Abstract

Concept, theory and simulations of a new type of waveguide device, a multiaperture Fourier-transform planar waveguide spectrometer, are presented. The spectrometer is formed by an array of Mach-Zehnder interferometers generating a wavelength dependent spatial fringe pattern at the array output. The input light spectrum is calculated using a discrete Fourier transformation of the output spatial fringes. The multiaperture input significantly increases the optical throughput (étendue) compared to conventional single input spectrometers. Design rules for the arrayed spectrometer are deduced from performance specifications such as wavelength range and spectral resolution. A design example with spectral resolution 0.025 nm and range 2.5 nm is presented, where the optical throughput is increased by a factor of 200 compared to a single input device.

© 2007 Optical Society of America

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  2. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, "A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with submicrometer aperture waveguides," Opt. Express 15, 2299-2306 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  21. K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
    [CrossRef]
  22. H. Yamada, K. Takada, Y. Inoue, Y. Ohmori, and S. Mitachi, "Statically-phase-compensated 10GHzspaced arrayed-waveguide grating," Electron. Lett.  32, 1580-1582-61 (1996).
    [CrossRef]
  23. B. Solheim, "Spatial Heterodyne Spectroscopy (SHS), Spatial Heterodyne Observations of Water (SHOW)," presented at the 12-th ASSFTS (Atmospheric Science from Space using Fourier Transform Spectrometry) workshop, Quebec City, Canada, 18 May 2005.
  24. Y. Lin, G. Shepherd, B. Solheim, M. Shepherd, S. Brown, J. Harlander, and J. Whiteway, "Introduction to spatial heterodyne observations of water (SHOW) project and its instrument development," Proc. XIV Int. TOVS Study Conf., 25-31 May 2005, Beijing, China, 835-843 (2005).
  25. G. P. Shepherd, Spectral Imaging of the Atmosphere (Academic Press, London, UK, 2002).
  26. S. Janz, "Silicon-based waveguide technology for wavelength division multiplexing," in Silicon Photonics, L. Pavesi and D. J. Lockwood, eds. (Springer-Verlag, Berlin, 2004).
    [CrossRef]
  27. L. Labadie, P. Kern, P. Labeye, E. LeCoarer, C. Vigreux-Bercovici, A. Pradel, J.-E. Broquin, and V. Kirschner, "Technology challenges for space interferometry: the option of mid-infrared integrated optics," Adv. Space Res., in press, available online 20 July 2007, http://dx.doi.org/10.1016/j.asr.2007.07.013.
  28. R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006).
    [CrossRef]

2007

2006

I. Powell and P. Cheben, "Modeling of the generic spatial heterodyne spectrometer and comparison with conventional spectrometer," Appl. Opt. 45, 9079-9086 (2006).
[CrossRef] [PubMed]

R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006).
[CrossRef]

2005

2003

2000

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

1994

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy," Electron. Lett. 30, 1671-1672 (1994).
[CrossRef]

1992

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

1991

1981

1974

1964

1958

P. Fellgett, "A propos de la théorie du spectromètre interférentiel multiplex," J. Phys. Radium 19, 187-191 (1958).
[CrossRef]

1954

Abe, M.

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

Alieva, T.

Buchwald, W. R.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006).
[CrossRef]

Calvo, M. L.

Cameron, D. G.

Cheben, P.

Delâge, A.

Densmore, A.

Emelett, S. J.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006).
[CrossRef]

Fellgett, P.

P. Fellgett, "A propos de la théorie du spectromètre interférentiel multiplex," J. Phys. Radium 19, 187-191 (1958).
[CrossRef]

Filler, A. H.

Florjanczyk, M.

Garcia, F. C.

Harlander, J.

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Horiguchi, M.

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy," Electron. Lett. 30, 1671-1672 (1994).
[CrossRef]

Ikonen, E.

Inoue, Y.

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy," Electron. Lett. 30, 1671-1672 (1994).
[CrossRef]

Ishii, M.

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

Jacquinot, P.

Janz, S.

Junttila, M.-L.

Kashyap, R.

Kauppinen, J.

Kauppinen, J. K.

Lamontagne, B.

Lapointe, J.

Mantsch, H. H.

Moffatt, D. J.

Okamoto, K.

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

Post, E.

Powell, I.

Reynolds, R. J.

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Rodrigo, J. A.

Roesler, F. L.

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Schmid, J. H.

Scott, A.

Solheim, B.

Soref, R. A.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006).
[CrossRef]

Steel, W. H.

Takada, K.

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy," Electron. Lett. 30, 1671-1672 (1994).
[CrossRef]

Tanaka, T.

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

Vogelaar, L.

Waldron, P.

Xu, D.-X.

Yamada, H.

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy," Electron. Lett. 30, 1671-1672 (1994).
[CrossRef]

Yanagisawa, T.

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

Appl. Opt.

Astrophys. J.

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Electron. Lett.

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy," Electron. Lett. 30, 1671-1672 (1994).
[CrossRef]

K. Takada, T. Tanaka, M. Abe, T. Yanagisawa, M. Ishii, and K. Okamoto, "Beam-adjustment-free crosstalk reduction in 10GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask," Electron. Lett. 36, 60-61 (2000).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Radium

P. Fellgett, "A propos de la théorie du spectromètre interférentiel multiplex," J. Phys. Radium 19, 187-191 (1958).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

M. Florja?czyk, P. Cheben, S. Janz, A. Scott, B. Solheim, and D.-X. Xu, "Planar waveguide spatial heterodyne spectrometer," Proc. SPIE 6796, 67963J-1 (2007).

Other

Ch. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley-Interscience, New York, 1999).

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley-Interscience, Chichester, UK, 1979).

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, Hoboken, New Jersey, 2007).
[CrossRef]

P. Cheben, "Wavelength dispersive planar waveguide devices: Echelle gratings and arrayed waveguide gratings," in Optical Waveguides: From Theory to Applied Technologies, M. L. Calvo and V. Laksminarayanan, eds. (CRC Press, London, 2007).

P. B. Fellgett, "The theory of infra-red sensitivities and its application to investigations of stellar radiation in the near infra-red," Ph.D. dissertation (University of Cambridge, Cambridge, UK, 1951).

R. H. Norton and R. Beer, "New apodizing functions for Fourier spectrometry," J. Opt. Soc. Am. 66, 259-264 (1976); erratum: 67, 419 (1977), http://www.opticsinfobase.org/abstract.cfm?URI=josa-67-3-419.
[CrossRef]

H. Yamada, K. Takada, Y. Inoue, Y. Ohmori, and S. Mitachi, "Statically-phase-compensated 10GHzspaced arrayed-waveguide grating," Electron. Lett.  32, 1580-1582-61 (1996).
[CrossRef]

B. Solheim, "Spatial Heterodyne Spectroscopy (SHS), Spatial Heterodyne Observations of Water (SHOW)," presented at the 12-th ASSFTS (Atmospheric Science from Space using Fourier Transform Spectrometry) workshop, Quebec City, Canada, 18 May 2005.

Y. Lin, G. Shepherd, B. Solheim, M. Shepherd, S. Brown, J. Harlander, and J. Whiteway, "Introduction to spatial heterodyne observations of water (SHOW) project and its instrument development," Proc. XIV Int. TOVS Study Conf., 25-31 May 2005, Beijing, China, 835-843 (2005).

G. P. Shepherd, Spectral Imaging of the Atmosphere (Academic Press, London, UK, 2002).

S. Janz, "Silicon-based waveguide technology for wavelength division multiplexing," in Silicon Photonics, L. Pavesi and D. J. Lockwood, eds. (Springer-Verlag, Berlin, 2004).
[CrossRef]

L. Labadie, P. Kern, P. Labeye, E. LeCoarer, C. Vigreux-Bercovici, A. Pradel, J.-E. Broquin, and V. Kirschner, "Technology challenges for space interferometry: the option of mid-infrared integrated optics," Adv. Space Res., in press, available online 20 July 2007, http://dx.doi.org/10.1016/j.asr.2007.07.013.

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Figures (6)

Fig. 1.
Fig. 1.

The schematics of the waveguide spectrometer formed by arrayed Mach-Zehnder interferometers.

Fig. 2.
Fig. 2.

Spatial fringe formation at the arrayed MZI outputs. Monochromatic inputs at a) the Littrow wavenumber σL, b) σL+δσ, and c) σL+2δσ, and the corresponding spatial fringes; d) Superposition of monochromatic inputs and the corresponding spatial fringe pattern.

Fig. 3.
Fig. 3.

Transfer matrix notation used in the model.

Fig. 4.
Fig. 4.

Transmission spectra of water vapor at 15 km altitude. The bandpass input filter spectrum is also shown.

Fig. 5.
Fig. 5.

Ideal input and apodized calculated spectra for the arrayed MZI spectrometer with 0.1 nm resolution.

Fig. 6.
Fig. 6.

Ideal input and apodized calculated spectra for the arrayed MZI spectrometer with 0.025 nm resolution.

Equations (26)

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E ( x , y , z , t ) = a e ( x , y ) e i ( ω t β z ) H ( x , y , z , t ) = a h ( x , y ) e i ( ω t β z )
P = 1 2 a 2 e × h * · z ̂ dx dy
[ a 1 , i out a 2 , i out ] = S i · [ a 1 , i in a 2 , i in ] = S c · S d , i · S s · [ a 1 , i in a 2 , i in ]
S s = γ s [ 1 κ s i κ s i κ s 1 κ s ] S c = γ c [ 1 κ c i κ c i κ c 1 κ c ]
S d , i = γ d , i e i β L 2 , i [ e α Δ L i e i β Δ L i 0 0 1 ]
P 1 out ( x i ) = P 1 , i out = 1 2 P in [ A 1 , i B i cos β Δ L i ]
P 2 out ( x i ) = P 2 , i out = 1 2 P in [ A 2 , i + B i cos β Δ L i ]
A 1 , i = 2 γ s 2 γ d , i 2 γ c 2 [ κ s κ c + ( 1 κ s ) ( 1 κ c ) 2 α Δ L i ]
A 2 , i = 2 γ s 2 γ d , i 2 γ c 2 [ κ s ( 1 κ c ) + κ c ( 1 κ c ) 2 α Δ L i ]
B i = 4 γ s 2 γ d , i 2 γ c 2 [ κ s κ c ( 1 κ s ) ( 1 κ c ) ] 1 2 e α Δ L i
0 p 1 , i out ( σ ) d σ = 1 2 0 p in ( σ ) [ A 1 , i B i cos ( 2 π σ n eff Δ L i ) ] d σ
0 p 2 , i out ( σ ) d σ = 1 2 0 p in ( σ ) [ A 2 , i + B i cos ( 2 π σ n eff Δ L i ) ] d σ
P 1 , i out = 1 2 A 1 , i P in 1 2 B i 0 p in ( σ ) cos ( 2 π σ n eff Δ L i ) d σ
P 2 , i out = 1 2 A 2 , i P in + 1 2 B i 0 p in ( σ ) cos ( 2 π σ n eff Δ L i ) d σ
F i = 1 B i ( 2 P 1 , i out A 1 , i P in ) = 1 B i ( 2 P 2 , i out A 2 , i P in )
F ( x ) = 0 p in ( σ ) cos 2 π σ x d σ = p in ( σ ¯ ) cos 2 π σ ¯ x d σ ¯
p in ( σ ¯ ) = F ( x ) cos 2 π σ ¯ x dx = 2 0 F ( x ) cos 2 π σ ¯ x dx
p in ( σ ¯ ) = Δ x N P in + 2 Δ x N i = 1 N F ( x i ) cos 2 π σ ¯ x i
P i in = 2 ( P 1 , i out + P 2 , i out ) ( A 1 , i + A 2 , i )
p in ( σ ¯ ) = Δ x N P in + 2 Δ x N i = 1 N W ( x i ) F ( x i ) cos 2 π σ ¯ x i
Δ φ = 2 π ( σ + δ σ ) Δ x 2 π σ Δ x = 2 π
δ σ = 1 λ 0 1 λ 0 + δ λ δ λ λ 0 2 = 1 R 1 λ 0
Δ L max = 1 δ σ n eff = R λ 0 n eff
N min = 2 Δ x Δ σ = 2 Δ σ δ σ = 2 Δ σ δ λ
δ σ pol σ 0 δ λ pol λ 0 = Δ n neff n neff
W ( x i ) = [ 1 ( x i x max ) 2 ] 2 = [ 1 ( Δ L i Δ L max ) 2 ] 2

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