HAL Id: hal-03004741
https://hal.archives-ouvertes.fr/hal-03004741
Submitted on 23 Nov 2020
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Polarization-resolved second harmonic generation from LiNbO3 powders
Oswaldo Sánchez-Dena, Zacharie Behel, Estelle Salmon, Emmanuel Benichou, Jorge-Alejandro Reyes-Esqueda, Pierre-François Brevet, Christian Jonin
To cite this version:
Oswaldo Sánchez-Dena, Zacharie Behel, Estelle Salmon, Emmanuel Benichou, Jorge-Alejandro Reyes-
Esqueda, et al.. Polarization-resolved second harmonic generation from LiNbO3 powders. Optical
Materials, Elsevier, 2020, 107, pp.110169. �10.1016/j.optmat.2020.110169�. �hal-03004741�
Polarization-Resolved Second Harmonic Generation from LiNbO 3 Powders
1
O SWALDO S ÁNCHEZ -D ENA ,
2Z ACHARIE B EHEL ,
2E STELLE S ALMON ,
1J ORGE A LEJANDRO R EYES -E SQUEDA ,
2*P IERRE -F RANCOIS B REVET 2,
2C HRISTIAN J ONIN
1Instituto de Física, Universidad National Autónoma de México, Circuito de la Investigación Científica, Ciudad Universitaria, Delegación Coyoacán, C.P. 4510, Ciudad de México, México
2 Institut Lumière Matière, UMR CNRS 5306 et Université Claude Bernard Lyon 1, Université de Lyon, Campus LyonTech La Doua, Bâtiment Alfred Kastler, 10 Rue Ada Byron, 69622 Villeurbanne, France
*Corresponding author: [email protected]
Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX
We report a polarization resolved analysis of the second harmonic intensity collected in retro-reflection from a Lithium Niobate microcrystals powder. Depth intensity profiles exhibit first an increase due to the beam focus entering the powder then a decrease due to multiple scattering. With a polarization analysis performed at selected depths, we show that there is a competition between ballistic and multiply scattered photons. The contribution from the multiply scattered photons dominates at all depths whereas at the maximum of the intensity depth profiles, the ballistic photons contribution is at its own maximum due to enhanced collection efficiency. This latter contribution from the ballistic photons is clearly observed through distortions in the polarization resolved plots.
http://dx.doi.org/10.1364/OL.99.099999
Optical second harmonic generation (SHG), the process whereby two photons at a fundamental frequency ω are annihilated and a single photon at the harmonic frequency 2ω is created is routinely used in many laboratory applications for sample characterization and imaging. SHG indeed stands as a convenient tool for biological- sample three-dimensional imaging microscopy [1], surface adsorption and reconstruction characterization [2, 3] or the probing of complex ferroic domain patterns [4] just to mention a few out of all those possibly envisioned [5]. This variety of use is essentially due to its non-invasiveness and inherent sensitivity to interfaces. Much remain to be done nevertheless to transfer the technique out of the laboratory as a standard control method. In this
way, one avenue is to explore the SHG response from many different types of materials. Hence, within this context, polarization- resolved experiments have been performed in weakly scattering suspensions of metallic nanoparticles. In this case much can be retrieved from the nanoparticles, and in particular the fine details of the local and non-local origin of their SHG responses [6, 7] as well as the competition between the roles of size and shape revealing the nanoparticles topology [8]. In scattering suspensions though, when linear optical scattering processes must be accounted for besides the nonlinear SHG events, this analysis also sheds some light on the problem of photon transport in random media and more precisely the transition from ballistic to multiple scattering regimes [9].
In the context of powdered materials, standard strongly scattering media, recent experiments have proposed a new paradigm to study quantitatively the SHG efficiency with notable implications for pharmaceutical materials [10]. Powder SHG experiments are no longer secondary, as initially conceived by Kurtz and Perry [11], their technique being principally devised to the determination of the nonlinear second order susceptibilities of materials unavailable under large single crystals. Yet, another feature that makes SHG attractive nowadays is the possible tuning of the SHG intensity that arises from Lithium Niobate (LiNbO3, LN) powders that can be ascribed to the proper control of the powder chemical composition and grain size [12].
In this Letter, we perform depth profiles with polarization resolution of the SHG intensity from a powder stack of the non- centrosymmetric LN microcrystals. We show that polarization distortions occur as the beam focus is translated from air into the powder. These distortions are shown to result from the competition between the multiply scattered and ballistic photons contributions during the focus longitudinal translation.
The studied LN powders had a [Li]:[Nb]=50:50 stoichiometric chemical composition and were made of nanosized single crystals with an average size of 100 to 300 nm as calculated by the Rietveld refinement method. These nanosized crystals were forming larger particles or grains with average size of 2.26 ± 0.09 µm as determined by Scanning Electron Microscopy. Details on the synthesis and characterization of these powders can be found elsewhere [20]. Because of the multiple scattering character of the LN powders, instead of samples of hundreds of microns thick, thin layers prepared by gentle pressure with a microscope coverslip were sufficient. The LN powders were deposited on a glass coverslip and the surplus was removed by gently knocking an edge of the coverslip on which was supported the adhered powders. A femtosecond laser (Coherent, model MIRA 900) delivering 180 fs pulses at a repetition rate of 80 MHz with an average power of at most about 0.5 mW at the sample was then used to perform the SHG depth profiles. The fundamental wavelength was set at 800 nm for convenience and no resonance features were observed. The laser beam was then passed through a half-wave plate to select the linear input polarization angle, passed through a filter to reject any unwanted harmonic spurious light and then sent to a dichroic mirror to impinge from the top onto the powders that were themselves supported on a microscope coverslip of 130 µm thick.
Of note, the powder/substrate interface was never observed. The fundamental beam was focused with a 16× objective (Melles Griot, model Plan N, NA = 0.32) mounted on a vertical motorized translation stage (Thorlabs, model KMTS50E). The retro-reflected SHG light intensity was then first separated from the fundamental beam with the dichroic mirror and sent into the detection line. The latter was constituted with a filter for fundamental light rejection, an analyzer and a lens with focal length f = 5 mm focusing the harmonic beam on the entrance slit of a spectrometer (Spex, model 500M). A Andor DU440 CCD was used as the final detector. Depth profiles were performed at different location in the transverse plane and were all similar. A typical profile recorded is shown on Figure 1.
The maximum SHG intensity of the profile corresponds to the physical situation in which the fundamental laser beam focus is located at the air/powder interface.
Figure 1 : SHG intensity depth profile through a LN powder. (Disks) experimental points, (line) fit using Eq.(1), see text.
The SHG intensity profile shown in Fig. 1 was obtained with vertical steps of 2 µm. The exposure time of the Andor CCD was set to 1 s. The depth profile graph is close to symmetric but careful inspection shows that it results from the squared intensity profile of the translated focused fundamental Gaussian beam on the rising edge and multiple scattering in the powder on the decreasing edge
[9]. As a result, the profile was adjusted with the following expression :
= Γ + − − − Θ − ⁄ (1)
combining a Lorentzian profile of width Γ and maximum location with an exponential decrease of characteristic length l. The exponential decrease was turned on at = using the Heaviside step-function Θ − such that Θ − = 0 for ≤ and Θ − = 1 for > . For the profile given in Figure 1 after a depth shift to locate the intensity maximum at the air/powder interface at depth = 0, we found Γ = 0.066 mm. This length is simply the Rayleigh parameter of the beam after the focusing with the x16 objective. The characteristic length for the intensity decrease due to multiple scattering was found to be = 0.034 mm.
The latter characteristic length results from the photon loss at both the fundamental and the harmonic wavelength due to multiple scattering and as expected is rather short. Hence, the collected photons can have undergone the four following trajectories : (i) direct trajectories at both the fundamental and harmonic frequencies, (ii) direct trajectory at the fundamental frequency and multiple scattering at the harmonic one, (iii) multiple scattering at the fundamental frequency and direct trajectory at the harmonic one and finally (iv) multiple scattering at both the fundamental and harmonic frequencies. Only Case (i) corresponds to truly ballistic photons whereas Case (iii) is unlikely because scattering cross- sections increase with decreasing wavelength.
Polarization resolved experiments were then performed as a function of the penetration depth, see Figure 2.
(a) (b)
(c)
Figure 2 : Polar plots of the SHG intensity collected for different relative depths of the fundamental laser beam focus as a function of the fundamental angle of polarization. (blue) Vertical polarization, (red) Horizontal polarization. The relative depth is indicated on each plot.
At negative profile relative depths, the vertically and horizontally polarized SHG intensities are very similar, almost superposed, see Fig. 2a. At the maximum of the SHG intensity profile, at near zero relative depths, however, the two polarized SHG intensities differ
1.2
1.0
0.8
0.6
0.4
0.2
0.0
SHG Intensity /arb. units
-0.2 -0.1 0.0 0.1 0.2
Depth /mm
0 45 90
135
180
225
270 315
z = -0.06 mm
0 45 90
135
180
225
270 315
z = 0 mm
0 45 90
135
180
225
270 315
z = +0.05 mm
dramatically, see Fig.2b, whereas they almost superpose again at large positive relative depths again, see Fig.2c.
Linearly polarized incident light in disordered media is strongly depolarized due to the very large number of elastic scattering events. This is in fact the reason behind the Kurtz-Perry method, by far the most popular approach to investigate powders with SHG.
This theory disregards the polarization state of the fundamental wave and still provides reliable results to predict the SHG efficiency of materials [11]. As a result, the method is to provide averaged effective nonlinear coefficients for powders. On the other hand, a revision of the Kurtz-Perry method in which scattering effects are considered, shows that the measured SHG intensity remains unaffected by the depolarization effects at the fundamental frequency [15]. Polarization resolved SHG measurements on powders have therefore been essentially omitted so far. Several problems have nevertheless been identified where polarization can play a significant role. One of them is the enhanced coherent nonlinear backscattering (CBS) signal readily identified as a sharp peak in the angular distribution of the reflected SHG intensity from nonlinear and disordered media [16, 17]. Recently, a general framework based on Mueller matrices has thus been proposed for the SHG process in powders [18-20].
From all these considerations, it appears that the polar plots shown on Figs. 2(a-c) are built from the superposition of cases (ii) and (iv), namely the multiply scattered photons, and case (i), i.e. the ballistic photons. When the contribution from the multiply scattered photons dominates, the two-crossed polarization plots must be identical and circular because the polarization information is lost, as observed in Figs. 2(a) and 2(c). However, strong distortions are expected when the ballistic photons contribution is no longer negligible, see for instance Fig. 2(b). It appears that the latter case occurs at the maximum intensity of the depth profile.
Ballistic photons preserve their polarization state as they propagate because they do not undergo any linear scattering event. In order to support quantitatively this analysis, the ballistic photons contribution was modeled by an assembly of nonlinear dipoles distributed in a volume with a size of the order of the fundamental wavelength. LN nano-sized crystals were replaced with local nonlinear dipoles induced with a hyperpolarizability the symmetry of which derived from the bulk LN susceptibility tensor. Only the single dominating element d33 was therefore considered, the other elements being at least ten times weaker [21].
The SHG intensity collected in the back-scattered geometry was then computed as the sum of the amplitudes of the individual nonlinear dipoles. Retardation between all nonlinear dipoles is therefore accounted for. The corresponding polarization plots for such a nonlinear dipoles assembly is given in Figure 3. This polar plot is the result of a single calculation with 100 nonlinear dipoles but similar results were obtained for 10 000 dipoles as well for example. In particular, Fig. 3 exhibits a dramatic difference between the two crossed polarizations. A direct comparison with the experimental data, see Fig. 2(b) for instance, shows that indeed the two crossed polarization are different but also shows that the multiply scattered photons contributions still dominates. Hence, the total SHG intensity stems from the multiply scattered photons and to a lesser extent to the ballistic photons. This latter contribution almost vanishes for large positive and negative relative depths far from the intensity maximum of the depth profile reported in Fig. 1.
The ratio of the two contributions from these photons trajectories
is therefore modified by the geometrical configuration and in particular the location of the fundamental beam focus. When the beam focus is set at or very close to the air/powder interface, the configuration is optimized to collect the ballistic photons. With the beam focus positioned too far below or above, ballistic photons escape back-collection due to multiple scattering. As a result, only multiply scattered photons are back-collected.
Figure 3 : Theoretical polar plots of the crossed-polarized SHG intensity for 100 nonlinear dipoles randomly distributed in space as a function of the fundamental angle of polarization. (blue) Vertical polarization, (red) Horizontal polarization
In order to quantitatively evaluate the contribution of the ballistic photons to that of the multiply scattered ones, we therefore developed further the model as follows. The total SHG intensity
!,# , where Γ indicates the output polarization, $ the incident angle of polarization and Ω = 2ω is the SHG intensity, is written as :
!,# = )#+ ∑4,5 +,#cos0 $ − Φ# sin4 0 $ − Φ# (2)
i.e. as the superposition of a purely dipolar ballistic photons contribution described by the five intensity parameters +,# and a multiply scattered photons contribution described with a constant value )# due to its lack of polarization. The ballistic contribution is also defined by its resulting dipole orientation Φ# whereas the relative weight of the ballistic photons contribution is given by the ratio +4#⁄ +4#+ )# .
Figure 4 : Multiply scattered photons contribution )# to the total SHG intensity. (filled disks) Vertical polarization, (empty disks) Horizontal polarization
Under these considerations, it can also be demonstrated that parameters +# and +4# must be real positive as well as the parameter )# because they are intensities whereas the other
0 25 50 75 100 125 25
50 75 100 125
0 45 90
135
180
225
270
315
160x103 140 120 100 80 60 40 20
HRS Intensity / arb. units
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
Depth / mm
parameters may take a negative value. Likewise, we have also assumed that +4#> +#≈ 0 in agreement with the theoretical polar plots obtained, see Fig. 3. With this simple model, we are therefore in position to analyze quantitatively all polarization plots as a function of relative depth. Figure 4 shows the multiply scattered photons contribution )# determined whereas Figures 5 and 6 display the dipolar ballistic photons contribution angle Φ7 and the ratio +4#⁄+4#+ )#.
Figure 5 : Dipolar ballistic photons contribution angle Φ7. (filled disks) Vertical polarization, (empty disks) Horizontal polarization
As expected, because the interaction volume is displaced during the depth profile measurement, the population and resulting contribution from the nonlinear dipoles contributing to the SHG signal changes. Because these nonlinear dipoles corresponding to the nano-sized LN crystals possess a random orientation, the Φ7 angle is also random for the two crossed polarizations as expected, see Fig. 5.
The contribution of the ballistic photons given by the ratio +4#⁄+4#+ )# is provided on Figure 6.
Figure 6 : Ballistic photons contribution +4#⁄ +4#+ )# . (filled disks) Vertical polarization, (empty disks) Horizontal polarization
It appears that this contribution never exceeds about 30% of the total, a value reached at the maximum of the depth profile intensity, when the geometrical configuration to collect them is optimized.
Finally, we provide also an example of the dipolar ballistic photons contribution, obtained from Eq.(2) by removing of the multiply scattered photons contribution )#. We observe two crossed polarization dipolar patterns in agreement with the theoretical one shown on Fig. 3. Interestingly, the two lobes patterns are distorted as a result of retardation between the nonlinear dipoles due to the non negligible size of the interaction volume containing the LN powder grains.
In conclusions, we have reported the depth profile of the SHG intensity collected from an LN powder. The SHG intensity results from the superposition of the ballistic and multiply scattered
photons contributions. A simple model of a nonlinear dipole assembly allows us to quantitatively determine the contributions from the two photons populations, the signal being always dominated by the multiply scattered photons.
Figure 7 : Polar plot of the polarized ballistic photons contribution experimentally collected at relative depth z = 0.
It is further shown that it is possible to retrieve the polarized dipolar contribution of the ballistic photons, the multiply scattered photons contribution being unpolarized. This work paves the way for a close and quantitative investigation of the SHG response from nonlinear optical powders.
Acknowledgments. The authors acknowledge financial support from the ANR under contract ANR-17-CE24-RACINE.
References
1. W. P. Dempsey, S. E. Fraser, and P. Pantazis, BioEssays 34, 351 (2012).
2. P. F. Brevet, Surface Second Harmonic Generation (Presses polytechniques et universitaires romandes, 1997).
3. T. Verbiest, K. Clays, and V. Rodriguez, Second-Order Nonlinear Optical Characterization Techniques: An Introduction (CRC Press, 2009). Chap. 3.
4. J. Nordlander, G. De Luca, N. Strkalj, M. Fiebig, and M. Trassin, Appl. Sci. 8, 570 (2018).
5. A. Rogov, Y. Mugnier, and L. Bonacina, J. Opt. 17, 033001 (2015).
6. J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F.
Brevet, Phys. Rev. B 71, 165407 (2005).
7. I. Russier-Antoine, H. J. Lee, A. W. Wark, J. Butet, E. Benichou, C. Jonin, O. J.
F. Martin, and P. F. Brevet, J. Phys. Chem. C 122, 17447 (2018).
8. J. Duboisset and P.F. Brevet, J. Phys. Chem. C, 123, 25303 (2019).
9. N. Khebbache, A. Maurice, S. Djabi, I. Russiere-Antoine, C. Jonin, S. E.
Skipetrov, and P. F. Brevet, ACS Photonics 4, 262 (2017).
10. A. U. Chowdhury, S. Zhang, and G. J. Simpson, Anal. Chem. 88, 3853 (2016).
11. D. Wanapun, U. S. Kestur, L. S. Taylor, and G. J. Simpson, Anal. Chem. 83, 4745 (2011).
12. S. K. Kurtz and T. T. Perry, J. Appl. Phys 39, 3798 (1968).
13. O. Sánchez-Dena, E. V. García-Ramírez, C. D. Fierro-Ruíz, E. Vigueras- Santiago, R. Farías, and J. A. Reyes-Esqueda, Mater. Res. Express 4, 035022 (2017).
14. M. B. van der Mark, M. P. van Albada, and A Lagendijk, Phys. Rev. B 37, 3575 (1988).
15. C. M. Aegerter and G. Maret, “Coherent Backscattering and Anderson Localization,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009).
16. J. Aramburu, J. Ortega, C. L. Folcia, and J. Etxebarria, Appl. Phys. B 116, 211 (2014).
-150 -100 -50 0 50 100 150
Angle / degrees
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
Depth / mm
0.4
0.3
0.2
0.1
0.0
Ballistic Photons
-60x10-3 -40 -20 0 20 40
Depth / mm
0 20000400006000080000 20000
40000 60000 80000
0 45 90
135
180
225
270
315
17. V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, Phys. Rev. B 44, 4931 (1991).
18. G.J. Simpson, J. Phys. Chem. B, 120, 3281 (2016)
19. J.R.W. Ulcickas, G.J. Simpson, J. Phys. Chem. B, 123, 6643 (2019) 20. R.W. Boyd, Nonlinear Optics, Academic Press, New York, 2008, 3rd edition 21. X. Zhang, J. Li, F. Shi, Y. Xu, Z. Wang, R. A. Rupp, J. Xu, Opt. Lett. 35, 1746
(2010).
