Abstract

In order to simplify the design process of microfabricated concave gratings, simplified algorithms for fast characterization of the concave grating were developed. These algorithms can be used to assist system designers using ray-tracing software in the determination of optimum design parameters considering the requirements and restrictions for specific applications. According to the algorithms, it is feasible to design a flat field microconcave grating with a 4 mm grating radius as a key component in a micro-Raman spectrometer system for inline environmental monitoring applications. This microspectrometer operates over the spectral wavelength band from 785 nm to 1000 nm and has a spectral resolution of 2 nm at 900 nm. The total size of the system is 1mm×4mm×3.7mm, making it one of the smallest for this wavelength range and spectrum resolution.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. R. K. Dutta, P. K. Sharma, and A. C. Pandey, “Surface enhanced Raman spectra of Escherichia Coli cell using ZnO nanoparticles,” Dig. J. Nanomater. Biostruct. 4, 83–87 (2009).
  15. “PCGrates,” http://www.iigrate.com/about/pcgrates .
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    [CrossRef]
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2010 (1)

M. M. Mariani, P. J. Day, and V. Deckert, “Applications of modern micro-Raman spectroscopy for cell analyses,” Integr. Biol. 2, 94–101 (2010).
[CrossRef]

2009 (1)

R. K. Dutta, P. K. Sharma, and A. C. Pandey, “Surface enhanced Raman spectra of Escherichia Coli cell using ZnO nanoparticles,” Dig. J. Nanomater. Biostruct. 4, 83–87 (2009).

2008 (3)

2007 (1)

H. K. Cheng, “Micrograting fabricated by deep x-ray lithography for optical communications,” Opt. Eng. 46, 048001 (2007).

2005 (1)

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

2004 (2)

T. Iliescu, M. Baia, and V. Miclaus, “A Raman spectroscopic study of the diclofenac sodium-beta-cyclodextrin interaction,” Eur. J. Pharmaceut. Sci. 22, 487–495 (2004).
[CrossRef]

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197–202 (2004).
[CrossRef]

2003 (1)

C. Xie and Y. Li, “Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,” J. Appl. Phys. 93, 2982–2986 (2003).
[CrossRef]

2001 (1)

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

1992 (1)

1989 (1)

1959 (1)

Baia, M.

T. Iliescu, M. Baia, and V. Miclaus, “A Raman spectroscopic study of the diclofenac sodium-beta-cyclodextrin interaction,” Eur. J. Pharmaceut. Sci. 22, 487–495 (2004).
[CrossRef]

Basu, P. K.

M. J. Deen and P. K. Basu, Silicon Photonics—Fundamentals and Devices (Wiley, 2012).

Brunner, R.

Burkhardt, M.

Cheng, H. K.

H. K. Cheng, “Micrograting fabricated by deep x-ray lithography for optical communications,” Opt. Eng. 46, 048001 (2007).

Correns, N.

Day, P. J.

M. M. Mariani, P. J. Day, and V. Deckert, “Applications of modern micro-Raman spectroscopy for cell analyses,” Integr. Biol. 2, 94–101 (2010).
[CrossRef]

Deckert, V.

M. M. Mariani, P. J. Day, and V. Deckert, “Applications of modern micro-Raman spectroscopy for cell analyses,” Integr. Biol. 2, 94–101 (2010).
[CrossRef]

Deen, M. J.

Dutta, R. K.

R. K. Dutta, P. K. Sharma, and A. C. Pandey, “Surface enhanced Raman spectra of Escherichia Coli cell using ZnO nanoparticles,” Dig. J. Nanomater. Biostruct. 4, 83–87 (2009).

Elliott, S.

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Emadi, A.

Grabarnik, S.

Grange, R.

Hamilton, T.

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Iliescu, T.

T. Iliescu, M. Baia, and V. Miclaus, “A Raman spectroscopic study of the diclofenac sodium-beta-cyclodextrin interaction,” Eur. J. Pharmaceut. Sci. 22, 487–495 (2004).
[CrossRef]

Jones, G.

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Klempner, M. S.

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Krieger, N.

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Li, Y.

C. Xie and Y. Li, “Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,” J. Appl. Phys. 93, 2982–2986 (2003).
[CrossRef]

Loewen, E. G.

E. G. Loewen, Diffraction Gratings and Applications (Marcel Dekker, 1997).

C. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

Mariani, M. M.

M. M. Mariani, P. J. Day, and V. Deckert, “Applications of modern micro-Raman spectroscopy for cell analyses,” Integr. Biol. 2, 94–101 (2010).
[CrossRef]

Miclaus, V.

T. Iliescu, M. Baia, and V. Miclaus, “A Raman spectroscopic study of the diclofenac sodium-beta-cyclodextrin interaction,” Eur. J. Pharmaceut. Sci. 22, 487–495 (2004).
[CrossRef]

Moir, D. T.

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Namilka, T.

Nelson, W. H.

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Palmer, C.

C. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

Pandey, A. C.

R. K. Dutta, P. K. Sharma, and A. C. Pandey, “Surface enhanced Raman spectra of Escherichia Coli cell using ZnO nanoparticles,” Dig. J. Nanomater. Biostruct. 4, 83–87 (2009).

Premasiri, W. R.

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Rudolf, K.

Sharma, P. K.

R. K. Dutta, P. K. Sharma, and A. C. Pandey, “Surface enhanced Raman spectra of Escherichia Coli cell using ZnO nanoparticles,” Dig. J. Nanomater. Biostruct. 4, 83–87 (2009).

Sokolova, E.

Sperry, J. F.

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Thompson, A. C.

A. C. Thompson and D. Vaudhn, X-Ray Data Booklet, 2nd ed. (Lawrence Berkeley Laboratory, 2001).

Thompson, E. D.

Vaudhn, D.

A. C. Thompson and D. Vaudhn, X-Ray Data Booklet, 2nd ed. (Lawrence Berkeley Laboratory, 2001).

Vdovin, G.

Wolffenbuttel, R. F.

Wu, M.

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Wu, Q.

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Xie, C.

C. Xie and Y. Li, “Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,” J. Appl. Phys. 93, 2982–2986 (2003).
[CrossRef]

Ziegler, L. D.

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Anal. Chem. (1)

Q. Wu, T. Hamilton, W. H. Nelson, S. Elliott, J. F. Sperry, and M. Wu, “UV Raman spectral intensities of E. coli and other bacteria excited at 228.9, 244.0, and 248.2 nm,” Anal. Chem. 73, 3432–3440 (2001).
[CrossRef]

Appl. Opt. (3)

Dig. J. Nanomater. Biostruct. (1)

R. K. Dutta, P. K. Sharma, and A. C. Pandey, “Surface enhanced Raman spectra of Escherichia Coli cell using ZnO nanoparticles,” Dig. J. Nanomater. Biostruct. 4, 83–87 (2009).

Eur. J. Pharmaceut. Sci. (1)

T. Iliescu, M. Baia, and V. Miclaus, “A Raman spectroscopic study of the diclofenac sodium-beta-cyclodextrin interaction,” Eur. J. Pharmaceut. Sci. 22, 487–495 (2004).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197–202 (2004).
[CrossRef]

Integr. Biol. (1)

M. M. Mariani, P. J. Day, and V. Deckert, “Applications of modern micro-Raman spectroscopy for cell analyses,” Integr. Biol. 2, 94–101 (2010).
[CrossRef]

J. Appl. Phys. (1)

C. Xie and Y. Li, “Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,” J. Appl. Phys. 93, 2982–2986 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. B (1)

W. R. Premasiri, D. T. Moir, M. S. Klempner, N. Krieger, G. Jones, and L. D. Ziegler, “Characterization of the surface enhanced Raman scattering (SERS) of bacteria,” J. Phys. Chem. B 109, 312–320 (2005).
[CrossRef]

Opt. Eng. (1)

H. K. Cheng, “Micrograting fabricated by deep x-ray lithography for optical communications,” Opt. Eng. 46, 048001 (2007).

Opt. Express (1)

Proc. SPIE (1)

S. Grabarnik, “Concave diffraction gratings fabricated with planar lithography,” Proc. SPIE 6992, 1–8 (2008).
[CrossRef]

Other (5)

M. J. Deen and P. K. Basu, Silicon Photonics—Fundamentals and Devices (Wiley, 2012).

C. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

“PCGrates,” http://www.iigrate.com/about/pcgrates .

A. C. Thompson and D. Vaudhn, X-Ray Data Booklet, 2nd ed. (Lawrence Berkeley Laboratory, 2001).

E. G. Loewen, Diffraction Gratings and Applications (Marcel Dekker, 1997).

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Figures (10)

Fig. 1.
Fig. 1.

Rowland-configuration-based concave grating.

Fig. 2.
Fig. 2.

Diffraction efficiency with different grating periods.

Fig. 3.
Fig. 3.

Geometry of a concave grating: A–point source, O–grating center, B–image of point source in image plane, P–arbitrary point on grating surface.

Fig. 4.
Fig. 4.

(a) Illuminated area of a point source. (b) Image of a point source.

Fig. 5.
Fig. 5.

(a) Power series coefficients with different incident angle. (b) Resolution when considering different power series coefficients.

Fig. 6.
Fig. 6.

Resolution caused by spot width when considering different number of power series coefficients.

Fig. 7.
Fig. 7.

(a) Ray tracing of a point source by Zemax. (b) Spot diagram of three different wavelengths, including 900 nm, 901.5 nm, and 903 nm.

Fig. 8.
Fig. 8.

Total resolutions when (a) the height h is close to the width w, and (b) the height h is much smaller than the width w.

Fig. 9.
Fig. 9.

(a) Groove density variation in x direction. (b) Horizontal focal curve.

Fig. 10.
Fig. 10.

Schematic diagram of concave micrograting spectrometer system.

Tables (1)

Tables Icon

Table 1. Parameters for Two Types of Different Configurations at 900 nm

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

sinα+sinβ=mGλ.
ΔλEntrance=Sdcosαmrin,
ΔλAberration=Δxcosβmrb,
ΔλDiffraction=λmN.
F=APBAOB0+mNλ=i,jxpizpii!j!Fij,
Dh=rbcosβFxp=rbcosβ(xpF20+12xp2F30+12zp2F12+16xp3F40+12xpzp2F22+)
Dv=rbFzp=rb(zpF02+xpzpF12+16zp3F04+12zpxp2F22+).
Dh=rbcosβFxp=rbcosβ(12zp2F12+124zp4F14+),
F14=3sinαR2rin2(13cos2α)9sinαrin4+3sinαcosαRrin(6rin21R2)+3sinβR2rb2(13cos2β)9sinβrb4+3sinβcosβRrb(6rb21R2).
Δλabr=dm(12zp2F12+124zp4F14).
Δλabr=12dmzp2(sinαrin(1rincosαR)+mGλsinαrb2mGλsinαRrb+(mGλsinα)32Rrb).
Δλabr=dmrbcosβFxp=dmrbcosβ(16xp3F40+124xp4F50+1120xp5F60+).
F40=3cos2αrin3(5sin2α1)+6cosαRrin2(13sin2α)+3sin2αR2rin3cosαR3+3cos2βrb3(5sin2β1)+6cosβRrb2(13sin2β)+3sin2βR2rb3cosβR3.
F40=3R3(1cosαcosα)+3(mGλsinα)2R3(112(mGλsinα)).
F20=(cos2αrincosαR)+(cos2βrbcosβR).
Fij=Mij+mG0λHij.
kQQ0=yy0xx0=C,
kQQ0(t)=rb0cosβ0rbcosβrbsinβrb0sinβ0=rb01(mG0λ0sinα)2rb1t2rb·trb0(mG0λ0sinα),
kQQ0(t)=g(t)=g0+g(0)t+12g(0)t2+16g(0)t3+.
H20=|mG0λ0sinα|RmG0λ0.
G=G0×(1+H20x+12H30x2+16H40x3).

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