Abstract

In this work, we present the design of a photonic structure for the generation of in-plane two-dimensional (2D) limited-diffraction beam. We have numerically investigated the characteristics of the light propagation passing through a 2D square-lattice annular-type photonic crystal shaped in an axicon configuration. Careful selection of the operating frequency as well as the optimization of the apex rod position creates a less diffracted beam whose transverse intensity profile closely resembles a zero-order Bessel function. The created beam dramatically resists against the spatial spreading over a propagation distance of 50 μm, after focusing with a spot size of 0.23μm. The self-healing capability of the generated limited-diffraction beam is demonstrated by placing obstacles with different sizes and shapes along the optical axis. The two features that accompany with such beams, i.e., diffraction-limited propagation and reconstruction ability after encountering obstructions, may strengthen its usage in manipulation of light propagation in various environments.

© 2012 Optical Society of America

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2011 (1)

Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, “Multiple beam splitting to free space from a V groove in a photonic crystal waveguide,” Appl. Phys. B 102, 857–861 (2011).
[CrossRef]

2010 (4)

M. Xin, L. Zhang, C. E. Png, J. H. Teng, and A. J. Danner, “Asymmetric open cavities for beam steering and switching from line-defect photonic crystals,” J. Opt. Soc. Am. B 27, 1153–1157 (2010).
[CrossRef]

M. S. Kumar, S. Menabde, S. Yu, and N. Park, “Directional emission from photonic crystal waveguide terminations using particle swarm optimization,” J. Opt. Soc. Am. B 27, 343–349 (2010).
[CrossRef]

G. Rui, Y. Lu, P. wang, H. Ming, and Q. Zhan, “Generation of enhanced evanescent Bessel beam using band-edge resonance,” J. Appl. Phys. 108, 074304 (2010).
[CrossRef]

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, 687–702 (2010).
[CrossRef]

2009 (3)

2008 (3)

2007 (2)

2006 (3)

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99, 113104 (2006).
[CrossRef]

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristic of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

2005 (6)

2002 (2)

V. Garces-Chavez, D. McGolin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, “High-resolution optical coherence tomography over a large depth range with an axicon lens,” Opt. Lett. 27, 243–245 (2002).
[CrossRef]

2001 (2)

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

2000 (2)

1999 (1)

C. A. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

1997 (1)

1992 (1)

A. Onae, T. Kurosawa, Y. Miki, and E. Sakuma, “Nearly diffraction-free CO2 laser beam,” J. Appl. Phys. 72, 4529–4532 (1992).
[CrossRef]

1991 (1)

1989 (2)

1988 (1)

1987 (1)

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1954 (1)

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, 1964).

Ahluwalia, B. P. S.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99, 113104 (2006).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

C. A. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Baida, F.

Bermel, P.

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, 687–702 (2010).
[CrossRef]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Broky, J.

Brzobohaty, O.

Bulu, I.

Caglayan, H.

Chen, L.

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Chen, Z.

Chen, Z.-H.

Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, “Multiple beam splitting to free space from a V groove in a photonic crystal waveguide,” Appl. Phys. B 102, 857–861 (2011).
[CrossRef]

Cheong, W. C.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99, 113104 (2006).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Christodoulides, D. N.

Citrin, D. S.

Cizmar, T.

Couairon, A.

Courjon, D.

Danner, A. J.

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

V. Garces-Chavez, D. McGolin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

C. A. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Di Trapani, P.

Ding, W.

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Ding, Z.

Dogariu, A.

Dubietis, A.

Durnin, J. E.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Elsaesser, T.

Faccio, D.

Friberg, A. T.

Fu, Y.

Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, “Multiple beam splitting to free space from a V groove in a photonic crystal waveguide,” Appl. Phys. B 102, 857–861 (2011).
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, D. McGolin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Grieber, U.

Grosjean, T.

Grunwald, R.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Hartmann, H.-J.

Herman, R. M.

Ibanescu, M.

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, 687–702 (2010).
[CrossRef]

Inoue, T.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristic of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

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, 687–702 (2010).
[CrossRef]

Johnson, S.

Johnson, S. G.

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, 687–702 (2010).
[CrossRef]

Jueptner, W.

Kebbel, V.

Kikuchi, H.

K. Uehara and H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[CrossRef]

Kivshar, Y. S.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

Kizuka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristic of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Kumar, M. S.

Kurosawa, T.

A. Onae, T. Kurosawa, Y. Miki, and E. Sakuma, “Nearly diffraction-free CO2 laser beam,” J. Appl. Phys. 72, 4529–4532 (1992).
[CrossRef]

Kurt, H.

H. Kurt, “Limited-diffraction light propagation with axicon-shape photonic crystals,” J. Opt. Soc. Am. B 26, 981–986 (2009).
[CrossRef]

H. Kurt, “The directional emission sensitivity of photonic crystal waveguides to air hole removal,” Appl. Phys. B 95, 341–344 (2009).
[CrossRef]

H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682–1684 (2008).
[CrossRef]

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13, 10316–10326 (2005).
[CrossRef]

Lanz, T.

Liu, Y.-M.

Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, “Multiple beam splitting to free space from a V groove in a photonic crystal waveguide,” Appl. Phys. B 102, 857–861 (2011).
[CrossRef]

Lu, P.-F.

Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, “Multiple beam splitting to free space from a V groove in a photonic crystal waveguide,” Appl. Phys. B 102, 857–861 (2011).
[CrossRef]

Lu, Y.

G. Rui, Y. Lu, P. wang, H. Ming, and Q. Zhan, “Generation of enhanced evanescent Bessel beam using band-edge resonance,” J. Appl. Phys. 108, 074304 (2010).
[CrossRef]

Maier, M.

Matsuoka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristic of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

McBridge, S.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

McGolin, D.

V. Garces-Chavez, D. McGolin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

McLeod, J. H.

McQueen, C. A.

C. A. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Melville, H.

V. Garces-Chavez, D. McGolin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Menabde, S.

Miceli, J. J.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Miki, Y.

A. Onae, T. Kurosawa, Y. Miki, and E. Sakuma, “Nearly diffraction-free CO2 laser beam,” J. Appl. Phys. 72, 4529–4532 (1992).
[CrossRef]

Ming, H.

G. Rui, Y. Lu, P. wang, H. Ming, and Q. Zhan, “Generation of enhanced evanescent Bessel beam using band-edge resonance,” J. Appl. Phys. 108, 074304 (2010).
[CrossRef]

Morrison, S. K.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

Nelson, J. S.

Nibbering, E. T. J.

Niggel, L.

Onae, A.

A. Onae, T. Kurosawa, Y. Miki, and E. Sakuma, “Nearly diffraction-free CO2 laser beam,” J. Appl. Phys. 72, 4529–4532 (1992).
[CrossRef]

Oskooi, A. F.

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, 687–702 (2010).
[CrossRef]

Ozbay, E.

Park, N.

Piskarkas, A.

Png, C. E.

Polesana, P.

Porras, M. A.

Prather, D. W.

Pustai, D.

Ren, H.

Roundy, D.

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, 687–702 (2010).
[CrossRef]

Rui, G.

G. Rui, Y. Lu, P. wang, H. Ming, and Q. Zhan, “Generation of enhanced evanescent Bessel beam using band-edge resonance,” J. Appl. Phys. 108, 074304 (2010).
[CrossRef]

Saj, W. M.

Sakuma, E.

A. Onae, T. Kurosawa, Y. Miki, and E. Sakuma, “Nearly diffraction-free CO2 laser beam,” J. Appl. Phys. 72, 4529–4532 (1992).
[CrossRef]

Sharkawy, A.

Shi, S.

Sibbett, W.

V. Garces-Chavez, D. McGolin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Siviloglou, G. A.

Soneson, J.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, 1964).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tang, D.

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Tao, S. H.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99, 113104 (2006).
[CrossRef]

Teng, J. H.

Tschirschwitz, F.

Turunen, J.

Uehara, K.

K. Uehara and H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[CrossRef]

Vasara, A.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

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Figures (16)

Fig. 1.
Fig. 1.

(a) Schematic presentation of 2D axicon-shape square-lattice APC and (b) its dispersion diagram calculated by the plane-wave expansion method. In (c) and (d), isofrequency contours of the second band and its gradient distribution are shown by small arrows.

Fig. 2.
Fig. 2.

(a) Spatial intensity profile of the generated limited-diffraction beam. The cross-sectional intensity profiles are shown at the focus point and at 75a propagation distance in (b) and (c), respectively.

Fig. 3.
Fig. 3.

Optimization of the maximum propagation distance Zmax=92a of the limited-diffraction beam’s central lobe by shifting the APC element at the apex location. (a) Spatial intensity distributions of a generated diffraction-limited beam. (b) On-axis intensity distributions for different longitudinal shifts of the apex rod.

Fig. 4.
Fig. 4.

Representation of the spatial intensity profile that corresponds to apex shifting value of ΔZ=1.4a.

Fig. 5.
Fig. 5.

Self-healing properties of the generated diffraction-limited beam. (a) Spatial intensity distribution of the generated diffraction-limited beam facing an obstacle of dimensions (dz=0.4a)×(dy=4a). The obstacle is placed at 40a distance from the tip of the axicon PC. (b) Spatial intensity distribution of the generated diffraction-limited beam with an obstacle of dimensions (dz=1a)×(dy=8a). The obstacle is placed 40a distance from the tip of the axicon PC. (c) Comparison of the cross-sectional intensity profiles just after the obstacle at 45a distance from the tip of the axicon PC of the diffraction-limited beams with different obstacle dimensions. (d) Comparison of the cross-sectional intensity profiles of the reconstructed diffraction-limited beams at 61a distance from the tip of the axicon PC, where cases for different obstacle dimensions are shown by different types of curves.

Fig. 6.
Fig. 6.

(a) Spatial intensity distribution of the tapered Gaussian beam in free space with 0.8 μm FWHM. (b) Spatial intensity distribution of the propagation of the tapered Gaussian beam with obstacle of (dz=0.4a)×(dy=1a) dimensions, which settled at 80a distance from source. (c) Comparison of the cross-sectional intensity profiles of the tapered Gaussian beams just after the obstacle at 85a distance from the source with different obstacle dimensions. (d) Comparison of the cross-sectional intensity profiles of the tapered Gaussian beams at 101a distance from the source. The different types of curves correspond to different obstacle dimensions.

Fig. 7.
Fig. 7.

(a) Subtracted spatial intensity distribution of the generated diffraction-limited beam propagation with and without an obstacle whose dimensions are (dz=1a)×(dy=8a). (b) The subtracted spatial intensity distribution of the Gaussian beam propagation with and without an obstacle whose dimensions are (dz=0.4a)×(dy=1a).

Fig. 8.
Fig. 8.

(a) On-axis intensity distributions for different widths of the axicon APC. (b) Width versus diffraction-limited propagation distance.

Fig. 9.
Fig. 9.

Spatial intensity profiles of the generated diffraction-limited beams for different width of the axicon PC. (a) to (f) correspond to width values of W=20a, 30a, 40a, 60a, 70a, and 80a, respectively.

Fig. 10.
Fig. 10.

Spatial intensity profiles of the generated diffraction-limited beams for different radii of obstacles placed behind the axicon PC. Frame (a) corresponds to the absence of an obstacle and frames (b)–(f) correspond to radii values of r=0.20a, 0.50a, 1.0a, 3.0a, and 5.0a, respectively.

Fig. 11.
Fig. 11.

Cross-sectional intensity profiles of beams in Fig. 10 are shown at a distance of 85a from the tip of the axicon PC.

Fig. 12.
Fig. 12.

On-axis intensity profiles of the beams in Fig. 10 are shown for different circular shape obstacle sizes.

Fig. 13.
Fig. 13.

Spatial intensity profiles of the generated diffraction-limited beams for different dimensions of rectangular-shaped obstacle. Frame (a) corresponds to the absence of an obstacle and frames (b)–(f) correspond to rectangular obstacles whose dimensions are (dz,dx)=(0.4a,0.2a), (0.4a,1.0a), (0.4a,4.0a), (0.4a,0.2a), (0.4a,9.0a), and (0.4a,12a), respectively.

Fig. 14.
Fig. 14.

Cross-sectional intensity profiles of the beams in Fig. 13 are shown at the distance 85a from the tip of the axicon PC.

Fig. 15.
Fig. 15.

On-axis intensity profiles of beams are shown for different rectangular-shape obstacle sizes.

Fig. 16.
Fig. 16.

(a) Schematic presentation of a 2D axicon-shape APC with graded indices of air holes. (b) Spatial intensity profiles of the generated diffraction-limited beam. (c) On-axis intensity profiles of the generated 2D beam.

Equations (3)

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(21c22t2)E(r,z,t)=0,
E(r,t)=E0exp(i(ωt+kzz))J0(krr).
J0(krr)=1π0πexp(ikrrcos(θ))dθ.

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