Abstract

Electromagnetic momentum is a fundamental physical concept that has been demonstrated experimentally and incorporated theoretically in various areas of physics. In spite of the weak character of the electromagnetic momentum transfer process, the combination of latter-day, high-energy laser light sources and microminiature mechanical elements suggested the possibility of optical excitation of these structures. One outcome of the present theoretical analysis is the prediction of an optopiezic effect wherein electromagnetic momentum causes a mechanical stress on a dielectric layer. If this is a valid prediction, such an optically induced, expansional pressure effect could be utilized as an extensional optical-to-mechanical transduction means.

© 1997 Optical Society of America

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References

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  1. J. H. Poynting, “Radiation pressure,” London Edinburgh Dublin Philos. Mag. J. Sci. 9, 393–406 (1905).
  2. G. E. Henry, “Radiation pressure,” Sci. Am. 196, 99–108 (1957).
  3. F. E. Borgnis, “Acoustic radiation pressure of plane compressional waves,” Rev. Mod. Phys. 25, 653–664 (1953).
    [CrossRef]
  4. E. J. Post, “Radiation pressure and dispersion,” J. Acoust. Soc. Am. 25, 55–60 (1953).
    [CrossRef]
  5. B. Halg, “On a nonvolatile memory cell based on micro-electro-mechanics,” in Proceedings of IEEE Micro Electro Mechanical Systems: An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 172–176.
  6. R. K. Wangsness, Electromagnetic Fields (Wiley, New York, 1986), p. 425.
  7. H. Minkowski, Nachr. Ges. Wiss. Gottingen, 53 (1908).
  8. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 51.
  9. P. Mulser, “Radiation pressure on macroscopic bodies,” J. Opt. Soc. Am. B 2, 1814–1829 (1985).
    [CrossRef]
  10. R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London, Ser. A 347, 475–491 (1976).
    [CrossRef]
  11. H. M. Lai, W. M. Suen, and K. Young, “Microscopic derivation of the force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
    [CrossRef]
  12. M. Abraham, Rend. Circ. Mat. Palermo 28, 1 (1909); 30, 33 (1910).

1985

1982

H. M. Lai, W. M. Suen, and K. Young, “Microscopic derivation of the force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

1976

R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London, Ser. A 347, 475–491 (1976).
[CrossRef]

1953

F. E. Borgnis, “Acoustic radiation pressure of plane compressional waves,” Rev. Mod. Phys. 25, 653–664 (1953).
[CrossRef]

E. J. Post, “Radiation pressure and dispersion,” J. Acoust. Soc. Am. 25, 55–60 (1953).
[CrossRef]

Borgnis, F. E.

F. E. Borgnis, “Acoustic radiation pressure of plane compressional waves,” Rev. Mod. Phys. 25, 653–664 (1953).
[CrossRef]

Lai, H. M.

H. M. Lai, W. M. Suen, and K. Young, “Microscopic derivation of the force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

Mulser, P.

Peierls, R.

R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London, Ser. A 347, 475–491 (1976).
[CrossRef]

Post, E. J.

E. J. Post, “Radiation pressure and dispersion,” J. Acoust. Soc. Am. 25, 55–60 (1953).
[CrossRef]

Suen, W. M.

H. M. Lai, W. M. Suen, and K. Young, “Microscopic derivation of the force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

Young, K.

H. M. Lai, W. M. Suen, and K. Young, “Microscopic derivation of the force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

J. Acoust. Soc. Am.

E. J. Post, “Radiation pressure and dispersion,” J. Acoust. Soc. Am. 25, 55–60 (1953).
[CrossRef]

J. Opt. Soc. Am. B

Phys. Rev. A

H. M. Lai, W. M. Suen, and K. Young, “Microscopic derivation of the force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

Proc. R. Soc. London, Ser. A

R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London, Ser. A 347, 475–491 (1976).
[CrossRef]

Rev. Mod. Phys.

F. E. Borgnis, “Acoustic radiation pressure of plane compressional waves,” Rev. Mod. Phys. 25, 653–664 (1953).
[CrossRef]

Other

J. H. Poynting, “Radiation pressure,” London Edinburgh Dublin Philos. Mag. J. Sci. 9, 393–406 (1905).

G. E. Henry, “Radiation pressure,” Sci. Am. 196, 99–108 (1957).

B. Halg, “On a nonvolatile memory cell based on micro-electro-mechanics,” in Proceedings of IEEE Micro Electro Mechanical Systems: An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 172–176.

R. K. Wangsness, Electromagnetic Fields (Wiley, New York, 1986), p. 425.

H. Minkowski, Nachr. Ges. Wiss. Gottingen, 53 (1908).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 51.

M. Abraham, Rend. Circ. Mat. Palermo 28, 1 (1909); 30, 33 (1910).

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Figures (11)

Fig. 1
Fig. 1

Optical interaction with dielectric layer.

Fig. 2
Fig. 2

Strain and momentum diagram.

Fig. 3
Fig. 3

Surface momentum transfers for quarter-wave layer.

Fig. 4
Fig. 4

Optically transferred momenta for quarter-wave layer.

Fig. 5
Fig. 5

Optically induced strains for quarter-wave layer.

Fig. 6
Fig. 6

Energy diagram.

Fig. 7
Fig. 7

Modified energy diagram.

Fig. 8
Fig. 8

Modified strain and momentum diagram.

Fig. 9
Fig. 9

Surface momentum transfers.

Fig. 10
Fig. 10

Optically induced strains.

Fig. 11
Fig. 11

Mechanical spring model of the optopiezic effect.

Equations (63)

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g=μ0ε0S=S/c2,
g=μεS=S/ν2,
GI=gIcos ϕΔτ=SIcos ϕΔtΔW cos ϕ/c
GR=gRcos ϕΔτ=SRcos ϕΔtΔW cos ϕ/c,
GT=gTcos ϕΔτ=STcos ϕΔtΔW cos ϕ/c
Gα=gαcos ΦΔτn=Sαcos ΦΔtΔW cos Φ/ν,
Gβ=gβcos ΦΔτn=Sβcos ΦΔtΔW cos Φ/ν,
ΔGfront=ΔtΔWcos ϕcSI cos ϕ-cos ΦνSα cos Φ-cos ΦνSβ cos Φ-cos ϕcSR cos ϕ,
ΔGback=ΔtΔWcos ΦνSα cos Φ-cos ϕcST cos ϕ-0-cos ΦνSβ cos Φ
P(pressure)=F(force)ΔW=ΔGnormal/ΔtΔW.
Pfront=SIccos2 ϕ+SRccos2 ϕ-Sανcos2 Φ-Sβνcos2 Φ,
Pback=Sανcos2 Φ+Sβνcos2 Φ-STccos2 ϕ.
SR/SI=|ER/EI|2R,
ST/SI=|ET/EI|2T.
Sα/SI=n|Eα/EI|2nA,
Sβ/SI=n|Eβ/EI|2nB.
Pfront=(SI/c)[(1+R)cos2 ϕ-n2(A+B)cos2 Φ],
Pback=(SI/c)[n2(A+B)cos2 Φ-T cos2 ϕ].
R=(n2-cos2 ϕ)2 sin2 δ(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ,
T=(2n cos ϕ)2(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ,
ATE=(n+cos ϕ)2 cos2 ϕ(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ;
n=n cos Φ,
ATM=1n2(n+cos ϕ)2 cos2 ϕ(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ;
n=cos Φn,
BTE=(n-cos ϕ)2 cos2 ϕ(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ;
n=n cos Φ,
BTM=1n2(n-cos ϕ)2 cos2 ϕ(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ;
n=cos Φn.
PPfront+Pback=(SI/c)[(1+R-T)cos2 ϕ]=2R(SI/c)cos2 ϕ;
σPfront-Pback=2(SI/c)[cos2 ϕ-n2(A+B)cos2 Φ].
ε(strain)=σ/2Γ,
(A+B)TE=1-RTE2n2 cos2 Φ+cos2 ϕn2 cos2 Φ,
(A+B)TM=1-RTM2cos2 Φ+n2 cos2 ϕn2 cos2 Φ.
σTE=(SI/c)[2 cos2 ϕ-(1-RTE)×(n2 cos2 Φ+cos2 ϕ)],
σTM=(SI/c)[2 cos2 ϕ-(1-RTM)×(cos2 Φ+n2 cos2 ϕ)].
RTE=RTMR0=(n2-1)2 sin2 δ(2n)2+(n2-1)2 sin2 δ.
σ0(Pfront-Pback)0=(SI/c)[-(n2-1)+(n2+1)R0],
P0=2R0 SIc.
R0,(m+1)π/2=(n2-1)2(n2+1)2,
σ0,(m+1)π/2(Pfront-Pback)0,(m+1)π/2=-2SIc(n2-1)(n2+1).
P0,(m+1)π/2=2SIc(n2-1)(n2+1)2.
R0,mπ=0,
σ0,mπ(Pfront-Pback)0,mπ=(SI/c)[-(n2-1)],
T=f2(2n cos ϕ)2(2n cos ϕ)2+(n2-cos2 ϕ)2 sin2 δ=f2(1-R)
gAbraham=1c2E×H=Sc2=1n2*gMinkowski,
g=1/2[n2+1-1/3(n2-1)2]S/c2
g=1/2[n2+1-1/5(n2-1)2]S/c2gS/c2,
Pfront=(SI/c)[(1+R)cos2 ϕ-g(A+B)cos2 Φ],
Pback=(SI/c)[g(A+B)cos2 Φ-T cos2 ϕ].
P=SIc{[1-f2+R(1+f2)]cos2 ϕ}2R SIccos2 ϕ,
σ=SIc{[1+f2+R(1-f2)]cos2 ϕ-2g(A+B)cos2 Φ}2 SIc[cos2 ϕ-g(A+B)cos2 Φ].
P=SIc2R=p=UmAδ,
SI(W/m2)=c UmAδ2R.
SIc2R=Um/Aδ
Um=kδ22=mν22,
δ=νmk=νω
SIc2R=Umω/Aν.
2k1x1+k3(x1-x2)-F1=0
2k2x2-k3(x1-x2)-F2=0,
-F3-F4=-2(k1x1+k2x2)=-F1-F2.
x1-x2=(F1-F2)/2k1+k3.
σPfront-Pback,
W=F1x1+F2x2=[(F1+F2)/2]2k1+[(F1-F2)/2]2k3+k1.

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