OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 2 — Jan. 22, 2007
  • pp: 652–659
« Show journal navigation

The anisotropic nanomovement of azo-polymers

H. Ishitobi, M. Tanabe, Z. Sekkat, and S. Kawata  »View Author Affiliations


Optics Express, Vol. 15, Issue 2, pp. 652-659 (2007)
http://dx.doi.org/10.1364/OE.15.000652


View Full Text Article

Acrobat PDF (299 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Nanoscale polymer movement is induced by a tightly focused laser beam in an azo-polymer film just at the diffraction limit of light. The deformation pattern that is produced by photoisomerization of the azo dye is strongly dependent on the incident laser polarization and the longitudinal focus position of the laser beam along the optical axis. The anisotropic photo-fluidity of the polymer film and the optical gradient force played important roles in the light induced polymer movement. We also explored the limits of the size of the photo-induced deformation, and we found that the deformation depends on the laser intensity and the exposure time. The smallest deformation size achieved was 200 nm in full width of half maximum; a value which is nearly equal to the size of the diffraction limited laser spot.

© 2007 Optical Society of America

1. Introduction

Light-induced patterns of surface deformations in azobenzene containing polymer films have attracted much attention because of possible applications in optical data storage and in micro/nano fabrication, and it is well known that such patterns reflect the state of the incident light polarization and the light intensity distribution [1–5

1. Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll ed., (Academic Press, USA, 2002).

]. Trans ↔ cis photoselective isomerization and molecular reorientation play important roles in the deformation process. Since photoisomerization was shown to enhance molecular mobility far below the glass transition temperature (Tg) of azo-polymers in the beginning of the past decade [6–9

6. Z. Sekkat and M. Dumont, “Photoassisted Poling of Azo Dye Doped Polymeric Films at Room Temperature,” Appl. Phys. B 54,486–489 (1992). [CrossRef]

], considerable exploration of sub-Tg photo-induced molecular movement was performed especially targeting polymer structural effects, including Tg, the free volume and free volume distribution, the mode of the attachment of the chromophore to a rigid or flexible chain, the molecular weight, and so on [10

10. Z. Sekkat, D. Yasumatsu, and S. Kawata, “Pure Photoorientation of Azo Dye in Polyurethanes and Quantification of Orientation of Spectrally Overlapping Isomers,” J. Phys. Chem. B 106,12407–12417 (2002). [CrossRef]

]. Light induced mass movement in azo polymers, i.e., surface relief gratings (SRGs) [8

8. P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66,136–138 (1995). [CrossRef]

,9

9. D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66,1166–1168 (1995). [CrossRef]

] triggered much studies to understand the mechanism of polymer migration, and most of the studies have focused on the SRGs that are fabricated by the interference pattern of two coherent laser beams [11–14

11. P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9,323–328 (1998). [CrossRef]

]. Yet, there are few reports on surface deformations that are induced by a single focused laser beam [15–17

15. S. Bian, J. M. Williams, D. Y. Kim, L. Lin, S. Balasubramanian, J. Kumar, and S. Tripathy, “Photoinduced surface deformations on azobenzene polymer films,” J. Appl. Phys. 86,4498–4508 (1999). [CrossRef]

]. To fabricate deformation structures with high spatial resolution, a small irradiation spot is required; a feature which can be achieved by focusing the laser beam by using a high numerical aperture (N.A.) objective lens. In this paper, we report on surface deformations of azo polymers by irradiation with a single tightly focused laser beam with a high N.A. objective lens (N.A. = 1.4). We discuss the effect of the incident light polarization and the position of the laser focus on the deformation pattern. In particular, we found that the deformation pattern is strongly dependent on the z- position of the focused laser spot. In addition to the well known trans ↔ cis surface deformation, it will be shown that a gradient force pertaining to laser trapping pulls the polymer towards the laser focus. Then we present a systematic study exploring the limits of the size of photo-induced deformation by changing the irradiation intensity and the exposure time.

2. Experiment

We prepared 50 nm thin films of poly(Disperse Red 1 methacrylate) (PMA-DR1, product No. 579009, Aldrich; Tg= 82 °C) by spin-casting from a chloroform solution. The remaining solvent was removed by heating the films for an hour at 100 °C. The chemical structure and the absorption spectrum of the film, i.e., trans-DR1 are shown in Fig. 1. Disperse Red 1 (DR1) is a nonlinear optical azo dye which is well known for its trans ↔ cis photoisomerization and for its ability to undergo efficient orientation and trigger important polymer movement when it is excited by polarized light [1

1. Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll ed., (Academic Press, USA, 2002).

]. The orientation effect is due to the highly anisometric nature of its polarizability tensor (rodlike molecule) [18

18. Z. Sekkat, J. Wood, W. Knoll, W. Volksen, and R. D. Miller, “Light-induced orientation in a high glass transition temperature polyimide with polar azo dyes in the side chain,” J. Opt. Soc. Am. B 13,1713–1724 (1996). [CrossRef]

]. The irradiation light source was a linearly polarized 460 nm light from a diode pumped frequency doubled laser (Sapphire 460 LP, Coherent Japan). The wavelength of the irradiation laser corresponds to the maximum absorption band of the film sample. The laser beam was focused by an objective lens (N. A. = 1.4) (Plan Apo 60×, Nikon). The diffraction limited spot diameters in the lateral (X or Y) and longitudinal (Z) axes are ∼ 400 nm and 1.0 μm, respectively. Computer controlled piezo stages (P-517 for X and Y axes and P-721 for Z axis, Physik Instruments (PI)) were used to control the position of the focused laser spot in three dimensions. The induced surface deformation of the films was measured by an atomic force microscope (AFM) (SPA-400, SEIKO Instruments Inc.). The AFM was operated in the tapping mode using a Si cantilever to eliminate the mechanical deformation of the films by the cantilever itself.

Fig. 1. Chemical structure (inset) and absorption spectrum of the trans-PMA-DR1 thin film. The wavelength of excitation is indicated.

3. Results and discussion

Figure 2 shows AFM images of the surface deformation induced by (a, b) linear and (c) circular polarizations. The polarizations were controlled by half and quarter wave plates. The estimated irradiation intensity at the sample film surface and the exposure time were 12.5 mW/cm2 and 30 s, respectively, and the laser beam was focused on the film surface. Irradiation with linearly polarized light induced the deformation pattern shown in Fig. 2 (a) and (b). It is clearly shown in this figure that the polymer moved along the polarization direction from the center to the outside of the focused spot, thus producing two side lobes along the polarization direction and a pit at the center. Indeed this polarization-dependent deformation was confirmed by an experiment in which the polarization direction of the irradiation light was rotated through an angle of 90 degrees and the surface relief followed the polarization of the light (see Fig. 2 (a) versus (b)). Similar polarization dependence was observed by Gilbert et al. [16

16. Y. Gilbert, R. Bachelot, P. Royer, A. Bouhelier, G. P. Wiederrecht, and L Novotny, “Longitudinal anisotropy of he photoinduced molecular migration in azobenzene polymer films,” Opt. Lett. 31,613–615 (2006). [CrossRef] [PubMed]

], who used an irradiation intensity of 40 kW/cm2. At such high intensities, photo-bleaching occurs and influences the surface deformation pattern [15

15. S. Bian, J. M. Williams, D. Y. Kim, L. Lin, S. Balasubramanian, J. Kumar, and S. Tripathy, “Photoinduced surface deformations on azobenzene polymer films,” J. Appl. Phys. 86,4498–4508 (1999). [CrossRef]

]. In our experiments, we used an appropriate light intensity range; e.g., 6.25 ∼ 62.5 W/cm2 (vide infra). In contrast to irradiation with linear polarization, irradiation with circularly polarized light induced a deformation pattern in which the polymer moved from the center to the outside of the focused laser spot, thus forming a doughnut shape pattern (Fig. 2 (c)). For both linear and circular polarizations, the polymer migrates in the direction of the polarization of the light from high to low light intensity regions, and the polarization dependence demonstrates that the light-induced polymer movement is anisotropically photo-fluidic [5

5. P. Karageorgiev, D. Neher, B. Schulz, B. Stiller, U. Pietsch, M. Giersig, and L. Brehmer, “From anisotropic photo-fluidity towards nanomanipulation in the optical near-field,” Nature Materials 4,699–703 (2005). [CrossRef] [PubMed]

].

Fig. 2. AFM images of the deformation induced by a tightly focused laser beam polarized (a) horizontally, (b) vertically, and (c) circularly, respectively.

The observed polarization dependence is consistent with the one obtained after irradiation with a low N.A. lens [15

15. S. Bian, J. M. Williams, D. Y. Kim, L. Lin, S. Balasubramanian, J. Kumar, and S. Tripathy, “Photoinduced surface deformations on azobenzene polymer films,” J. Appl. Phys. 86,4498–4508 (1999). [CrossRef]

]. When a laser beam is tightly focused by a high N.A. objective lens, a non negligible electric field Ez component is created along the optical axis. The intensity distributions corresponding to Ex, Ey, and Ez at the focal position are different, and shown in Fig. 3, and they should lead to different deformation patterns. However, in our experimental conditions, only Ex contributes appreciably to the deformation. With N.A. = 1.4 and wavelength = 460 nm, the maximum intensity corresponding to Ez and Ey are 7 and 200 times smaller than that of Ex, respectively.

Fig. 3. Calculated distributions of squared electric field components created by a tightly focused linearly polarized laser beam. The each components of electric field of (a) Ex, (b) Ey, and (c) Ez are shown. The polarization direction is X, Z is perpendicular to the film, and Y is perpendicular to both X and Z. The distribution was calculated assuming a refractive index of the surrounding medium equal to 1.5.

Fig. 4. AFM images of the surface deformation induced by changing the Z-position of the focused laser spot. The Z-position was varied from -500 nm to +500 nm with an interval of 100 nm. The values inside each figure represent the Z-position of the focus (unit is nm). The polarization direction is indicated.
Fig. 5. (Left column) Line plots of the surface deformation at (a) Z = +500 nm, (b) Z = 0 nm, and (c) Z = -500 nm. The positions of the each plot correspond to the directions that are between the arrows indicated in Fig. 4. (Right column) Schematics describing the relationship between the Z-position of the focus and the film surface. The arrows oriented laterally and longitudinally in these schematics indicate the direction of the anisotropic photo-fluidity and the optical gradient force, respectively.

In a systematic set of experiments, we studied the dependence of the size of the photo-induced deformation on the intensity of the irradiation light and the exposure time. In those experiments, the irradiation light is linearly polarized and focused by a 1.4 N.A. objective lens. The deformation pattern was studied just at the laser focus, i.e., Z = 0 nm, for three irradiation intensities (6.25, 12.5, 62.5 mW/cm2), and exposure times according to the series 1 to 500 s for 6.25 and 12.5 mW/cm2, and 1 to 100 s for 62.5 mW/cm2. The deformation patterns obtained at all intensities at all times of irradiation were the same, but the size of the deformation was different. Figure 6 shows the dependence of the height and the full width at half maximum (FWHM) of deformation pattern along the direction parallel to the light polarization on the irradiation intensity and the exposure time. The height is defined as the difference between the top of the side lobes and the bottom of the central pit as shown in Fig. 6. As is can be seen as well from this figure, the rate of the deformation of the height and FWHM decreased with the increasing irradiation dose, and the higher the irradiation intensity, the faster the increase of both the height and FWHM. The height increases more rapidly than FWHM which needs more time to reach saturation. The height increases rapidly at small irradiation doses, and saturates at larger irradiation doses near 90 nm. 90 nm corresponds to near twice the initial film thickness; a thickness modulation which is usually observed in SRGs [13

13. A. Natansohn and P. Rochon, “Photoinduced Motions in Azobenzene-Based Polymers,” in Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll, ed. (Academic Press, USA, 2002), Chap. 13, and references therein.

,14

14. O. N. Oliveira, L. Li, J. Kumar, and S. Tripathy, “Surface-Relief Gratings on Azobenzene-Containing Films,” in Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll, ed. (Academic Press, USA, 2002), Chap. 14 and references therein.

]. The minimum FWHM of the fabricated pattern is about 200 nm; a value which corresponds to the size of the diffraction limited laser spot.

Fig. 6. Size dependence of the surface deformation on the irradiation intensity and the exposure time. A typical deformation pattern and the corresponding line pot are shown in the left of the figure and the definitions of the height and FWHM are indicated. Scatters are experimental data, and solid lines are exponential empirical theoretical fits.

4. Conclusion

We studied anisotropic nanoscale polymer movement induced by a tightly focused laser beam in an azo-polymer film. We found that the deformation pattern strongly depends on the incident laser polarization and the z-position of the focus. Light induced anisotropic photo-fluidity moves the polymer along the polarization direction in the film plane, and the optical gradient force pulls the polymer along the optical axis; a feature which allows for the control of the deformation pattern (protrusion versus pit) by changing the z-position of the focus. From a set of systematic studies, we found that the smallest deformation size that could be achieved is 200 nm in full width of half maximum; a value which is nearly equal to the size of the diffraction limited laser spot. The present work unambiguously demonstrates light induced nanoscale polymer movement, and it will trigger future studies addressing near field fabrication with a resolution beyond the diffraction limit of light as well as fundamental studies and theories of photo-induced nano movements in polymers.

References and links

1.

Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll ed., (Academic Press, USA, 2002).

2.

K. Koyayashi, C. Egami, and Y. Kawata, “Optical Storage Media with Dye-Doped Minute Sphere on Polymer Films,” Opt. Rev. 10,262–266 (2003). [CrossRef]

3.

C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S-H Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, “Near-Field Photochemical Imaging of Nobel Metal Nanostructures,” Nano Lett. 5,615–619 (2005). [CrossRef] [PubMed]

4.

Y. Gilbert, R. Bachelot, A. Vial, G. Lerondel, P. Royer, A. Bouhelier, and G. P. Wiederrecht, “Photoresponsive polymers for topographic simulation of the optical near-field of a nanometer sized gold tip in a highly focused laser beam,” Opt. Express 13,3619–3624 (2005). [CrossRef] [PubMed]

5.

P. Karageorgiev, D. Neher, B. Schulz, B. Stiller, U. Pietsch, M. Giersig, and L. Brehmer, “From anisotropic photo-fluidity towards nanomanipulation in the optical near-field,” Nature Materials 4,699–703 (2005). [CrossRef] [PubMed]

6.

Z. Sekkat and M. Dumont, “Photoassisted Poling of Azo Dye Doped Polymeric Films at Room Temperature,” Appl. Phys. B 54,486–489 (1992). [CrossRef]

7.

F. Charra, F. Kajzar, J. M. Nunzi, P. Raimond, and E. Idiart, “Light-induced second-harmonic generation in azo-dye polymers,” Opt. Lett. 18,941–943 (1993). [CrossRef] [PubMed]

8.

P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66,136–138 (1995). [CrossRef]

9.

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66,1166–1168 (1995). [CrossRef]

10.

Z. Sekkat, D. Yasumatsu, and S. Kawata, “Pure Photoorientation of Azo Dye in Polyurethanes and Quantification of Orientation of Spectrally Overlapping Isomers,” J. Phys. Chem. B 106,12407–12417 (2002). [CrossRef]

11.

P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9,323–328 (1998). [CrossRef]

12.

F. L. Labarthet, J. L. Bruneel, T. Buffeteau, and C. Sourisseau, “Chromophore Orientations upon Irradiation in Gratings Inscribed on Azo-Dye Polymer Films: A Combined AFM and Confocal Raman Microscopic Study,” J. Phys. Chem. B 108,6949–6960 (2004). [CrossRef]

13.

A. Natansohn and P. Rochon, “Photoinduced Motions in Azobenzene-Based Polymers,” in Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll, ed. (Academic Press, USA, 2002), Chap. 13, and references therein.

14.

O. N. Oliveira, L. Li, J. Kumar, and S. Tripathy, “Surface-Relief Gratings on Azobenzene-Containing Films,” in Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll, ed. (Academic Press, USA, 2002), Chap. 14 and references therein.

15.

S. Bian, J. M. Williams, D. Y. Kim, L. Lin, S. Balasubramanian, J. Kumar, and S. Tripathy, “Photoinduced surface deformations on azobenzene polymer films,” J. Appl. Phys. 86,4498–4508 (1999). [CrossRef]

16.

Y. Gilbert, R. Bachelot, P. Royer, A. Bouhelier, G. P. Wiederrecht, and L Novotny, “Longitudinal anisotropy of he photoinduced molecular migration in azobenzene polymer films,” Opt. Lett. 31,613–615 (2006). [CrossRef] [PubMed]

17.

T. Grosjean and D Courjon, “Photopolymers as vectorial sensors of the electric field,” Opt. Express 14,2203–2210 (2006). [CrossRef] [PubMed]

18.

Z. Sekkat, J. Wood, W. Knoll, W. Volksen, and R. D. Miller, “Light-induced orientation in a high glass transition temperature polyimide with polar azo dyes in the side chain,” J. Opt. Soc. Am. B 13,1713–1724 (1996). [CrossRef]

19.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11,288–290 (1986). [CrossRef] [PubMed]

OCIS Codes
(160.5470) Materials : Polymers
(210.4810) Optical data storage : Optical storage-recording materials
(240.6670) Optics at surfaces : Surface photochemistry

ToC Category:
Optics at Surfaces

History
Original Manuscript: October 18, 2006
Revised Manuscript: December 5, 2006
Manuscript Accepted: December 11, 2006
Published: January 22, 2007

Citation
H. Ishitobi, M. Tanabe, Z. Sekkat, and S. Kawata, "The anisotropic nanomovement of azo-polymers," Opt. Express 15, 652-659 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-652


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Z. Sekkat and W. Knoll, ed., Photoreactive Organic Thin Films, (Academic Press, USA, 2002).
  2. K. Koyayashi, C. Egami and Y. Kawata, "Optical storage media with Dye-Doped Minute Sphere on Polymer Films," Opt. Rev. 10, 262-266 (2003). [CrossRef]
  3. C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S-H Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, "Near-field photochemical imaging of Nobel Metal Nanostructures," Nano Lett. 5, 615-619 (2005). [CrossRef] [PubMed]
  4. Y. Gilbert, R. Bachelot, A. Vial, G. Lerondel, P. Royer, A. Bouhelier, and G. P. Wiederrecht," Photoresponsive polymers for topographic simulation of the optical near-field of a nanometer sized gold tip in a highly focused laser beam," Opt. Express 13, 3619-3624 (2005). [CrossRef] [PubMed]
  5. P. Karageorgiev, D. Neher, B. Schulz, B. Stiller, U. Pietsch, M. Giersig, and L. Brehmer, "From anisotropic photo-fluidity towards nanomanipulation in the optical near-field," Nat. Mater. 4, 699-703 (2005). [CrossRef] [PubMed]
  6. Z. Sekkat and M. Dumont, "Photoassisted poling of Azo Dye Doped Polymeric Films at room temperature," Appl. Phys. B 54, 486-489 (1992). [CrossRef]
  7. F. Charra, F. Kajzar, J. M. Nunzi, P. Raimond, and E. Idiart, "Light-induced second-harmonic generation in azo-dye polymers," Opt. Lett. 18, 941-943 (1993). [CrossRef] [PubMed]
  8. P. Rochon, E. Batalla, and A. Natansohn, "Optically induced surface gratings on azoaromatic polymer films," Appl. Phys. Lett. 66, 136-138 (1995). [CrossRef]
  9. D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, "Laser-induced holographic surface relief gratings on nonlinear optical polymer films," Appl. Phys. Lett. 66, 1166-1168 (1995). [CrossRef]
  10. Z. Sekkat, D. Yasumatsu, and S. Kawata, "Pure photo orientation of Azo dye in polyurethanes and quantification of orientation of spectrally overlapping Isomers," J. Phys. Chem. B 106, 12407-12417 (2002). [CrossRef]
  11. P. Lefin, C. Fiorini, J. M. Nunzi, "Anisotropy of the photoinduced translation diffusion of azo-dyes," Opt. Mater. 9, 323-328 (1998). [CrossRef]
  12. F. L. Labarthet, J. L. Bruneel, T. Buffeteau, and C. Sourisseau, "Chromophore Orientations upon irradiation in gratings inscribed on Azo-Dye Polymer Films: A combined AFM and Confocal Raman Microscopic Study," J. Phys. Chem. B 108, 6949-6960 (2004). [CrossRef]
  13. A. Natansohn and P. Rochon, "Photo induced motions in Azobenzene-based polymers," in Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll, ed., (Academic Press, USA, 2002), Chap. 13, and references therein.
  14. O. N. Oliveira, L. Li, J. Kumar, and S. Tripathy, "Surface-relief gratings on Azobenzene-containing films," in Photoreactive Organic Thin Films, Z. Sekkat and W. Knoll, ed., (Academic Press, USA, 2002), Chap. 14 and references therein.
  15. S. Bian, J. M. Williams, D. Y. Kim, L. Lin, S. Balasubramanian, J. Kumar and S. Tripathy, "Photo induced surface deformations on Azobenzene polymer films," J. Appl. Phys. 86, 4498-4508 (1999). [CrossRef]
  16. Y. Gilbert, R. Bachelot, P. Royer, A. Bouhelier, G. P. Wiederrecht, and L Novotny, "Longitudinal anisotropy of he photo induced molecular migration in Azobenzene polymer films," Opt. Lett. 31, 613-615 (2006). [CrossRef] [PubMed]
  17. T. Grosjean and D Courjon, "Photopolymers as vectorial sensors of the electric field," Opt. Express 14, 2203-2210 (2006). [CrossRef] [PubMed]
  18. Z. Sekkat, J. Wood, W. Knoll, W. Volksen, R. D. Miller, "Light-induced orientation in a high glass transition temperature polyimide with polar azo dyes in the side chain," J. Opt. Soc. Am. B 13, 1713-1724 (1996). [CrossRef]
  19. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited