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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 12 — Dec. 1, 2008
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Enhancement of laser-induced fluorescence at 473 nm excitation with subwavelength resonant waveguide gratings

Petri Karvinen, Tarmo Nuutinen, Outi Hyvärinen, and Pasi Vahimaa  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 16364-16370 (2008)
http://dx.doi.org/10.1364/OE.16.016364


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Abstract

A dielectric subwavelength resonant waveguide grating was designed and fabricated in order to enhance fluorescence of biomolecules. More than 80 times higher laser-induced fluorescence yield was observed from enhanced green fluorescence protein on the structure when compared to same material on a flat surface.

© 2008 Optical Society of America

1. Introduction

In quantifying and visualizing biomolecules the use of fluorescent labels is one of the most wide-spread methods. Besides the improvements in excitation illumination methods and in the detection of the emitted light also various amplification schemes have been developed to boost the fluorescence yield. A few of these schemes are based on the enhancement of local field intensities of the coherent light used as an excitation beam; for example total internal reflection configurations, evanescent fields in and near waveguides, surface plasmon resonances [1

1. K. Tawa, H. Hori, K. Kintaka, K. Kiyosue, Y. Tatsu, and J. Nishii, “Optical microscopic observation of fluorescence enhanced by grating-coupled surface plasmon resonance,” Opt. Express 16, 9781–9790 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-13-9781. [CrossRef] [PubMed]

, 2

2. F.-C. Chien, C.-Y. Lin, J.-N. Yih, K.-L. Lee, C.-W. Chang, P.-K. Wei, and S.-J. Chen, “Plasmon-enhanced optical waveguide biosensors constructed with sub-wavelength gold grating,” Proc. SPIE 6323, 63230M (2006). [CrossRef]

, 3

3. J. Zhang and J. R. Lakowicz, “Metal-enhanced fluorescence of an organic fluorophore using gold particles,” Opt. Express 15, 2598–2606 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2598. [CrossRef] [PubMed]

], and various photonic crystal devices [4

4. N. Ganesh, W. Zhang, P. C. Mathias, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nanotechnology 2, 515–520 (2007). [CrossRef]

, 5

5. 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, 2351–2360 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-12-2351. [CrossRef] [PubMed]

] can be used.

On the other hand, resonant waveguide grating (RWG) [6

6. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32 (14), 2606–2613 (1993), http://www.opticsinfobase.org/abstract.cfm?URI=ao-32-14-2606. [CrossRef]

] is a one type of a structure studied extensively lately. Besides their commonly known sharp and tunable filtering properties also their use in pulse shaping [7

7. T. Vallius, P. Vahimaa, and J. Turunen, “Pulse deformations at guided-mode resonance filters,” Opt. Express 10, 840–843 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-16-840. [PubMed]

] and in the enhancement of light-matter interaction, e.g. in the case of second harmonic generation [8

8. 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, 111109 (2007). [CrossRef]

], has been examined. The phenomenon examined in the latter example is due to very high local energy densities that exist inside these RWG structures, and this field enhancement can also be used to increase fluorescence in analytical applications in biosciences or in medicine.

2. Theory

A resonant waveguide grating is basically a diffractive grating and a waveguide in one element. A dielectric subwavelength transmission-type RWG couples a certain, typically very narrow wavelength band into a waveguide mode. This mode is then slowly coupled back into the direction of reflection, and these elements are commonly considered to be good narrow band filters. The filtering and other common properties of these structures are described in more detail elsewhere [6

6. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32 (14), 2606–2613 (1993), http://www.opticsinfobase.org/abstract.cfm?URI=ao-32-14-2606. [CrossRef]

, 9

9. J. Saarinen, E. Noponen, and J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34 (9), 2560–2566 (1995). [CrossRef]

]. The resonance conditions are also very sensitive to the refractive index of the surrounding material. This attribute of the RWGs can be used for example in sensors measuring concentration or other properties that alter the refractive index of liquids [10

10. B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002). [CrossRef]

, 11

11. P. Y. Li, B. Lin, J. Gerstenmaier, and B. T. Cunningham, “A new method for label-free imaging of biomolecular interactions,” Sens. Actuators B 996–13 (2004). [CrossRef]

, 12

12. J. Yih, Y. Chu, Y. Mao, W. Wang, F. Chien, C. Lin, K. Lee, P. Wei, and S. Chen, “Optical waveguide biosensors constructed with subwavelength gratings,” Appl. Opt. 45, 1938–1942 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-9-1938. [CrossRef] [PubMed]

].

The interesting fact in our case is that these propagating waveguide modes also lead to very high local energy densities inside the grating. Because the structure can be designed to be a surface relief grating which also functions as the waveguide layer, these high intensity hot spots can be exposed to the transmission medium (in our case water-based solution) in the grooves of the grating. Fluorescent material can now be introduced into these grooves, and the structure can be used as an aforementioned fluorescence amplification scheme.

3. Design and fabrication

The waveguide resonance occurs at a certain wavelength, which depends on the polarization of the incident light, physical dimensions of the structure and the angle of incidence. Numerical calculations based on rigorous diffraction theory [13

13. J. Turunen, “Diffraction theory of microrelief gratings,” in Micro-optics: Elements, Systems and Applications, ed. H.P. Herzig, (Taylor & Fracis, London, 1997)

] were used to design a resonant grating for the wavelength λ=473 nm, with the angle of incidence around 5 °. The designed resonant grating consists of a binary SiO2 grating (period 250 nm, fill factor 0.5, height 200 nm), which is coated with an evaporated 170 nm thick TiO2 layer. A schematic diagram of the structure as well as of the measurement setup is presented in Fig. 1. It should be noted that the thickness of TiO2 coating is not the same on top of the grating and in the bottom of the grooves; this is due to the fabrication process and it was taken into account already during the design step.

Fig. 1. A schematic diagram of the measurement setup and the sample. A RWG fabricated on SiO2 substrate is covered with fluorescent proteins (EGFP) and illuminated from the substrate side. Resulting fluorescence is detected with a CCD while the incident angle is varied (the sample is rotated).

The aim in the design was to achieve as high energy densities as possible in the grooves and near the surface of the grating. In "f2">Fig. 2 the calculated time average of the energy density is plotted inside one grating period. For the optimization process a numerical model was devised: the time average of the energy density was integrated along a path 2 nm away from the TiO 2 surface and the result was then divided with a same type of integral 2 nm away from a flat, unstructured TiO2 layer. This value is also later on used as a rough theoretical estimation of the fluorescence gain, plotted with measurement results in Fig. 5.

Fig. 2. Calculated enhancement of the energy density when compared to the incoming field. Cross-section of one period is shown on the left: white lines denote boundaries between different materials (as from left to right: SiO2 substrate, TiO2 coating and water) and dashed red and blue lines show the sections examined more closely in the plotted curves on the right. Illumination is from the left, and the angle of incidence is 2.35° in relative to the z-axis.

For the fabrication of the designed element standard electron beam lithography processes commonly used in micro-optics [14

14. P. Rai-Choudhury, Handbook of Microlithography, Micromachining, and Microfabrication: Volume 1: Microlithography, (SPIE—The International Society for Optical Engineering, 1997)

] were used. A 5” x 5” x 0.09” fused silica mask plate was first spin-coated with PMMA resist. Resist was exposed by an electron beam pattern generator (Vistec EBPG 5000+ESHR) and then developed in a mixture of methyl-isobutyl-ketone and isopropanol. The resulting resist structure was then used in a lift-off process to create a chromium structure. This was in turn used as a mask in reactive ion etching of the substrate in CHF3/Ar plasma (Oxford Instruments PlasmaLab 80). After the removal of the residual chromium the sample was coated with TiO2 by vacuum deposition. A SEM image of one of the final elements can be seen in Fig. 3. The dimensions of the grating are within the fabrication tolerances from the design, but naturally slight deviations exist both in the physical dimensions and the shape of the structure. Especially it should be noted that in the evaporation process the top part of the TiO2 coating is rounded and expanded from the designed rectangular shape, which results in more narrow gap leading to the bottom of the grooves than was intended. From the cross-section SEM image the depth of the SiO2 grating was measured to be 215 nm, fill factor 0.52, and the thickness of the TiO2 layer on top of the grating 172 nm. TiO2 thickness on the bottom of the grooves was 48 nm and on the sidewalls 38 nm. With these parameters the resonance should occur with an incident angle of 2.35 ° when the refractive index of the buffer solution is estimated to be same as water’s. These same measured grating parameters are used throughout this paper where theoretical results are presented (mainly Figs. 2 and 5) for the sake of consistency.

Fig. 3. SEM image of the RWG structure.

In the measurements Enhanced Green Fluorescent Protein (EGFP) was used as a fluorescent material. EGFP exhibits excitation and emission maxima at 488 nm and 509 nm (respectively). In this work, EGFP was produced as recombinant protein with affinity tags in Escherichia coli. Coding sequence for the enhanced green fluorescent protein (EGFP) was amplified by polymerase chain reaction (PCR) from pEGFP-N1 vector (Clontech) and inserted to bacterial expression vector pGEX-1λ T (Amersham). By the PCR primers coding sequence for some extra amino acids e.g. for carboxy terminal histidine tag were introduced to the construct. Proteins were expressed and purified applying manufacturers protocols. Protein solution containing 1.0 µM EGFP (Purity >95% by SDS-PAGE) in 0.1% triton-X-100 in phosphate buffered saline (PBS) was prepared and applied to the surfaces. Proteins were allowed to freely adsorb from the solution 2 hours in the room temperature and excess of unbound or loosely bound proteins were washed from the surface with the Triton-PBS-solution. Finally, samples were sealed under glass cover-slips to avoid the samples to dry out (Fig. 1 right). Smooth distribution of the proteins over the surfaces and the absence of any visible protein aggregates were confirmed by epifluorescence microscopy.

4. Measurements, results and discussion

A TM-polarized DPSS-laser beam at the wavelength of 473 nm and power of 46mW, manufactured by Changhun New Industries Optoelectronics, Ltd was used as an excitation light source. The measuring system was introduced earlier in the figure 1. First after the laser there was a diaphragm to decrease the intensity of light on the sample. Too high intensities caused the EGFP fluorescence to bleach out in a rate visible to the eye (photobleaching). The sample was placed on a rotatable table to detect the incident angle dependence of the fluorescence, caused by the incident angle dependence of the resonant waveguide grating.

The grating was on the camera side face of the sample. The grating lines were in vertical direction, so that the plane of incidence is the horizontal plane. The emitted fluorescent light was detected with a CCD-camera, using a bandpass interference filter (center wavelength at 510 nm and passband of ±10nm) in between the sample and the CCD-cell to collect only the fluorescent light. The camera was fixed in relative to the incident laser beam, so the detection angle in relative to the substrate normal varied between 35 and 45 degrees when the sample was rotated. Within these limits the angular distribution of the emitted fluorescence resembles that of a lambertian source both in and out of resonance (and with the flat surface used as a control); this was noted in the theoretical calculations and also checked in practice during the measurements. Thus the effect of this change in the measurement angle was canceled out when the gain was calculated.

Camera is SBIG STL-4020M with a CCD-array of 2048×2048 pixels, 7.4×7.4 µm each. In our images each pixel is a mean value of 3×3 pixels. Three scaled sample images are presented in Fig. 4: first one from a flat reference surface, second taken from the sample when the incident angle is not the resonant angle, and finally an image from the RWG sample in resonance. The buffer controls (samples without EGFP, only buffer solution on RWG) did not emit any detectable fluorescence.

Fig. 4. Scaled intensity images (in arbitrary units) taken from (a) flat TiO2 surface, (b) the RWG structure when incident angle is outside resonance and (c) the RWG when the resonance conditions are met.

The camera was connected to pc for analyzing the results. Intensity of fluorescence signal was calculated from the images and divided by the intensity of a TiO 2 surface without structure covered with the same fluorescent proteins. This calculated gain from two different samples is presented as a function of incident angle in figure 5: the intensity of the fluorescence signal was observed to be over 80 times higher when the resonance conditions were met when compared to the flat surface.

Also the polarization of the emission was measured by adding a rotatable linear polarizer in front of the CCD-camera. The emitted fluorescence was noted to be partially linearly polarized in all configurations: roughly two thirds (66%) of the emission of the proteins on the flat surface and on the structured surface (both out of resonance and in resonance) was TM-polarized. This was expected, because the incident laser beam is fully TM-polarized, and the statistical excitation probability of a single molecule depends on its orientation in relative to the polarization of the excitation. Thus, if we roughly model the fluorescent molecules as dipoles attached into the surface (not in completely free motion), we get emission which is partially polarized in the same direction as the light used in excitation. The more noteworthy result of this measurement is the fact that the polarization of the emission does not significantly change when the RWG is used to enhance the fluorescence.

Fig. 5. Measured gain in fluorescence when compared to unstructured surface for two similar samples (blue dots and red diamonds), and a rough theoretical estimation of the fluorescence gain made during the design step (black solid curve).

The seemingly large difference between estimated and measured maximum gain is mostly due to combination of unideal component and possible uneven distribution of adsorbed proteins on a surface with micro- and nanostructures. As was already mentioned, in the final element the gap leading to the bottom of the grooves turned out to be only a few nanometers wide. It is reasonable to assume that the amount of adsorbed proteins inside the grooves (where the highest energy densities reside in) is smaller when compared to a flat surface, while the reference basis of the calculated enhancement was to assume the adsorbtion to be even in both cases. Also it should be kept in mind that the rough theoretical model used here is devised to get relative information of the fluorescence enhancement capabilities of different structures, not to give absolute gain ratios. For example if the path integral is taken further than 2 nm away from the structure surface, the resulting theoretical gain drops.

The shift of the incident angle of the resonant conditions is mainly due to the change in the refractive index of the solution containing the proteins near the structure, which depends on the amount of molecules adsorbed. As was already mentioned, this phenomenon is used in various measurement schemes. In our case the resonant angle was not of interest, so what amount of the deviation is due to unideal component and what is caused by the distribution and adsorbtion of the proteins is not studied here. However, it should be noted that a change of about 0.05 in the refractive index of the water solution near the TiO2 surface can solely be responsible of the shift in the incident angle seen in Fig. 5.

Despite the above-mentioned shortcomings of the theoretical gain estimation, it still served its original purpose and also provides the explanation of the significant fluorescence enhancement observed with the fabricated samples. The fact that the width of the measured and calculated enhancement peaks in the Fig. 5 correspond to each other is a strong indicator that the calculated resonance is responsible for the measured fluorescence enhancement. Other possible reasons for higher fluorescence yield, like stronger adsorbtion on the grating surface than on a flat one, can be ruled out because enhancement occurs only with certain incident angles (that correspond to the resonant angles).

5. Conclusion

A subwavelength resonant grating was designed and fabricated to operate at the wavelength of 473 nm. Fluorescence emitted from enhanced green fluorescent protein on top of the grating was detected and compared to fluorescence from same molecules on a flat surface. Over 80 times higher fluorescence yield was detected from the molecules on the grating when resonance conditions were met. This significant gain is due to local enhancement of electromagnetic field inside the structure.

Acknowledgment

The work of P. Karvinen was financed by the Graduate School on Modern Optics and Photonics, and T. Nuutinen would like to thank ISB (The National Graduate School in Informational and Structural Biology) for support. Authors also gratefully acknowledge H. J. Hyvärinen for coding support and also NEMO (Network of Excellence on Micro-Optics).

References and links

1.

K. Tawa, H. Hori, K. Kintaka, K. Kiyosue, Y. Tatsu, and J. Nishii, “Optical microscopic observation of fluorescence enhanced by grating-coupled surface plasmon resonance,” Opt. Express 16, 9781–9790 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-13-9781. [CrossRef] [PubMed]

2.

F.-C. Chien, C.-Y. Lin, J.-N. Yih, K.-L. Lee, C.-W. Chang, P.-K. Wei, and S.-J. Chen, “Plasmon-enhanced optical waveguide biosensors constructed with sub-wavelength gold grating,” Proc. SPIE 6323, 63230M (2006). [CrossRef]

3.

J. Zhang and J. R. Lakowicz, “Metal-enhanced fluorescence of an organic fluorophore using gold particles,” Opt. Express 15, 2598–2606 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2598. [CrossRef] [PubMed]

4.

N. Ganesh, W. Zhang, P. C. Mathias, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nanotechnology 2, 515–520 (2007). [CrossRef]

5.

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, 2351–2360 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-12-2351. [CrossRef] [PubMed]

6.

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32 (14), 2606–2613 (1993), http://www.opticsinfobase.org/abstract.cfm?URI=ao-32-14-2606. [CrossRef]

7.

T. Vallius, P. Vahimaa, and J. Turunen, “Pulse deformations at guided-mode resonance filters,” Opt. Express 10, 840–843 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-16-840. [PubMed]

8.

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, 111109 (2007). [CrossRef]

9.

J. Saarinen, E. Noponen, and J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34 (9), 2560–2566 (1995). [CrossRef]

10.

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002). [CrossRef]

11.

P. Y. Li, B. Lin, J. Gerstenmaier, and B. T. Cunningham, “A new method for label-free imaging of biomolecular interactions,” Sens. Actuators B 996–13 (2004). [CrossRef]

12.

J. Yih, Y. Chu, Y. Mao, W. Wang, F. Chien, C. Lin, K. Lee, P. Wei, and S. Chen, “Optical waveguide biosensors constructed with subwavelength gratings,” Appl. Opt. 45, 1938–1942 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-9-1938. [CrossRef] [PubMed]

13.

J. Turunen, “Diffraction theory of microrelief gratings,” in Micro-optics: Elements, Systems and Applications, ed. H.P. Herzig, (Taylor & Fracis, London, 1997)

14.

P. Rai-Choudhury, Handbook of Microlithography, Micromachining, and Microfabrication: Volume 1: Microlithography, (SPIE—The International Society for Optical Engineering, 1997)

OCIS Codes
(170.1420) Medical optics and biotechnology : Biology
(300.2530) Spectroscopy : Fluorescence, laser-induced
(050.5745) Diffraction and gratings : Resonance domain

ToC Category:
Diffraction and Gratings

History
Original Manuscript: July 18, 2008
Revised Manuscript: August 28, 2008
Manuscript Accepted: September 2, 2008
Published: September 29, 2008

Virtual Issues
Vol. 3, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Petri Karvinen, Tarmo Nuutinen, Outi Hyvärinen, and Pasi Vahimaa, "Enhancement of laser-induced fluorescence at 473 nm excitation with subwavelength resonant waveguide gratings," Opt. Express 16, 16364-16370 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-21-16364


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References

  1. K. Tawa, H. Hori, K. Kintaka, K. Kiyosue, Y. Tatsu, and J. Nishii, "Optical microscopic observation of fluorescence enhanced by grating-coupled surface plasmon resonance," Opt. Express 16, 9781-9790 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-13-9781. [CrossRef] [PubMed]
  2. F.-C. Chien, C.-Y. Lin, J.-N. Yih, K.-L. Lee, C.-W. Chang, P.-K. Wei, and S.-J. Chen, "Plasmon-enhanced optical waveguide biosensors constructed with sub-wavelength gold grating," Proc. SPIE 6323, 63230M (2006). [CrossRef]
  3. J. Zhang and J. R. Lakowicz, "Metal-enhanced fluorescence of an organic fluorophore using gold particles," Opt. Express 15, 2598-2606 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2598. [CrossRef] [PubMed]
  4. N. Ganesh, W. Zhang, P. C. Mathias, and B. T. Cunningham, "Enhanced fluorescence emission from quantum dots on a photonic crystal surface," Nature Nanotech. 2, 515-520 (2007). [CrossRef]
  5. 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, 2351-2360 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-12-2351. [CrossRef] [PubMed]
  6. S. S. Wang and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32, 2606-2613 (1993), http://www.opticsinfobase.org/abstract.cfm?URI=ao-32-14-2606. [CrossRef]
  7. T. Vallius, P. Vahimaa, and J. Turunen, "Pulse deformations at guided-mode resonance filters," Opt. Express 10, 840-843 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-16-840. [PubMed]
  8. 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, 111109 (2007). [CrossRef]
  9. J. Saarinen, E. Noponen, and J. Turunen, "Guided-mode resonance filters of finite aperture," Opt. Eng. 34, 2560-2566 (1995). [CrossRef]
  10. B. Cunningham, P. Li, B. Lin, and J. Pepper, "Colorimetric resonant reflection as a direct biochemical assay technique," Sens. Actuators B 81, 316-328 (2002). [CrossRef]
  11. P. Y. Li, B. Lin, J. Gerstenmaier, and B. T. Cunningham, "A new method for label-free imaging of biomolecular interactions," Sens. Actuators B 996-13 (2004). [CrossRef]
  12. J. Yih, Y. Chu, Y. Mao, W. Wang, F. Chien, C. Lin, K. Lee, P. Wei, and S. Chen, "Optical waveguide biosensors constructed with subwavelength gratings," Appl. Opt. 45, 1938-1942 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-9-1938. [CrossRef] [PubMed]
  13. J. Turunen, "Diffraction theory of microrelief gratings," in Micro-optics: Elements, Systems and Applications, ed. H.P. Herzig, (Taylor & Fracis, London, 1997)
  14. P. Rai-Choudhury, Handbook of Microlithography, Micromachining, and Microfabrication: Volume 1: Microlithography, (SPIE-The International Society for Optical Engineering, 1997)

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