Abstract

We present a new design for the integration of a tunable Fabry–Perot (FP) filter and the grating etched on top of the cavity (IGFP) in the miniature spectrometer. It is based on the predispersion of the grating with the capacity of spatial separation of the spectral component and filter effect of the tunable FP filter. The free spectral range (FSR) of the IGFP is determined by the FSR of the grating, and its resolution depends on the filtering capacity of the FP filter. In the experiment, the high-resolution and wavelength scanning process of the IGFP were demonstrated with a narrowband and broadband light source, respectively. The results of the sub-nanometer resolution agree well with those from a commercial optical spectrum analyzer. Further, the IGFP provides an effective approach to solve the problem of the decrease of spectral resolution in the miniaturization process.

© 2013 Optical Society of America

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    [CrossRef]
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  5. S. C. Truxal, K. Kurabayashi, and Y.-C. Tung, “Design of a MEMS tunable polymer grating for single detector spectroscopy,” Int. J. Optomechatron. 2, 75–87 (2008).
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2013 (1)

2012 (3)

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

N. Gupta, S. Tan, and D. R. Zander, “Microelectromechanical systems-based visible-near infrared Fabry–Perot tunable filters using quartz substrate,” Opt. Eng. 51, 074007 (2012).
[CrossRef]

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photon. 4, 379–440 (2012).
[CrossRef]

2010 (1)

2008 (2)

S. C. Truxal, K. Kurabayashi, and Y.-C. Tung, “Design of a MEMS tunable polymer grating for single detector spectroscopy,” Int. J. Optomechatron. 2, 75–87 (2008).
[CrossRef]

N. Neumann, M. Ebermann, S. Kurth, and K. Hiller, “Tunable infrared detector with integrated micromachined Fabry–Perot filter,” J. Micro/Nanolithogr., MEMS, MOEMS 7, 021004 (2008).
[CrossRef]

2007 (1)

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

2006 (1)

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

2004 (1)

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

2001 (2)

S. Kong, D. Wijngaards, and R. Wolffenbuttel, “Infrared micro-spectrometer based on a diffraction grating,” Sens. Actuators A 92, 88–95 (2001).
[CrossRef]

D. Sander and J. Müller, “Self-focussing phase transmission grating for an integrated optical microspectrometer,” Sens. Actuators A 88, 1–9 (2001).
[CrossRef]

2000 (1)

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A 82, 191–197 (2000).
[CrossRef]

1999 (2)

1997 (1)

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[CrossRef]

1992 (1)

T. A. Kwa and R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sens. Actuators A 31, 259–266 (1992).
[CrossRef]

1991 (2)

J. Mohr, B. Anderer, and W. Ehrfeld, “Fabrication of a planar grating spectrograph by deep-etch lithography with synchrotron radiation,” Sens. Actuators A 27, 571–575 (1991).
[CrossRef]

K. C. Harvey and C. J. Myatt, “External-cavity diode laser using a grazing-incidence diffraction grating,” Opt. Lett. 16, 910–912 (1991).
[CrossRef]

1972 (1)

Alphonse, G. A.

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[CrossRef]

Anderer, B.

J. Mohr, B. Anderer, and W. Ehrfeld, “Fabrication of a planar grating spectrograph by deep-etch lithography with synchrotron radiation,” Sens. Actuators A 27, 571–575 (1991).
[CrossRef]

Bach, K.

Baillard, X.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Bartek, M.

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A 82, 191–197 (2000).
[CrossRef]

Benech, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Bize, S.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Blaize, S.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Born, M.

Breede, M.

Carmo, J. P.

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

Chang-Hasnain, C. J.

Chase, C.

Ching, B. C.

Clairon, A.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Connolly, J. C.

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[CrossRef]

Correia, J. H.

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A 82, 191–197 (2000).
[CrossRef]

de Graaf, G.

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A 82, 191–197 (2000).
[CrossRef]

de Rooij, N. F.

Delfyett, P. J.

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[CrossRef]

Ebermann, M.

N. Neumann, M. Ebermann, S. Kurth, and K. Hiller, “Tunable infrared detector with integrated micromachined Fabry–Perot filter,” J. Micro/Nanolithogr., MEMS, MOEMS 7, 021004 (2008).
[CrossRef]

Ehrfeld, W.

J. Mohr, B. Anderer, and W. Ehrfeld, “Fabrication of a planar grating spectrograph by deep-etch lithography with synchrotron radiation,” Sens. Actuators A 27, 571–575 (1991).
[CrossRef]

Euteneuer, A.

Fedeli, J. M.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Finlay, J.

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[CrossRef]

Gauguet, A.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Goncalves, L.

C. Pinheiro, J. Rocha, L. Goncalves, S. Lanceros-Mendez, and G. Minas, “A tunable Fabry–Perot optical filter for application in biochemical analysis of human’s fluids,” in IEEE International Symposium on Industrial Electronics (IEEE, 2006), pp. 2778–2783.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Gupta, N.

N. Gupta, S. Tan, and D. R. Zander, “Microelectromechanical systems-based visible-near infrared Fabry–Perot tunable filters using quartz substrate,” Opt. Eng. 51, 074007 (2012).
[CrossRef]

Hänsch, T. W.

Harvey, K. C.

Herzig, H. P.

Hildebrand, L.

Hiller, K.

N. Neumann, M. Ebermann, S. Kurth, and K. Hiller, “Tunable infrared detector with integrated micromachined Fabry–Perot filter,” J. Micro/Nanolithogr., MEMS, MOEMS 7, 021004 (2008).
[CrossRef]

Hofmann, M.

Hofmann, W.

Kern, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Kong, S.

S. Kong, D. Wijngaards, and R. Wolffenbuttel, “Infrared micro-spectrometer based on a diffraction grating,” Sens. Actuators A 92, 88–95 (2001).
[CrossRef]

Kong, S. H.

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A 82, 191–197 (2000).
[CrossRef]

Kurabayashi, K.

S. C. Truxal, K. Kurabayashi, and Y.-C. Tung, “Design of a MEMS tunable polymer grating for single detector spectroscopy,” Int. J. Optomechatron. 2, 75–87 (2008).
[CrossRef]

Kurth, S.

N. Neumann, M. Ebermann, S. Kurth, and K. Hiller, “Tunable infrared detector with integrated micromachined Fabry–Perot filter,” J. Micro/Nanolithogr., MEMS, MOEMS 7, 021004 (2008).
[CrossRef]

Kwa, T. A.

T. A. Kwa and R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sens. Actuators A 31, 259–266 (1992).
[CrossRef]

Lanceros-Mendez, S.

C. Pinheiro, J. Rocha, L. Goncalves, S. Lanceros-Mendez, and G. Minas, “A tunable Fabry–Perot optical filter for application in biochemical analysis of human’s fluids,” in IEEE International Symposium on Industrial Electronics (IEEE, 2006), pp. 2778–2783.

Laurent, P.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Le Coarer, E.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Leblond, G.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Lemonde, P.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Lérondel, G.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Lerose, D.

Manzardo, O.

Marxer, C. R.

Minas, G.

C. Pinheiro, J. Rocha, L. Goncalves, S. Lanceros-Mendez, and G. Minas, “A tunable Fabry–Perot optical filter for application in biochemical analysis of human’s fluids,” in IEEE International Symposium on Industrial Electronics (IEEE, 2006), pp. 2778–2783.

Mohr, J.

J. Mohr, B. Anderer, and W. Ehrfeld, “Fabrication of a planar grating spectrograph by deep-etch lithography with synchrotron radiation,” Sens. Actuators A 27, 571–575 (1991).
[CrossRef]

Morand, A.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Müller, J.

D. Sander and J. Müller, “Self-focussing phase transmission grating for an integrated optical microspectrometer,” Sens. Actuators A 88, 1–9 (2001).
[CrossRef]

Myatt, C. J.

Neumann, N.

N. Neumann, M. Ebermann, S. Kurth, and K. Hiller, “Tunable infrared detector with integrated micromachined Fabry–Perot filter,” J. Micro/Nanolithogr., MEMS, MOEMS 7, 021004 (2008).
[CrossRef]

Pinheiro, C.

C. Pinheiro, J. Rocha, L. Goncalves, S. Lanceros-Mendez, and G. Minas, “A tunable Fabry–Perot optical filter for application in biochemical analysis of human’s fluids,” in IEEE International Symposium on Industrial Electronics (IEEE, 2006), pp. 2778–2783.

Rao, Y.

Rocha, J.

C. Pinheiro, J. Rocha, L. Goncalves, S. Lanceros-Mendez, and G. Minas, “A tunable Fabry–Perot optical filter for application in biochemical analysis of human’s fluids,” in IEEE International Symposium on Industrial Electronics (IEEE, 2006), pp. 2778–2783.

Rocha, R. P.

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

Rosenbusch, P.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[CrossRef]

Royer, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Sacher, J.

Sander, D.

D. Sander and J. Müller, “Self-focussing phase transmission grating for an integrated optical microspectrometer,” Sens. Actuators A 88, 1–9 (2001).
[CrossRef]

Schmidt, A.

Schmidt, F.

Schulze, F. M.

Shi, H.

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[CrossRef]

Siaw Hei, E. K.

Smarsly, B.

Stefanon, I.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Sterger, M.

Struckmeier, J.

Tan, S.

N. Gupta, S. Tan, and D. R. Zander, “Microelectromechanical systems-based visible-near infrared Fabry–Perot tunable filters using quartz substrate,” Opt. Eng. 51, 074007 (2012).
[CrossRef]

Truxal, S. C.

S. C. Truxal, K. Kurabayashi, and Y.-C. Tung, “Design of a MEMS tunable polymer grating for single detector spectroscopy,” Int. J. Optomechatron. 2, 75–87 (2008).
[CrossRef]

Tung, Y.-C.

S. C. Truxal, K. Kurabayashi, and Y.-C. Tung, “Design of a MEMS tunable polymer grating for single detector spectroscopy,” Int. J. Optomechatron. 2, 75–87 (2008).
[CrossRef]

Wijngaards, D.

S. Kong, D. Wijngaards, and R. Wolffenbuttel, “Infrared micro-spectrometer based on a diffraction grating,” Sens. Actuators A 92, 88–95 (2001).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980).

Wolffenbuttel, R.

S. Kong, D. Wijngaards, and R. Wolffenbuttel, “Infrared micro-spectrometer based on a diffraction grating,” Sens. Actuators A 92, 88–95 (2001).
[CrossRef]

Wolffenbuttel, R. F.

J. P. Carmo, R. P. Rocha, M. Bartek, G. de Graaf, R. F. Wolffenbuttel, and J. H. Correia, “A review of visible-range Fabry–Perot microspectrometers in silicon for the industry,” Opt. Laser Technol. 44, 2312–2320 (2012).
[CrossRef]

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

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A 82, 191–197 (2000).
[CrossRef]

T. A. Kwa and R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sens. Actuators A 31, 259–266 (1992).
[CrossRef]

Yang, W.

Yaw, L. C.

Zander, D. R.

N. Gupta, S. Tan, and D. R. Zander, “Microelectromechanical systems-based visible-near infrared Fabry–Perot tunable filters using quartz substrate,” Opt. Eng. 51, 074007 (2012).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

H. Shi, J. Finlay, G. A. Alphonse, J. C. Connolly, and P. J. Delfyett, “Multiwavelength 10-GHz picosecond pulse generation from a single-stripe semiconductor diode laser,” IEEE Photon. Technol. Lett. 9, 1439–1441 (1997).
[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]

Int. J. Optomechatron. (1)

S. C. Truxal, K. Kurabayashi, and Y.-C. Tung, “Design of a MEMS tunable polymer grating for single detector spectroscopy,” Int. J. Optomechatron. 2, 75–87 (2008).
[CrossRef]

J. Micro/Nanolithogr., MEMS, MOEMS (1)

N. Neumann, M. Ebermann, S. Kurth, and K. Hiller, “Tunable infrared detector with integrated micromachined Fabry–Perot filter,” J. Micro/Nanolithogr., MEMS, MOEMS 7, 021004 (2008).
[CrossRef]

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E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[CrossRef]

Opt. Commun. (1)

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[CrossRef]

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N. Gupta, S. Tan, and D. R. Zander, “Microelectromechanical systems-based visible-near infrared Fabry–Perot tunable filters using quartz substrate,” Opt. Eng. 51, 074007 (2012).
[CrossRef]

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Sens. Actuators A (5)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Device concept and operational principle of the IGFP. (b) and (c) Schematic of spectrum data acquisition at the cavity length L1 and L1+δL, respectively. (d) Whole spectrum by the overlay of two spectrums from (b) and (c).

Fig. 2.
Fig. 2.

Schematic diagram of the spatial separation of spectral component by the grating.

Fig. 3.
Fig. 3.

Schematic diagram of the wavelength scanning.

Fig. 4.
Fig. 4.

Schematic diagram of definition of the resolution (finesse=29.8).

Fig. 5.
Fig. 5.

Schematic diagram of the experiment (OAP: 60° off-axis parabolic reflector).

Fig. 6.
Fig. 6.

(a) Spectrums of narrowband light source by the IGFP and the spectrum profile by the grating, the dotted lines with the different symbols representing the spectrums of the different cavity lengths. (b) Spectrum measured by a commercial optical spectrum analyzer (OSA).

Fig. 7.
Fig. 7.

Spectrums of broadband light source from IGFP, and the spectrum curve obtained by the grating. Inset, three detailed drawing of the spectrums from IGFP.

Equations (20)

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t(x)={exp[iφ](l1)d<x<b+(l1)d1b+(l1)d<x<ld0(x>Nd)and(x<0)(l=1,2,3)withφ=2πh(n1)λcosα,
IG(β)=(2wλz)2m=+cm2sinc2[2wλ(sinβsinαmd)]withmas an integer,wherecm=1d0dt(x)eim2π/ddx,
tFP=(1R)21+R22Rcosη,
whereη=4πn0Lcosβ/λ,
Ifinal=IG×tFP=(2wλz)2m=+cm2sinc2[2wλ(sinβsinαmd)]×(1R)21+R22Rcosη.
d(sinβmaxsinα)=λmin,
d[sin(βmax)sinα]=λmax.
d=(λmax+λmin)/2sinα,
d(sinβsinα)=mλ,(m=1),
2n0Lcosβ=kλ,(k=1,2,3),
4πn0Lλdd2(dsinαλ)2=2kπ.
2n0L1cosβ1=kλ1,
2n0L1cosβ2=(k+1)λ2.
2n0L2cosβ2=kλ2.
ΔL=L1L2=λ/2n0cosβ.
tFP(ηk±ηFWHM/2)=1/2,withηk=2kπ.
ηFWHM=2πF,
Δλk=λk22nLF.
Δη=4πn0cosβλδL.
δL<λ6n0cosβF.

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