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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 18 — Sep. 8, 2003
  • pp: 2126–2133
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Multimodal multiplex spectroscopy using photonic crystals

Zhaochun Xu, Zhanglei Wang, Michael E. Sullivan, David J. Brady, Stephen H. Foulger, and Ali Adibi  »View Author Affiliations


Optics Express, Vol. 11, Issue 18, pp. 2126-2133 (2003)
http://dx.doi.org/10.1364/OE.11.002126


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Abstract

Spatio-spectral transmission patterns induced on low coherence fields by disordered photonic crystals can be used to construct optical spectrometers. Experimental results suggest that 1–10 nm resolution multimodal spectrometers for diffuse source analysis may be constructed using a photonic crystal mounted on a focal plane array. The relative independence of spatial and spectral modal response in photonic crystals enables high efficiency spectral analysis of diffuse sources.

© 2003 Optical Society of America

1. Introduction

Optical spectroscopy for chemical and biological sensing is based on spectral structure induced by absorption, refraction, fluorescence or scattering [1

1. R. Narayanaswamy, “Proceedings of the 6th European Conference on Optical Chemical Sensors and Biosensors EUROPT(R)ODE VI,” Sensors and Actuators B 90, 1–345 (2003). [CrossRef]

]. Spectroscopic analysis of incoherent phenomena, such as fluorescence and Raman scattering, is inefficient because spatially diffuse sources couple poorly to spatial filtering spectrometers. Conventional spectrometers spatially filter to reduce ambiguity between spatial and spectral modes. To date, surface enhanced spectroscopy [2

2. M. Moskovits, “Surface-Enhanced Spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985). [CrossRef]

] has been the best approach to overcoming this mismatch. By localizing the fluorescing or scattering source, surface enhancement improves coupling between source and spectrometer. We propose an alternative approach to overcoming this mismatch using multimodal multiplex spectroscopy. Multiplex spectrometers measure weighted projections of multiple wavelength channels and have been common for the past half century [3

3. J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman & Hall, London, 1969).

]. Multimodal spectrometers are designed to measure the spectral density averaged over multiple spatial modes. Integrated multimodal spectroscopy is enabled by recent progress in photonic crystals and is to our knowledge first explicitly introduced in this report. A spectrometer capable of averaging spectral densities over many modes would improve the optical throughput of low coherence sources by several orders of magnitude (similar to the enhancements observed using surface enhancement) and could thereby enable volume Raman and fluorescence spectroscopy of diffuse sources, such as tissue and gases.

Multimodal multiplex spectrometers may be constructed using the spectral diversity of transmission through inhomogeneous photonic crystals. Several groups have used homogeneous photonic crystals to produce spectral filters and prisms. For example, Lin, et al., demonstrated a dispersive prism in two dimensional microwave photonic crystals [4

4. S. Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett.21, 1771–1773 (1996). [CrossRef] [PubMed]

]. Later, Kosaka et al., considered anomalous dispersion photonic crystals near resonance [5

5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998). [CrossRef]

] and proposed use of the resulting superprism effect for wavelength demultiplexing applications [6

6. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: Toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999). [CrossRef]

]. The theory of the superprism effect is well developed [7

7. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000). [CrossRef]

, 8

8. B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012–1020 (2000). [CrossRef]

] and wavelength separation in a planar photonic crystal structure is demonstrated in good agreement with the theory [9

9. L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38, 915–918 (2002). [CrossRef]

]. In all these demonstrations, the incident optical beam has been spatially coherent and the photonic crystal has been assumed to be homogeneous.

Spatio-spectral structure in the transmittance of inhomogeneous disordered photonic crystals can convert spatially incoherent input signals with spatially uniform spectral density into spatially non-uniform spectral densities over a detection plane. The inhomogeneity induced in the transmitted spectrum can be sampled to measure multiplex spectral projections. These projections can be computationally inverted to estimate the mean spectrum over all the modes.

The proposed microspectromer consists of a photonic crystal mating directly to a detector array as shown in Fig. 1. The photonic crystal in this case is a 3D opal structure that is an inhomogeneous quasi-periodic array of microcavities that cause spectral variation in the near field. Advantages of the photonic crystal filter compared to an array of thin film filters are: insensitivity to angle of incidence, ability to characterize large etendue sources, and spectral diversity as a function of position on a small scale less than 10 microns.

Fig. 1. Proposed microspectromer based on spatio-spectral structure in the transmittance of inhomogeneous disordered photonic crystals for diffuse source characterization.

2. Multimodal spectral diversity in photonic crystals

The capacity of photonic crystals to break the ambiguity between spatial and spectral modes was the core of their original conception [12

12. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

, 13

13. S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

]. The idea has been to form “band gaps” such that no modes exist at specific frequencies and then to use dislocations or impurities to introduce localized states. Here we propose a new class of photonic crystal applications that do not require full band gaps, but do rely on inhomogeneous spectral properties due to crystal disorder. We use the local spatio-spectral distribution of fields in photonic crystals to build linear distributed devices for spectral estimation. As an example of a crystal appropriate for these applications, Fig. 2 is a true color image of a colloidal crystal formed of a quasi-periodic array of polymer spheres. The crystal is uniformly illuminated by a halogen light source subtending a solid angle of 0.1 steradians. The half angle is 10 degrees. One is accustomed to observing color separation with gratings, but only for narrow spatial bandwidth fields observed in the far field of the structure. As shown in Fig. 2, a photonic crystal can induce complex multidimensional spectral diversity in the near field of the device. This structure is illustrated in more detail in Fig. 3, which plots the spectral transmission at points distributed on a rectangular grid spaced by 100 microns. The photonic crystal structure is illuminated by the halogen source with an effective source spatial bandwidth of 25mm diameter. The distance of the source to the photonic crystal was 75mm. An Ocean Optics USB2000 fiber optic spectrometer was used to measure the transmission spectrum at a grid of points in a plane 0.5mm behind the opal structure.

Fig. 2. True color photographs of the photonic crystal opal structure illuminated by a white light source. (A) 20X magnification. (B) 4X magnification.

The photonic crystal composites used in our measurements were prepared as described in [14

14. S. H. Foulger, P. Jiang, A. Lattam, D. W. Smith, J. Ballato, D. E. Dausch, S. Grego, and B. R. Stoner, “Photonic crystal composites with reversible high-frequency stop band shifts,” Adv. Mater. 15, 685–689 (2003). [CrossRef]

]. Fabrication begins with a crystalline colloidal array composed of monodispersed crosslinked polystyrene spheres dispersed in water. The sphere diameter is 109±26 nm (mean and standard deviation) and the particle density is 1013–1014 cm-3. The particles formed in a hydrogel using photoinitiated free radical polymerized methacrylate functionalized poly(ethylene glycol)(PEG) [15

15. S. H. Foulger, P. Jiang, Y. R. Ying, A. C. Lattam, D. W. Smith, and J. Ballato, “Photonic bandgap composites,” Adv. Mater. 13, 1898–1901 (2001). [CrossRef]

, 16

16. S. H. Foulger, S. Kotha, B. Sweryda-Krawiec, T. W. Baughman, J. M. Ballato, P. Jiang, and D. W. Smith, “Robust polymer colloidal crystal photonic bandgap structures,” Opt. Lett. 25, 1300–1302 (2000). [CrossRef]

]. Upon hydrogel encapsulation, the long range order of the particles is stable to ionic contamination and minor mechanical deformation. The opalescing hydrogel based film is removed from the glass slide assembly in which it is fabricated [16

16. S. H. Foulger, S. Kotha, B. Sweryda-Krawiec, T. W. Baughman, J. M. Ballato, P. Jiang, and D. W. Smith, “Robust polymer colloidal crystal photonic bandgap structures,” Opt. Lett. 25, 1300–1302 (2000). [CrossRef]

] and allowed to air dry for 2 days, then placed in a vacuum oven at 35 C. The resulting clear film is then swollen in a monomer solution of 2-methoxyethyl acrylate, 2-methoxyethyl methacrylate, or a mixture of the monomers for 2 days. Ethylene glycol dimethacrylate and DEAP are added to this solution and the formulation crosslinked by a 3-minute exposure to a UV lamp. All chemicals were purchased from Aldrich or Acros Organics.

Fig. 3. Transmission curves as a function of wavelength at points p1 through p7. The points are on a 100 micron spaced grid immediately behind the photonic crystal.

Most photonic crystal analyses and applications focus on perfectly periodic structures with perhaps a few defects added to create localized states. Self-assembled colloidal crystals, in contrast, vary slightly in order and period. Such natural inhomogeneity enables multimodal spectroscopy. We searched for regions of the crystal with particularly strong spatio-spectral inhomogeneity. Figure 4 is a spectral diversity map of the crystal used in Fig. 2. The map shows the variance of the spectral transmission of each pixel relative to the mean spectral transmission. The map shows three regions with particularly high spectral variations. Figure 5 is a movie of the crystal images at different illumination wavelengths.

Fig. 4. Spectral diversity map of the opal structure. The standard deviation of transmission curves (Fig. 3) was used as a metric of spectral diversity for each point of the photonic crystal. Regions 1,2, and 3 in the plot exhibit strong spectral diversities, and those regions were chosen in our spectral estimation algorithm.
Fig. 5. (800 KB movie) A series of images at different illumination wavelength. Click here to start the movie. One can see that there are three regions with strong pattern variations corresponding to those in Fig. 4.

3. Spectral estimation

10,000 contiguous pixel measurements covering regions 1–3 of Fig. 4 were used to estimate source spectra with 5 nm resolution over 500–650 nm wavelength range. Because the spectral filter response H̿ is not known in advance, a set of calibration sources is used to characterize H̿. A ½ meter focal length Acton Research grating monochromator with a halogen lamp input illumination source was used for calibration. The output beam from the monochromator illuminated a diffuser such that the effective source for the photonic crystal was a uniform diffuse spot with a diameter of 12mm. The photonic crystal was placed 30mm from the diffuser so that each point on the photonic crystal subtends a full angle of 22 degrees. The image size of the photonic crystal was 5mm square. Images were captured using a Roper Scientific CoolSnap monochrome camera with a 1.2X relay lens. A series of narrow band spectra (each of 8 nm width spaced in 2 nm steps over the 500–650 nm spectral range) were generated from the monochromator and their corresponding filter responses were recorded on the CCD camera. These training spectra formed a banded spectral intensity matrix. The transfer function matrix H̿ is estimated using non-negative least squares optimization.

The calibrated photonic crystal was used to estimate the spectra of unknown sources over the wavelength range from 500 to 650 nanometers (nm) at resolutions varying from 2 to 20 nm. Since the number of spectral channels estimated (between 8 and 75) is much less than the number of pixel measurements (10,000) pixel, the measurements over-determine the spectrum. Over-determined problems do not have globally consistent solutions due to the presence of noise, but one can find a solution in the least squares sense. In finding the solution, we add the additional constraint that the spectral density is non-negative, which makes direct linear least squares inversion impossible. Instead we used the Matlab Optimization Toolbox to solve the general nonlinear optimization problem: minsHsm2 , such that s≥0, where ║▯║2 denotes the Euclidean norm.

Reconstruction at resolutions varying from 2 to 20 nm were attempted, 2 nm reconstruction failed to achieve high fidelity. Example spectral reconstruction results are shown in Fig. 6 with 5 nm resolution. Figure 6(a) shows the spectrum of a 15 inch LCD computer monitor set to a uniform screen color and apertured to 12 mm on the same optical path as the calibration signal. Figure 6(b) shows the spectrum of a mercury neon discharge lamp illuminating the same diffuser as was used for calibration.

4. Conclusion

Fig. 6. Spectra reconstruction. (A) Liquid crystal display (LCD) spectrum reconstruction. (B) Neon lamp spectrum reconstruction. In both (A) and (B), the red lines are true spectra taken by Ocean Optics USB2000 optic fiber spectrometer; the cyan bar plots are numerically reconstructed spectra using the photonic crystal spectrometer.

Acknowledgments

This work was supported by the National Institute on Alcohol Abuse and Alcoholism through the Integrated Alcohol Sensing and Data Analysis program under contract N01-AA-23013 and the Applied and Computational Mathematic Program of the Defense Advanced Research Projects Agency through the ARO contract DAAD 19-01-1-0641.

Refererences and links

1.

R. Narayanaswamy, “Proceedings of the 6th European Conference on Optical Chemical Sensors and Biosensors EUROPT(R)ODE VI,” Sensors and Actuators B 90, 1–345 (2003). [CrossRef]

2.

M. Moskovits, “Surface-Enhanced Spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985). [CrossRef]

3.

J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman & Hall, London, 1969).

4.

S. Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett.21, 1771–1773 (1996). [CrossRef] [PubMed]

5.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998). [CrossRef]

6.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: Toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999). [CrossRef]

7.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000). [CrossRef]

8.

B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012–1020 (2000). [CrossRef]

9.

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38, 915–918 (2002). [CrossRef]

10.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge Univ. Press, Cambridge, 1995).

11.

D. L. Marks, R. A. Stack, and D. J. Brady, “Digital refraction distortion correction with an astigmatic coherence sensor,” Appl. Opt. 41, 6050–6054 (2002). [CrossRef] [PubMed]

12.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

13.

S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

14.

S. H. Foulger, P. Jiang, A. Lattam, D. W. Smith, J. Ballato, D. E. Dausch, S. Grego, and B. R. Stoner, “Photonic crystal composites with reversible high-frequency stop band shifts,” Adv. Mater. 15, 685–689 (2003). [CrossRef]

15.

S. H. Foulger, P. Jiang, Y. R. Ying, A. C. Lattam, D. W. Smith, and J. Ballato, “Photonic bandgap composites,” Adv. Mater. 13, 1898–1901 (2001). [CrossRef]

16.

S. H. Foulger, S. Kotha, B. Sweryda-Krawiec, T. W. Baughman, J. M. Ballato, P. Jiang, and D. W. Smith, “Robust polymer colloidal crystal photonic bandgap structures,” Opt. Lett. 25, 1300–1302 (2000). [CrossRef]

OCIS Codes
(070.4790) Fourier optics and signal processing : Spectrum analysis
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

ToC Category:
Focus Issue: Integrated computational imaging systems

History
Original Manuscript: July 15, 2003
Revised Manuscript: August 14, 2003
Published: September 8, 2003

Citation
Zhaochun Xu, Zhanglei Wang, Michael Sullivan, David Brady, Stephen Foulger, and Ali Adibi, "Multimodal multiplex spectroscopy using photonic crystals," Opt. Express 11, 2126-2133 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-18-2126


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References

  1. R. Narayanaswamy, "Proceedings of the 6th European Conference on Optical Chemical Sensors and Biosensors EUROPT(R)ODE VI," Sensors and Actuators B 90, 1-345 (2003). [CrossRef]
  2. M. Moskovits, "Surface-Enhanced Spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985). [CrossRef]
  3. J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman & Hall, London, 1969).
  4. S. Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, "Highly dispersive photonic band-gap prism," Opt. Lett. 21, 1771-1773 (1996). [CrossRef] [PubMed]
  5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998). [CrossRef]
  6. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: Toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999). [CrossRef]
  7. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000). [CrossRef]
  8. B. Gralak, S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000). [CrossRef]
  9. L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002). [CrossRef]
  10. L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge Univ. Press, Cambridge, 1995).
  11. D. L. Marks, R. A. Stack, and D. J. Brady, "Digital refraction distortion correction with an astigmatic coherence sensor," Appl. Opt. 41, 6050-6054 (2002). [CrossRef] [PubMed]
  12. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  13. S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  14. S. H. Foulger, P. Jiang, A. Lattam, D. W. Smith, J. Ballato, D. E. Dausch, S. Grego, and B. R. Stoner, "Photonic crystal composites with reversible high-frequency stop band shifts," Adv. Mater. 15, 685-689 (2003). [CrossRef]
  15. S. H. Foulger, P. Jiang, Y. R. Ying, A. C. Lattam, D. W. Smith, and J. Ballato, "Photonic bandgap composites," Adv. Mater. 13, 1898-1901 (2001). [CrossRef]
  16. S. H. Foulger, S. Kotha, B. Sweryda-Krawiec, T. W. Baughman, J. M. Ballato, P. Jiang, and D. W. Smith, "Robust polymer colloidal crystal photonic bandgap structures," Opt. Lett. 25, 1300-1302 (2000). [CrossRef]

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