Abstract

A simulation of arbitrary beam array generation by ultrashort pulses using diffractive optical elements (DOEs) will help us to understand and optimize various pulse propagation effects in the target plane prior to the design and fabrication of optical systems for a variety of applications. The spatial-temporal distortion of a few femtosecond optical pulses in the imaging plane on propagation through a DOE is numerically studied with an efficient algorithm. A visualization of the pulse evolution is presented in three-dimensional space and time. The propagation effects include pulse front delay, lateral walk-off of the various spectral components in the imaging plane and the time dependence of the diffraction pattern in the target plane.

© 2007 Optical Society of America

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References

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2006 (5)

2005 (2)

2004 (1)

2003 (2)

N. H. Rizvi, "Femtosecond laser micromachining: current status and applications," RIKEN Rev. 50, 107-115 (2003).

S. Zhang, Y. Ren, and G. Lupke, "Ultrashort laser pulse beam shaping," Appl. Opt. 42, 715-718 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (4)

1999 (1)

Amako, J.

Andres, P.

Caraquitena, J.

Dai, E.

Fainman, Y.

Fuchs, U.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hasegawa, S.

Hayasaki, Y.

Hirao, K.

Ichikawa, H.

Judkazis, S.

T. Kondo, S. Matsuo, S. Judkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-730 (2001).
[CrossRef]

Kazuhiro, N.

Kondo, T.

T. Kondo, S. Matsuo, S. Judkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-730 (2001).
[CrossRef]

Kuroiwa, Y.

Lancis, J.

Li, G.

Lupke, G.

Matsuo, S.

T. Kondo, S. Matsuo, S. Judkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-730 (2001).
[CrossRef]

Miller, D. A. B.

Misawa, H.

T. Kondo, S. Matsuo, S. Judkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-730 (2001).
[CrossRef]

Mnguez-Vega, G.

Nagasaka, K.

Nakagawa, W.

Narita, Y.

Nishida, N.

Piestun, R.

Ren, Y.

Rizvi, N. H.

N. H. Rizvi, "Femtosecond laser micromachining: current status and applications," RIKEN Rev. 50, 107-115 (2003).

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Schimmel, H.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Sampling rules in the frequency domain for numerical propagation of ultra short pulses through linear homogenous dielectrics," J. Opt. Soc. Am. B 23, 2227-2236 (2006).
[CrossRef]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Diffraction induced space-time splitting effects in ultra short pulse propagation," J. Mod. Opt. 53, 1819-1828 (2006).
[CrossRef]

Sharma, D. K.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Diffraction induced space-time splitting effects in ultra short pulse propagation," J. Mod. Opt. 53, 1819-1828 (2006).
[CrossRef]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Sampling rules in the frequency domain for numerical propagation of ultra short pulses through linear homogenous dielectrics," J. Opt. Soc. Am. B 23, 2227-2236 (2006).
[CrossRef]

Sun, P. C.

Takeshima, N.

Tanaka, S.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Torres-Company, V.

Tunnermann, A.

Tyan, R. C.

Veetil, S. P.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Diffraction induced space-time splitting effects in ultra short pulse propagation," J. Mod. Opt. 53, 1819-1828 (2006).
[CrossRef]

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski, "Spectral and temporal evolution of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Sampling rules in the frequency domain for numerical propagation of ultra short pulses through linear homogenous dielectrics," J. Opt. Soc. Am. B 23, 2227-2236 (2006).
[CrossRef]

Vijayan, C.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Sampling rules in the frequency domain for numerical propagation of ultra short pulses through linear homogenous dielectrics," J. Opt. Soc. Am. B 23, 2227-2236 (2006).
[CrossRef]

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski, "Spectral and temporal evolution of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Diffraction induced space-time splitting effects in ultra short pulse propagation," J. Mod. Opt. 53, 1819-1828 (2006).
[CrossRef]

Viswanathan, N. K.

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski, "Spectral and temporal evolution of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

Wyrowski, F.

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski, "Spectral and temporal evolution of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Diffraction induced space-time splitting effects in ultra short pulse propagation," J. Mod. Opt. 53, 1819-1828 (2006).
[CrossRef]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Sampling rules in the frequency domain for numerical propagation of ultra short pulses through linear homogenous dielectrics," J. Opt. Soc. Am. B 23, 2227-2236 (2006).
[CrossRef]

Xu, F.

Zeitner, U. D.

Zhang, S.

Zhou, C.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

T. Kondo, S. Matsuo, S. Judkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-730 (2001).
[CrossRef]

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski, "Spectral and temporal evolution of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

J. Mod. Opt. (1)

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, "Diffraction induced space-time splitting effects in ultra short pulse propagation," J. Mod. Opt. 53, 1819-1828 (2006).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (5)

RIKEN Rev. (1)

N. H. Rizvi, "Femtosecond laser micromachining: current status and applications," RIKEN Rev. 50, 107-115 (2003).

Other (2)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (4)

Fig. 1
Fig. 1

Schematic for the multifocal imaging with a diffractive optical element.

Fig. 2
Fig. 2

Intensity of the spot arrays formed by a monochromatic Gaussian beam at design wavelength 800 nm .

Fig. 3
Fig. 3

Snapshots of 3D visualization of multibeam imaging with ultrashort pulse in the observation plane. The gray scale on the right side of each figure shows the intensity at that instant of time. (a) Pulse at 0 fs ; (b) pulse at 5.8 fs ; (c) pulse at 11.6 fs .

Fig. 4
Fig. 4

Equivalent to Fig. 3a (not to scale) rendered in color to explain the chromatic and angular dispersion.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

U ( x , y , z , t ) = u ( x , y , z ) P ( t ) exp [ j ω 0 t ] .
U ̃ ( x , y , z , ω ) = T ( x , y , ω ) U ̃ i n ( x , y , z , ω ) .
U ̃ i n ( x , y , z , ω ) = FT { U ( x , y , z , t ) } .
T ( x , y , ω ) = T A ( x , y , ω ) exp [ j Φ ( x , y , ω ) ] .
Φ ( x , y , ω ) = n ( ω ) ω c [ ( K ( x , y ) 1 ) h ] ,
U ̃ ( x , y , z , ω i ) in = { U ̃ 1 ( x , y , z , ω 1 ) , U ̃ 2 ( x , y , z , ω 2 ) , , , U ̃ n ( x , y , z , ω I ) }
U ̃ ( x , y , z f , ω i ) out exp [ i k 2 f ( 1 d f ) ( x 2 + y 2 ) ] U ̃ ( x , y , z , ω i ) in × exp [ i k f ( x x + y y ) ] d x d y .
U ( x , y , z , t i ) = IFT U ̃ ( x , y , z , ω i )

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