Abstract

Abstract

In this paper, a simple confocal laser scanning microscopic (CLSM) image mapping technique based on the finite-difference time domain (FDTD) calculation has been proposed and evaluated for characterization of a subwavelength-scale three-dimensional (3D) void structure fabricated inside polymer matrix. The FDTD simulation method adopts a focused Gaussian beam incident wave, Berenger’s perfectly matched layer absorbing boundary condition, and the angular spectrum analysis method. Through the well matched simulation and experimental results of the xz-scanned 3D void structure, we first characterize the exact position and the topological shape factor of the subwavelength-scale void structure, which was fabricated by a tightly focused ultrashort pulse laser. The proposed CLSM image mapping technique based on the FDTD can be widely applied from the 3D near-field microscopic imaging, optical trapping, and evanescent wave phenomenon to the state-of-the-art bio- and nano-photonics area.

© 2007 Optical Society of America

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E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, and B. Luther-Davies, "Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation," Phys. Rev. B 73, 214101 (2006).

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

2005 (4)

Y. Cheng, K. Sugioka, and K. Midorikawa, "Freestanding optical fibers fabricated in a glass chip using femtosecond laser micromachining for lab-on-a-chip application," Opt. Express 13, 7225-7232 (2005).
[CrossRef] [PubMed]

A. Vogel, J. Noack, G. Huttmann, and G. Paultauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).

T. C. Chu, W.-C. Liu, and D. P. Tsai, "Enhanced resolution induced by random silver nanoparticles in near-field optical disks," Opt. Commun. 246, 561-567 (2005).
[CrossRef]

R. C. Gauthier, "Computation of the optical trapping force using an FDTD based technique," Opt. Express 13, 3707-3718 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

M. Straub, M. Ventura, and M. Gu, "Multiple higher-order stop gaps in infrared polymer photonic crystals," Phys. Rev. Lett. 91, 043901 (2003).
[CrossRef] [PubMed]

2002 (1)

D. Day and M. Gu, "Formation of voids in a doped polymethylmethacrylate polymer," Appl. Phys. Lett. 80, 2404-2406 (2002).
[CrossRef]

2001 (3)

2000 (1)

1999 (3)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

D. W. Prather and S. Shi, "Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements," J. Opt. Soc. Am. A 16, 1131-1142 (1999).
[CrossRef]

R. Drezek, A. Dunn, and R. Richards-Kortum, "Light scattering from cells: finite-difference time-domain simulations and goniometric measurements," Appl. Opt. 38, 3651-3661 (1999).
[CrossRef]

1996 (2)

1995 (2)

R. X. Bian, R. C. Dunn, and X. S. Xie, "Single molecule emission characteristics in near-field microscopy," Phys. Rev. Lett. 75, 4772-4775 (1995).
[CrossRef] [PubMed]

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

1994 (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1989 (1)

D. A. Parthenopoulos and P. M. Rentzepis, "Three-dimensional optical data storage memory," Science 245, 843-845 (1989).
[CrossRef] [PubMed]

1966 (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Alda, J.

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Barlow, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Bian, R. X.

R. X. Bian, R. C. Dunn, and X. S. Xie, "Single molecule emission characteristics in near-field microscopy," Phys. Rev. Lett. 75, 4772-4775 (1995).
[CrossRef] [PubMed]

Callan, J. P.

Chang, S.

Cheng, Y.

Chu, T. C.

T. C. Chu, W.-C. Liu, and D. P. Tsai, "Enhanced resolution induced by random silver nanoparticles in near-field optical disks," Opt. Commun. 246, 561-567 (2005).
[CrossRef]

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Day, D.

D. Day and M. Gu, "Formation of voids in a doped polymethylmethacrylate polymer," Appl. Phys. Lett. 80, 2404-2406 (2002).
[CrossRef]

Dereux, A.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Drezek, R.

Dunn, A.

Dunn, R. C.

R. X. Bian, R. C. Dunn, and X. S. Xie, "Single molecule emission characteristics in near-field microscopy," Phys. Rev. Lett. 75, 4772-4775 (1995).
[CrossRef] [PubMed]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Finlay, R. J.

Fujimoto, J. G.

Gamaly, E. G.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, and B. Luther-Davies, "Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation," Phys. Rev. B 73, 214101 (2006).

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Gauthier, R. C.

Girard, C.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Glezer, E. N.

Gu, M.

M. Straub, M. Ventura, and M. Gu, "Multiple higher-order stop gaps in infrared polymer photonic crystals," Phys. Rev. Lett. 91, 043901 (2003).
[CrossRef] [PubMed]

D. Day and M. Gu, "Formation of voids in a doped polymethylmethacrylate polymer," Appl. Phys. Lett. 80, 2404-2406 (2002).
[CrossRef]

Haggans, C. W.

Hallo, L.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Hartl, I.

Hayashi, K. -I.

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Her, T. -H.

Huang, L.

Huttmann, G.

A. Vogel, J. Noack, G. Huttmann, and G. Paultauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).

Ippen, E. P.

Itoh, K.

Judkins, J. B.

Juodkazis, S.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, and B. Luther-Davies, "Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation," Phys. Rev. B 73, 214101 (2006).

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Kawata, S.

S. Kawata, H. -B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

Kowalevicz, A. M.

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Lee, I. -Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Liu, W.-C.

T. C. Chu, W.-C. Liu, and D. P. Tsai, "Enhanced resolution induced by random silver nanoparticles in near-field optical disks," Opt. Commun. 246, 561-567 (2005).
[CrossRef]

López-Alonso, J. M.

Luther-Davies, B.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, and B. Luther-Davies, "Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation," Phys. Rev. B 73, 214101 (2006).

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Marder, S. R.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Martin, O. J. F.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Maughon, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
[CrossRef]

Mazur, E.

Mellin, S.

Midorikawa, K.

Milosavljevic, M.

Minoshima, K.

Misawa, H.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, and B. Luther-Davies, "Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation," Phys. Rev. B 73, 214101 (2006).

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Nicolai, P.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Nishii, J.

Nishimura, K.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, and B. Luther-Davies, "Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation," Phys. Rev. B 73, 214101 (2006).

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, "Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures," Phys. Rev. Lett. 96, 166101 (2006).
[CrossRef] [PubMed]

Noack, J.

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B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. -Y. S. Lee, S. M. Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51 (1999).
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Supplementary Material (2)

» Media 1: AVI (1628 KB)     
» Media 2: AVI (946 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of a general CLSM system (a) and 2D FDTD calculation structure (b).

Fig. 2.
Fig. 2.

2D TE/TM FDTD simulation of laser beam focused in a void structure with different NAs: (a) TE Hz -field, NA=0.9, (b) TM Ez -field, NA=0.9, see Supplementary Animation A [Media 1]. (c) TE Hz -field, NA=1.4, and (d) TM Ez -field, NA=1.4 (oil-immersion), see Supplementary Animation B [Media 2]. The following parameters were used in the calculations: the incident amplitude of Hz (Ez ) is 1 A/m (V/m), the refractive index of the PVA is 1.5; the refractive index of the void is 1.0 at the incident wavelength of 632.8nm.

Fig. 3.
Fig. 3.

2D TE/TM FDTD-based transmission- and reflection-type CLSM images with different NAs and different incident Gaussian beam modes: (a) TE, NA=0.9, (b) TM, NA=0.9, (c) TE, NA=1.4 (oil-immersion), and (d) TM, NA=1.4 (oil-immersion). The white arrows indicate the bright points of the transmission and reflection CLSM, and the black arrow indicates the dark point of the transmission CLSM image. The red lines are drawn to indicate the extracted axial size of the void (See text). One pixel size means the scanning distance with the minimum resolution of 0.1µm. The inserted elliptical shapes represent the center position and topological shape of the assumed subwavelength-scale void structure.

Fig. 4.
Fig. 4.

2D TE/TM FDTD-based transmission- and reflection-type CLSM images with different subwavelength-scale elliptical structures with different refractive indices in PVA polymer matrix under the tightly focused Gaussian beams incidence with a high NA of 1.4 (the oil-immersion) objective: TE (a) and TM (b) with the refractive indices difference Δn=0.01, TE (c) and TM (d) with the refractive index difference Δn=0.05 (high density, voxel), TE (e) and TM (f) with the refractive index difference Δn=0.1 (phase change, liquid), and its comparison of the contrast ratio about the transmission-type CLSM (g) and reflection-type CLSM (h).

Fig. 5.
Fig. 5.

2D TM FDTD-based transmission- and reflection-type CLSM images with different size, shape, and multilayered refractive index variation: (a) small-size sphere (0.28×0.28 µm) structure, (b) medium-size sphere (0.56×0.56 µm), (c) small-size (0.28×0.79 µm) void (nv=1.0) with 20% solidized shell (ns=1.55), (d) small-size (0.4×0.984 µm) void (nv=1.0) with 20% solidized shell (ns=1.55), (e) medium-size (0.56×0.1.38 µm) void (nv=1.0) with 40% solidized shell (ns=1.55), and (f) large-size (0.72×1.1725 µm) void (nv=1.0) with 40% solidized shell (ns=1.55).

Fig. 6.
Fig. 6.

Fabricated subwavelength-scale 3D void structures: (a) Recording input pattern, (b) SEM image of the recorded bits at the boundary region between the PVA polymer and air interface, (c) transmission-type CLSM image of the recorded pattern inside the PVA polymer matrix, (d) reflection-type CLSM image of the recorded pattern inside the PVA polymer matrix, and (e) and (f) the cross-section depth-scanned images (x-z plane) of (c) and (d), respectively.

Fig. 7.
Fig. 7.

Transmission-type CLSM image of the microexploded single void structure inside the PVA polymer matrix (a) and its xz-scanned images (b) of experiments (right) and FDTD-based simulation (left) and comparison of each xz-direction cross-sectional intensity profile at the center (minimum intensity) point in the shadow region (c).

Fig. 8.
Fig. 8.

Transmission-type CLSM image of the microexploded single void structure inside the PVA polymer matrix (a) and its xz-scanned images (b) of experiments (right) and FDTD-based simulation (left) and comparison of each xz-direction cross-sectional intensity profile at the phase transition (maximum intensity) point (c).

Tables (1)

Tables Icon

Table 1. Contrast ratio of the TE/TM FDTD-based transmission- and reflection-type CLSM image with respect to different refractive index variations in the PVA polymer matrix

Equations (10)

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× E = μ 0 H t , × H = σ E + ε 0 ε r E t ,
E z n + 1 ( i , j , k + 1 2 ) = ( 1 Δ t σ ( i , j , k + 1 2 ) ε ( i , j , k + 1 2 ) ) E z n ( i , j , k + 1 2 )
+ ( Δ t Δ u ε ( i , j , k + 1 2 ) ) [ H y n + 1 2 ( i + 1 2 , j , k + 1 2 ) H y n + 1 2 ( i 1 2 , j , k + 1 2 ) + H x n + 1 2 ( i , j 1 2 , k + 1 2 ) H x n + 1 2 ( i , j + 1 2 , k + 1 2 ) ]
H z n + 1 2 ( i + 1 2 , j + 1 2 , k ) = ( 1 Δ t σ ( i + 1 2 , j + 1 2 , k ) ε ( i + 1 2 , j + 1 2 , k ) ) H z n 1 2 ( i + 1 2 , j + 1 2 , k )
+ ( Δ t Δ u ε ( i + 1 2 , j + 1 2 , k ) ) [ E x n ( i + 1 2 , j + 1 , k ) E x n ( i + 1 2 , j , k ) + E y n ( i , j + 1 2 , k ) E y n ( i + 1 , j + 1 2 , k ) ]
I Source = τ d × e i ω m Δ t × e [ x Δ u × ( D x 2 ) w 0 ] 2 × e ik f 2 + ( x D x / 2 ) 2 f
τ d = 1 2 × [ 1 + erf { ( m 20 ) 5 2 } ]
E ( f m , x ) = t T t PH t T E ( t , x ) · e j 2 π f m t d t ,
U ( x , z ) = D x 2 D x 2 T ( f x ) e i 2 π { f x x + β ( z z 0 ) } d f x + D x 2 D x 2 R ( f x ) e i 2 π { f x x β ( z z 0 ) } d f x ,
β = { ( n m λ ) 2 ( f x 2 ) when ( f x 2 ) ( n m λ ) 2 i ( f x 2 ) ( n m λ ) 2 otherwise

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