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Research Papers

Optomechanics of Soft Materials

[+] Author and Article Information
Ruobing Bai

School of Engineering and Applied Sciences,
Kavli Institute for Bionano Science and Technology,
Harvard University,
Cambridge, MA 02138

Zhigang Suo

Fellow ASME
School of Engineering and Applied Sciences,
Kavli Institute for Bionano Science and Technology,
Harvard University,
Cambridge, MA 02138
e-mail: suo@seas.harvard.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 20, 2014; final manuscript received February 18, 2015; published online June 3, 2015. Assoc. Editor: Erik van der Giessen.

J. Appl. Mech 82(7), 071011 (Jul 01, 2015) (9 pages) Paper No: JAM-14-1592; doi: 10.1115/1.4030324 History: Received December 20, 2014; Revised February 18, 2015; Online June 03, 2015

Some molecules change shape upon receiving photons of certain frequencies, but here we study light-induced deformation in ordinary dielectrics with no special optical effects. All dielectrics deform in response to light of all frequencies. We derive a dimensionless number to estimate when light can induce large deformation. For a structure made of soft dielectrics, with feature size comparable to the wavelength of light, the structure shapes the light, and the light deforms the structure. We study this two-way interaction between light and structure by combining the electrodynamics of light and the nonlinear mechanics of elasticity. We show that optical forces vary nonlinearly with deformation and readily cause optomechanical snap-through instability. These theoretical ideas may help to create optomechanical devices of soft materials, complex shapes, and small features.

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Figures

Grahic Jump Location
Fig. 2

The Maxwell stress in the vacuum between two parallel plates of conductor separated by a narrow gap of vacuum. The applied voltage Φ induces electric charges ±Q on the two plates, as well as an electric field E and a Maxwell-stress field in the vacuum between the two plates. The Maxwell stress is a tensor with three principal components, tensile in the vertical direction, and compressive in the two horizontal directions. The three components have the same magnitude, ɛ0E2/2, where ɛ0 is the permittivity of the vacuum. The tensile Maxwell stress in the vertical direction causes the two plates to attract each other. This attractive electrostatic force is balanced by a mechanical force P.

Grahic Jump Location
Fig. 1

Optical forces cause motions of various kinds. (a) Optical tweezers trap a rigid particle and move it in a liquid. (b) A beam of light deforms the interface between two liquids. (c) Light in two waveguides causes an evanescent optical field in the space between the waveguides, and bends them. (d) Two beams of laser stretch a cell.

Grahic Jump Location
Fig. 3

Two antiparallel lasers deform a thin sheet of a soft dielectric. The refractive index is n in the dielectric, and nout in the outside medium. (a) In the undeformed state, the dielectric has the dimensions (L1,L2,L3). (b) In the deformed state, the dielectric deforms to the dimensions (l1,l2,l3). The electromagnetic fields of the left and right lasers are (EL,HL) and (ER,HR), respectively. The lasers generate the Maxwell stress in the dielectric and outside. (c) The Maxwell stress causes equivalent mechanical stress acting on the dielectric.

Grahic Jump Location
Fig. 6

Maxwell stresses in a dielectric optically mismatched with the outside. Because 〈T2〉=-〈T1〉, only 〈T1〉 and 〈T3〉 are plotted. (a) When l3 = Λ, both 〈T1〉 and 〈T2〉 average to zero, but 〈T3out〉≠〈T3〉. (b) When l3 = 1.5Λ, all three components of the optical force vanish.

Grahic Jump Location
Fig. 7

Deformation induced by optical forces in a dielectric optically mismatched with the outside. (a) The out-of-plane stretch changes with the amplitude of the optical field. At l3 = Λ, the optical mismatch gives rise to a nonzero optical force, so that the deformation is maintained by a finite amplitude of the optical field, E0. By contrast, at l3 = 1.5Λ, all components of the optical force vanish, so that the deformation cannot be maintained by an optical field of finite amplitude. (b) and (c) The in-plane stretches as functions of the out-of-plane stretch. (d) When the dielectric and the outside are optically mismatched, 〈T3out〉≠〈T3〉 in general, and the out-of-plane component of the optical force deforms the dielectric even when L3/Λ→∞.

Grahic Jump Location
Fig. 4

Deformation induced by optical forces in a dielectric optically matched to the outside. Λ is the wavelength of the laser inside the dielectric. (a) The out-of-plane stretch as a function of the amplitude of the input optical field. When the thickness of the deformed dielectric, l3, approaches the multiples of the half wavelength, 0.5Λ,1.0Λ,1.5Λ…, all components of the optical force approach zero, so that amplitude of the input optical field, E0, becomes larger and larger to maintain the deformation. (b) and (c) The in-plane stretches as functions of the out-of-plane stretch. (d) The stretches depend on the thickness of the undeformed dielectric, L3.

Grahic Jump Location
Fig. 5

Optomechanical snap-through instability. (a) A thin sheet of dielectric is placed in the optical field of two antiparallel lasers. The dielectric is clamped at the top and bottom, and is pulled by a mechanical force f in the vertical direction. (b) In the presence of the optical field, the force–displacement curve is not monotonic, leading to a snap-through instability.

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