Abstract

A passively stable laser-driven lightsail is described, which makes use of a spatially variant “bi-grating” sail with a mass (payload) attached to a boom (patent pending). A two-dimensional analytical model of the system, a linear stability analysis, and numerical solutions of the equations of motion are reported. The acceleration of the light sail along the beam path is found to depend on the grating parameters. We identify stability conditions that depend on the grating design, beam parameters, and boom length. The inclusion of damping is found to enhance the dynamic range of stability.

© 2019 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

O. Ilic and H. A. Atwater, Nat. Photonics 13, 289 (2019).
[Crossref]

2018 (4)

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

G. A. Swartzlander, J. Br. Interplanet. Soc. 71, 130 (2018).

Y.-J. L. Chu, E. M. Jansson, and G. A. Swartzlander, Phys. Rev. Lett. 121, 063903 (2018).
[Crossref]

2017 (3)

Z. Manchester and A. Loeb, Astrophys. J. Lett. 837, L20 (2017).
[Crossref]

E. Popova, M. Efendiev, and I. Gabitov, Math. Methods Appl. Sci. 40, 1346 (2017).
[Crossref]

G. A. Swartzlander, J. Opt. Soc. Am. B 34, C25 (2017).
[Crossref]

2016 (1)

2011 (1)

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

2006 (1)

2003 (1)

J. Benford and G. Benford, Beamed Energy Propul. 664, 303 (2003).
[Crossref]

2001 (1)

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

1999 (1)

1992 (1)

1991 (1)

1986 (1)

1984 (1)

R. L. Forward, J. Spacecr. Rockets 21, 187 (1984).
[Crossref]

1982 (1)

M. H. Johnson and E. Teller, Proc. Natl. Acad. Sci. USA 79, 1340 (1982).
[Crossref]

1979 (1)

R. F. Weiss, A. N. Pirri, and N. H. Kemp, Astronaut. Aeronaut. 17, 50 (1979).

1972 (1)

W. Moeckel, J. Spacecr. Rockets 9, 942 (1972).
[Crossref]

1967 (1)

J. Redding, Nature 213, 588 (1967).
[Crossref]

Abdallah, C. T.

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Adams, C.

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

Allen, J.

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Allen, M.

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Ashkin, A.

Astilean, S.

Atwater, H. A.

O. Ilic and H. A. Atwater, Nat. Photonics 13, 289 (2019).
[Crossref]

Benford, G.

J. Benford and G. Benford, Beamed Energy Propul. 664, 303 (2003).
[Crossref]

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Benford, J.

J. Benford and G. Benford, Beamed Energy Propul. 664, 303 (2003).
[Crossref]

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Bjorkholm, J.

Cambril, E.

Chavel, P.

Chu, S.

Chu, Y.-J. L.

Y.-J. L. Chu, E. M. Jansson, and G. A. Swartzlander, Phys. Rev. Lett. 121, 063903 (2018).
[Crossref]

Ciolkowski, K. E.

K. E. Ciolkowski, Extension of Man into Outer Space (1921) [see also, Tsiolkovsky, K.E., Symposium Jet Propulsion, No. 2, United Scientific and Technical Presses, 1936].

Dziedzic, J. M.

Efendiev, M.

E. Popova, M. Efendiev, and I. Gabitov, Math. Methods Appl. Sci. 40, 1346 (2017).
[Crossref]

Fan, Z.

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Farn, M. W.

Forward, R. L.

R. L. Forward, J. Spacecr. Rockets 21, 187 (1984).
[Crossref]

Gabitov, I.

E. Popova, M. Efendiev, and I. Gabitov, Math. Methods Appl. Sci. 40, 1346 (2017).
[Crossref]

Georgiev, D.

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Glebov, L. B.

Gupta, S.

Haidner, H.

Heaton, A.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

Ilic, O.

O. Ilic and H. A. Atwater, Nat. Photonics 13, 289 (2019).
[Crossref]

Jansson, E. M.

Y.-J. L. Chu, E. M. Jansson, and G. A. Swartzlander, Phys. Rev. Lett. 121, 063903 (2018).
[Crossref]

Johnson, L.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

Johnson, M. H.

M. H. Johnson and E. Teller, Proc. Natl. Acad. Sci. USA 79, 1340 (1982).
[Crossref]

Kailath, T.

T. Kailath, Linear Systems (Prentice-Hall, 1980).

Kemp, N. H.

R. F. Weiss, A. N. Pirri, and N. H. Kemp, Astronaut. Aeronaut. 17, 50 (1979).

Kim, S. M.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Kipfer, P.

Kung, P.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Lalanne, P.

Landis, G. A.

G. A. Landis, in 46th International Astronautical Congress (IAF) (1995).

Laue, G.

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

Launois, H.

Loeb, A.

Z. Manchester and A. Loeb, Astrophys. J. Lett. 837, L20 (2017).
[Crossref]

Manchester, Z.

Z. Manchester and A. Loeb, Astrophys. J. Lett. 837, L20 (2017).
[Crossref]

Miller, K. A.

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Moeckel, W.

W. Moeckel, J. Spacecr. Rockets 9, 942 (1972).
[Crossref]

Orphee, J.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Pinson, R.

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

Pirri, A. N.

R. F. Weiss, A. N. Pirri, and N. H. Kemp, Astronaut. Aeronaut. 17, 50 (1979).

Popova, E.

E. Popova, M. Efendiev, and I. Gabitov, Math. Methods Appl. Sci. 40, 1346 (2017).
[Crossref]

Redding, J.

J. Redding, Nature 213, 588 (1967).
[Crossref]

Rotar, V.

Sarkissian, H.

Schamiloglu, E.

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Serak, S. V.

Shcherbakov, M. R.

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Shvets, G.

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Singh, G.

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Soleymani, S.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Sood, R.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Stork, W.

Streibl, N.

Swartzlander, G. A.

Y.-J. L. Chu, E. M. Jansson, and G. A. Swartzlander, Phys. Rev. Lett. 121, 063903 (2018).
[Crossref]

G. A. Swartzlander, J. Br. Interplanet. Soc. 71, 130 (2018).

G. A. Swartzlander, J. Opt. Soc. Am. B 34, C25 (2017).
[Crossref]

Tabiryan, N. V.

Teller, E.

M. H. Johnson and E. Teller, Proc. Natl. Acad. Sci. USA 79, 1340 (1982).
[Crossref]

Ullery, D. C.

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Weiss, R. F.

R. F. Weiss, A. N. Pirri, and N. H. Kemp, Astronaut. Aeronaut. 17, 50 (1979).

Wenner, B.

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Whorton, M.

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

Zeldovich, B. Y.

ACS Photon. (1)

Z. Fan, M. R. Shcherbakov, M. Allen, J. Allen, B. Wenner, and G. Shvets, ACS Photon. 5, 4303 (2018).
[Crossref]

Acta Astronaut. (1)

L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, Acta Astronaut. 68, 571 (2011).
[Crossref]

AIP Conf. Proc. (1)

E. Schamiloglu, C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, AIP Conf. Proc. 552, 559 (2001).
[Crossref]

Appl. Opt. (1)

Astronaut. Aeronaut. (1)

R. F. Weiss, A. N. Pirri, and N. H. Kemp, Astronaut. Aeronaut. 17, 50 (1979).

Astrophys. J. Lett. (1)

Z. Manchester and A. Loeb, Astrophys. J. Lett. 837, L20 (2017).
[Crossref]

Beamed Energy Propul. (1)

J. Benford and G. Benford, Beamed Energy Propul. 664, 303 (2003).
[Crossref]

J. Br. Interplanet. Soc. (1)

G. A. Swartzlander, J. Br. Interplanet. Soc. 71, 130 (2018).

J. Opt. Soc. Am. A (2)

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

J. Spacecr. Rockets (2)

W. Moeckel, J. Spacecr. Rockets 9, 942 (1972).
[Crossref]

R. L. Forward, J. Spacecr. Rockets 21, 187 (1984).
[Crossref]

Math. Methods Appl. Sci. (1)

E. Popova, M. Efendiev, and I. Gabitov, Math. Methods Appl. Sci. 40, 1346 (2017).
[Crossref]

Nat. Photonics (1)

O. Ilic and H. A. Atwater, Nat. Photonics 13, 289 (2019).
[Crossref]

Nature (1)

J. Redding, Nature 213, 588 (1967).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

Y.-J. L. Chu, E. M. Jansson, and G. A. Swartzlander, Phys. Rev. Lett. 121, 063903 (2018).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

M. H. Johnson and E. Teller, Proc. Natl. Acad. Sci. USA 79, 1340 (1982).
[Crossref]

Sci. Rep. (1)

D. C. Ullery, S. Soleymani, A. Heaton, J. Orphee, L. Johnson, R. Sood, P. Kung, and S. M. Kim, Sci. Rep. 8, 10026 (2018).
[Crossref]

Other (4)

T. Kailath, Linear Systems (Prentice-Hall, 1980).

K. E. Ciolkowski, Extension of Man into Outer Space (1921) [see also, Tsiolkovsky, K.E., Symposium Jet Propulsion, No. 2, United Scientific and Technical Presses, 1936].

G. A. Landis, in 46th International Astronautical Congress (IAF) (1995).

Breakthrough Starshot, “Breakthrough initiatives,” https://breakthroughinitiatives.org/ .

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Figures (5)

Fig. 1.
Fig. 1. Beam of full-width 2 w 0 is incident from the left on a sail composed of two diffractive panels A and B, each of length L . A payload of mass M p is attached to the sail by a boom of length D b and mass M b . Sail displacement and attitude with respect to the beam axis, x s and Θ . Forces on each panel are shown as F A and F B . Incident and diffracted wave vectors, k i , k m A , k m B .
Fig. 2.
Fig. 2. Relative power on panels A , B as a function of relative sail displacement x s / L for flattop (dark lines) and Gaussian (gray lines) beams having full-width 2 w 0 = L for angles of incidence: 0 ° and 10 ° .
Fig. 3.
Fig. 3. (a) Transverse force F x and (b) torque N y as a function of angle Θ and transverse displacement x s owing to radiation pressure from a (top) flattop and (bottom) Gaussian beam profile of power P 0 . Normalization, F 0 = 2 P 0 / c and N 0 = F 0 D b / 2 , where c is the speed of light and D b is the boom length. System parameters are listed in Table 1.
Fig. 4.
Fig. 4. Numerical solutions for a flattop beam with parameters listed in Table 1. (a) Phase plot and (b) frequency spectrum for transverse displacement, x s . (c) Phase plot and (d) frequency spectrum for attitude Θ . Undamped (black line) and critically damped (blue line) examples are shown.
Fig. 5.
Fig. 5. Numerical solutions for a Gaussian beam with parameters listed in Table 1. (a) Phase plot and (b) frequency spectrum for transverse displacement, x s . (c) Phase plot and (d) frequency spectrum for attitude Θ . Undamped (black line) and critically damped (blue line) examples are shown.

Tables (1)

Tables Icon

Table 1. Parameters and Values Used in Numerical Model

Equations (22)

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

sin θ m A , B = m A , B λ / Λ sin θ ,
I f ( p ) = ( P 0 / 4 w 0 2 ) cos Θ rect ( ( p cos Θ + x s ) / w 0 ) ,
I g ( p ) = P 0 2 w 0 2 π / 2 cos Θ exp ( 2 ( p cos Θ + x s ) 2 w 0 2 ) .
P A , B = ( P 0 / 2 w 0 ) ( w 0 x s ) , | x s | < w 0 ,
F A , B = F A , B ( p ) p ^ + F A , B ( n ) n ^ = ( P A , B / c ) ( κ A , B p ^ + Γ A , B n ^ ) ,
κ A , B = m A , B λ / Λ .
N A = 2 w 0 c 0 L I ( p ) d p ( D cm n ^ + p p ^ ) × ( κ A p ^ + Γ A n ^ ) ,
N B = 2 w 0 c L 0 I ( p ) d p ( D cm n ^ + p p ^ ) × ( κ B p ^ + Γ B n ^ ) ,
N A , B = P 0 2 w 0 c ( w 0 x s ) [ D cm κ A , B ( w 0 x s ) Γ A , B 2 cos Θ ] y ^ .
N = ( N A + N B ) y ^ = J Θ ¨ y ^ ,
F z = M z ¨ s = ( F A n + F B n ) cos Θ ( F A p + F B p ) sin Θ ,
F x = M x ¨ s = ( F A p + F B p ) cos Θ + ( F A n + F B n ) sin Θ .
z ¨ s = α K 1 Θ x s ,
x ¨ s = K 1 x s + K 2 Θ ,
Θ ¨ = K 3 x s + K 4 Θ ,
α = P 0 ( 1 + 1 κ A 2 ) / M c ,
K 1 = P 0 κ A / M c w 0 ,
K 2 = P 0 ( 1 + 1 κ A 2 ) / M c ,
K 3 = P 0 D b κ A / 2 w 0 J c + M K 2 / J ,
D cr = 2 w 0 ( 1 + 1 κ A 2 ) / κ A .
ϵ 1 , 2 = ω 0 2 [ 1 ± 1 Δ ] ,
| x s | / x cr + | Θ | / Θ cr < 1 ,