Shear Brillouin light scattering microscope Moonseok Kim,1,2 Sebastien Besner,1 Antoine Ramier,1,3 Sheldon J. J. Kwok,1,3 Jeesoo An,1 Giuliano Scarcelli,1,4 and Seok Hyun Yun1,3,* 1

Harvard Medical School and Wellman Center for Photomedicine, Massachusetts General Hospital, Cambridge, MA 02139, USA 2 Department of Physics, Korea University, Seoul 136-701, South Korea 3 Harvard-MIT Health Sciences and Technology, Cambridge, MA 02139, USA 4 The Fischell Department of Bioengineering, University of Maryland, College Park, MD 20742, USA *[email protected]

Abstract: Brillouin spectroscopy has been used to characterize shear acoustic phonons in materials. However, conventional instruments had slow acquisition times over 10 min per 1 mW of input optical power, and they required two objective lenses to form a 90° scattering geometry necessary for polarization coupling by shear phonons. Here, we demonstrate a confocal Brillouin microscope capable of detecting both shear and longitudinal phonons with improved speeds and with a single objective lens. Brillouin scattering spectra were measured from polycarbonate, fused quartz, and borosilicate in 1-10 s at an optical power level of 10 mW. The elastic constants, phonon mean free path and the ratio of the Pockels coefficients were determined at microscopic resolution. ©2016 Optical Society of America OCIS codes: (290.5830) Scattering, Brillouin; (300.6190) Spectrometers.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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1. Introduction Brillouin scattering spectroscopy is a useful technique for noncontact and nondestructive measurements in material sciences [1–4], mineralogy [5,6] and biology [7]. The acoustic and thermodynamic properties of a material can be determined from the spectrum of Brillouin light scattering resulting from the phase-matched interaction of an incident light and the acoustic phonons in the sample [8–10]. The complete stiffness tensor of a material can be characterized by measuring Brillouin scattering from both longitudinal and shear phonons along the principal axis of symmetry of a material [11]. The technique has been used to characterize various polymers and optical glass [12–15]. In previous studies, multi-pass Fabry-Perot interferometers [16], optical beating instruments [17], or scanning-grating monochromators [18] are employed due to their high spectral resolution and extinction ratio. However, a single spectral analysis of shear Brillouin light scattering typically requires more than a few minutes due to the slow data acquisition speeds of these instruments. Faster acquisition of a few seconds was demonstrated by the use of angle-dispersive Fabry-Perot interferometry at an optical power of 100-200 mW in quartz [19–21]. However, this approach achieves the data acquisition speed only at the expense of the spectral resolution, as the throughput efficiency is inversely proportional to the Finesse (F). We have previously demonstrated a non-scanning Brillouin spectrometer using virtuallyimaged phased array (VIPA) etalons [9,22,23]. The ability to acquire all spectral components simultaneous with minimal incident loss owing to the special coating of VIPA tremendously increased data acquisition speed without the loss of spectral resolution. This innovation has enabled measurement of the age-related stiffening in the crystalline lens [24], in situ and in vivo mapping of the longitudinal modulus of the human cornea [25,26]. However, the instruments based on this parallel spectrometer have so far been configured to collect near 180° back scattering. With the back scattering measurement, the magnitude of Brillouin scattering from shear phonons in isotropic materials vanishes. Therefore, the previous Brillouin microscopes are suited only for the measurements of longitudinal phonons.

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Received 14 Oct 2015; revised 7 Dec 2015; accepted 13 Dec 2015; published 6 Jan 2016 11 Jan 2016 | Vol. 24, No. 1 | DOI:10.1364/OE.24.000319 | OPTICS EXPRESS 320

Here, we describe an off-axis confocal microscope that is capable of measuring both longitudinal and shear Brillouin scattering and offers high acquisition speed by employing a two-stage VIPA spectrometer. The off-axis beam geometry allows a single objective lens with high numerical aperture (NA) to be used for both illumination and collection. In comparison with traditional approaches using two lenses to achieve a 90° scattering angle between the input and scattered beams, our approach offers a more simple and convenient approach that is well-suited for high-resolution microscopy. The polarization state of the scattered light from shear phonons is orthogonal to the input polarization state where as the longitudinal Brillouin scattering maintains the polarization state. Therefore, polarization-based filtering allowed us to discriminate shear and longitudinal Brillouin signals. We achieved a reduction in data acquisition time by more than an order-of-magnitude compared to previous measurement of shear phonons using scanning Fabry-Perot interferometers. 2. Theoretical background Spontaneous Brillouin scattering is a process in which light is inelastically scattered via phase-matched interaction with acoustic phonons: either by receiving energy from thermally activated acoustic waves (Stokes) or by giving energy to acoustic waves (anti-Stokes). The acoustic waves (phonons) in a medium cause local fluctuations of density and pressure, and the resulting spatial variation of refractive index causes light scattering. Because such waves are not static but propagate inside the material, the scattered light also experiences a frequency shift Ω B given by ΩB =

2nv

θ

(1)

sin( ) 2 λ

where n is the refractive index of the medium, v is the velocity of the acoustic wave, λ is the wavelength, and θ is the angle between the incident and scattered beams. The Brillouin shifts are in the order of a few GHz for visible light in backward (θ = 180°) or right-angle (θ = 90°) scattering. The acoustic velocity can be related to the mechanical properties of the material. The mechanical properties of the material are generally described by a stiffness tensor, Cijkl commonly written as a 6 × 6 matrix Cmn. In the case of isotropic materials, the stiffness tensor reduces to two independent components: longitudinal modulus M = c11 and shear modulus G = c44. Similarly, the acoustic modes of isotropic solids are either longitudinal (velocity vL) or shear (velocity vS). The acoustic velocities and elastic constants are related by:

ρ vL2 = M , ρ vS2 = G.

(2)

where ρ is the density. Therefore, the Brillouin spectrum of a homogeneous isotropic material has two peaks corresponding to the longitudinal and shear phonons, respectively. The magnitude of shear Brillouin scattering in isotropic materials is zero in backscattering angle of θ = 180°. To observe shear Brillouin peaks, an appropriate scattering angle, θ ≠180° is required. For 90° scattering, the differential scattering cross section [27] is expressed as: dσ dΩ

VV

 k T π 2ε 4V  p 2 =  B 4 s  122  2λ ρ  vL

(3)

for the longitudinal acoustic phonons, and dσ dΩ

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VH

 k T π 2ε 4V = B 4 s  2λ ρ

2  p44  2  2vS

(4)

Received 14 Oct 2015; revised 7 Dec 2015; accepted 13 Dec 2015; published 6 Jan 2016 11 Jan 2016 | Vol. 24, No. 1 | DOI:10.1364/OE.24.000319 | OPTICS EXPRESS 321

for the shear phonons, where k B is Boltzmann’s constant, T is the absolute temperature, ∈ is the dielectric permittivity, Vs is the scattering volume, and pij are the Pockels elasto-optic coefficients. Here, the subscript VV indicates that the polarization states of the input and scattered waves are both vertical to the scattering plane (i.e. s-pol), and VH indicates that the polarization state of the scattered wave is horizontal (p-pol)—orthogonal to the input polarization. From (3) and (4), the magnitude ratio of shear and longitudinal Brillouin scattering is given by 2

I S  vS   p44  =    I L  vL   p12 

2

(5)

The ratio of the Pockels coefficients, (p44/p12)2, ranges from 0.01 in solid materials with high mechanical strength to 0 in liquids. Since (p44/p12)2

Shear Brillouin light scattering microscope.

Brillouin spectroscopy has been used to characterize shear acoustic phonons in materials. However, conventional instruments had slow acquisition times...
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