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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 12 — Jun. 7, 2010
  • pp: 12298–12303
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Giant enhancement of second-harmonic generation in multiple diffraction orders from sub-wavelength resonant waveguide grating

A. Saari, G. Genty, M. Siltanen, P. Karvinen, P. Vahimaa, M. Kuittinen, and M. Kauranen  »View Author Affiliations


Optics Express, Vol. 18, Issue 12, pp. 12298-12303 (2010)
http://dx.doi.org/10.1364/OE.18.012298


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Abstract

We demonstrate a purely dielectric resonant waveguide structure that enhances the efficiency of second-harmonic generation by a factor of at least 5500 compared to a flat reference surface in the same geometry. We also show that the structure emits second-harmonic radiation in four different directions when the sample is illuminated with fundamental radiation incident at the resonant angle of the sample.

© 2010 OSA

1. Introduction

Structural details that are smaller than wavelength of light can give rise to strongly enhanced local electric fields and very sharp resonances. Resonant waveguide gratings (RWG) [1

1. R. Magnusson and S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]

,2

2. D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997). [CrossRef]

] constructed from all-dielectric, low-loss materials are one example of such sub-wavelength structures. A RWG consists of a surface waveguide, which is lossy due to a surface grating diffracting light both in and out of the waveguide mode. On resonance, the fields diffracted out of the waveguide mode interfere with the transmitted and reflected fields in such a way that it is theoretically possible to achieve 100% reflection [1

1. R. Magnusson and S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]

]. Simultaneously, the field strengths in the waveguide mode can be significantly enhanced. RWGs can thus provide efficient and convenient coupling of freely propagating laser beams to nanosized structures and waveguide modes while avoiding problems such as those arising from tight focusing.

Due to their unique characteristics, RWGs are commonly used as narrow bandpass filters or selective mirrors [3

3. P. Priambodo, T. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003). [CrossRef]

7

7. S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, “Theoretical analysis on the tuning dynamics of the waveguide-grating structures,” Opt. Express 17(2), 426–436 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-2-426. [CrossRef] [PubMed]

]. In filter use, the strongest local fields are often inside the grating material and the enhanced field is not used directly. Instead, an effort to minimize the enhancement can be beneficial to, e.g., decrease the damage threshold [8

8. T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008). [CrossRef]

]. However, designing the RWG using, e.g., deep grooves so that the local field is both strong and accessible at the surface, can lead to applications such as improved fluorescence detection [9

9. P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt. 46(12), 2351–2360 (2007). [CrossRef] [PubMed]

,10

10. P. Karvinen, T. Nuutinen, J. Rahomäki, O. Hyvärinen, and P. Vahimaa, “Strong fluorescence-signal gain with single-excitation-enhancing and emission-directing nanostructured diffraction grating,” Opt. Lett. 34(20), 3208–3210 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-20-3208. [CrossRef] [PubMed]

]. In particular, the high enhancement of the local fields at the surface of the RWG is interesting for nonlinear optical effects, which scale with a high field intensity, as can also occur in a total-internal-reflection geometry [11

11. B. U. Felderhof, A. Bratz, G. Marowsky, O. Roders, and F. Sieverdes, “Optical second-harmonic generation from adsorbate layers in total-reflection geometry,” J. Opt. Soc. Am. B 10(10), 1824–1833 (1993). [CrossRef]

].

2. Experiments

The present sample was designed for optimum coupling into the waveguide mode of p-polarized light at the fundamental wavelength of 1064 nm and for a resonance angle of incidence of about 21°. These parameters were chosen because the surface nonlinearity of the sample has a strong out-of-plane nature and the nonlinear response is therefore expected to be particularly enhanced for p-polarized fundamental radiation. The local field enhancement resulting from the grating resonance was thus optimized for this particular polarization on the basis of numerical calculations and rigorous diffraction theory. The theoretically calculated linear transmission as a function of the incident angle is shown in Fig. 1
Fig. 1 (a) Theoretically calculated transmission of the RWG at 1064 nm as a function of incident angle, (b) scanning electron microscope image of the RWG, and (c) calculated time-average energy density in the RWG (delimited by the white lines) at 1064 nm.
.

The period of the grating is 580 nm and the depth of the grooves is 237 nm. The thickness of the TiO2 coating is 237 nm on top of the grooves and 60% and 30% of that on the bottom of the grooves and on the sidewalls, respectively. The calculation of the local field [see Fig. 1(b)] reveals that its energy density can be enhanced by a factor exceeding 200 in certain areas of the grating structure compared to the field in free space. Although the strongest field is located at the sharp grating corners, the actual structure exhibits rounded corners, which decrease the field strength at these locations. Beyond the corners, the strongest local fields appear in the TiO2 layer and at the air-TiO2 interface throughout the structure. While the TiO2 layer may give rise to quadrupolar bulk nonlinearities [13

13. F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8704. [CrossRef] [PubMed]

], the air-TiO2 interface is favorable for the coupling with the surface nonlinearity arising from the broken centrosymmetry of the interface. Although one cannot separate the bulk and surface contribution to the nonlinearity, we expect the bulk contribution to be significantly smaller than that of the interfaces. The enhancement factor of 200 means that the intensity of the SH signal generated from the grating could ideally be over four orders of magnitude larger than from a flat surface. This estimation is simply based on the local field enhancement. For a more detailed analysis, one should account for the coupling of the radiation fields (at the fundamental and harmonic frequency) to the local fields, the locally varying nonlinearity and the local nonlinear sources.

Our structure has a sub-wavelength period for a fundamental wavelength of 1064 nm. Therefore, only zero diffraction orders in transmission and reflection can propagate in air, although the waveguide mode propagates within the structure. The period is, however, larger than the SH wavelength of 532 nm. As a consequence, SH light can be emitted also into non-zero diffraction orders. From momentum conservation along the surface and taking into account the additional momentum induced by the grating, we find that the possible magnitudes of the in-plane wave vectors of SH light are given by
n2sinθm=n1sinθi+m(λ/a),
(1)
where m is the diffraction order, subscripts i and m refer to the angles of incident and diffracted plane waves, respectively. The wavelength λ corresponds to that of the SH and a is the period of the grating. Here, n 1 and n 2 are the indices of refraction of the medium in which the fundamental and SH beams propagate, respectively. In the present case light propagates in air and n 1 and n 2 are equal to 1. From this it follows that only the reflected and transmitted diffraction orders m = 0 and m = −1 can propagate and we should therefore observe SH light in four different directions as illustrated in Fig. 2(a)
Fig. 2 (a) Directions of the SH light diffracted by the RWG. T 0 (T -1) and R 0 (R -1) represent the directions of the transmitted and reflected 0 (−1) order. The direction of the incident fundamental beam is marked in red and the normal to the surface with the dashed line. (b) Experimental setup. λ/2: half-wave plate, Vis-block: filter blocking any visible radiation from the laser, IR-filter: filter blocking any IR radiation from the RWG, PMT: photomultiplier.
.

A schematic of the experimental setup is shown in Fig. 2(b). The RWG was placed in a computer-controlled rotation mount which allows the SH signal to be measured as a function of the angle of incidence, thereby allowing the angle to be optimized for maximum SH radiation. The sample was illuminated with a pulsed Nd:YAG laser operating at 1064 nm and producing pulses of 70 ps duration. This fundamental beam was linearly polarized using a Glan-polarizer. Special care was taken in order to minimize the beam divergence which may decrease the coupling efficiency into the waveguide mode. The laser spot on the sample surface had a diameter of ~1 mm. The beam was subsequently filtered to remove all possible SH light that might be generated by the optics before the sample. In this way, the radiation incident onto the sample was purely at the fundamental wavelength and p-polarized. A photomultiplier tube for the detection of SH light was placed at the end of a computer-controlled rotating arm, thus making it possible to detect SH light over the whole 360° range. The fundamental wavelength was filtered out after the RWG and another Glan-polarizer was used to polarize the SH light along the p-direction before detection with a photomultiplier tube. The detector area was limited by a 200 µm wide slit, which is significantly narrower than the beam diameter at the detector allowing for better resolution of the SHG signals.

3. Results and discussion

We first determined the resonance angle for maximum SH enhancement by detecting the transmitted 0 diffraction order while changing the angle of incidence. The resonance was found to occur at the 21.98° angle of incidence, close to the design target of 21°.

We subsequently investigated the directions in which SH light is emitted by the RWG sample and compared them with those predicted by diffraction theory. For this purpose, the detection arm was rotated over the whole 360° range in the plane of incidence while keeping the angle of incidence fixed at the 21.98° resonance. The detected SHG intensity as a function of the detection angle is shown in Fig. 3
Fig. 3 Second harmonic vs. detection angle. The 0° angle corresponds to the normal to the RWG. T 0 and R 0 represent the directions of the transmitted and reflected 0 order while T -1 and R -1 represent that of the −1 order. Inset: detailed view of the 0th diffraction order in transmission.
where we clearly observe SH radiation in four different directions corresponding to detection angles of −147.42°, −33.28°, 21.98° and 157.98°, respectively. The zero angle corresponds to transmission direction through the RWG, normal to the sample surface (see Fig. 2). Positive and negative angles indicate clockwise and counterclockwise rotation with respect to the zero angle. The SH radiations detected at negative angles correspond to −1 diffraction order, while SH radiations detected at positive angles correspond to 0 diffraction order. Assuming a resonant incident angle of 21.98°, the directions of the detected SH radiation for reflected 0 order and reflected/transmitted −1 order agree very well with the values of −147.12°, −32.88°, and 158.02° estimated from Eq. (1). The small discrepancy can be attributed to the uncertainty of the grating period. When limiting the detector area by the 200 µm slit, all the SHG beams exhibited comparable angular widths of ~0.2° at a 0.5 m distance from the sample, showing evidence of strong directionality.

We further observed an azimuthal angular dependence in the SH intensity, i.e., dependence on the orientation of the sample about the surface normal, but this dependence was only observed for the SH signals detected at negative angles, i.e., for the −1 diffraction order, which makes it impossible to unambiguously determine the relative magnitudes of all the four SH beams. Indeed, when the azimuthal angle was optimized to maximize the SH intensity detected in the −1 diffraction order, the SH signal in those directions was significantly larger than that detected in the 0-order directions for which the tuning of the azimuthal angle had little effect. Furthermore, depending on the measurement geometry, some weak side-maxima (not shown here) were observed on either both transmitted or both reflected peaks. In this case the weak side-maxima are caused typically by the working field borders in the electron-beam writing that cause additional periodicity on the structure. We believe that the azimuthal dependence of the SH intensity may be caused by unaccounted interference and diffraction effects in the RWG sample. The fact that the SH intensity seemingly depends on the azimuthal angle of incidence may induce a further increase in the enhancement factor if the azimuthal angle is optimized for a particular diffraction order.

4. Conclusions

We have demonstrated a purely dielectric resonant waveguide structure that enhances the efficiency of second-harmonic generation by a factor of at least 5500 compared to a flat reference surface in the same geometry. Even when the difference in the optimal conditions for the grating and the reference are taken into account, the enhancement factor is about 1000. The enhancement is associated with strong local fields at the interfaces of the grating when the resonant waveguide mode is excited. This remarkable enhancement in second-harmonic generation is of interest for applications that uses the sensitivity of the structure such as molecular fluorescence enhancement and biomolecule detection [9

9. P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt. 46(12), 2351–2360 (2007). [CrossRef] [PubMed]

,10

10. P. Karvinen, T. Nuutinen, J. Rahomäki, O. Hyvärinen, and P. Vahimaa, “Strong fluorescence-signal gain with single-excitation-enhancing and emission-directing nanostructured diffraction grating,” Opt. Lett. 34(20), 3208–3210 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-20-3208. [CrossRef] [PubMed]

,15

15. P. Karvinen, T. Nuutinen, O. Hyvärinen, and P. Vahimaa, “Enhancement of laser-induced fluorescence at 473 nm excitation with subwavelength resonant waveguide gratings,” Opt. Express 16(21), 16364–16370 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16364. [CrossRef] [PubMed]

]. We have further demonstrated that the present structure emits second-harmonic radiation in four different directions when the sample is illuminated with fundamental radiation incident at the resonant angle of the sample. The additional signals arise from the fact that the period of the structure is sub-wavelength only for the fundamental wavelength used, but not for the second-harmonic wavelength. The relative magnitudes of the four peaks were found to be very sensitive to minute variations in the measurement geometry and merit further investigations.

We emphasize that the present results were obtained using a structure that supports a waveguide resonance for the fundamental wavelength only. In the future, it will be interesting to design new types of structures that are simultaneously resonant for both the fundamental and second-harmonic wavelengths so as to obtain even higher enhancement factors. Finally, we point out that even higher enhancement may be expected for third-order processes, because of their higher-order dependence on the local field amplitude and because their origin is not constrained to the surface nonlinearity by symmetry.

Acknowledgments

We acknowledge the Academy of Finland (grant #107009) for financial support. The work of P. Karvinen was financed by the Graduate School of Modern Optics and Photonics. We also acknowledge “The Research and Development Project on Nanophotonics” funded by the Ministry of Education of Finland.

References and links

1.

R. Magnusson and S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]

2.

D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997). [CrossRef]

3.

P. Priambodo, T. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003). [CrossRef]

4.

C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B 21(6), 1127–1136 (2004). [CrossRef]

5.

M. Bader, A. Selle, O. Stenzel, R. Delmdahl, G. Spiecker, and C. Fischer, “High spectral resolution analysis of tunable narrowband resonant grating waveguide structures,” Appl. Phys. B 89(2-3), 151–154 (2007). [CrossRef]

6.

F. Brückner, D. Friedrich, T. Clausnitzer, O. Burmeister, M. Britzger, E.-B. Kley, K. Danzmann, A. Tünnermann, and R. Schnabel, “Demonstration of a cavity coupler based on a resonant waveguide grating,” Opt. Express 17(1), 163–169 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-163. [CrossRef] [PubMed]

7.

S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, “Theoretical analysis on the tuning dynamics of the waveguide-grating structures,” Opt. Express 17(2), 426–436 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-2-426. [CrossRef] [PubMed]

8.

T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008). [CrossRef]

9.

P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt. 46(12), 2351–2360 (2007). [CrossRef] [PubMed]

10.

P. Karvinen, T. Nuutinen, J. Rahomäki, O. Hyvärinen, and P. Vahimaa, “Strong fluorescence-signal gain with single-excitation-enhancing and emission-directing nanostructured diffraction grating,” Opt. Lett. 34(20), 3208–3210 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-20-3208. [CrossRef] [PubMed]

11.

B. U. Felderhof, A. Bratz, G. Marowsky, O. Roders, and F. Sieverdes, “Optical second-harmonic generation from adsorbate layers in total-reflection geometry,” J. Opt. Soc. Am. B 10(10), 1824–1833 (1993). [CrossRef]

12.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007). [CrossRef]

13.

F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8704. [CrossRef] [PubMed]

14.

V. Chukharev, N. Tkachenko, A. Efimov, P. Vainiotalo, and H. Lemmetyinen, “Spectroscopy of a terthiophene-vinylbenzoate,” Photochem. Photobiol. Sci. 2(10), 1044–1049 (2003). [CrossRef] [PubMed]

15.

P. Karvinen, T. Nuutinen, O. Hyvärinen, and P. Vahimaa, “Enhancement of laser-induced fluorescence at 473 nm excitation with subwavelength resonant waveguide gratings,” Opt. Express 16(21), 16364–16370 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16364. [CrossRef] [PubMed]

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 30, 2010
Revised Manuscript: April 26, 2010
Manuscript Accepted: April 26, 2010
Published: May 25, 2010

Citation
A. Saari, G. Genty, M. Siltanen, P. Karvinen, P. Vahimaa, M. Kuittinen, and M. Kauranen, "Giant enhancement of second-harmonic generation in multiple diffraction orders from sub-wavelength resonant waveguide grating," Opt. Express 18, 12298-12303 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12298


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References

  1. R. Magnusson and S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]
  2. D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997). [CrossRef]
  3. P. Priambodo, T. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003). [CrossRef]
  4. C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B 21(6), 1127–1136 (2004). [CrossRef]
  5. M. Bader, A. Selle, O. Stenzel, R. Delmdahl, G. Spiecker, and C. Fischer, “High spectral resolution analysis of tunable narrowband resonant grating waveguide structures,” Appl. Phys. B 89(2-3), 151–154 (2007). [CrossRef]
  6. F. Brückner, D. Friedrich, T. Clausnitzer, O. Burmeister, M. Britzger, E.-B. Kley, K. Danzmann, A. Tünnermann, and R. Schnabel, “Demonstration of a cavity coupler based on a resonant waveguide grating,” Opt. Express 17(1), 163–169 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-163 . [CrossRef] [PubMed]
  7. S. Feng, X. Zhang, J. Song, H. Liu, and Y. Song, “Theoretical analysis on the tuning dynamics of the waveguide-grating structures,” Opt. Express 17(2), 426–436 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-2-426 . [CrossRef] [PubMed]
  8. T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008). [CrossRef]
  9. P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt. 46(12), 2351–2360 (2007). [CrossRef] [PubMed]
  10. P. Karvinen, T. Nuutinen, J. Rahomäki, O. Hyvärinen, and P. Vahimaa, “Strong fluorescence-signal gain with single-excitation-enhancing and emission-directing nanostructured diffraction grating,” Opt. Lett. 34(20), 3208–3210 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-20-3208 . [CrossRef] [PubMed]
  11. B. U. Felderhof, A. Bratz, G. Marowsky, O. Roders, and F. Sieverdes, “Optical second-harmonic generation from adsorbate layers in total-reflection geometry,” J. Opt. Soc. Am. B 10(10), 1824–1833 (1993). [CrossRef]
  12. M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007). [CrossRef]
  13. F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8704 . [CrossRef] [PubMed]
  14. V. Chukharev, N. Tkachenko, A. Efimov, P. Vainiotalo, and H. Lemmetyinen, “Spectroscopy of a terthiophene-vinylbenzoate,” Photochem. Photobiol. Sci. 2(10), 1044–1049 (2003). [CrossRef] [PubMed]
  15. P. Karvinen, T. Nuutinen, O. Hyvärinen, and P. Vahimaa, “Enhancement of laser-induced fluorescence at 473 nm excitation with subwavelength resonant waveguide gratings,” Opt. Express 16(21), 16364–16370 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16364 . [CrossRef] [PubMed]

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