Abstract

We propose and show experimentally axisymmetric spatial (angular) filtering of two-dimensional light beams by axisymmetric photonic microstructures. Such three-dimensional microstructures (similar to photonic crystals), in gapless configuration, were recorded in bulk of glass, where the refractive index has been point-by-point modulated using tightly focused femtosecond laser pulses. Axisymmetric angular filtering of approximately 25 mrad is demonstrated experimentally.

© 2014 Optical Society of America

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2013 (2)

R. Pico, I. Pérez-Arjona, V. J. Sánchez-Morcillo, and K. Staliunas, Appl. Acoust. 74, 945 (2013).
[CrossRef]

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

2012 (1)

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

2011 (2)

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

K. Staliunas, Phys. Rev. A 84, 013626 (2011).
[CrossRef]

2010 (2)

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

2009 (2)

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Rev. A 79, 053807 (2009).
[CrossRef]

2007 (1)

2005 (1)

2003 (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

1996 (1)

1993 (1)

A. E. Siegman, Proc. SPIE 1868, 2 (1993).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Araiza, J. J.

Avendano-Alejo, M.

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Cakmak, A. O.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Chen, S.

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

Cojocaru, C.

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Colak, E.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Dai, R.

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

Davis, K. M.

Fan, D.

Gailevicius, D.

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

Gertus, T.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Hirao, K.

Juodkazis, S.

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

Liu, D.

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

Luo, H.

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

Luo, Z.

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

Maigyte, L.

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Malinauskas, M.

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

Miura, K.

Mizeikis, V.

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

Moreno, I.

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Ozbay, E.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Peckus, M.

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Pérez-Arjona, I.

R. Pico, I. Pérez-Arjona, V. J. Sánchez-Morcillo, and K. Staliunas, Appl. Acoust. 74, 945 (2013).
[CrossRef]

Pico, R.

R. Pico, I. Pérez-Arjona, V. J. Sánchez-Morcillo, and K. Staliunas, Appl. Acoust. 74, 945 (2013).
[CrossRef]

Purlys, V.

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

Ren, Z.

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

Rutkauskas, M.

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

Sánchez-Morcillo, V. J.

R. Pico, I. Pérez-Arjona, V. J. Sánchez-Morcillo, and K. Staliunas, Appl. Acoust. 74, 945 (2013).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Rev. A 79, 053807 (2009).
[CrossRef]

Serebryannikov, A. E.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Proc. SPIE 1868, 2 (1993).
[CrossRef]

Sirutkaitis, V.

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Staliunas, K.

R. Pico, I. Pérez-Arjona, V. J. Sánchez-Morcillo, and K. Staliunas, Appl. Acoust. 74, 945 (2013).
[CrossRef]

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

K. Staliunas, Phys. Rev. A 84, 013626 (2011).
[CrossRef]

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Rev. A 79, 053807 (2009).
[CrossRef]

Sugimoto, N.

Tang, Z.

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

Z. Tang, D. Fan, S. Wen, Y. Ye, and C. Zhao, Chin. Opt. Lett. 5, 211 (2007).

Trull, J.

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Tuennermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Wang, Z.

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

Wen, S.

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

Z. Tang, D. Fan, S. Wen, Y. Ye, and C. Zhao, Chin. Opt. Lett. 5, 211 (2007).

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Xiang, Y.

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Ye, Y.

Zhao, C.

Appl. Acoust. (1)

R. Pico, I. Pérez-Arjona, V. J. Sánchez-Morcillo, and K. Staliunas, Appl. Acoust. 74, 945 (2013).
[CrossRef]

Appl. Phys. A (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Appl. Phys. B (2)

R. Dai, S. Chen, Z. Ren, Z. Wang, and D. Liu, Appl. Phys. B 109, 15 (2012).
[CrossRef]

Z. Luo, Z. Tang, Y. Xiang, H. Luo, and S. Wen, Appl. Phys. B 94, 641 (2009).
[CrossRef]

Chin. Opt. Lett. (1)

J. Appl. Phys. (1)

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (5)

J. Trull, L. Maigyte, V. Mizeikis, M. Malinauskas, S. Juodkazis, C. Cojocaru, M. Rutkauskas, M. Peckus, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 84, 033812 (2011).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Rev. A 79, 053807 (2009).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, Phys. Rev. A 82, 043819 (2010).
[CrossRef]

V. Purlys, L. Maigyte, D. Gailevičius, M. Peckus, M. Malinauskas, and K. Staliunas, Phys. Rev. A 87, 033805 (2013).
[CrossRef]

K. Staliunas, Phys. Rev. A 84, 013626 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Proc. SPIE (1)

A. E. Siegman, Proc. SPIE 1868, 2 (1993).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Illustration of spatial filtering in a 2D PhC, in spatial Fourier domain (k,k) in configuration (a) with and (b) without the angular bandgaps. Filtering occurs when the waves in indicated areas are resonantly scattered due to periodic modulation of refractive index with wave vectors q⃗=(q,q) (red arrows). Thick arrows show the direction of deflected angular components. Angle α indicates central angle of spatial filtering and φ shows the angular width of the filtering.

Fig. 2.
Fig. 2.

(a), (c), and (e) Geometries of the photonic structures; and (b), (d), and (f) their far field distributions obtained by numerical calculations. (a) and (b) 2D case as considered in [10]; (c) and (d) square symmetry case in transverse plane case as considered in [9]; (e) and (f) spatial filtering in axisymmetric structures as considered in this Letter. The inset in (f) shows 5 times enhanced field intensity for visualization of the outer ring. The parameters for simulations are given in the main text.

Fig. 3.
Fig. 3.

Experimentally recorded far field distributions behind the axisymmetric structure for N=6, 8, and 12 longitudinal periods of the structure. (a), (c), and (e) show the large scale distributions; and (b), (d), and (f) show the small scale distributions together with their vertical cross sections through the axis of the beam. The radii of dark inner and light outer circles are 65 and 396 mrad, respectively. The insets in (b), (d), and (f) show 5 times enhanced field intensity for visualization of the bright outer ring.

Fig. 4.
Fig. 4.

(a) Numerically calculated width and (b) depth of the angular filtering range, depending on the length of the structure for three different s parameter values: 0.05, 0.15, and 0.25. The data from experimental measurements are shown by points with error bars. The red solid line corresponds to experimental values of s.

Equations (1)

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sin(α)=q2k0(Q1)=λ2d(Q1).

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