OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 11 — Oct. 22, 2008
« Show journal navigation

Probing dielectric interfaces on the nanoscale with elastic scattering patterns of single gold nanorods

Tina Züchner, Antonio Virgilio Failla, Mathias Steiner, and Alfred J. Meixner  »View Author Affiliations


Optics Express, Vol. 16, Issue 19, pp. 14635-14644 (2008)
http://dx.doi.org/10.1364/OE.16.014635


View Full Text Article

Acrobat PDF (1177 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We study spatially isolated, individual gold nanorods placed at a planar interface between two dielectric media using confocal interference scattering microscopy in combination with higher order laser modes. Approaching refractive index matching conditions, we observe that the elastic scattering patterns of individual nanorods exhibit an exponential increase of both the scattering intensity and the signal-to-background ratio. In case refractive index matching conditions are fullfilled, the data acquisition rates are maximized and suitable for in-vivo biological measurements. In all cases, the characteristic two-lobe shape of the scattering patterns of single nanorods remains unchanged while the sign of the image contrast is a direct consequence of the refractive index variation occurring at the interface.

© 2008 Optical Society of America

1. Introduction

Metallic nanoparticles have a promising future in nano-science and -technology due to their favorable and tunable optical properties originating from particle plasmons (PPs), i.e. collective oscillations of free electrons in the conduction band. PPs are determined by material, size and shape of the nanoparticles [1

1. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402, (2002). [CrossRef] [PubMed]

8

8. F. Tam, C. Moran, and N. Halas, “Geometrical parameters controlling sensitivity of nanoshell plasmon resonances to changes in dielectric environment,” J. Phys. Chem. B 108, 17290–17294, (2004). [CrossRef]

] as well as by their aggregation [9

9. M. Steiner, C. Debus, A. V. Failla, and A. J. Meixner, “Plasmon-enhanced emission in gold nanoparticle aggregates,” J. Phys. Chem. C 112, 3103–3108, (2008). [CrossRef]

]. Moreover, PPs have been recognized to be strongly influenced by extrinsic parameters like the dielectric properties of the local surrounding medium [10

10. A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express 13, 2668–2677, (2005). [CrossRef] [PubMed]

, 11

11. J. J. Mock, D. R. Smith, and S. Schult, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3, 485–491, (2003). [CrossRef]

]. Novel applications comprise utilization of metal nanoparticles as non-toxic and non-bleaching labels in biology and biomedicine, e.g. [12

12. D. Yelin, D. Oron, S. Thiberge, E. Moses, and Y. Silberberg, “Multiphoton plasmon-resonance microscopy,” Opt. Express 11, 1385–1391, (2003). [CrossRef] [PubMed]

15

15. H. Hess and Y. Tseng, “Active intracellular transport of nanoparticles: Opportunity or threat?” ACS Nano 1, 390–392, (2007). [CrossRef] [PubMed]

] and references therein, as well as highly sensitive biochemical nano-sensors [10

10. A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express 13, 2668–2677, (2005). [CrossRef] [PubMed]

, 11

11. J. J. Mock, D. R. Smith, and S. Schult, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3, 485–491, (2003). [CrossRef]

, 16

16. C. Sönnichsen, B.M. Reinhard, J. Liphardt, and A.P. Alivisatos. “A molecular ruler based on plasmon coupling of single gold and silver nanoparticles,” Nature Biotech. 23, 741–745, (2005). [CrossRef]

19

19. S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” PNAS 97, 996–1001, (2000). [CrossRef] [PubMed]

].

Metallic nanoparticles have been studied extensively in combination with optical microscopy [1

1. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402, (2002). [CrossRef] [PubMed]

, 20

20. M.R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B , 68, 1154331–11543310, (2003). [CrossRef]

22

22. C.J. Orendorff, L. Gearheart, N.R. Jana, and C.J. Murphy, “Aspect ratio dependence on surface enhanced raman scattering using silver and gold nanorod substrates,” Phys. Chem. Chem. Phys. 8, 165–170, (2006). [CrossRef] [PubMed]

] and considerable effort has been spent on detection and visualization of individual metallic nanoparticles with diameters down to 1.4 nm [23

23. F.V. Ignatovich, A. Hartschuh, and L. Novotny, “Detection of nanoparticles using optical gradient forces,” J. Mod. Opt. 50, 1509–1520, (2003).

27

27. S. Berciaud, L. Cognet, G.A. Blab, and B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402–257406, (2004). [CrossRef]

]. In this context, confocal interference scattering microscopy (CISM) in combination with tightly focused fundamental as well as higher order laser beams has been used for imaging elastic scattering pattern of individual, spatially isolated metallic nanoparticles [28

28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

]. In CISM, see for example [29

29. C.J.R. Sheppard and D.M. Shotton, Confocal Laser Scanning Microscopy, (Bios Scientific Publishers, London, 1997).

,30

30. C.J.R. Sheppard and Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik 87, 129–132, (1991).

], the image contrast results from the interference between the light scattered by an object and the light reflected from the interface where the object is located. This method allows topological measurements with nanometer-precision as well as the determination of the shape and the orientation of single nanoparticles having dimensions much smaller than the wavelength of the excitation laser lig! ht [28

28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

, 31

31. T. Züchner, A.V. Failla, A. Hartschuh, and A.J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au-nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343, (2008). [CrossRef] [PubMed]

, 32

32. A.V. Failla, S.W. Jäger, T. Züchner, M. Steiner, and A.J. Meixner, “Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy,” Opt. Express 15, 8532–8542, (2007). [CrossRef] [PubMed]

]. The possibility of combining fast imaging and high topological sensitivity recommends implementation of CISM on the single nanoparticle level for applications like chemical sensing or time lapse imaging of biological processes occurring at the cell membrane. In a preliminary step, however, the influence of changes in the local environment, either liquid or solid, on the elastic scattering properties of individual metal nanoparticles acting as optical nanosprobes has to be investigated.

In this article, we study experimentally and theoretically the scattering patterns of the same group of spatially isolated, individual gold nanorods placed at a planar interface between two transparent dielectric media under controlled variation of their refractive indices. The intensities of both the excitation light elastically scattered by individual nanorods and the excitation light locally reflected at the nearby interface were found to vary by up to three orders of magnitude while the ratio between them is enhanced by up to five orders of magnitude if refractive index matching conditions are fulfilled. In this case, the signal-to-background ratios of measured single nanorod scattering patterns reach a level sufficient for in-vivo biological measurements. Our simulations reproduce the experimental results by accounting for both the aspect ratio and the volume of individual gold nanorods and the changes of the reflection coefficients occurring at the local interfa! ce. Changing the transition direction of the interface (high n/low n to low n/high n) results in a sign inversion of the image contrast; an effect that could be utilized for detecting even weak dielectric interfaces.

2. Materials and methods

2.1. Sample preparation

Gold nanorods were synthesized utilizing a seed-mediated approach [34

34. B. Nikoobakht and M.A. El-Sayed, “Preparation and growth mechanism of gold nanorods (NRs) using seed-mediated growth method,” Chem. Mater. 15, 1957–1962, (2003). [CrossRef]

], subsequently purified from excess surfactant and characterized both individually on a glass surface using atomic force microscopy (AFM) and in aqueous solution using extinction spectroscopy (see Fig. 1). Throughout this work we will neglect the effect of the surfactant belayer capping the gold nanorods [35

35. B. Nikoobakht and M.A. El-Sayed, “Evidence for Bilayer Assembly of Cationic Surfactants on The Surface of Gold Nanorods,” Langmuir 17, 6368–6374, (2001). [CrossRef]

]. The AFM image Fig. 1(a) shows a spatially isolated, individual gold nanorod having a height of 15 nm on a glass cover slip spin coated from a high diluted aqueous solution (0.5 rods per µm 2) for optical measurements (for details, see [28

28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

]). The extinction spectrum of the nanorod solution (see Fig. 1(c)) exhibits two maxima reflecting their plasmon resonances along the short axis b and the long axis a. The measured spectrum was fitted with an analytical expression based on Mie theory [33

33. S. Link, M.B. Mohamed, and M.A. El-Sayed, “Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant,” J. Phys. Chem. B 103, 3073–3077, (1999). [CrossRef]

,36

36. G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 25, 377–445, (1908). [CrossRef]

]. From the fit results, we estimate that the particles have an average aspect ratio R=a/b of 2.6. By combining the results obtained from both AFM and spectroscopic measurements, we estimate the average dimensions of gold nanorods to be 15 nm x 38 nm in good agreement with the values given in [34

34. B. Nikoobakht and M.A. El-Sayed, “Preparation and growth mechanism of gold nanorods (NRs) using seed-mediated growth method,” Chem. Mater. 15, 1957–1962, (2003). [CrossRef]

].

Fig. 1. (a) AFM image of a single, spatially isolated Au nanorod as spin coated from aqueous solution on a microscope cover slip. (b) Cross sections taken along the dashed lines in (a). (c) Extinction spectrum of the nanorod solution exhibiting the plasmon resonances along the short and long axis b and a, respectively. The fit (dashed line) to the experimental spectrum (solid line) is used to determine the average aspect ratio R=a/b=2.6 of the nanorods in solution [33].

For the optical experiments, droplets of water (n 2=1.34) and immersion oil (n 2=1.518) were successively deposited on the surface of a microscope glass cover slip (n 1=1.518) bearing spatially isolated, individual gold nanorods for studying the influence of the changing interface as well as the modified local dielectric environment on the scattering patterns of the same nanorods. In a second step, we prepared samples by sealing a diluted nanoparticle solution between two glass cover slips to investigate the influence of the change of the transition direction of the interface (high n/low n and low n/high n, respectively) on the scattering patterns of individual nanorods. Here, the distance of the cover slips was determined by confocal microscopy to be approximately 2 µm.

2.2. Optical setup and signal detection

All scattering images were acquired with a home-built inverted confocal microscope as sketched in Fig. 2 that was equipped with a HeNe-Laser operated at 633 nm. A higher order laser mode, i.e. an azimuthally polarized doughnut mode (APDM), having a diameter of 4 mm, was tightly focussed on individual gold nanorods and the elastically scattered light was collected on a point-like detector. Details regarding the experimental arrangement can be found in [28

28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

,31

31. T. Züchner, A.V. Failla, A. Hartschuh, and A.J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au-nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343, (2008). [CrossRef] [PubMed]

]. The detected signal IAPD consists of the coherent interference between the excitation light reflected at the interface where the nanorod is located and the light elastically scattered by the particle:

IAPDEr+Es2=Er2+Es2+2EsErcosϕ
(1)

Here, |E r|2 represents the intensity of the excitation light reflected at the interface, i.e. the image background intensity IBKG. |E s|2 represents the pure scattering signal of the particle and is proportional to its squared volume [37

37. C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles, (JohnWiley & Sons, New York, 1983).

]. The interference term 2|E s||E r |cosϕ depends critically on the phase ϕ between the reflected and the scattered field. The sum of the second and third term on the right hand side of Eq. 1 describes the image contrast in the scattering pattern of a single particle. The phase of the scattered field is determined by the spectral properties of the PPs, the material and the dimensions of the nanoparticle as well as the refractive index of the surrounding media whereas the phase of the reflected field is affected by the numerical aperture of the microscope objective. Importantly, the refractive index mismatch, i.e., the difference between the refractive indices of the two dielectrics forming the interface, is critical for the phases of both fields so that small variations can switch the sign of the image contrast.

Fig. 2. Schematic of the optical setup. MC: Mode converter, L: Lens, SF: Spatial filter, BS: Beam splitter, MO: Microscope objective, SC: (x,y)-Scanning stage, S: Sample, APD: Avalanche photodiode. (Inset (I)) (a) Representative experimental scattering pattern of a gold nanorod excited at λ=633 nm with an azimuthally polarized doughnut mode (APDM). (b) Reconstruction of the pattern shown in (a) obtained by fitting the experimental data with a model function. (c) Simulated theoretical scattering pattern of the same particle. (Inset (II)) Visualization of the intensity distribution and the polarization orientation (arrows) in the collimated laser excitation beam.

Starting from Eq. 1 the scattering pattern of an individual gold nanorod (I Nano) can be described in the following way:

INano=IAPDIBKG=2EsErcosϕifErEs
(2)
INano=Es2ifEsEr
(3)
INano=2EsErcosϕ+Es2ifEsEr.
(4)

Equation 2 is valid if the reflected field at the interface is comparable to or smaller than the transmitted field. Eq. 3 can only be used if the dielectric interface fulfills index matching conditions, i.e. E r=0, while Eq. 4 also holds close to the index matching regime. Depending on the actual size and shape of a specific nanoparticle as well as the excitation wavelength used, more complex approaches might be required.

An individual gold nanorod renders a characteristic two-lobe scattering pattern that reveals the particle’s position and orientation with nanometer-accuracy [28

28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

, 31

31. T. Züchner, A.V. Failla, A. Hartschuh, and A.J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au-nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343, (2008). [CrossRef] [PubMed]

]. In Fig. 2 Inset (I, a), a typical scattering pattern imaged for a spatially isolated gold nanorod deposited on glass, covered by water and excited using an APDM is shown. In order to estimate the orientation and the position of single gold nanorods [32

32. A.V. Failla, S.W. Jäger, T. Züchner, M. Steiner, and A.J. Meixner, “Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy,” Opt. Express 15, 8532–8542, (2007). [CrossRef] [PubMed]

], we used a two dimensional fit algorithm running on Matlab® that produces a virtual scattering pattern (see Fig. 2, Inset (I, b) by fitting the experimental data with a model function (Eq. 8 of [32

32. A.V. Failla, S.W. Jäger, T. Züchner, M. Steiner, and A.J. Meixner, “Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy,” Opt. Express 15, 8532–8542, (2007). [CrossRef] [PubMed]

]). The corresponding theoretical scattering pattern is shown in Fig. 2, Inset (I, c). It was simulated based on Mie theory and analytical calculations of the optical field distribution of an APDM in the focal regime of a high NA objective lens ! accounting for Eq. 1. The simulation does not require free parameters and constitutes a physical interpretation of the imaging process. A detailed discussion of the underlying model is subject of a parallel publication.

3. Results and discussion

3.1. The refractive index mismatch at the interface

Fig. 3. Experimental (a-c) and corresponding simulated (g-i) scattering patterns of the same set of individual, spatially isolated gold nanorods (aspect ratio R=2.6, excited with an APDM at λ=633 nm) imaged for three different interfaces as indicated in the schematics on top. (d-f) Scattering intensity profiles taken along the lines in (a), (b) and (c), respectively. The simulations account for the contrast of the experimental scattering patterns.

To investigate the effect of the interface and the local dielectric environment, we recorded successively scattering patterns of the same set of spatially isolated, individual gold nanorods in three different configurations: First, deposited on a microscope glass cover slip exposed to air (glass-air interface; see Fig. 3, left schematic), second, covered with a droplet of water (glass-water interface; see Fig. 3, middle schematic) and, third, after evaporation of the water, covered with a droplet of immersion oil (glass-oil interface; see Fig. 3, right schematic) effectively achieving refractive index matching conditions. A detailed description of the sample and the confocal microscopy setup can be found in the Materials and Methods section. There, we also outline the analytical description of the detectable scattering signal.

We utilized the model function (see Eq. 8 of [32

32. A.V. Failla, S.W. Jäger, T. Züchner, M. Steiner, and A.J. Meixner, “Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy,” Opt. Express 15, 8532–8542, (2007). [CrossRef] [PubMed]

]) to determine the signal amplitude, position and orientation of individual nanorods as well as the relative distances between them. The orientation could be determined with a standard deviation of approximately 1 degree corresponding to a rotational arch of 0.8 nm assuming a nanorod length of 45 nm. Relative particle distances were extracted with nanometer-precision and relative errors below 1 percent. The results for scattering amplitudes, orientations and relative distances of the particles were used as parameters for simulating the corresponding theoretical scattering patterns that are shown in Fig. 3(d)–(f). For simulating the scattering patterns at the glass-air and glass-water interface, respectively, we used Eq. 2 as specified in the Materials and Methods section. In fact, in these cases, the electric field reflected at the interface E r is not negligible and strongly affects the amplitude and the phase of the overall scattering signal. For the glass-oil interface, the scattering patterns are well-described by Eq. 3 (see Materials and Methods section). In this case, the inversion of the image contrast is a direct consequence of E r⋍0 as will be discussed in the following.

The scattering patterns shown in Fig. 3 can be rationalized by decomposing the total scattering signal into contributions arising from the reflected field E r and the scattered field E s. We investigate the influence of E r by measuring the image background intensity |E r|2 as a function of the laser excitation power for the three different interfaces discussed above. As can be seen in Fig. 4, we obtain a linear dependence between |E r|2 and the laser excitation power for each of them, as expected. As an important result, for a given laser excitation power (as indicated by the dashed vertical line in Fig. 4), the measured background intensity |E r |2 reaches a minimum at the oil-glass interface and is two (three) orders of magnitude smaller as measured for the glass-water (glass-air) interface. Simultaneously, the contribution of the scattered field E s! to the overall detected intensity, i.e. (|E s|/|E r|)2, increases exponentially by five orders of magnitude towards the index matching regime, i.e. n 2=n 1=1.518, as can be seen from the calculation result shown in the inset in Fig. 4. As a result, we expect the image contrast (see Fig. 3(d)–(f)) to increase for a decreasing difference between the refractive indices n 1, n 2 of the dielectrics and to invert the sign approaching the index matching regime, i.e. n 1n 2. Under this condition, the interference term in Eq. 1 becomes negligible and Eq. 3 delivers a valid approximation assuming perfect focusing conditions as well as a perfect dielectric interface. As a key result, the

index matching condition delivers optimized imaging conditions for small metallic nanoparticles, in particular for low laser excitation powers, that are suitable for 1! t in-vivo measurements in biological environments.

Fig. 4. Measured background intensity |E r|2 as a function of the laser excitation power (λ=633 nm) for the three different interfaces glass-air (squares), glass-water (circles) and glass-oil (triangles) according to the schematics in Fig. 3. The lines represent linear fits to the respective data sets. (Inset) Relative nanorod scattering intensity (|E s|/|E r|)2 (normalized with respect to (|E s|/|E r|)2 for n 2=1, see also Eq. 1) as a function of the refractive index n 2.

3.2. Particle geometry and image contrast

To visualize the influence of R on the shape of the scattering pattern, we calculated the integrated scattering intensity as a function of the aspect ratio for a single gold nanorod and the result is shown in Fig. 5. The curve suggests that, despite the sharp maximum occurring at R⋍2.1 due to the plasmon resonance of gold nanorods embedded in oil, the total scattering intensity of the nanorod increases moderately, proportional to the volume of the particle. Three representative simulated scattering patterns for R=2.5, 4 and 7, respectively, are also shown in Fig. 5. Apparently, the nanorod with R=2.5 appears as the strongest scatterer offering the brightest signal and represents the average aspect ratio of gold nanorods observed in our experiments. For an increasing R, the overall scattering intensity as well as the shape of the scattering patterns are modified. Hence, we conclude that variations of the aspect ratio are ma! inly responsible for the differences of the scattering patterns observed for different nanorods in our experiments (compare, for example, the scattering patterns in Fig. 3(c)).

Fig. 5. Integrated scattering intensity of a gold nanorod as function of the aspect ratio R=a/b calculated for the excitation wavelength 633 nm assuming a constant nanorod width b of 15 nm as well as refractive index matching conditions n 2=n 1 (i.e the particle is located at a glass-oil interface, see also Fig. 3). (Insets) Corresponding scattering patterns of gold nanorods simulated for R=2.5, 4 and 7, respectively. The intensity scale provided by the underlying color map is optimized for R=7 and kept constant in all three images.

3.3. Direction of refractive index transition and contrast inversion

In the following, we demonstrate that CISM allows to localize even weak dielectric interfaces and to distinguish the direction of the refractive index transition (high n to low n or low n to high n) by analyzing the contrast of the scattering pattern of an individual gold nanorods. As sketched in Fig. 6, spatially isolated, individual gold nanorods were located at either a glass-water (high n to low n) or water-glass (low n to high n) interface with respect to the microscope objective focused on the sample from below (see also Fig. 2). All scattering patterns acquired from nanorods located at the lower interface (transition high n to low n) exhibit negative image contrast as can be seen in Fig. 6, Inset(I). In contrary, all the scattering images measured from nanorods located at the upper interface (transition low n to high n) show inverted, i.e. positive, image contrast (see Fig. ! 6, Inset (II)). The explanation of this phenomenon is that the reflection coefficients of the two interfaces differ by a phase factor of π effectively switching the overall phase of the reflected field E r [38

38. M. Born and E. Wolf.Principles of optics, Pergamon Pr., Oxford,1964).

].

Measuring the sign or varitions of the image contrast could represent a promising experimental approach to determine the position of a particle within an interface between two dielectric media or to detect small local changes in the dielectric properties of the interface itself. Monitoring dielectric modifications in active interfaces like, for example, a cell membrane with high spatial resolution could allow for tracking the flow of single proteins into and out of a cell or to determine the amount of particles passing through a membrane.

4. Conclusion

We have investigated the scattering patterns of individual, spatially isolated gold nanorods placed at a planar interface between two transparent media. We measured the effect of the refractive index mismatch on the scattering intensity, the signal-to-background ratio as well as the image contrast and its sign. We found that the scattering properties of each single particle could be modified by varying in-situ the dielectric properties of the surrounding media. As a major result, the signal-to-background ratio was found to be maximized in the index matching regime, i.e. for diminishing reflection of excitation light at the interface. Under this condition, the scattering patterns are determined exclusively by the geometrical and, hence, plasmonic properties of the particles. Moreover, we demonstrated that scattering patterns of individual gold nanorods reveal the nature of closely spaced dielectric interfaces due to a sign inversion of the image contrast.

Fig. 6. Schematic of a sample with individual, spatially isolated gold nanorods attached to a lower (glass-water) and an upper (water-glass) interface with respect to the optical setup as sketched in Fig. 2. (Inset (I)/(II)) The corresponding experimental scattering patterns measured for single nanorods (excitation with an APDM at λ=633 nm) at the lower/upper interface show negative/positive contrast. The intensity scale provided by the underlying color map is optimized for each image separately.

The combination of CISM and higher order laser modes provides simultaneously accurate topological information like the position, the shape and the orientation of metallic nanoparticles [28

28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

,31

31. T. Züchner, A.V. Failla, A. Hartschuh, and A.J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au-nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343, (2008). [CrossRef] [PubMed]

,32

32. A.V. Failla, S.W. Jäger, T. Züchner, M. Steiner, and A.J. Meixner, “Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy,” Opt. Express 15, 8532–8542, (2007). [CrossRef] [PubMed]

] and allows for monitoring small variations in their local dielectric environment. Our results demonstrate the potential of advanced confocal microscopy techniques, see also e.g. [39

39. S. Martin, A.V. Failla, U. Spöri, C. Cremer, and A. Pombo, “Measuring the Size of Biological Nanostructures with Spatially Modulated Illumination Microscopy,” Mol. Biol. Cell. 15, 2449–2455, (2004). [CrossRef] [PubMed]

, 40

40. E.J. Botcherby, R. Juškaitis, M.J. Booth, and T. Wilson, “Aberration-free optical refocusing in high numerical aperture microscopy,” Opt. Lett. 32, 2007–2009, (2007). [CrossRef] [PubMed]

], for the in-vivo detection of metallic sensors attached to or incorporated in biological systems.

Acknowledgments

We acknowledge stimulating discussions with Achim Hartschuh (LMU, Munich, Germany) and Stefanie Reichelt (Cancer Research UK, Cambridge, UK) as well as experimental assistance by Frank Wackenhut. Financial support was provided by the Deutsche Forschungsgemeinschaft DFG (Me 1600/6-1/2) and the Landesstiftung Baden-Württemberg. Scan images were in part processed using WSxM software from nanotec [41

41. I. Horcas, R. Fernandez, J.M. Gomez-Rodriguez, J. Colchero, J. Gomez-Herrero, and A.M. Baro. “WSXM: A software for scanning probe microscopy and a tool for nanotechnology.” Rev. Sci. Instrum. , 78, 013705–8, (2007). [CrossRef] [PubMed]

].

References and links

1.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402, (2002). [CrossRef] [PubMed]

2.

A. Bouhelier, R. Bachelot, G. Lerondel, S. Kostcheev, P. Royer, and G.P. Wiederrecht, “Surface plasmon characteristics of tunable photoluminescence in single gold nanorods,” Phys. Rev. Lett. 95, 267405, (2005). [CrossRef]

3.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314, (2004). [CrossRef]

4.

J.J. Mock, M. Barbic, D.R. Smith, D.A. Schultz, and S. Schultz, “Shape effects in plasmon resonance of individual colloidal silver nanoparticles,” J. Chem. Phys. 116, 6755–6758, (2002). [CrossRef]

5.

K.-S. Lee and M. A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: Sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110, 19220–19225, (2006). [CrossRef] [PubMed]

6.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in biological imaging and biomedicine,” J. Phys. Chem. B 110, 7238–7248, (2006). [CrossRef] [PubMed]

7.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677, (2003). [CrossRef]

8.

F. Tam, C. Moran, and N. Halas, “Geometrical parameters controlling sensitivity of nanoshell plasmon resonances to changes in dielectric environment,” J. Phys. Chem. B 108, 17290–17294, (2004). [CrossRef]

9.

M. Steiner, C. Debus, A. V. Failla, and A. J. Meixner, “Plasmon-enhanced emission in gold nanoparticle aggregates,” J. Phys. Chem. C 112, 3103–3108, (2008). [CrossRef]

10.

A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express 13, 2668–2677, (2005). [CrossRef] [PubMed]

11.

J. J. Mock, D. R. Smith, and S. Schult, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3, 485–491, (2003). [CrossRef]

12.

D. Yelin, D. Oron, S. Thiberge, E. Moses, and Y. Silberberg, “Multiphoton plasmon-resonance microscopy,” Opt. Express 11, 1385–1391, (2003). [CrossRef] [PubMed]

13.

X. Huang, I.H. El-Sayed, W. Qian, and M.A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120, (2006). [CrossRef] [PubMed]

14.

H. Wang, T.B. Huff, D.A. Zweifel, W. He, P.S. Low, A. Wei, and J.-X. Cheng, “In vitro and in vivo two-photon luminescence imaging of single gold nanorods,” PNAS 102, 15752–15756, (2005). [CrossRef] [PubMed]

15.

H. Hess and Y. Tseng, “Active intracellular transport of nanoparticles: Opportunity or threat?” ACS Nano 1, 390–392, (2007). [CrossRef] [PubMed]

16.

C. Sönnichsen, B.M. Reinhard, J. Liphardt, and A.P. Alivisatos. “A molecular ruler based on plasmon coupling of single gold and silver nanoparticles,” Nature Biotech. 23, 741–745, (2005). [CrossRef]

17.

G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kürzinger, “Biomolecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3, 935–938, (2003). [CrossRef]

18.

K. J. Lee, P. D. Nallathamby, L. M. Browning, C. J. Osgood, and X. -H. N. Xu, “In Vivo Imaging of Transport and Biocompatibility of Single Silver Nanoparticles in Early Development of Zebrafish Embryos,” ACS Nano 1, 133–143, 2007. [CrossRef] [PubMed]

19.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” PNAS 97, 996–1001, (2000). [CrossRef] [PubMed]

20.

M.R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B , 68, 1154331–11543310, (2003). [CrossRef]

21.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett, 96, 113002, (2006).

22.

C.J. Orendorff, L. Gearheart, N.R. Jana, and C.J. Murphy, “Aspect ratio dependence on surface enhanced raman scattering using silver and gold nanorod substrates,” Phys. Chem. Chem. Phys. 8, 165–170, (2006). [CrossRef] [PubMed]

23.

F.V. Ignatovich, A. Hartschuh, and L. Novotny, “Detection of nanoparticles using optical gradient forces,” J. Mod. Opt. 50, 1509–1520, (2003).

24.

V. Jacobsen, P. Stoller, C. Brunner, V. Vogel, and V. Sandoghdar, “Interferometric optical detection and tracking of very small gold nanoparticles at a water-glass interface,” Opt. Express 14, 405–414, (2006). [CrossRef] [PubMed]

25.

O.L. Muskens, N. Del Fatti, F. Vallée, J.R. Huntzinger, P. Billaud, and M. Broyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109, (2006). [CrossRef]

26.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163, (2002). [CrossRef] [PubMed]

27.

S. Berciaud, L. Cognet, G.A. Blab, and B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402–257406, (2004). [CrossRef]

28.

A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A.J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6, 1374–1378, (2006). [CrossRef] [PubMed]

29.

C.J.R. Sheppard and D.M. Shotton, Confocal Laser Scanning Microscopy, (Bios Scientific Publishers, London, 1997).

30.

C.J.R. Sheppard and Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik 87, 129–132, (1991).

31.

T. Züchner, A.V. Failla, A. Hartschuh, and A.J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au-nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343, (2008). [CrossRef] [PubMed]

32.

A.V. Failla, S.W. Jäger, T. Züchner, M. Steiner, and A.J. Meixner, “Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy,” Opt. Express 15, 8532–8542, (2007). [CrossRef] [PubMed]

33.

S. Link, M.B. Mohamed, and M.A. El-Sayed, “Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant,” J. Phys. Chem. B 103, 3073–3077, (1999). [CrossRef]

34.

B. Nikoobakht and M.A. El-Sayed, “Preparation and growth mechanism of gold nanorods (NRs) using seed-mediated growth method,” Chem. Mater. 15, 1957–1962, (2003). [CrossRef]

35.

B. Nikoobakht and M.A. El-Sayed, “Evidence for Bilayer Assembly of Cationic Surfactants on The Surface of Gold Nanorods,” Langmuir 17, 6368–6374, (2001). [CrossRef]

36.

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 25, 377–445, (1908). [CrossRef]

37.

C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles, (JohnWiley & Sons, New York, 1983).

38.

M. Born and E. Wolf.Principles of optics, Pergamon Pr., Oxford,1964).

39.

S. Martin, A.V. Failla, U. Spöri, C. Cremer, and A. Pombo, “Measuring the Size of Biological Nanostructures with Spatially Modulated Illumination Microscopy,” Mol. Biol. Cell. 15, 2449–2455, (2004). [CrossRef] [PubMed]

40.

E.J. Botcherby, R. Juškaitis, M.J. Booth, and T. Wilson, “Aberration-free optical refocusing in high numerical aperture microscopy,” Opt. Lett. 32, 2007–2009, (2007). [CrossRef] [PubMed]

41.

I. Horcas, R. Fernandez, J.M. Gomez-Rodriguez, J. Colchero, J. Gomez-Herrero, and A.M. Baro. “WSXM: A software for scanning probe microscopy and a tool for nanotechnology.” Rev. Sci. Instrum. , 78, 013705–8, (2007). [CrossRef] [PubMed]

OCIS Codes
(180.0180) Microscopy : Microscopy
(180.1790) Microscopy : Confocal microscopy
(180.3170) Microscopy : Interference microscopy
(290.5850) Scattering : Scattering, particles

ToC Category:
Microscopy

History
Original Manuscript: June 10, 2008
Revised Manuscript: July 24, 2008
Manuscript Accepted: July 24, 2008
Published: September 3, 2008

Virtual Issues
Vol. 3, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Tina Züchner, Antonio Virgilio Failla, Mathias Steiner, and Alfred J. Meixner, "Probing dielectric interfaces on the nanoscale with elastic scattering patterns of single gold nanorods," Opt. Express 16, 14635-14644 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-19-14635


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, "Drastic reduction of plasmon damping in gold nanorods," Phys. Rev. Lett. 88, 077402 (2002). [CrossRef] [PubMed]
  2. A. Bouhelier, R. Bachelot, G. Lerondel, S. Kostcheev, P. Royer, and G. P. Wiederrecht, "Surface plasmon characteristics of tunable photoluminescence in single gold nanorods," Phys. Rev. Lett. 95, 267405 (2005). [CrossRef]
  3. T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, "Tomographic plasmon spectroscopy of a single gold nanoparticle," Nano Lett. 4, 2309-2314 (2004). [CrossRef]
  4. J. J. Mock, M. Barbic, D. R. Smith, D. A. Schultz, and S. Schultz, "Shape effects in plasmon resonance of individual colloidal silver nanoparticles," J. Chem. Phys. 116, 6755-6758 (2002). [CrossRef]
  5. K.-S. Lee and M. A. El-Sayed, "Gold and silver nanoparticles in sensing and imaging: Sensitivity of plasmon response to size, shape, and metal composition," J. Phys. Chem. B 110, 19220-19225 (2006). [CrossRef] [PubMed]
  6. P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, "Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in biological imaging and biomedicine," J. Phys. Chem. B 110, 7238-7248 (2006). [CrossRef] [PubMed]
  7. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment," J. Phys. Chem. B 107, 668-677 (2003). [CrossRef]
  8. F. Tam, C. Moran, and N. Halas, "Geometrical parameters controlling sensitivity of nanoshell plasmon resonances to changes in dielectric environment," J. Phys. Chem. B 108, 17290-17294 (2004). [CrossRef]
  9. M. Steiner, C. Debus, A. V. Failla, and A. J. Meixner, "Plasmon-enhanced emission in gold nanoparticle aggregates," J. Phys. Chem. C 112, 3103-3108 (2008). [CrossRef]
  10. A. Curry, G. Nusz, A. Chilkoti, and A. Wax, "Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy," Opt. Express 13, 2668-2677 (2005). [CrossRef] [PubMed]
  11. J. J. Mock, D. R. Smith, and S. Schult, "Local refractive index dependence of plasmon resonance spectra from individual nanoparticles," Nano Lett. 3, 485-491 (2003). [CrossRef]
  12. D. Yelin, D. Oron, S. Thiberge, E. Moses, and Y. Silberberg, "Multiphoton plasmon-resonance microscopy," Opt. Express 11, 1385-1391 (2003). [CrossRef] [PubMed]
  13. X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006). [CrossRef] [PubMed]
  14. H. Wang, T. B. Huff, D. A. Zweifel, W. He, P. S. Low, A. Wei, and J.-X. Cheng, "In vitro and in vivo two-photon luminescence imaging of single gold nanorods," PNAS 102, 15752-15756 (2005). [CrossRef] [PubMed]
  15. H. Hess and Y. Tseng, "Active intracellular transport of nanoparticles: Opportunity or threat?" ACS Nano 1, 390-392 (2007). [CrossRef] [PubMed]
  16. C. Sönnichsen, B. M. Reinhard, J. Liphardt, and A. P. Alivisatos, "A molecular ruler based on plasmon coupling of single gold and silver nanoparticles," Nature Biotech. 23, 741-745 (2005). [CrossRef]
  17. G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kürzinger, "Biomolecular recognition based on single gold nanoparticle light scattering," Nano Lett. 3, 935-938 (2003). [CrossRef]
  18. K. J. Lee, P. D. Nallathamby, L. M. Browning, C. J. Osgood, and X. -H. N. Xu, "In Vivo Imaging of Transport and Biocompatibility of Single Silver Nanoparticles in Early Development of Zebrafish Embryos," ACS Nano 1, 133-143 (2007). [CrossRef] [PubMed]
  19. S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, "Single-target molecule detection with nonbleaching multicolor optical immunolabels," PNAS 97, 996-1001 (2000). [CrossRef] [PubMed]
  20. M. R. Beversluis, A. Bouhelier, and L. Novotny, "Continuum generation from single gold nanostructures through near-field mediated intraband transitions," Phys. Rev. B 68, 1154331-11543310 (2003). [CrossRef]
  21. P. Anger, P. Bharadwaj, and L. Novotny, "Enhancement and quenching of single-molecule fluorescence," Phys. Rev. Lett,  96, 113002 (2006).
  22. C. J. Orendorff, L. Gearheart, N. R. Jana, and C. J. Murphy, "Aspect ratio dependence on surface enhanced raman scattering using silver and gold nanorod substrates," Phys. Chem. Chem. Phys. 8, 165-170 (2006). [CrossRef] [PubMed]
  23. F. V. Ignatovich, A. Hartschuh, and L. Novotny, "Detection of nanoparticles using optical gradient forces," J. Mod. Opt. 50, 1509-1520 (2003).
  24. V. Jacobsen, P. Stoller, C. Brunner, V. Vogel, and V. Sandoghdar, "Interferometric optical detection and tracking of very small gold nanoparticles at a water-glass interface," Opt. Express 14, 405-414 (2006). [CrossRef] [PubMed]
  25. O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, "Single metal nanoparticle absorption spectroscopy and optical characterization," Appl. Phys. Lett. 88, 063109 (2006). [CrossRef]
  26. D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, "Photothermal imaging of nanometer-sized metal particles among scatterers," Science 297, 1160-1163 (2002). [CrossRef] [PubMed]
  27. S. Berciaud, L. Cognet, G. A. Blab, and B. Lounis, "Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals," Phys. Rev. Lett. 93, 257402-257406 (2004). [CrossRef]
  28. A.V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006). [CrossRef] [PubMed]
  29. C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (Bios Scientific Publishers, London, 1997).
  30. C. J. R. Sheppard and Y. Gong, "Improvement in axial resolution by interference confocal microscopy," Optik 87, 129-132 (1991).
  31. T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au-nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2008). [CrossRef] [PubMed]
  32. A. V. Failla, S. W. Jäger, T. Züchner, M. Steiner, and A. J. Meixner, "Topology measurements of metal nanoparticles with 1 nm accuracy by confocal interference scattering microscopy," Opt. Express 15, 8532-8542 (2007). [CrossRef] [PubMed]
  33. S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999). [CrossRef]
  34. B. Nikoobakht and M. A. El-Sayed, "Preparation and growth mechanism of gold nanorods (NRs) using seedmediated growth method," Chem. Mater. 15, 1957-1962 (2003). [CrossRef]
  35. B. Nikoobakht and M. A. El-Sayed, "Evidence for Bilayer Assembly of Cationic Surfactants on The Surface of Gold Nanorods," Langmuir 17, 6368-6374 (2001). [CrossRef]
  36. G. Mie, "Beiträge zur optik trüber medien, speziell kolloidaler metallösungen," Ann. Phys. 25, 377-445 (1908). [CrossRef]
  37. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (JohnWiley & Sons, New York, 1983).
  38. M. Born and E. Wolf. Principles of optics (Pergamon Pr., Oxford,1964).
  39. S. Martin, A. V. Failla, U. Spöri, C. Cremer, and A. Pombo, "Measuring the Size of Biological Nanostructures with Spatially Modulated Illumination Microscopy," Mol. Biol. Cell. 15, 2449-2455 (2004). [CrossRef] [PubMed]
  40. E. J. Botcherby, R. Ju¡skaitis, M. J. Booth, and T. Wilson, "Aberration-free optical refocusing in high numerical aperture microscopy," Opt. Lett. 32, 2007-2009 (2007). [CrossRef] [PubMed]
  41. I. Horcas, R. Fernandez, J. M. Gomez-Rodriguez, J. Colchero, J. Gomez-Herrero, and A. M. Baro. "WSXM: A software for scanning probe microscopy and a tool for nanotechnology." Rev. Sci. Instrum.,  78, 013705-8 (2007). [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