Abstract

High-sensitivity spectroscopy of methane around 3 μm was carried out by means of a 5.5-mW cw difference-frequency generator in conjunction with a high finesse cavity in off-axis alignment. By cavity-output integration a minimum detectable absorption coefficient of 5.7∙10-9 cm-1Hz-1/2 was achieved, which compares well with results already reported in the literature. Detection of methane in natural abundance was also performed in ambient air, for different values of total pressure, allowing direct concentration measurements via evaluation of the integrated absorbance of the spectra. In particular, at atmospheric pressure, a minimum detectable concentration of 850 parts per trillion by volume (pptv)∙Hz-1/2 was demonstrated.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2005 (5)

J. T. Hodges and R. Ciurylo, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum. 76, 023112 (2005).
[CrossRef]

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O’Keefe, “Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser,” Appl. Phys. B 81, 705–710 (2005).
[CrossRef]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy,” Appl. Phys. B 80, 141–145 (2005).
[CrossRef]

C. R. Webster, “Measuring methane and its isotopes 12CH4, 13CH4 and CH3D on the surface of Mars with in situ laser spectroscopy,” Appl. Opt. 44, 1226–1234 (2005).
[CrossRef] [PubMed]

D. Halmer, G. von Basum, P. Hering, and M. Mürtz, “Mid-infrared cavity leak-out spectroscopy for ultrasensitive detection of carbonyl sulfide,” Opt. Lett. 30, 2314–2316 (2005).
[CrossRef] [PubMed]

2004 (4)

2003 (2)

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

2002 (8)

G. Gagliardi and L. Gianfrani, “Trace-gas anlysis using diode lasers in the near-IR and long-path techniques,” Opt. Lasers. Eng. 37, 509–520 (2002).
[CrossRef]

D. S. Baer, J. B. Paul, M. Gupta, and A. O’Keefe, “Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy,” Appl. Phys. B 75, 261–265 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, “Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers,” Appl. Phys. B 75, 755–761 (2002).
[CrossRef]

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

S. Stry, P. Hering, and M. Mürtz, “Portable difference-frequency laser-based cavity leak-out spectrometer for trace-gas analysis,” Appl. Phys. B 75, 297–303 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

J. Morville, D. Romanini, M. Chenevier, and A. Kachanov, “Effects of laser phase noise on the injection of a high-finesse cavity,” Appl. Opt. 41, 6980–6990 (2002).
[CrossRef] [PubMed]

2001 (6)

E. V. Kovalchuk, D. Dekorsy, A. I. Lvovsky, C. Braxmaier, J. Mlynek, A. Peters, and S. Schiller, “High-resolution doppler-free molecular spectroscopy with a continuous-wave optical parametric oscillator,” Opt. Lett. 26, 1430–1433 (2001).
[CrossRef]

J. B. Paul, L. Lapson, and J. Anderson, “Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment,” Appl. Opt. 40, 4904–4910 (2001).
[CrossRef]

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, “Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 121–125 (2001).
[CrossRef]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

H. Dahnke, D. Kleine, P. Hering, and M. Mürtz, “Real-time monitoring of ethane in human breath using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 971–975 (2001).
[CrossRef]

2000 (2)

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem 19, 565–607 (2000).
[CrossRef]

R. Peeters, G. Berden, A. Apituley, and G. Meijer, “Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy,” Appl. Phys. B 71, 231–236 (2000).
[CrossRef]

1998 (2)

J. Ye, Long-Sheng Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am B 15, 6–15 (1998).
[CrossRef]

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

1997 (1)

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

1994 (2)

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

G. J. German and D. J. Rokestraw, “Multiplex spectroscopy: determining the transition moments and absolute concentrations of molecular species,” Science 264, 1750–1753 (1994).
[CrossRef]

1964 (1)

Allen, M. G.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O’Keefe, “Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser,” Appl. Phys. B 81, 705–710 (2005).
[CrossRef]

Anderson, J.

Apituley, A.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, “Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy,” Appl. Phys. B 71, 231–236 (2000).
[CrossRef]

Baer, D. S.

S. Williams, M. Gupta, T. Owano, D. S. Baer, A O’Keefe, D. R. Yarkony, and S. Matsika, “Quantitative detection of O2 by cavity-enhanced spectroscopy,” Opt. Lett. 29, 1066–1068 (2004).
[CrossRef] [PubMed]

D. S. Baer, J. B. Paul, M. Gupta, and A. O’Keefe, “Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy,” Appl. Phys. B 75, 261–265 (2002).
[CrossRef]

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

Baillargeon, J. N.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Bakhirkin, Y. A.

Bakowski, B.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

Berden, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem 19, 565–607 (2000).
[CrossRef]

R. Peeters, G. Berden, A. Apituley, and G. Meijer, “Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy,” Appl. Phys. B 71, 231–236 (2000).
[CrossRef]

Borri, S.

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

Braxmaier, C.

Cancio, P.

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

Canosa-Mas, C. E.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, “Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers,” Appl. Phys. B 75, 755–761 (2002).
[CrossRef]

Capasso, F.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Chapman, W. B.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

Chenevier, M.

Cho, A.Y.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Ciurylo, R.

J. T. Hodges and R. Ciurylo, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum. 76, 023112 (2005).
[CrossRef]

Corner, L.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

Cotrufo, F.

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

Curl, R. F.

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, “Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection,” Appl. Opt. 43, 2257–2266 (2004).
[CrossRef] [PubMed]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Dahnke, H.

H. Dahnke, D. Kleine, P. Hering, and M. Mürtz, “Real-time monitoring of ethane in human breath using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 971–975 (2001).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, “Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 121–125 (2001).
[CrossRef]

De Biasio, G.

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

de Labachelerie, M.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

De Natale, G.

A. Rocco, G. De Natale, P. De Natale, G. Gagliardi, and L. Gianfrani, “A diode-laser-based spectrometer for in-situ measurements of volcanic gases,” Appl. Phys. B 78, 235–240 (2004).
[CrossRef]

De Natale, P.

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy,” Appl. Phys. B 80, 141–145 (2005).
[CrossRef]

A. Rocco, G. De Natale, P. De Natale, G. Gagliardi, and L. Gianfrani, “A diode-laser-based spectrometer for in-situ measurements of volcanic gases,” Appl. Phys. B 78, 235–240 (2004).
[CrossRef]

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

Dekorsy, D.

Ebrahimzadeh, M.

M. Ebrahimzadeh: in Solid-State Mid-Infrared Laser Sources, Topics in Appl. Phys.89, I. T. Sorokina and K. L. Vodopyanov, eds. (Spriger-Verlag, Berlin2003) p. 179.

Feller, G. S.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

Fried, A

F. K. Tittel, D. Richter, and A Fried: in Solid-State Mid-Infrared Laser Sources, Topics in Appl. Phys.89, I. T. Sorokina and K. L. Vodopyanov, eds. (Spriger-Verlag, Berlin2003) p. 445.

Fried, A.

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

Gagliardi, G.

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy,” Appl. Phys. B 80, 141–145 (2005).
[CrossRef]

A. Rocco, G. De Natale, P. De Natale, G. Gagliardi, and L. Gianfrani, “A diode-laser-based spectrometer for in-situ measurements of volcanic gases,” Appl. Phys. B 78, 235–240 (2004).
[CrossRef]

G. Gagliardi and L. Gianfrani, “Trace-gas anlysis using diode lasers in the near-IR and long-path techniques,” Opt. Lasers. Eng. 37, 509–520 (2002).
[CrossRef]

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

German, G. J.

G. J. German and D. J. Rokestraw, “Multiplex spectroscopy: determining the transition moments and absolute concentrations of molecular species,” Science 264, 1750–1753 (1994).
[CrossRef]

Gianfrani, L.

A. Rocco, G. De Natale, P. De Natale, G. Gagliardi, and L. Gianfrani, “A diode-laser-based spectrometer for in-situ measurements of volcanic gases,” Appl. Phys. B 78, 235–240 (2004).
[CrossRef]

G. Gagliardi and L. Gianfrani, “Trace-gas anlysis using diode lasers in the near-IR and long-path techniques,” Opt. Lasers. Eng. 37, 509–520 (2002).
[CrossRef]

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

Giusfredi, G.

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

Gmachl, C.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Gupta, M.

S. Williams, M. Gupta, T. Owano, D. S. Baer, A O’Keefe, D. R. Yarkony, and S. Matsika, “Quantitative detection of O2 by cavity-enhanced spectroscopy,” Opt. Lett. 29, 1066–1068 (2004).
[CrossRef] [PubMed]

D. S. Baer, J. B. Paul, M. Gupta, and A. O’Keefe, “Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy,” Appl. Phys. B 75, 261–265 (2002).
[CrossRef]

Hall, J. L.

J. Ye, Long-Sheng Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am B 15, 6–15 (1998).
[CrossRef]

Halmer, D.

Hancock, G.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

Hanson, R. K.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

Hering, P.

D. Halmer, G. von Basum, P. Hering, and M. Mürtz, “Mid-infrared cavity leak-out spectroscopy for ultrasensitive detection of carbonyl sulfide,” Opt. Lett. 30, 2314–2316 (2005).
[CrossRef] [PubMed]

G. von Basum, D. Halmer, P. Hering, M Mürtz, S. Schiller, F. Müller, A. Popp, and F. Kühnemann, “Parts per trillion sensitivity for ethane in air with an optical parametric oscillator cavity leak-out spectrometer,” Opt. Lett. 29, 797–799 (2004).
[CrossRef] [PubMed]

S. Stry, P. Hering, and M. Mürtz, “Portable difference-frequency laser-based cavity leak-out spectrometer for trace-gas analysis,” Appl. Phys. B 75, 297–303 (2002).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, “Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 121–125 (2001).
[CrossRef]

H. Dahnke, D. Kleine, P. Hering, and M. Mürtz, “Real-time monitoring of ethane in human breath using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 971–975 (2001).
[CrossRef]

Herriott, D.

Hodges, J. T.

J. T. Hodges and R. Ciurylo, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum. 76, 023112 (2005).
[CrossRef]

Hutchinson, A. L.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Kachanov, A.

Kachanov, A. A.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Kasyutich, V. L.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, “Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers,” Appl. Phys. B 75, 755–761 (2002).
[CrossRef]

Katsuda, T.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Kelly, K. K.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Kleine, D.

H. Dahnke, D. Kleine, P. Hering, and M. Mürtz, “Real-time monitoring of ethane in human breath using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 971–975 (2001).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, “Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 121–125 (2001).
[CrossRef]

Kogelnik, H.

Kompfner, R.

Kosterev, A. A.

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, “Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection,” Appl. Opt. 43, 2257–2266 (2004).
[CrossRef] [PubMed]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Kotchie, R.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

Kovalchuk, E. V.

Kühnemann, F.

Lapson, L.

Lvovsky, A. I.

Ma, Long-Sheng

J. Ye, Long-Sheng Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am B 15, 6–15 (1998).
[CrossRef]

Maddaloni, P.

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy,” Appl. Phys. B 80, 141–145 (2005).
[CrossRef]

Malara, P.

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy,” Appl. Phys. B 80, 141–145 (2005).
[CrossRef]

Matsika, S.

Mazzotti, D.

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

Mclaughlin, R. J.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Meijer, G.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, “Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy,” Appl. Phys. B 71, 231–236 (2000).
[CrossRef]

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem 19, 565–607 (2000).
[CrossRef]

Menzel, L.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Mihalcea, R. M.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

Mlynek, J.

Morville, J.

Müller, F.

Mürtz, M

Mürtz, M.

D. Halmer, G. von Basum, P. Hering, and M. Mürtz, “Mid-infrared cavity leak-out spectroscopy for ultrasensitive detection of carbonyl sulfide,” Opt. Lett. 30, 2314–2316 (2005).
[CrossRef] [PubMed]

S. Stry, P. Hering, and M. Mürtz, “Portable difference-frequency laser-based cavity leak-out spectrometer for trace-gas analysis,” Appl. Phys. B 75, 297–303 (2002).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, “Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 121–125 (2001).
[CrossRef]

H. Dahnke, D. Kleine, P. Hering, and M. Mürtz, “Real-time monitoring of ethane in human breath using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 971–975 (2001).
[CrossRef]

Nakagawa, K.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

O’Keefe, A

O’Keefe, A.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O’Keefe, “Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser,” Appl. Phys. B 81, 705–710 (2005).
[CrossRef]

D. S. Baer, J. B. Paul, M. Gupta, and A. O’Keefe, “Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy,” Appl. Phys. B 75, 261–265 (2002).
[CrossRef]

Ohtsu, M.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Owano, T.

Paul, J. B.

D. S. Baer, J. B. Paul, M. Gupta, and A. O’Keefe, “Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy,” Appl. Phys. B 75, 261–265 (2002).
[CrossRef]

J. B. Paul, L. Lapson, and J. Anderson, “Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment,” Appl. Opt. 40, 4904–4910 (2001).
[CrossRef]

Peeters, R.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, “Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy,” Appl. Phys. B 71, 231–236 (2000).
[CrossRef]

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem 19, 565–607 (2000).
[CrossRef]

Peters, A.

Peverall, R.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

Pfrang, C.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, “Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers,” Appl. Phys. B 75, 755–761 (2002).
[CrossRef]

Popp, A.

Restieri, R.

G. Gagliardi, R. Restieri, G. De Biasio, P. De Natale, F. Cotrufo, and L. Gianfrani, “Quantitative diode laser absorption spectroscopy near 2 μm with high precision measurements of CO2 concentration,” Rev. Sci. Instrum. 72, 4228–4233 (2001).
[CrossRef]

Richard, E. C.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Richter, D.

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

F. K. Tittel, D. Richter, and A Fried: in Solid-State Mid-Infrared Laser Sources, Topics in Appl. Phys.89, I. T. Sorokina and K. L. Vodopyanov, eds. (Spriger-Verlag, Berlin2003) p. 445.

Ritchie, G. A. D.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002).
[CrossRef]

Rocco, A.

A. Rocco, G. De Natale, P. De Natale, G. Gagliardi, and L. Gianfrani, “A diode-laser-based spectrometer for in-situ measurements of volcanic gases,” Appl. Phys. B 78, 235–240 (2004).
[CrossRef]

Rokestraw, D. J.

G. J. German and D. J. Rokestraw, “Multiplex spectroscopy: determining the transition moments and absolute concentrations of molecular species,” Science 264, 1750–1753 (1994).
[CrossRef]

Roller, C.

Romanini, D.

J. Morville, D. Romanini, M. Chenevier, and A. Kachanov, “Effects of laser phase noise on the injection of a high-finesse cavity,” Appl. Opt. 41, 6980–6990 (2002).
[CrossRef] [PubMed]

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Rosen, D. I.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O’Keefe, “Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser,” Appl. Phys. B 81, 705–710 (2005).
[CrossRef]

Sadeghi, N.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Schiller, S.

Schmeltekopf, A. L.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Shelkovnikov, A. S.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Silva, M. L.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O’Keefe, “Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser,” Appl. Phys. B 81, 705–710 (2005).
[CrossRef]

Sivco, D. L.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

Sonnenfroh, D. M.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O’Keefe, “Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser,” Appl. Phys. B 81, 705–710 (2005).
[CrossRef]

Stockel, F.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Stry, S.

S. Stry, P. Hering, and M. Mürtz, “Portable difference-frequency laser-based cavity leak-out spectrometer for trace-gas analysis,” Appl. Phys. B 75, 297–303 (2002).
[CrossRef]

Tamassia, F.

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

Thompson, T .L.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Tittel, F. K.

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, “Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection,” Appl. Opt. 43, 2257–2266 (2004).
[CrossRef] [PubMed]

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

F. K. Tittel, D. Richter, and A Fried: in Solid-State Mid-Infrared Laser Sources, Topics in Appl. Phys.89, I. T. Sorokina and K. L. Vodopyanov, eds. (Spriger-Verlag, Berlin2003) p. 445.

Tuck, A. F.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Urban, W.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A.Y. Cho, and W. Urban, “Spectroscopic detection of biological NO with a quantum cascade laser,” Appl. Phys. B 72, 1–5 (2001).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, “Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy,” Appl. Phys. B 72, 121–125 (2001).
[CrossRef]

Vaughan, S.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, “Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers,” Appl. Phys. B 75, 755–761 (2002).
[CrossRef]

von Basum, G.

Walega, J. G.

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

Wayne, R. P.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, “Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers,” Appl. Phys. B 75, 755–761 (2002).
[CrossRef]

Webber, M. E.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, “Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm,” Appl. Phys. B 67, 283–288 (1998).
[CrossRef]

Webster, C. R.

Wert, B. P.

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

Williams, S.

Wilson, R.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Winkler, R. H.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T .L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, “A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere,” Appl. Phys. B 75, 183–194 (2002).
[CrossRef]

Yarkony, D. R.

Ye, J.

J. Ye, Long-Sheng Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am B 15, 6–15 (1998).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (16)

D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, “Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,” Appl. Phys. B 75, 281–288 (2003).
[CrossRef] [PubMed]

S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia, “Power-boosted difference-frequency source for high-resolution infrared spectroscopy,” Appl. Phys. B 76, 473–477 (2003).
[CrossRef]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy,” Appl. Phys. B 80, 141–145 (2005).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental set-up. OI: optical isolator, FP: fiber port, C: collimating lens, HWP/QWP: half/quarter wave plate, L1/L2: lenses for spatial mode-matching, DM: dichroic mirror, AL: achromatic lens, PPLN: periodically-poled lithium-niobate non-linear crystal, Ge-F: Germanium filter. The function generator on the external cavity diode laser provides current modulation, while the one connected to the cavity piezo element is used for cavity-lenght modulation.

Fig. 2.
Fig. 2.

Effective free-spectral-range of the off-axis cavity over a 6 GHz scan (recorded on a timescale of 400 ms). Inset: mode spacing (15 MHz) shown on an expanded horizontal scale.

Fig. 3.
Fig. 3.

Absorption line profiles from the cavity, corresponding to ro-vibrational transitions of the CH3D ν4 and CH4 ν24 bands, respectively at 2960.617586 cm-1 and 2960.65530 cm-1. The cavity was filled with pure methane in natural isotopic abundance at 100 mTorr pressure. The inset shows the background baseline (recorded in absence of gas) used to extract the noise level (S/N=600 Hz1/2).

Fig. 4.
Fig. 4.

Integrated absorbance (experimental points) as a function of the air-sample total pressure for the CH4 transition at 2948.107924 cm-1. The IA values and the error bars were obtained from the fit lineshapes according to the procedure described in the text. A weighted linear fit was performed on these points in order to extract the gas concentration c from the slope Eq. (5). Inset a) shows the spectra recorded at increasing pressure values, while the corresponding fit lineshapes are plotted in inset b). At atmospheric pressure a signal-to-noise ratio S/N=1150 Hz1/2 was measured.

Equations (5)

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

dI dt = c 2 L [ I 0 MT 2 I ( 1 R ) ]
I t ( ω ) = I 0 M T 2 2 [ ( 1 R ) + ( ω ) PL ]
σ min = α p S N = 5.7 10 9 cm 1 Hz .
IA I t , α = 0 I t ( ω ) I t , α = 0 = α ( ω ) α ( ω ) + 1 R PLR
IA = P tot π ( B C P + B 2 ) 1

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