5858
OPTICS LETTERS / Vol. 39, No. 20 / October 15, 2014
Practical way to avoid spurious geometrical contributions in Brillouin light scattering experiments at variable scattering angles Andrea Battistoni,1,2,* Filippo Bencivenga,1 Daniele Fioretto,3 and Claudio Masciovecchio1 1
Sincrotrone Trieste S.C.p.A., S.S. 14 km 163, 5 in Area Science Park, I-34149 Basovizza, Italy 2
3
Dipartimento di Fisica, Università Degli Studi di Trieste, I-34127 Trieste, Italy
Dipartimento di Fisica e Geologia, Università Degli Studi di Perugia, Via Pascoli, I-06123 Perugia, Italy *Corresponding author: [email protected] Received June 19, 2014; accepted August 21, 2014; posted September 12, 2014 (Doc. ID 214424); published October 9, 2014
In this Letter, we present a simple method to avoid the well-known spurious contributions in the Brillouin light scattering (BLS) spectrum arising from the finite aperture of collection optics. The method relies on the use of special spatial filters able to select the scattered light with arbitrary precision around a given value of the momentum transfer (Q). We demonstrate the effectiveness of such filters by analyzing the BLS spectra of a reference sample as a function of scattering angle. This practical and inexpensive method could be an extremely useful tool to fully exploit the potentiality of Brillouin acoustic spectroscopy, as it will easily allow for effective Q-variable experiments with unparalleled luminosity and resolution. © 2014 Optical Society of America OCIS codes: (290.5830) Scattering, Brillouin; (330.6110) Spatial filtering; (300.6250) Spectroscopy, condensed matter; (290.5820) Scattering measurements; (050.2230) Fabry-Perot; (000.2170) Equipment and techniques. http://dx.doi.org/10.1364/OL.39.005858
Brillouin light scattering (BLS) spectroscopy is a longstanding hypersonic technique, widely used both for fundamental studies of different kind of dynamics (e.g., phonons [1], relaxation processes [2], and magnetic modes [3]) and for sophisticated technological applications, ranging from thin film characterization [4] to atmospheric survey [5]. Spontaneous BLS is a “photon in/photon out” method in which a monochromatic beam of frequency/wavevector ωin ; k⃗ in interacts with the sample, giving rise to a frequency ωout and wavevector k⃗ out distribution of scattered photons. Energy and momentum conservation allows us to express such a ⃗ ω] as a function of the energy distribution [IQ; (ℏω ℏωout − ℏωin ) and momentum (ℏQ⃗ ℏk⃗ out − ℏk⃗ in ) transferred to the sample’s excitations. ⃗ ω is usually determined as a In BLS experiments, IQ; ⃗ function of ω at a given Q-value, and it is typically featured by a quasi elastic (Rayleigh) peak centered at ω 0 and two symmetric side peaks, termed Brillouin doublet. The frequency shifts (Ω) and linewidths (Γ) of the latter are related to the frequencies and lifetimes ⃗ In isotropic of acoustic modes at the selected Q. ⃗ systems, the BLS spectrum only depends on Q jQj 2ns kin sinθ∕2 [6], where ns and θ are the refraction index of the sample and the scattering angle, respectively. Nowadays BLS is mainly used in two geometrical configurations, corresponding to θ 90° and θ 180° (or close to 180°). This limited range in θ is essentially due to the finite angular acceptance of collection optics, which simultaneously collect a finite distribution of scattering angles around the selected value. Such a distribution turns into a Q distribution (P Q ) with a characteristic extension (2ΔQ ) centered on the selected value (Q0 ). As shown in Fig. 1, as θ decreases, the relative Q-spread (2ΔQ ∕Q0 ) increases, mostly due to the decreasing of Q0 with sinθ∕2. This introduces an ineluctable artifact ⃗ ω, which results in a in the determination of IQ; 0146-9592/14/205858-04$15.00/0
weighted sum of spectra corresponding to the different ⃗ Q-values convoluted with the instrumental response function. Sophisticated experimental setups [7] and special data analysis procedures [8–10] have been proposed to cope with this issue. However, the former are not easily implementable in most BLS setups (mainly based on Fabry–Perot interferometers of the “Sandercock” type [11]), while the latter require ansatzes on the functional ⃗ which are not necessarily a dependency of Ω and Γ on Q, priori known. On the contrary, their determination is often the object of the experiment, in particular in studies focused on the acoustic dynamics of disordered systems [12–17]. In this Letter, we propose a simple and inexpensive approach that relies on the use of special spatial filters
Fig. 1. P Q profiles sampled by an optics of 0.25 numerical aperture at various values of θ (see legend). The full and dashed lines are the P Q profiles with and without a mask, respectively, with ΔQ 0.1 μm−1 . © 2014 Optical Society of America
October 15, 2014 / Vol. 39, No. 20 / OPTICS LETTERS
Fig. 2. Scattering from the sample (embedded in a cylindrical container) originates from O. k⃗ in and θ are the wavevector of incoming photons and the scattering angle, respectively, while the green cone is the locus of the k⃗ out vectors corresponding to the equal-Q scattering. The shape of the slit (highlighted in green) is determined by the intersection between the cone and the plane of the collection optics (highlighted in blue). The inset shows a 2 in. diameter mask designed with the following parameters: γ θ 30°, dM 10 cm, ds 3.5 mm, dq 1 mm, ns 1.33, nq 1.5, and ΔQ ∕Q0 3.7%. At λ 532 nm, this mask selects photons scattered by acoustic modes with Q-values in the 8.1 0.3 μm−1 range.
(hereafter referred to as “masks”) that are able to select the desired P Q profile in isotropic samples. Figure 2 shows the rationale of the mask’s design for an isotropic sample contained in a cylindrical holder with an axis orthogonal to the scattering plane and crossing the scattering volume. We assume that the scattering comes from a point-like source (O), chosen as the origin of a Cartesian x; y; z reference frame and corresponding to the intersection between the z axis (normal to the plane of collection optics) and k⃗ in [located in the y; zplane]; we further assume that the divergence of the incoming beam is negligible with respect to that of the scattered one. The locus of the kout vectors corresponding to the same Q-value is thus given by the surface of the cone having an axis k⃗ in and an angular aperture θ. The scattered photons with a given Q are located at the intersection between such a cone and the plane of the collection optics. Given a plane parallel to the one of the collection optics and placed at a distance dM ≤ f 2 from O (where f 2 is the distance between O and the plane of the collection optics), the intersection curve can be calculated from the following parametric equation, in which α ranges from −αm to αm (where αm depends on the geometry and is
OPTICS LETTERS / Vol. 39, No. 20 / October 15, 2014
Practical way to avoid spurious geometrical contributions in Brillouin light scattering experiments at variable scattering angles Andrea Battistoni,1,2,* Filippo Bencivenga,1 Daniele Fioretto,3 and Claudio Masciovecchio1 1
Sincrotrone Trieste S.C.p.A., S.S. 14 km 163, 5 in Area Science Park, I-34149 Basovizza, Italy 2
3
Dipartimento di Fisica, Università Degli Studi di Trieste, I-34127 Trieste, Italy
Dipartimento di Fisica e Geologia, Università Degli Studi di Perugia, Via Pascoli, I-06123 Perugia, Italy *Corresponding author: [email protected] Received June 19, 2014; accepted August 21, 2014; posted September 12, 2014 (Doc. ID 214424); published October 9, 2014
In this Letter, we present a simple method to avoid the well-known spurious contributions in the Brillouin light scattering (BLS) spectrum arising from the finite aperture of collection optics. The method relies on the use of special spatial filters able to select the scattered light with arbitrary precision around a given value of the momentum transfer (Q). We demonstrate the effectiveness of such filters by analyzing the BLS spectra of a reference sample as a function of scattering angle. This practical and inexpensive method could be an extremely useful tool to fully exploit the potentiality of Brillouin acoustic spectroscopy, as it will easily allow for effective Q-variable experiments with unparalleled luminosity and resolution. © 2014 Optical Society of America OCIS codes: (290.5830) Scattering, Brillouin; (330.6110) Spatial filtering; (300.6250) Spectroscopy, condensed matter; (290.5820) Scattering measurements; (050.2230) Fabry-Perot; (000.2170) Equipment and techniques. http://dx.doi.org/10.1364/OL.39.005858
Brillouin light scattering (BLS) spectroscopy is a longstanding hypersonic technique, widely used both for fundamental studies of different kind of dynamics (e.g., phonons [1], relaxation processes [2], and magnetic modes [3]) and for sophisticated technological applications, ranging from thin film characterization [4] to atmospheric survey [5]. Spontaneous BLS is a “photon in/photon out” method in which a monochromatic beam of frequency/wavevector ωin ; k⃗ in interacts with the sample, giving rise to a frequency ωout and wavevector k⃗ out distribution of scattered photons. Energy and momentum conservation allows us to express such a ⃗ ω] as a function of the energy distribution [IQ; (ℏω ℏωout − ℏωin ) and momentum (ℏQ⃗ ℏk⃗ out − ℏk⃗ in ) transferred to the sample’s excitations. ⃗ ω is usually determined as a In BLS experiments, IQ; ⃗ function of ω at a given Q-value, and it is typically featured by a quasi elastic (Rayleigh) peak centered at ω 0 and two symmetric side peaks, termed Brillouin doublet. The frequency shifts (Ω) and linewidths (Γ) of the latter are related to the frequencies and lifetimes ⃗ In isotropic of acoustic modes at the selected Q. ⃗ systems, the BLS spectrum only depends on Q jQj 2ns kin sinθ∕2 [6], where ns and θ are the refraction index of the sample and the scattering angle, respectively. Nowadays BLS is mainly used in two geometrical configurations, corresponding to θ 90° and θ 180° (or close to 180°). This limited range in θ is essentially due to the finite angular acceptance of collection optics, which simultaneously collect a finite distribution of scattering angles around the selected value. Such a distribution turns into a Q distribution (P Q ) with a characteristic extension (2ΔQ ) centered on the selected value (Q0 ). As shown in Fig. 1, as θ decreases, the relative Q-spread (2ΔQ ∕Q0 ) increases, mostly due to the decreasing of Q0 with sinθ∕2. This introduces an ineluctable artifact ⃗ ω, which results in a in the determination of IQ; 0146-9592/14/205858-04$15.00/0
weighted sum of spectra corresponding to the different ⃗ Q-values convoluted with the instrumental response function. Sophisticated experimental setups [7] and special data analysis procedures [8–10] have been proposed to cope with this issue. However, the former are not easily implementable in most BLS setups (mainly based on Fabry–Perot interferometers of the “Sandercock” type [11]), while the latter require ansatzes on the functional ⃗ which are not necessarily a dependency of Ω and Γ on Q, priori known. On the contrary, their determination is often the object of the experiment, in particular in studies focused on the acoustic dynamics of disordered systems [12–17]. In this Letter, we propose a simple and inexpensive approach that relies on the use of special spatial filters
Fig. 1. P Q profiles sampled by an optics of 0.25 numerical aperture at various values of θ (see legend). The full and dashed lines are the P Q profiles with and without a mask, respectively, with ΔQ 0.1 μm−1 . © 2014 Optical Society of America
October 15, 2014 / Vol. 39, No. 20 / OPTICS LETTERS
Fig. 2. Scattering from the sample (embedded in a cylindrical container) originates from O. k⃗ in and θ are the wavevector of incoming photons and the scattering angle, respectively, while the green cone is the locus of the k⃗ out vectors corresponding to the equal-Q scattering. The shape of the slit (highlighted in green) is determined by the intersection between the cone and the plane of the collection optics (highlighted in blue). The inset shows a 2 in. diameter mask designed with the following parameters: γ θ 30°, dM 10 cm, ds 3.5 mm, dq 1 mm, ns 1.33, nq 1.5, and ΔQ ∕Q0 3.7%. At λ 532 nm, this mask selects photons scattered by acoustic modes with Q-values in the 8.1 0.3 μm−1 range.
(hereafter referred to as “masks”) that are able to select the desired P Q profile in isotropic samples. Figure 2 shows the rationale of the mask’s design for an isotropic sample contained in a cylindrical holder with an axis orthogonal to the scattering plane and crossing the scattering volume. We assume that the scattering comes from a point-like source (O), chosen as the origin of a Cartesian x; y; z reference frame and corresponding to the intersection between the z axis (normal to the plane of collection optics) and k⃗ in [located in the y; zplane]; we further assume that the divergence of the incoming beam is negligible with respect to that of the scattered one. The locus of the kout vectors corresponding to the same Q-value is thus given by the surface of the cone having an axis k⃗ in and an angular aperture θ. The scattered photons with a given Q are located at the intersection between such a cone and the plane of the collection optics. Given a plane parallel to the one of the collection optics and placed at a distance dM ≤ f 2 from O (where f 2 is the distance between O and the plane of the collection optics), the intersection curve can be calculated from the following parametric equation, in which α ranges from −αm to αm (where αm depends on the geometry and is
