase shift as a function of concentration of PMMA solution. The phase shift at the center the circular polymer structure is analyzed from the shift of the fringes. One fringe shift corresponds to 2π phase shift.

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For this particular phase modulator, a 7wt% PMMA toluene solution and 10 µl of a 10wt% PVA aqueous solution were used as polymer phase retardation material and protection layer, respectively. The diameter of the polymer film is 2.7 mm. The phase shift at the center the circular polymer structure is analyzed from the shift of the fringes, and it is determined to be π. The thickness of the polymer film is calculated to be 646 nm from Eq. (1), taking into account a refractive index of 1.49 for PMMA.

 

Fig. 5. Interferogram of phase shaper recorded at 633nm. The diameter of the polymer film is 2.7mm.

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Next, we analyzed the intensity distribution of the phase modulated laser beam at the focus changing the ratio of the phase retarded over non retarded part of the laser beam. A plano-convex lens (f=100 mm) was used to focus the phase shifted laser beam on a CCD camera. The alignment of the phase shaper is critical to the shape of the ‘doughnut’. The alignment procedure is as follows. The diameter of the laser beam is adjusted to be ~1.4 times the diameter of phase shifted area, and the position of the phase shaper is manipulated to make the intensity distribution at the focus to be symmetrical. Then, the diameter of the laser beam with respect to the diameter of the phase shifting area are precisely adjusted by an iris to get the maximum contrast ratio in the ‘doughnut’. The effect of the beam size on ‘doughnut shape’ at the focus is shown in Fig. 6.

 

Fig. 6. The Intensity distribution of phase shaped laser beam. (a) Schematic of the diameter of the phase shaper (A) and that of the laser beam (B). The ratio of the diameter of the laser beam and that of the phase shaper (B/A) are (b) 1.30, (c) 1.39, (d) 1.41, (e) 1.48, and (f) 1.56, respectively.

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The intensity distribution of the phase modulated laser beam focused by a microscope objective (Olympus, numerical aperture 1.3, ×100) on a cover slip is evaluated by using single molecules as a probe for the electric field, since single molecules can be regard as ideal dipole emitter [11]. Scanning fluorescence images of single phenoxy substituted terylenediimide (TDI) molecules are shown in Fig. 7. The bin-time for each pixel is 5 ms, and the imaged areas are 10 µm×10 µm or 2 µm×2µm. Without phase shaper, the fluorescence originating from an individual molecule has a Gaussian intensity distribution, reflecting the intensity distribution of the applied excitation beam [Fig. 7(a)]. When the polymer phase shaper is placed at the center of the laser beam, the images resulting from single molecules change drastically [Fig. 7(b)]. Single molecules show up now as ‘doughnuts’, effectively reflecting the intensity distribution of the applied excitation beam. The intensity ratio of the center (of the hole) and the surrounding doughnut in Fig. 7(c) is 1/20–1/200.

 

Fig. 7. Fluorescence images of single TDI molecules. (a) without phase shaper, (b) with phase shaper, (c) zoom of one molecule in image b. The scale represents photon counts per 5 ms.

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4. Conclusion

We demonstrate the fabrication of a circular polymeric π phase shaper. The π phase retarding properties were confirmed by interferometric measurements. Next, we demonstrate the application of this phase shaper for generating laser beams with a doughnut shape intensity distribution at the focus. The latter was unambiguously confirmed by imaging single molecules. The method proposed here allows for easy fabrication of phase shapers that can be used over a wide range of wavelengths just by controlling the concentration of phase retarding polymer and/or spin coating speed. The phase shapers proposed here and the doughnut shaped beams that can be generated have a potential for application in for example STED microscopy.

Acknowledgments

Support from the FWO, the Flemish Ministry of Education (GOA 2006/2) the Federal Science Policy of Belgium (IAP-V-03) is acknowledged. J.Hotta thanks the KULeuven Research fund for a fellowship, H.Uji-i thanks the KULeuven Center of Excellence CECAT for a fellowship.

References and links

1. T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).

2. D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740–742 (2003). [CrossRef]   [PubMed]  

3. P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time interactive optical micromanipulation of a mixture of high- and low-index particles,” Opt. Express 12, 1417–1425 (2004). [CrossRef]   [PubMed]  

4. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001). [CrossRef]   [PubMed]  

5. M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005). [CrossRef]   [PubMed]  

6. G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004). [CrossRef]  

7. Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999). [CrossRef]  

8. T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004). [CrossRef]  

9. M. Born and E. Wolf, Principal of Optics, (Pergamon Press, Oxford, 1980) Chap. 7, Chap. 8, and Chap. 9.

10. O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999). [CrossRef]  

11. J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000). [CrossRef]  

References

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  1. T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).
  2. D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740–742 (2003).
    [Crossref] [PubMed]
  3. P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time interactive optical micromanipulation of a mixture of high- and low-index particles,” Opt. Express 12, 1417–1425 (2004).
    [Crossref] [PubMed]
  4. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  5. M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
    [Crossref] [PubMed]
  6. G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
    [Crossref]
  7. Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999).
    [Crossref]
  8. T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
    [Crossref]
  9. M. Born and E. Wolf, Principal of Optics, (Pergamon Press, Oxford, 1980) Chap. 7, Chap. 8, and Chap. 9.
  10. O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
    [Crossref]
  11. J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
    [Crossref]

2005 (1)

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
[Crossref] [PubMed]

2004 (3)

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time interactive optical micromanipulation of a mixture of high- and low-index particles,” Opt. Express 12, 1417–1425 (2004).
[Crossref] [PubMed]

2003 (1)

2001 (2)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

2000 (1)

1999 (1)

O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
[Crossref]

Born, M.

M. Born and E. Wolf, Principal of Optics, (Pergamon Press, Oxford, 1980) Chap. 7, Chap. 8, and Chap. 9.

Daria, V. R.

Eggeling, C.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
[Crossref] [PubMed]

Enderlein, J.

Engel, E.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).

Fujii, M.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Fukuchi, N.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Glückstad, J.

Grasjo, L.

O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
[Crossref]

Hell, S. W.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
[Crossref] [PubMed]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).

Hofmann, M.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
[Crossref] [PubMed]

Igasaki, Y.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Iketaki, Y.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Ishiuchi, S.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Jakobs, S.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
[Crossref] [PubMed]

Karthaus, O.

O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
[Crossref]

Klar, T. A.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Maruyama, N.

O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
[Crossref]

Masuda, M.

Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999).
[Crossref]

Miyaji, G.

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

Miyamoto, Y.

Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999).
[Crossref]

Miyanaga, N.

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

Ohbayashi, K.

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

Omatsu, T.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Rodrigo, P. J.

Sakai, M.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Shimomura, M.

O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
[Crossref]

Sueda, K.

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

Takeda, M.

Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999).
[Crossref]

Tsubakimoto, K.

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Wada, A.

Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999).
[Crossref]

Watanabe, T.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principal of Optics, (Pergamon Press, Oxford, 1980) Chap. 7, Chap. 8, and Chap. 9.

Yamamoto, K.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Yuan, X.-C.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Zhang, D. W.

Chaos (1)

O. Karthaus, L. Grasjo, N. Maruyama, and M. Shimomura, “Formation of ordered mesoscopic polymer arrays by dewetting,” Chaos 9, 308–314 (1999).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Opt. Eng. (1)

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, and Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613-1–066613-9 (2001).

PNAS (1)

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS 102, 17565–17569 (2005).
[Crossref] [PubMed]

Rev. Laser Eng. (1)

G. Miyaji, K. Ohbayashi, K. Sueda, K. Tsubakimoto, and N. Miyanaga, “Generation of Vector Beams with Axially-Symmetric Polarization,” Rev. Laser Eng. 32, 259–264 (2004).
[Crossref]

Other (2)

Y. Miyamoto, M. Masuda, A. Wada, and M. Takeda “Electron-beam lithography fabrication of phase holograms to generate Laguerre-Gaussian beams,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi ed, Proc. SPIE3740, 232–235 (1999).
[Crossref]

M. Born and E. Wolf, Principal of Optics, (Pergamon Press, Oxford, 1980) Chap. 7, Chap. 8, and Chap. 9.

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Figures (7)

Fig. 1.
Fig. 1.

Electric field of the laser beam passing through the phase shaper. (a0: radius of the laser beam, a1: radius of circular thin film).

Fig. 2.
Fig. 2.

Simulated intensity distribution at the focus (a) in x-y plane, (b) in x-z plane (λ=633 nm, f=2.3 mm, a0=3 mm (incident laser beam radius), a1=2.12 mm (phase shifted field)). The intensity value is normalized to that of the non-apodized beam at the focus.

Fig. 3.
Fig. 3.

Scheme of phase shaper fabrication.

Fig. 4.
Fig. 4.

Phase shift as a function of concentration of PMMA solution. The phase shift at the center the circular polymer structure is analyzed from the shift of the fringes. One fringe shift corresponds to 2π phase shift.

Fig. 5.
Fig. 5.

Interferogram of phase shaper recorded at 633nm. The diameter of the polymer film is 2.7mm.

Fig. 6.
Fig. 6.

The Intensity distribution of phase shaped laser beam. (a) Schematic of the diameter of the phase shaper (A) and that of the laser beam (B). The ratio of the diameter of the laser beam and that of the phase shaper (B/A) are (b) 1.30, (c) 1.39, (d) 1.41, (e) 1.48, and (f) 1.56, respectively.

Fig. 7.
Fig. 7.

Fluorescence images of single TDI molecules. (a) without phase shaper, (b) with phase shaper, (c) zoom of one molecule in image b. The scale represents photon counts per 5 ms.

Equations (3)

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Δ ϕ = 2 π d λ 0 ( n polymer n air )
U ( P ) = 2 π i a 2 A λ f 2 e i ( f a ) 2 u 0 1 J 0 ( v ρ ) e 1 2 i u ρ 2 ρ d ρ
u = 2 π λ ( a f ) 2 z , v = 2 π λ ( a f ) r = 2 π λ a f x 2 + y 2

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