Abstract

A hybrid device that we term G-Fresnel (i.e., grating and Fresnel) is demonstrated. It fuses the functions of a grating and a Fresnel lens into a single device. We have fabricated the G-Fresnel device by using polydimethylsiloxane (PDMS) based soft lithography. Three-dimensional surface profilometry has been performed to examine the device quality. We have also conducted optical characterizations to confirm its dual focusing and dispersing properties. The G-Fresnel can be useful for the development of miniature optical spectrometers as well as emerging optofluidic applications.

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References

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    [CrossRef]
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2009

F. Schneider, J. Draheim, R. Kamberger, and U. Wallrabe, “Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS,” Sens. Actuators, A 151(2), 95–99 (2009).
[CrossRef]

2005

2003

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003).
[CrossRef]

2000

1996

Adibi, A.

Atkin, D. M.

Birks, T. A.

Camou, S.

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003).
[CrossRef]

Chang-Yen, D. A.

Draheim, J.

F. Schneider, J. Draheim, R. Kamberger, and U. Wallrabe, “Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS,” Sens. Actuators, A 151(2), 95–99 (2009).
[CrossRef]

Eich, R. K.

Fujii, T.

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003).
[CrossRef]

Fujita, H.

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003).
[CrossRef]

Gale, B. K.

Hsieh, C.

Kamberger, R.

F. Schneider, J. Draheim, R. Kamberger, and U. Wallrabe, “Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS,” Sens. Actuators, A 151(2), 95–99 (2009).
[CrossRef]

Karbaschi, A.

Knight, J. C.

Momtahan, O.

Nuzzo, R. G.

J. A. Rogers and R. G. Nuzzo, “Recent progress in soft lithography,” Mater. Today 8(2), 50–56 (2005).
[CrossRef]

Ranka, J. K.

Rogers, J. A.

J. A. Rogers and R. G. Nuzzo, “Recent progress in soft lithography,” Mater. Today 8(2), 50–56 (2005).
[CrossRef]

Russell, P. S.

Schneider, F.

F. Schneider, J. Draheim, R. Kamberger, and U. Wallrabe, “Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS,” Sens. Actuators, A 151(2), 95–99 (2009).
[CrossRef]

Stentz, A. J.

Wallrabe, U.

F. Schneider, J. Draheim, R. Kamberger, and U. Wallrabe, “Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS,” Sens. Actuators, A 151(2), 95–99 (2009).
[CrossRef]

Windeler, R. S.

J. Lightwave Technol.

Lab Chip

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003).
[CrossRef]

Mater. Today

J. A. Rogers and R. G. Nuzzo, “Recent progress in soft lithography,” Mater. Today 8(2), 50–56 (2005).
[CrossRef]

Opt. Lett.

Sens. Actuators, A

F. Schneider, J. Draheim, R. Kamberger, and U. Wallrabe, “Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS,” Sens. Actuators, A 151(2), 95–99 (2009).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optic (Roberts & Company, Englewood, Colorado, 1996).

F. T. S. Yu, An introduction to diffraction,information processing, and holography (The MIT Press, 1973).

K. Shi, “Supercontinuum Imaging and Spectroscopy,” The Pennsylvania State University Doctoral Dissertation, 2007.

J. James, Spectrograph Design Fundamentals (Cambridge University Press, Cambridge, 2007).

C. Palmer, and E. Loewen, Diffraction grating handbook (Newport Corporation, 2005).

Y. Fainman, L. P. Lee, D. Psaltis, and C. Yang, Optofluidics-Fundamentals, Devices and Applications (McGraw-Hill, 2010).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram illustrating the dual focusing and dispersing properties of a transmission-type G-Fresnel.

Fig. 2
Fig. 2

Schematic diagram showing a thin hologram recorded with diverging and converging spherical waves.

Fig. 3
Fig. 3

Schematic diagram illustrating the procedure of fabricating a G-Fresnel; (a): PDMS pre-polymer mix is poured onto the surface of a Fresnel lens; (b): after it is in situ cured, a negative Fresnel lens mold is formed and can be peeled off; (c) PDMS pre-polymer is sandwiched between the negative Fresnel mold and a grating; (d): after curing a transmission-type G-Fresnel is fabricated; (e): a reflection-type G-Fresnel can be readily obtained by coating the grating side of a transmission-type G-Fresnel with a thin layer of reflective film; (f): a photo of a fabricated negative Fresnel mold; (g): a photo of a fabricated transmission-type G-Fresnel (h): a photo of a fabricated reflection-type G-Fresnel (Fresnel surface on top).

Fig. 4
Fig. 4

Typical surface profiles of a negative Fresnel mold and the Fresnel side of a G-Fresnel measured by optical profilometry. (a) and (b): 3D surface profile near the central parts of a negative Fresnel mold and the Fresnel side of a G-Fresnel respectively; (c) and (d): 3D surface profiles near the peripheral parts of the negative mold and the G-Fresnel respectively; (e) comparison of surface height profiles along the radial direction near the central parts of the mold and the G-Fresnel; (f) comparison of surface height profiles along the radial direction near the peripheral parts of the mold and the G-Fresnel.

Fig. 5
Fig. 5

Optical characterization results; (a) schematic diagram of the experimental system; (b) a photo of a focused diffraction pattern produced by passing a collimated supercontinuum through a transmission-type G-Fresnel; (c) diffraction pattern produced by a grating; (d) measured intensity distribution of several exemplary wavelengths (486.0 nm, 525.3 nm, 564.7 nm, 604.1 nm, 643.5 nm, 682.8 nm).

Equations (6)

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t ( x , y ) η ( λ ) e j π λ F ( x 2 + y 2 ) e j 2 π Λ x
f ( x , y , z ) e j π λ d [ ( x ' x 0 ) 2 + ( y ' y 0 ) 2 ] p ( x ' , y ' ) e j π λ F ( x ' 2 + y ' 2 ) e j 2 π Λ x ' e j π λ z [ ( x x ' ) 2 + ( y y ' ) 2 ] d x ' d y ' e j π λ ( 1 d 1 F + 1 z ) ( x ' 2 + y ' 2 ) p ( x ' , y ' ) e j 2 π [ ( x 0 λ d 1 Λ + x λ z ) x ' + ( y 0 λ d + y λ z ) y ' ] d x ' d y '
x i = L d x 0 + L λ Λ , y i = L d y 0 , L = F d d F = d λ d / λ 0 F 0 1
L = Λ d λ 0 F 0 x 0 Λ x i λ 0 F 0 d λ 0 F 0 x 0 Λ
t ( x , y ) η ( λ ) e j π λ F x c 2 e j π λ F [ ( x x c ) 2 + y 2 ]
t H | e j π λ l ( x 2 + y 2 ) + e j π λ l [ ( x Δ x ) 2 + y 2 ] | 2 = 2 + { e j π λ l ( x 2 + y 2 ) e j π λ l [ ( x Δ x ) 2 + y 2 ] + c . c . } = 2 + [ e j π λ l Δ x 2 e j 2 π λ l ( x 2 + y 2 ) e j 2 π λ l / Δ x x + c . c . ]

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