Abstract

We demonstrate a second-order bandpass filter using a single gradient index lens (GRIN) coated with mirrors. The filter becomes possible because of the residual and externally introduced small birefringence of the GRIN lens material. We show that the filter function can be trimmed by mechanical strain of the lens. Applications of the filter in microwave photonics are discussed.

© 2010 Optical Society of America

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References

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  1. G. Meltz, W. W. Morey, and W. H. Glenn, Opt. Lett. 14, 823 (1989).
    [CrossRef] [PubMed]
  2. J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
    [CrossRef]
  3. B. E. Little, S. T. Chu, and H. A. Haus, Opt. Lett. 23, 1570 (1998).
    [CrossRef]
  4. J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
    [CrossRef]

2007

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

2000

J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
[CrossRef]

1998

1989

Capmany, J.

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

Chu, S. T.

Glenn, W. H.

Haus, H. A.

Ho, P. T.

J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
[CrossRef]

Little, B. E.

J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
[CrossRef]

B. E. Little, S. T. Chu, and H. A. Haus, Opt. Lett. 23, 1570 (1998).
[CrossRef]

Meltz, G.

Novak, D.

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

W., W.

Wilson, R. A.

J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
[CrossRef]

IEEE Photonics Technol. Lett.

J. V. Hryniewicz, B. E. Little, R. A. Wilson, and P. T. Ho, IEEE Photonics Technol. Lett. 12, 320 (2000).
[CrossRef]

Nat. Photonics

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

Opt. Lett.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the second-order optical filter based on a birefringent GRIN lens end-coated with mirrors.

Fig. 2
Fig. 2

(a) Setup used to study the optical filter. (b) Setup used to study the rf photonic filter based on the GRIN lens optical filter.

Fig. 3
Fig. 3

(a) Reflection and (b) transmission of the filter and (c) demonstration of the filter function trimming with stress application. To observe the spectrum, we scanned the laser frequency through the filter line (the scan speed and sweep time were not calibrated in frequency units) and measured the intensity of the reflected and transmitted light with an oscilloscope.

Fig. 4
Fig. 4

(Left) Logarithmic measurement of the transmission function of the optical filter, and (right) an rf photonic filter based on the optical filter. The middle curve describes the filter transmission when light interacts only with one mode of the polarization doublet. The uppermost curve shows the filter transmission when light interacts with two modes of the doublet but there is no polarizer at the output of the GRIN lens. The bottommost curve is taken for the same conditions as the uppermost curve and with a polarizer inserted.

Equations (6)

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T r x = T x 1 R x exp ( 4 i π n x L / λ ) ,
T r y = T y 1 R y exp ( 4 i π n y L / λ ) ,
E out E 0 = i T ( 1 T ) e i ϕ ¯ sin ϕ Δ ( 1 ( 1 T ) e i ϕ ¯ ) 2 + 2 ( 1 T ) e i ϕ ¯ ( 1 cos ϕ Δ ) ,
E out E 0 i T ϕ Δ ( T + i ϕ ¯ ) 2 + ϕ Δ 2 .
| n y n x | = λ T 2 π L ;
P out P in T 4 ϕ ¯ 4 + 4 T 4 = γ 4 ( ω ω 0 ) 4 + 4 γ 4 ,

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