Abstract

We present a simple broadband gradient-index antireflective coating, fabricated directly on a single mode telecom fiber tip. A regular array of hemi-ellipsoidal protrusions significantly reduce the Fresnel reflection from the glass-air interface. The parameters of the structure were optimized with numerical simulation for the best performance at and around 1550 nm and the coating was fabricated with Direct Laser Writing. The measured reflectance decreased by a factor of 30 at 1550 nm and was below 0.28% for the 100 nm spectral band around the central wavelength. Compared to quarter wavelength antireflective coatings the demonstrated approach offers significantly reduced technological challenges, in particular processing of a single optical material with low sensitivity to imperfections in the fabrication process.

© 2014 Optical Society of America

1. Introduction

Antireflection coatings are indispensable in today’s optics – from eyeglasses to compound camera lenses, from binoculars to microscope objectives, reducing Fresnel reflections is vital for high performance optical devices. The most common approach is based on quarter wavelength antireflection (AR) coating. Advanced thin film deposition technologies allow for nanometer layer thickness precision and high purity coating material compositions. This technique has its limitations, though: unless complex multilayer coatings are employed the spectral range is limited, the deposition is a costly process and integration with microscale (opto)electronics is problematic. The traditional AR coating technology is also limited to several materials and in particular suffers from the scarcity of these with low refractive index [1].

A fundamentally different approach to eliminating (or at least minimizing) the reflection from the material-air interface is replacing the abrupt change of the refractive index with a gradual matching layer – the idea dating back to lord Rayleigh [2]. As the choice of low-index transparent optical materials is limited, the gradient-index coating must be fabricated with a structured AR coatings. By adjusting the filling factor between the structure building material(s) and the surrounding medium it is thus possible to affect the effective refractive index [3,4].

If properly designed, such coating can significantly reduce the interface reflectivity over a broad spectral range [411] and a number of techniques have been demonstrated to date for fabrication of nanostructured AR coatings: ion-etching [57], oblique angle deposition [8], interference lithography [9], nanoimprint lithography [10, 11] or electron beam lithography [12].

In this paper we demonstrate a simple periodic structure fabricated with Direct Laser Writing (DWL) on the cleaved surface of a single mode optical fiber. With a regular pattern of hemi-ellipsoidal protrusions made of transparent polymer, a significant reduction of the Fresnel reflection from the fiber-air interface has been achieved in a broad spectral range around the telecom band at 1.55 micron. We compare the experimental results with the simulations of the light propagation in the structure and summarize some practical aspects of its fabrication.

2. Design

There has been a significant effort invested into the gradient-index AR coating design [1316] and it has been demonstrated that the quintic-polynomial refractive index profile can approach the optimum [13]. Since the experimental realization of such index profile is far from trivial, a number of techniques were proposed to generate simplified structures that still perform as efficient AR coatings in terms of the low reflectivity, spectral band covered, the incidence angle, or these parameters combined [59].

The departure point of our AR structure design is the resolution characteristics of the DLW setup (Photonic Professional with the IP-L negative photoresist, both from Nanoscribe GmbH). As, upon irradiation with 780 nm infrared femtosecond pulses, the liquid resin photopolymerization occurs only when the laser light intensity exceeds a certain threshold, the solidified volume defines a single three dimensional writing point – the voxel. In our setup the voxel is approximately a prolate ellipsoid of revolution with the minor and major axes being 420 nm and 1000 nm respectively. The design must also take the so called “proximity effect” into account – if the two voxels are written too close to each other they merge due to diffusion of the resin components. The AR structure is made of an array of transparent protrusions, each of which has the shape of a part of the voxel extending partially above the glass substrate – see Fig. 1(a). The refractive index profile of such structure, calculated with a 3D finite-difference time-domain (FDTD) simulation package (MEEP [17]) is plotted in Fig. 1(b). The optical path length of a plane wave travelling within the structure was determined by evaluating the phase accumulated during propagation and the refractive index was found as the derivative of this optical path length with respect to the distance travelled.

 

Fig. 1 Schematic (drawn to scale) of the gradient-index AR structure – a square grid of hemi-ellipsoidal protrusions (turquoise, made of the photopolymerized IPL resin) are deposited on the glass surface (light blue). The dashed line shows the complete DWL voxel shape. The black scale bar at the bottom is 500 nm long (a). Calculated refractive index of the structure (dashed red line) plotted along the optimum quintic profile (solid black line) (b).

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For a broadband AR coating centered at 1550 nm, the structure parameters – the height h and the grid constant d – were optimized with the full 3D FDTD numerical code used to simulate the light propagation in the structure (FDTD Solutions, Lumerical). The propagation direction was from the substrate (the fiber) towards the free space and the plane wave incident on the structure was assumed. The simulation has been run for a number of parameter sets and the minimum reflectivity at 1550 nm was used as the fitness function in the manual optimization. For the model with the dispersionless solid polymer with the refractive index of 1.5, the optimum height was found to be 450 nm with the optimum spacing of 450 nm, which readily satisfies the condition that the structure is a zero-order diffraction grating at 1550 nm [16]. The pink curves in Fig. 2 represent the calculated reflectivity spectrum for the optimized structure. At 1550 nm the reflectivity from the glass-air interface drops as low as 0.065% and remains well below 0.2% across the entire 1400-1700 nm band. Interestingly, even far-from-optimum geometries still perform well as antireflective coating – compare other curves in Figs. 2(a) and 2(b).

 

Fig. 2 Calculated performance of the AR coating deposited on SMF-28 optical fiber for different structure height h (a) and grid spacing d (b). The grid spacing d = 450 nm in (a) and the structure height h = 450 nm in (b).

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3. Fabrication and characterization

To verify the performance of the structure, it was fabricated on a cleaved end of the standard telecommunication SMF-28 fiber (NA = 0.14, ncore = 1.4682 and mode field diameter 10.4 ± 0.5 μm at 1550 nm). The cleaved fiber was inserted into a drop of the liquid photoresist and the structure was written on the glass surface – compare Fig. 3(a). Details of the setup and the DLW process can be found in [18].

 

Fig. 3 Schematic of the DWL process of the AR structure fabrication (a); the cleaved fiber tip is dipped into the liquid resin. 100 × high numerical aperture objective focuses a beam of NIR femtosecond pulses at the fiber surface. False-color SEM images of the SMF-28 optical fiber with the AR structure covering the central part of the cleaved fiber end (b). Oblique view of the structure (c). Close-up of the AR structure with the array of hemi-ellipsoidal protrusions packed on a square grid (d). The scale bars are 50, 2 and 0.5 μm in (b), (c) and (d), respectively.

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The reflection from the fiber end with and without the AR coating was measured with a superluminescent diode (FWHM = 55 nm, centered at 1547 nm) coupled via the optical circulator (FCIR-1550-3L10-FC/APC, Haphit). First, a piece of the uncoated (bare) fiber was used to measure the transmitted light spectra at both the circulator output ports with an optical spectrum analyzer (OSA, AQ6370C, Yokogawa) and their sum was used as the incident intensity in subsequent reflectivity estimation. Next, the coated fiber was fused with an arc splicer (FSM-60S, Fujikura) and the reflected spectrum was recorded - see Fig. 4(a). Subsequently, the AR coated fiber end was cut off and the measurements were repeated for the bare cleaved fiber as reference. The far field image of the fiber output was recorded with the InGaAs camera (Xeva-1.7-320, XenICs) to ensure no light scattering from the AR structure is present – Fig. 4(c). The structure geometry was examined with a scanning electron microscope (SEM, EVO MA 10, Zeiss).

 

Fig. 4 Schematic of the setup used for the reflectivity measurements, SLD – superluminescent diode, OSA – optical spectrum analyzer (a). Measured reflectivity of the SMF-28 fiber end with (red) and without (green) gradient-index AR coating (ARC, solid lines) plotted along the results of numerical simulations for the fabricated structure (dash-dot lines) (b). Measured far field image of the fiber output with the AR structure (c).

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4. Results and discussion

Figures 3(b), 3(c) and 3(d) show the false-color SEM images of the SMF-28 fiber with the AR structure fabricated on the fiber core. The entire array is a square with 22 hemi-ellipsoids in each of the 22 rows, separated by 450 nm. The measured single protrusion diameter at the bottom was 367 ± 7 nm and the height varied from 280 nm to 520 nm across the coating, due to the fiber tilt during laser writing.

Figure 4(b) presents the measured back-reflection spectra from the AR coated and bare fiber end. With the gradient-index structure the reflectivity is 0.12% at 1550 nm and remains below 0.28% across the 1500-1600 nm spectral band. The measurement results are compared with the numerical simulations performed for the structure parameters measured from the SEM images. The ripple visible in the spectrum measured for the uncoated fiber is also present in the other (coated fiber) reflectivity spectrum. We attribute this, as well as the discrepancies in the curve slope, to the transmission characteristics of the optical circulator and the residual etaloning effects in the measurement setup and the structure itself. The latter can be further reduced by optimizing the protrusion shape and spacing.

5. Conclusions

Although the geometry (especially the height) of the fabricated structure differed from the designed optimum, it performed very well as an efficient antireflective coating for a telecom single mode optical fiber.

In particular, we have demonstrated that a broadband gradient-index AR coating:

  • 1. does not need to be far sub-wavelength – the feature size and the characteristic spacing of the order of one third of the wavelengths are sufficiently small,
  • 2. can have a refractive index profile that follows a smooth curve, not necessarily close to the optimum quintic polynomial,
  • 3. can have large dimension tolerances, especially in the structure height – contrary to the interference-based quarter wavelength layers – and still work effectively in the significant spectral range.

As the AR coating is based on forming a homogenous, transparent material, and no high aspect ratio structures are used, it can be fabricated with one of the inexpensive replication techniques, e.g. hot embossing [1921].

Acknowledgments

This work has been generously supported by the National Science Center (Poland) within the DEC-2012/05/E/ST3/03281 grant funds. Partial support by ERDF within the POIG.02.01.00-14-122/09-00 is also acknowledged.

References and links

1. A. Macleod, Thin-Film Optical Filters (Institute of Physics Publishing, 2001), Chap. 15.

2. J. S. Rayleigh, “On reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880).

3. U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011).

4. U. Schulz, “Review of modern techniques to generate antireflective properties on thermoplastic polymers,” Appl. Opt. 45(7), 1608–1618 (2006). [CrossRef]   [PubMed]  

5. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997). [CrossRef]  

6. H. L. Chen, S. Y. Chuang, C. H. Lin, and Y. H. Lin, “Using colloidal lithography to fabricate and optimize sub-wavelength pyramidal and honeycomb structures in solar cells,” Opt. Express 15(22), 14793–14803 (2007). [CrossRef]   [PubMed]  

7. C.-H. Sun, P. Jiang, and B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008). [CrossRef]  

8. J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

9. K. Hadobás, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000). [CrossRef]  

10. Y. Kanamori, M. Okochi, and K. Hane, “Fabrication of antireflection subwavelength gratings at the tips of optical fibers using UV nanoimprint lithography,” Opt. Express 21(1), 322–328 (2013). [CrossRef]   [PubMed]  

11. Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, and S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009). [CrossRef]  

12. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999). [CrossRef]   [PubMed]  

13. W. H. Southwell, “Gradient-index antireflection coatings,” Opt. Lett. 8(11), 584–586 (1983). [CrossRef]   [PubMed]  

14. J. A. Dobrowolski, D. Poitras, P. Ma, H. Vakil, and M. Acree, “Toward perfect antireflection coatings: Numerical investigation,” Appl. Opt. 41(16), 3075–3083 (2002). [CrossRef]   [PubMed]  

15. D. Poitras and J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. Theory,” Appl. Opt. 43(6), 1286–1295 (2004). [CrossRef]   [PubMed]  

16. E. B. Grann, M. G. Varga, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995). [CrossRef]  

17. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]  

18. M. S. Rill, Three-Dimensional Photonic Metamaterials by Direct Laser Writing and Advanced Metallization Techniques (Ph.D. Thesis, Karlsruhe School of Optics & Photonics, 2010), Chap. 3, http://digbib.ubka.uni-karlsruhe.de/volltexte/1000018614.

19. H. Becker and U. Heim, “Hot embossing as a method for the fabrication of polymer high aspect ratio structures,” Sens. Actuators A Phys. 83(1–3), 130–135 (2000). [CrossRef]  

20. K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, and C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002). [CrossRef]  

21. H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, and L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000). [CrossRef]  

References

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  1. A. Macleod, Thin-Film Optical Filters (Institute of Physics Publishing, 2001), Chap. 15.
  2. J. S. Rayleigh, “On reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880).
  3. U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011).
  4. U. Schulz, “Review of modern techniques to generate antireflective properties on thermoplastic polymers,” Appl. Opt. 45(7), 1608–1618 (2006).
    [Crossref] [PubMed]
  5. P. Lalanne, G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
    [Crossref]
  6. H. L. Chen, S. Y. Chuang, C. H. Lin, Y. H. Lin, “Using colloidal lithography to fabricate and optimize sub-wavelength pyramidal and honeycomb structures in solar cells,” Opt. Express 15(22), 14793–14803 (2007).
    [Crossref] [PubMed]
  7. C.-H. Sun, P. Jiang, B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008).
    [Crossref]
  8. J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).
  9. K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
    [Crossref]
  10. Y. Kanamori, M. Okochi, K. Hane, “Fabrication of antireflection subwavelength gratings at the tips of optical fibers using UV nanoimprint lithography,” Opt. Express 21(1), 322–328 (2013).
    [Crossref] [PubMed]
  11. Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
    [Crossref]
  12. Y. Kanamori, M. Sasaki, K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
    [Crossref] [PubMed]
  13. W. H. Southwell, “Gradient-index antireflection coatings,” Opt. Lett. 8(11), 584–586 (1983).
    [Crossref] [PubMed]
  14. J. A. Dobrowolski, D. Poitras, P. Ma, H. Vakil, M. Acree, “Toward perfect antireflection coatings: Numerical investigation,” Appl. Opt. 41(16), 3075–3083 (2002).
    [Crossref] [PubMed]
  15. D. Poitras, J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. Theory,” Appl. Opt. 43(6), 1286–1295 (2004).
    [Crossref] [PubMed]
  16. E. B. Grann, M. G. Varga, D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995).
    [Crossref]
  17. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
    [Crossref]
  18. M. S. Rill, Three-Dimensional Photonic Metamaterials by Direct Laser Writing and Advanced Metallization Techniques (Ph.D. Thesis, Karlsruhe School of Optics & Photonics, 2010), Chap. 3, http://digbib.ubka.uni-karlsruhe.de/volltexte/1000018614 .
  19. H. Becker, U. Heim, “Hot embossing as a method for the fabrication of polymer high aspect ratio structures,” Sens. Actuators A Phys. 83(1–3), 130–135 (2000).
    [Crossref]
  20. K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
    [Crossref]
  21. H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
    [Crossref]

2013 (1)

2011 (1)

U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011).

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

2009 (1)

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

2008 (1)

C.-H. Sun, P. Jiang, B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008).
[Crossref]

2007 (2)

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

H. L. Chen, S. Y. Chuang, C. H. Lin, Y. H. Lin, “Using colloidal lithography to fabricate and optimize sub-wavelength pyramidal and honeycomb structures in solar cells,” Opt. Express 15(22), 14793–14803 (2007).
[Crossref] [PubMed]

2006 (1)

2004 (1)

2002 (2)

J. A. Dobrowolski, D. Poitras, P. Ma, H. Vakil, M. Acree, “Toward perfect antireflection coatings: Numerical investigation,” Appl. Opt. 41(16), 3075–3083 (2002).
[Crossref] [PubMed]

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

2000 (3)

H. Becker, U. Heim, “Hot embossing as a method for the fabrication of polymer high aspect ratio structures,” Sens. Actuators A Phys. 83(1–3), 130–135 (2000).
[Crossref]

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

1999 (1)

1997 (1)

P. Lalanne, G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[Crossref]

1995 (1)

1983 (1)

1880 (1)

J. S. Rayleigh, “On reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880).

Abbott, S.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Acet, M.

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

Acree, M.

Ahn, C. H.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Allsopp, D. W. E.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Becker, H.

H. Becker, U. Heim, “Hot embossing as a method for the fabrication of polymer high aspect ratio structures,” Sens. Actuators A Phys. 83(1–3), 130–135 (2000).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Carl, A.

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

Chen, H. L.

Chen, M.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Chen, Q.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Chuang, S. Y.

David, C.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Desta, Y.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Dobrowolski, J. A.

Gabriel, M.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Gobrecht, J.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Grann, E. B.

Hadobás, K.

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

Hane, K.

Heim, U.

H. Becker, U. Heim, “Hot embossing as a method for the fabrication of polymer high aspect ratio structures,” Sens. Actuators A Phys. 83(1–3), 130–135 (2000).
[Crossref]

Heyderman, L. J.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Hubbard, G.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Jiang, B.

C.-H. Sun, P. Jiang, B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008).
[Crossref]

Jiang, P.

C.-H. Sun, P. Jiang, B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008).
[Crossref]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Kaiser, W.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Kanamori, Y.

Kim, J. K.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Kim, K.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Kirsch, S.

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

Koppel, S.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Lalanne, P.

P. Lalanne, G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[Crossref]

Lee, J.-B.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Lin, C. H.

Lin, S.-Y.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Lin, Y. H.

Liu, C.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Liu, W.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Ma, P.

Manohara, H.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Morris, G. M.

P. Lalanne, G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[Crossref]

Murphy, M.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Okochi, M.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Park, S.

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Poitras, D.

Pommet, D. A.

Rayleigh, J. S.

J. S. Rayleigh, “On reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880).

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Sasaki, M.

Scandella, L.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Schallenberg, U. B.

U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011).

Schift, H.

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Schubert, E. F. S.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Schubert, M. F.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Schulz, U.

Shields, P. A.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Smart, J. A.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Southwell, W. H.

Sun, C.-H.

C.-H. Sun, P. Jiang, B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008).
[Crossref]

Vakil, H.

Varga, M. G.

Wang, W. N.

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

Wassermann, E. F.

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

Xi, J.-Q.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Appl. Opt. (3)

Appl. Phys. Lett. (2)

Q. Chen, G. Hubbard, P. A. Shields, C. Liu, D. W. E. Allsopp, W. N. Wang, S. Abbott, “Broadband moth-eye antireflection coatings fabricated by low-cost nanoimprinting,” Appl. Phys. Lett. 94(26), 263118 (2009).
[Crossref]

C.-H. Sun, P. Jiang, B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008).
[Crossref]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

J. Opt. Soc. Am. A (1)

Microelectron. Eng. (1)

H. Schift, C. David, M. Gabriel, J. Gobrecht, L. J. Heyderman, W. Kaiser, S. Koppel, L. Scandella, “Nanoreplication in polymers using hot embossing and injection molding,” Microelectron. Eng. 53(1–4), 171–174 (2000).
[Crossref]

Microsyst. Technol. (1)

K. Kim, S. Park, J.-B. Lee, H. Manohara, Y. Desta, M. Murphy, C. H. Ahn, “Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology,” Microsyst. Technol. 9(1–2), 5–10 (2002).
[Crossref]

Nanotechnology (2)

K. Hadobás, S. Kirsch, A. Carl, M. Acet, E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology 11(3), 161–164 (2000).
[Crossref]

P. Lalanne, G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997).
[Crossref]

Nat. Photonics (1)

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. S. Schubert, M. Chen, S.-Y. Lin, W. Liu, J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Opt. Express (2)

Opt. Lett. (2)

Proc. Lond. Math. Soc. (1)

J. S. Rayleigh, “On reflection of vibrations at the confines of two media between which the transition is gradual,” Proc. Lond. Math. Soc. 11, 51–56 (1880).

Proc. SPIE (1)

U. B. Schallenberg, “Nanostructures versus thin films in the design of antireflection coatings,” Proc. SPIE 8168, 81681N (2011).

Sens. Actuators A Phys. (1)

H. Becker, U. Heim, “Hot embossing as a method for the fabrication of polymer high aspect ratio structures,” Sens. Actuators A Phys. 83(1–3), 130–135 (2000).
[Crossref]

Other (2)

A. Macleod, Thin-Film Optical Filters (Institute of Physics Publishing, 2001), Chap. 15.

M. S. Rill, Three-Dimensional Photonic Metamaterials by Direct Laser Writing and Advanced Metallization Techniques (Ph.D. Thesis, Karlsruhe School of Optics & Photonics, 2010), Chap. 3, http://digbib.ubka.uni-karlsruhe.de/volltexte/1000018614 .

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Figures (4)

Fig. 1
Fig. 1 Schematic (drawn to scale) of the gradient-index AR structure – a square grid of hemi-ellipsoidal protrusions (turquoise, made of the photopolymerized IPL resin) are deposited on the glass surface (light blue). The dashed line shows the complete DWL voxel shape. The black scale bar at the bottom is 500 nm long (a). Calculated refractive index of the structure (dashed red line) plotted along the optimum quintic profile (solid black line) (b).
Fig. 2
Fig. 2 Calculated performance of the AR coating deposited on SMF-28 optical fiber for different structure height h (a) and grid spacing d (b). The grid spacing d = 450 nm in (a) and the structure height h = 450 nm in (b).
Fig. 3
Fig. 3 Schematic of the DWL process of the AR structure fabrication (a); the cleaved fiber tip is dipped into the liquid resin. 100 × high numerical aperture objective focuses a beam of NIR femtosecond pulses at the fiber surface. False-color SEM images of the SMF-28 optical fiber with the AR structure covering the central part of the cleaved fiber end (b). Oblique view of the structure (c). Close-up of the AR structure with the array of hemi-ellipsoidal protrusions packed on a square grid (d). The scale bars are 50, 2 and 0.5 μm in (b), (c) and (d), respectively.
Fig. 4
Fig. 4 Schematic of the setup used for the reflectivity measurements, SLD – superluminescent diode, OSA – optical spectrum analyzer (a). Measured reflectivity of the SMF-28 fiber end with (red) and without (green) gradient-index AR coating (ARC, solid lines) plotted along the results of numerical simulations for the fabricated structure (dash-dot lines) (b). Measured far field image of the fiber output with the AR structure (c).

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