Abstract

We propose planar, high numerical aperture (NA), low loss, focusing reflectors and lenses using subwavelength high contrast gratings (HCGs). By designing the reflectance and the phase of non-periodic HCGs, both focusing reflectors and lenses can be constructed. Numerical aperture values as high as 0.81 and 0.96 are achieved for a reflector and lens with very low losses of 0.3 and 0.2 dB, respectively. The design algorithm is also shown to be readily extended to a 2D lens. Furthermore, HCG optics can simultaneously focus the reflected and transmitted waves, with important technological implications. HCG focusing optics are defined by one-step photolithography and thus can be readily integrated with many devices including VCSELs, saturable absorbers, telescopes, CCDs and solar cells.

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  10. V. Karagodsky, M. C. Y. Huang, and C. J. Chang-Hasnain, “Analytical Solution and Design Guideline for Highly Reflective Subwavelength Gratings,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2008), paper JTuA128.
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    [CrossRef]
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  13. Yu. V. Troitski, “The Energy Conservation Law for Optical Two-Port Devices,” Opt. Spectrosc. 92(4), 555–559 (2002).
    [CrossRef]

2009

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

2008

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large Fabrication Tolerance for VCSELs Using High-Contrast Grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

2004

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

2002

Yu. V. Troitski, “The Energy Conservation Law for Optical Two-Port Devices,” Opt. Spectrosc. 92(4), 555–559 (2002).
[CrossRef]

1991

1990

1989

T. Shiono, M. Kitagawa, K. Setsune, and T. Mitsuyu, “Reflection micro-Fresnel lenses and their use in an integrated focus sensor,” Appl. Opt. 28, 15 (1989).

1982

1981

1979

D. C. Shaver and D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16(6), 1626 (1979).
[CrossRef]

Chang-Hasnain, C. J.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large Fabrication Tolerance for VCSELs Using High-Contrast Grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Chase, C.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Flanders, D. C.

D. C. Shaver and D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16(6), 1626 (1979).
[CrossRef]

Fujita, T.

Gaylord, T. K.

Gilchrist, H.

Habiby, S. F.

Haruna, M.

Huang, M. C. Y.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large Fabrication Tolerance for VCSELs Using High-Contrast Grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Hubbard, W. M.

Karagodsky, V.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Kitagawa, M.

T. Shiono, M. Kitagawa, K. Setsune, and T. Mitsuyu, “Reflection micro-Fresnel lenses and their use in an integrated focus sensor,” Appl. Opt. 28, 15 (1989).

Koyama, J.

Marrakchi, A.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Mitsuyu, T.

T. Shiono, M. Kitagawa, K. Setsune, and T. Mitsuyu, “Reflection micro-Fresnel lenses and their use in an integrated focus sensor,” Appl. Opt. 28, 15 (1989).

Moewe, M.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Moharam, M. G.

Nahory, R. E.

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Nishihara, H.

Pesala, B.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Rastani, K.

Sedgwick, F. G.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Setsune, K.

T. Shiono and K. Setsune, “Blazed reflection micro-Fresnel lenses fabricated by electron-beam writing and dry development,” Opt. Lett. 15(1), 84 (1990).
[CrossRef] [PubMed]

T. Shiono, M. Kitagawa, K. Setsune, and T. Mitsuyu, “Reflection micro-Fresnel lenses and their use in an integrated focus sensor,” Appl. Opt. 28, 15 (1989).

Shaver, D. C.

D. C. Shaver and D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16(6), 1626 (1979).
[CrossRef]

Shiono, T.

T. Shiono and K. Setsune, “Blazed reflection micro-Fresnel lenses fabricated by electron-beam writing and dry development,” Opt. Lett. 15(1), 84 (1990).
[CrossRef] [PubMed]

T. Shiono, M. Kitagawa, K. Setsune, and T. Mitsuyu, “Reflection micro-Fresnel lenses and their use in an integrated focus sensor,” Appl. Opt. 28, 15 (1989).

Takahashi, M.

Troitski, Yu. V.

Yu. V. Troitski, “The Energy Conservation Law for Optical Two-Port Devices,” Opt. Spectrosc. 92(4), 555–559 (2002).
[CrossRef]

Wakahayashi, K.

Zhou, Y.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large Fabrication Tolerance for VCSELs Using High-Contrast Grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009).
[CrossRef]

IEEE Photon. Technol. Lett.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, “Large Fabrication Tolerance for VCSELs Using High-Contrast Grating,” IEEE Photon. Technol. Lett. 20(6), 434–436 (2008).
[CrossRef]

J. Opt. Soc. Am.

J. Vac. Sci. Technol.

D. C. Shaver and D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16(6), 1626 (1979).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

Yu. V. Troitski, “The Energy Conservation Law for Optical Two-Port Devices,” Opt. Spectrosc. 92(4), 555–559 (2002).
[CrossRef]

Other

E. Hecht, Optics (Addison Wesley, 2007), Chap. 5.
[PubMed]

V. Karagodsky, M. C. Y. Huang, and C. J. Chang-Hasnain, “Analytical Solution and Design Guideline for Highly Reflective Subwavelength Gratings,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2008), paper JTuA128.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of a non-periodic high contrast grating (HCG). High index gratings (blue) are surrounded by low index material, typically air. High reflectivity or high transmissivity in a subwavelength grating (s + a < λSurrounding Material) can be achieved by proper choice of grating parameters (b) Phase distribution of a non-periodic HCG focusing reflector or lens. The blue curve is the ideal phase distribution for a lens modulo 2π. Green circles are the phases of each HCG bar. Focusing can be achieved by proper design of the grating phases.

Fig. 2
Fig. 2

Reflectance contour, phase contour, and actual dimensions for an HCG focusing reflector. Reflectance is shown in gray and white color in logarithmic scale as a function of bar width and air gap. The red lines are the phase in the unit of degree. Actual dimensions of an HCG focusing design are circles in different colors, indicating different 2π-windows. All the actual dimensions are chosen on a line where R>0.9 and maximum phase change is 2π.

Fig. 3
Fig. 3

(a) H-field intensity distribution (normalized by incident field intensity) on both the reflection side and the transmission side of an HCG focusing reflector. HCG bars are denoted by yellow boxes (b) H-field intensity distribution (normalized by incident field intensity) at the reflection focal plane. This field distribution is plotted after the incident wave is subtracted (c) H-field intensity distribution (normalized by incident field intensity) for both reflected wave and transmitted wave along z axis at the center of the reflector (x = 0). The blue curve is H-field intensity of the transmitted wave, amplified by ten. The yellow curve is H-field intensity of reflected wave, with the interference pattern. The red curve is H-field intensity of reflected wave after the incident wave is subtracted (the reflected wave component of the yellow curve).

Fig. 4
Fig. 4

(a) H-Field intensity distribution (normalized by incident field intensity) of an HCG lens. A plane wave is incident from the positive z direction and focused to a spot 4.0 μm from the bottom edge of the HCG lens (b) H-field intensity distribution at the focal plane, normalized to incident field intensity, demonstrating a FWHM of just 650 nm.

Fig. 5
Fig. 5

(a) Top view of a 2D HCG lens (b) Gaussian beam source E-field intensity distribution (c) E-field intensity distribution at the focal plane. The Gaussian beam is focused from 3.5 μm (waist radius) down to 0.89 μm, a 15X reduction in area. The corresponding increase in peak intensity is 12X, a value which can be improved by applying a bar-by-bar optimization procedure described in the text.

Fig. 6
Fig. 6

(a) Full width half maximum (FWHM) at the focal spot as a function of focal length f. The blue curve is the continuous ideal phase distribution results. The red, pink, yellow, green curves are discrete ideal phase distribution results for different constant phase element of widths δx. The black crosses are the FDTD results for HCG focusing reflectors (b) Field intensity distributions (normalized by peak field intensity) at the focal plane for an HCG focusing reflector (blue solid line) and a corresponding ideal phase lens (red dashed line). Both cases have 30 μm width and 15 μm focal length. These two curves show excellent agreement.

Equations (2)

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ϕ ( x ) = 2 π λ ( f + ϕ max 2 π λ x 2 + f 2 )
ϕ R ϕ T = π 2 + m π m = 1 , 2 ,

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