Abstract

The feasibility of a broadband, miniature, and low loss optical delay line composed of a coiled microfiber with several-micron radius is demonstrated theoretically. Under the introduced low-loss condition, the fundamental mode of the microfiber is shifted away and does not scatter from the interfaces with the central rod and adjacent turns. Dimensions of the designed 100 ns feedforward microfiber delay line containing 20 m of microfiber are 5 mm × 5 mm × 20 mm at the radiation wavelength 1.5 μm and can be much smaller for the recirculating loop delay line. These dimensions can be further optimized by varying the radii of the microfiber and coil. The predicted insertion loss of this device is ~ 0.004 dB/ns, which is two orders of magnitude smaller than the loss achieved presently for the miniature delay lines. A curved microfiber taper is proposed as a compact, low-loss, and broadband connection to this optical delay line. The taper adiabatically converts the input fundamental mode of a straight microfiber into the shifted mode of the coiled microfiber.

© 2009 Optical Society of America

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2009 (2)

2008 (3)

2007 (3)

B. Min, L. Yang, and K. Vahala, "Perturbative analytic theory of an ultrahigh-Q toroidal microcavity," Phys. Rev. A 76, 013823 (2007).
[CrossRef]

M. Hossein-Zadeh and K. J. Vahala, "Free ultra-high-Q microtoroid: a tool for designing photonic devices," Opt. Express 15, 166-175 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-1-166.
[CrossRef] [PubMed]

J. D. Love and C. Durniak, "Bend Loss, Tapering, and Cladding-Mode Coupling in Single-Mode Fibers," IEEE Photon. Technol. Lett. 19, 1257-1259 (2007).
[CrossRef]

2006 (5)

M. Sumetsky, Y. Dulashko, J. M. Fini, A. Hale, and D. J. DiGiovanni, "The Microfiber Loop Resonator: Theory, Experiment, and Application," J. Lightwave Technol. 24, 242-250 (2006).
[CrossRef]

M. Sumetsky, "How thin can a microfiber be and still guide light?," Opt. Lett. 31, 870-872 (2006).
[CrossRef] [PubMed]

R. S. Tucker, "The Role of Optics and Electronics in High-Capacity Routers," J. Lightwave Technol. 26, 4655-4673 (2006).
[CrossRef]

A. B. Matsko and V. S. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

2005 (1)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics," Phys. Rev. A 71, 013817 (2005).
[CrossRef]

2004 (4)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip," Appl. Phys. Lett. 85, 6113-6115 (2004).
[CrossRef]

M. Sumetsky, "Optical fiber microcoil resonator," Opt. Express 12, 2303-2316 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-10-2303.
[CrossRef] [PubMed]

F. L. Kien, J. Q. Lianga, K. Hakuta, and V. I. Balykin, "Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber," Opt. Commun. 242, 445-455 (2004).
[CrossRef]

M. Sumetsky, Y. Dulashko, and A. Hale, "Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer," Opt. Express 12, 3521-3531 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3521.
[CrossRef] [PubMed]

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

2001 (2)

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).
[CrossRef]

V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, and L. Maleki, "Microtorus: a high-finesse microcavity with whispering-gallery modes," Opt. Lett. 26, 256-258 (2001).
[CrossRef]

1998 (1)

1996 (1)

1994 (1)

R. Adar, M. R. Serbin, and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

1991 (1)

1985 (1)

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

1975 (1)

Heiblum and J. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75- 83 (1975).
[CrossRef]

Adar, R.

R. Adar, M. R. Serbin, and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Balykin, V. I.

F. L. Kien, J. Q. Lianga, K. Hakuta, and V. I. Balykin, "Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber," Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Birks, T. A.

Blumenthal, D. J.

Bowers, J. E.

Burmeister, E. F.

Byer, R. L.

Coldren, L. A.

Cutler, C. C.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

DiGiovanni, D. J.

Dulashko, Y.

Durniak, C.

J. D. Love and C. Durniak, "Bend Loss, Tapering, and Cladding-Mode Coupling in Single-Mode Fibers," IEEE Photon. Technol. Lett. 19, 1257-1259 (2007).
[CrossRef]

Eggleton, B. J.

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).
[CrossRef]

Fini, J. M.

Goodman, J. W.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Gorodetsky, M. L.

Hakuta, K.

F. L. Kien, J. Q. Lianga, K. Hakuta, and V. I. Balykin, "Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber," Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Hale, A.

Hossein-Zadeh, M.

Ilchenko, V. S.

Jackson, K. P.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Kien, F. L.

F. L. Kien, J. Q. Lianga, K. Hakuta, and V. I. Balykin, "Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber," Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Kimble, H. J.

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics," Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip," Appl. Phys. Lett. 85, 6113-6115 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Klamkin, J.

Knight, J. C.

Lenz, G.

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).
[CrossRef]

Lianga, J. Q.

F. L. Kien, J. Q. Lianga, K. Hakuta, and V. I. Balykin, "Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber," Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Love, J. D.

J. D. Love and C. Durniak, "Bend Loss, Tapering, and Cladding-Mode Coupling in Single-Mode Fibers," IEEE Photon. Technol. Lett. 19, 1257-1259 (2007).
[CrossRef]

Mabuchi, H.

Mack, J. P.

Madsen, C. K.

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).
[CrossRef]

Maleki, L.

Mašanovic, M. L.

Matsko, A. B.

A. B. Matsko and V. S. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

Min, B.

B. Min, L. Yang, and K. Vahala, "Perturbative analytic theory of an ultrahigh-Q toroidal microcavity," Phys. Rev. A 76, 013823 (2007).
[CrossRef]

Mizrahi, V.

R. Adar, M. R. Serbin, and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

Moslehi, B.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Newton, S. A.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Poulsen, H. N.

Savchenkov, A. A.

Schiller, S.

Serbin, M. R.

R. Adar, M. R. Serbin, and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

Shaw, H. J.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Slusher, R. E.

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics," Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip," Appl. Phys. Lett. 85, 6113-6115 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Stamenic, B.

Streed, E. W.

Sumetsky, M.

Tucker, R. S.

R. S. Tucker, "The Role of Optics and Electronics in High-Capacity Routers," J. Lightwave Technol. 26, 4655-4673 (2006).
[CrossRef]

Tur, M.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Vahala, K.

B. Min, L. Yang, and K. Vahala, "Perturbative analytic theory of an ultrahigh-Q toroidal microcavity," Phys. Rev. A 76, 013823 (2007).
[CrossRef]

Vahala, K. J.

M. Hossein-Zadeh and K. J. Vahala, "Free ultra-high-Q microtoroid: a tool for designing photonic devices," Opt. Express 15, 166-175 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-1-166.
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics," Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip," Appl. Phys. Lett. 85, 6113-6115 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Vernooy, D. W.

Yang, L.

B. Min, L. Yang, and K. Vahala, "Perturbative analytic theory of an ultrahigh-Q toroidal microcavity," Phys. Rev. A 76, 013823 (2007).
[CrossRef]

Yao, L.

Yao, X. S.

Appl. Phys. Lett. (1)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip," Appl. Phys. Lett. 85, 6113-6115 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).
[CrossRef]

Heiblum and J. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75- 83 (1975).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

A. B. Matsko and V. S. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. D. Love and C. Durniak, "Bend Loss, Tapering, and Cladding-Mode Coupling in Single-Mode Fibers," IEEE Photon. Technol. Lett. 19, 1257-1259 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

J. Lightwave Technol. (4)

R. Adar, M. R. Serbin, and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

M. Sumetsky, "Basic elements for microfiber photonics: micro/nanofibers and microfiber coil resonators," J. Lightwave Technol. 26, 21-27 (2008).
[CrossRef]

R. S. Tucker, "The Role of Optics and Electronics in High-Capacity Routers," J. Lightwave Technol. 26, 4655-4673 (2006).
[CrossRef]

M. Sumetsky, Y. Dulashko, J. M. Fini, A. Hale, and D. J. DiGiovanni, "The Microfiber Loop Resonator: Theory, Experiment, and Application," J. Lightwave Technol. 24, 242-250 (2006).
[CrossRef]

Nature (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

F. L. Kien, J. Q. Lianga, K. Hakuta, and V. I. Balykin, "Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber," Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Opt. Express (6)

E. F. Burmeister, J. P. Mack, H. N. Poulsen, M. L. Mašanovic, B. Stameni?, D. J. Blumenthal, and J. E. Bowers, "Photonic integrated circuit optical buffer for packet-switched networks," Opt. Express 17, 6629-6635 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6629.
[CrossRef] [PubMed]

M. Sumetsky, "Optical fiber microcoil resonator," Opt. Express 12, 2303-2316 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-10-2303.
[CrossRef] [PubMed]

E. F. Burmeister, J. P. Mack, H. N. Poulsen, J. Klamkin, L. A. Coldren, D. J. Blumenthal, and J. E. Bowers, "SOA gate array recirculating buffer with fiber delay loop," Opt. Express 16, 8451-8456 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8451.
[CrossRef] [PubMed]

L. Yao, T. A. Birks, and J. C. Knight, "Low bend loss in tightly-bent fibers through adiabatic bend transitions," Opt. Express 17, 2962-2967 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-4-2962.
[CrossRef] [PubMed]

M. Hossein-Zadeh and K. J. Vahala, "Free ultra-high-Q microtoroid: a tool for designing photonic devices," Opt. Express 15, 166-175 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-1-166.
[CrossRef] [PubMed]

M. Sumetsky, Y. Dulashko, and A. Hale, "Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer," Opt. Express 12, 3521-3531 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3521.
[CrossRef] [PubMed]

Opt. Lett. (5)

Opt. Switch. Net. (1)

E. F. Burmeister, D. J. Blumenthal, and J. E. Bowers, "A comparison of optical buffering technologies," Opt. Switch. Net. 5, 10-18 (2008).
[CrossRef]

Phys. Rev. A (2)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics," Phys. Rev. A 71, 013817 (2005).
[CrossRef]

B. Min, L. Yang, and K. Vahala, "Perturbative analytic theory of an ultrahigh-Q toroidal microcavity," Phys. Rev. A 76, 013823 (2007).
[CrossRef]

Other (5)

J. B. Khurgin and R. Tucker, Eds., Slow Light: Science and Applications (CRC Press, 2008).
[CrossRef]

V. M. Babi? and V. S. Buldyrev, Short-Wavelength Diffraction Theory: Asymptotic Methods (Springer-Verlag, Berlin, 1991).

It is assumed that the elasto-optic effects are removed by reflowing of the coiled microfiber so that the refractive index is isotropic.

S. Leon-Saval, T. Birks, W. Wadsworth, P. St. J. Russell, and M. Mason, "Supercontinuum generation in submicron fibre waveguides," Opt. Express 12, 2864-2869 (2004), http://www.opticsinfobase.org/oe/ abstract.cfm?URI=oe-12-13-2864.
[CrossRef] [PubMed]

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman & Hall, London, 1983).

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Figures (6)

Fig. 1.
Fig. 1.

(a) – Optical microsphere resonator; (b) – Optical microtoroid resonator; (c) Optical microfiber coil delay line (MCDL). Surface plots illustrate the fundamental mode distribution.

Fig. 2.
Fig. 2.

Local coordinates (x,y,s) along the geodesic s situated at the outer side of the microfiber surface.

Fig. 3.
Fig. 3.

(a) – Distribution of the fundamental mode field along the cross-section of the curved microfiber for R =2.5 mm, r = 15 μm, and λ = 1.5 μm calculated using the vector BPM method; (b) – The same distribution calculated with Eq. (1); (c) – Comparison of the distributions shown in (a) and (b) along the axis x (curves 1) and axis y 1 (curves 2) crossing the maximum point of the mode: BPM – solid curves, Eq. (1) – dashed curves; (d) – Cross-sections of the distribution shown in (a) along the axis x (curve 1) and axis y 0 (curve 2).

Fig. 4.
Fig. 4.

(a) – An optical coiled microfiber taper; (b) – A coiled microfiber taper connecting a planar waveguide/single mode fiber with an MCDL; (c) – A uniform radius coiled microfiber taper connecting a tapered optical fiber to an MCDL. In (b) and (c), the diagrams illustrate the evolution of the transverse propagation constants along the taper length.

Fig. 5.
Fig. 5.

(a) – Illustration of conformal transformation of a coiled microfiber taper into a straight microfiber taper; (b) – evolution of the fundamental mode along the coiled nonadiabatic microfiber taper with L =0.3 mm in the cross-section y =0 (see Fig.2); (c) – evolution of the fundamental mode along the coiled adiabatic microfiber taper with L =1 mm in the same crosssection. The upper (lower) scale correspond to the upper (lower) parts of (b) and (c) separated by dashed lines.

Fig. 6.
Fig. 6.

(a) – Illustration of the conformal transformation of a bent microfiber into a straight microfiber; (b) – evolution of the fundamental mode along the bent microfiber with L= 2 mm, (c) – evolution of the fundamental mode along the bent microfiber with L= 6 mm.

Equations (5)

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E mn ( x , y , s ) exp [ i β mn s ] exp ( 1 2 Y 2 ) H m ( Y ) Ai ( X t n ) ,
X = ( 2 β 2 R ) 1 3 ( x y 2 2 r ) , Y = ( β 2 Rr ) 1 4 y , β = 2 π n f λ .
β mn = β 2 1 2 t n β 1 3 R 2 3 ( m + 1 2 ) ( Rr ) 1 2 .
r ( R β 2 ) 1 3 .
L t 1 min ( 1.3 β 1 3 R 2 3 , ( R ) 1 2 ) .

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