Abstract

In this study, inspired by the frequency-modulated continuous-wave (FMCW) method, an operation scheme of continuous-wave (CW) terahertz (THz) homodyne system is proposed and evaluated. For this purpose, we utilized the fast and stable wavelength tuning characteristics of a dual-mode laser (DML) as a beating source. Using the frequency-modulated THz waves generated by DML, a cost-effective and robust operation of CW THz system to be applicable to the measurements of thickness or refractive index of a sample is demonstrated. We believe that the proposed scheme shows a potential to the implementations of compact and fast CW THz measurement systems that can be useful in many THz applications.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2014 (2)

2013 (4)

S.-P. Han, H. Ko, J.-W. Park, N. Kim, Y.-J. Yoon, J. H. Shin, D. Y. Kim, D. H. Lee, and K. H. Park, “InGaAs Schottky barrier diode array detector for a real-time compact terahertz line scanner,” Opt. Express 21(22), 25874–25882 (2013).
[Crossref] [PubMed]

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

B. Apicella, A. Bruno, X. Wang, and N. Spinelli, “Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra,” Int. J. Mass Spectrom. 338, 30–38 (2013).
[Crossref]

2012 (3)

2011 (4)

H.-J. Song and T. Nagatsuma, ““Present and future of terahertz communications,” IEEE Trans. THz Sci. Technol. 1(1), 256–263 (2011).

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

2010 (5)

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96(15), 151112 (2010).
[Crossref]

Z. W. Barber, W. R. Babbitt, B. Kaylor, R. R. Reibel, and P. A. Roos, “Accuracy of active chirp linearization for broadband frequency modulated continuous wave ladar,” Appl. Opt. 49(2), 213–219 (2010).
[Crossref] [PubMed]

A. Vasilyev, N. Satyan, S. Xu, G. Rakuljic, and A. Yariv, “Multiple source frequency-modulated continuous-wave optical reflectometry: theory and experiment,” Appl. Opt. 49(10), 1932–1937 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (3)

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

2006 (1)

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49(2), 513–517 (2006).

2003 (1)

2002 (1)

P. H. Siegel, “Terahertz technology,” IEEE T. Microw. Theory 50(3), 910–928 (2002).
[Crossref]

1998 (1)

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

1997 (1)

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997).
[Crossref]

1995 (1)

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8-THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
[Crossref]

Ajito, K.

S. Hisatake, J.-Y. Kim, K. Ajito, and T. Nagatsuma, “Self-heterodyne spectrometer using uni-traveling-carrier photodiodes for terahertz-wave generators and optoelectronic mixers,” J. Lightwave Technol. 32(20), 3683–3689 (2014).
[Crossref]

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

Apicella, B.

B. Apicella, A. Bruno, X. Wang, and N. Spinelli, “Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra,” Int. J. Mass Spectrom. 338, 30–38 (2013).
[Crossref]

Baaske, K.

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96(15), 151112 (2010).
[Crossref]

Babbitt, W. R.

Barber, Z. W.

Bigourd, D.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

Blary, K.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

Bocquet, R.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

Brown, E. R.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8-THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
[Crossref]

Bruno, A.

B. Apicella, A. Bruno, X. Wang, and N. Spinelli, “Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra,” Int. J. Mass Spectrom. 338, 30–38 (2013).
[Crossref]

Calawa, S.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

Chang, C.-H.

C.-S. Yang, C.-H. Chang, M.-H. Lin, P. Yu, O. Wada, and C.-L. Pan, “THz conductivities of indium-tin-oxide nanowhiskers as a graded-refractive-index structure,” Opt. Express 20(S4Suppl 4), A441 (2012).
[Crossref] [PubMed]

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

Chen, C.-W.

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Cuisset, A.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

Cunningham, J.

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997).
[Crossref]

Deninger, A.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Dennis, C. L.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8-THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
[Crossref]

Dinatale, W. F.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

Döhler, G. H.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

Duerr, E. K.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

Fukada, Y.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

Geva, M.

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997).
[Crossref]

Gossard, A. C.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

Grüninger, M.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Güsten, R.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Han, S.-P.

Hemberger, J.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Hindle, F.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

Hisatake, S.

S. Hisatake, J.-Y. Kim, K. Ajito, and T. Nagatsuma, “Self-heterodyne spectrometer using uni-traveling-carrier photodiodes for terahertz-wave generators and optoelectronic mixers,” J. Lightwave Technol. 32(20), 3683–3689 (2014).
[Crossref]

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

Inoue, H.

Jang, Y.

Jeon, M. Y.

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

N. Kim, J. Shin, E. Sim, C. W. Lee, D.-S. Yee, M. Y. Jeon, Y. Jang, and K. H. Park, “Monolithic dual-mode distributed feedback semiconductor laser for tunable continuous-wave terahertz generation,” Opt. Express 17(16), 13851–13859 (2009).
[Crossref] [PubMed]

Jeon, S.-G.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49(2), 513–517 (2006).

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Jin, Y.-S.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49(2), 513–517 (2006).

Kawase, K.

Kaylor, B.

Kim, D. Y.

Kim, G.-J.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49(2), 513–517 (2006).

Kim, J.-Y.

Kim, N.

K. Moon, N. Kim, J.-H. Shin, Y.-J. Yoon, S.-P. Han, and K. H. Park, “Continuous-wave terahertz system based on a dual-mode laser for real-time non-contact measurement of thickness and conductivity,” Opt. Express 22(3), 2259–2266 (2014).
[Crossref] [PubMed]

S.-P. Han, H. Ko, J.-W. Park, N. Kim, Y.-J. Yoon, J. H. Shin, D. Y. Kim, D. H. Lee, and K. H. Park, “InGaAs Schottky barrier diode array detector for a real-time compact terahertz line scanner,” Opt. Express 21(22), 25874–25882 (2013).
[Crossref] [PubMed]

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

H.-C. Ryu, N. Kim, S.-P. Han, H. Ko, J.-W. Park, K. Moon, and K. H. Park, “Simple and cost-effective thickness measurement terahertz system based on a compact 1.55 μm λ/4 phase-shifted dual-mode laser,” Opt. Express 20(23), 25990–25999 (2012).
[Crossref] [PubMed]

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

N. Kim, J. Shin, E. Sim, C. W. Lee, D.-S. Yee, M. Y. Jeon, Y. Jang, and K. H. Park, “Monolithic dual-mode distributed feedback semiconductor laser for tunable continuous-wave terahertz generation,” Opt. Express 17(16), 13851–13859 (2009).
[Crossref] [PubMed]

Kinder, T.

M. Scheller, T. Kinder, O. Peters, T. Müller-Wirts, and M. Koch, “Single sampling point detection of frequency modulated terahertz waves,” J. Infrared Milli. Thz Waves 33(1), 36–42 (2012).
[Crossref]

Kitahara, G.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

Ko, H.

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

S.-P. Han, H. Ko, J.-W. Park, N. Kim, Y.-J. Yoon, J. H. Shin, D. Y. Kim, D. H. Lee, and K. H. Park, “InGaAs Schottky barrier diode array detector for a real-time compact terahertz line scanner,” Opt. Express 21(22), 25874–25882 (2013).
[Crossref] [PubMed]

H.-C. Ryu, N. Kim, S.-P. Han, H. Ko, J.-W. Park, K. Moon, and K. H. Park, “Simple and cost-effective thickness measurement terahertz system based on a compact 1.55 μm λ/4 phase-shifted dual-mode laser,” Opt. Express 20(23), 25990–25999 (2012).
[Crossref] [PubMed]

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

Koch, M.

M. Scheller, T. Kinder, O. Peters, T. Müller-Wirts, and M. Koch, “Single sampling point detection of frequency modulated terahertz waves,” J. Infrared Milli. Thz Waves 33(1), 36–42 (2012).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96(15), 151112 (2010).
[Crossref]

Lampin, J. F.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

Lee, C. W.

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

N. Kim, J. Shin, E. Sim, C. W. Lee, D.-S. Yee, M. Y. Jeon, Y. Jang, and K. H. Park, “Monolithic dual-mode distributed feedback semiconductor laser for tunable continuous-wave terahertz generation,” Opt. Express 17(16), 13851–13859 (2009).
[Crossref] [PubMed]

Lee, D.

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

Lee, D. H.

Leem, Y. A.

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

Lin, M.-H.

Lin, Y.-C.

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

Lippens, D.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

Malzer, S.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

Matton, S.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

Mayorga, I. C.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

McIntosh, K. A.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8-THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
[Crossref]

Mittleman, D. M.

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997).
[Crossref]

Molvar, K. A.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

Moon, K.

Mouret, G.

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

Müller-Wirts, T.

M. Scheller, T. Kinder, O. Peters, T. Müller-Wirts, and M. Koch, “Single sampling point detection of frequency modulated terahertz waves,” J. Infrared Milli. Thz Waves 33(1), 36–42 (2012).
[Crossref]

Nagatsuma, T.

S. Hisatake, J.-Y. Kim, K. Ajito, and T. Nagatsuma, “Self-heterodyne spectrometer using uni-traveling-carrier photodiodes for terahertz-wave generators and optoelectronic mixers,” J. Lightwave Technol. 32(20), 3683–3689 (2014).
[Crossref]

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

H.-J. Song and T. Nagatsuma, ““Present and future of terahertz communications,” IEEE Trans. THz Sci. Technol. 1(1), 256–263 (2011).

Nichols, K. B.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8-THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
[Crossref]

Nuss, M. C.

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997).
[Crossref]

Ogawa, Y.

Pan, C.-L.

C.-S. Yang, C.-H. Chang, M.-H. Lin, P. Yu, O. Wada, and C.-L. Pan, “THz conductivities of indium-tin-oxide nanowhiskers as a graded-refractive-index structure,” Opt. Express 20(S4Suppl 4), A441 (2012).
[Crossref] [PubMed]

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

Park, J.-W.

Park, K. H.

K. Moon, N. Kim, J.-H. Shin, Y.-J. Yoon, S.-P. Han, and K. H. Park, “Continuous-wave terahertz system based on a dual-mode laser for real-time non-contact measurement of thickness and conductivity,” Opt. Express 22(3), 2259–2266 (2014).
[Crossref] [PubMed]

S.-P. Han, H. Ko, J.-W. Park, N. Kim, Y.-J. Yoon, J. H. Shin, D. Y. Kim, D. H. Lee, and K. H. Park, “InGaAs Schottky barrier diode array detector for a real-time compact terahertz line scanner,” Opt. Express 21(22), 25874–25882 (2013).
[Crossref] [PubMed]

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

H.-C. Ryu, N. Kim, S.-P. Han, H. Ko, J.-W. Park, K. Moon, and K. H. Park, “Simple and cost-effective thickness measurement terahertz system based on a compact 1.55 μm λ/4 phase-shifted dual-mode laser,” Opt. Express 20(23), 25990–25999 (2012).
[Crossref] [PubMed]

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

N. Kim, J. Shin, E. Sim, C. W. Lee, D.-S. Yee, M. Y. Jeon, Y. Jang, and K. H. Park, “Monolithic dual-mode distributed feedback semiconductor laser for tunable continuous-wave terahertz generation,” Opt. Express 17(16), 13851–13859 (2009).
[Crossref] [PubMed]

Peters, O.

M. Scheller, T. Kinder, O. Peters, T. Müller-Wirts, and M. Koch, “Single sampling point detection of frequency modulated terahertz waves,” J. Infrared Milli. Thz Waves 33(1), 36–42 (2012).
[Crossref]

Preu, S.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

Rakuljic, G.

Reibel, R. R.

Roggenbuck, A.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Roos, P. A.

Ryu, H.-C.

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

H.-C. Ryu, N. Kim, S.-P. Han, H. Ko, J.-W. Park, K. Moon, and K. H. Park, “Simple and cost-effective thickness measurement terahertz system based on a compact 1.55 μm λ/4 phase-shifted dual-mode laser,” Opt. Express 20(23), 25990–25999 (2012).
[Crossref] [PubMed]

Satyan, N.

Scheller, M.

M. Scheller, T. Kinder, O. Peters, T. Müller-Wirts, and M. Koch, “Single sampling point detection of frequency modulated terahertz waves,” J. Infrared Milli. Thz Waves 33(1), 36–42 (2012).
[Crossref]

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96(15), 151112 (2010).
[Crossref]

Schmitz, H.

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Shieh, J.-M.

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

Shin, J.

Shin, J. H.

Shin, J.-H.

Siegel, P. H.

P. H. Siegel, “Terahertz technology,” IEEE T. Microw. Theory 50(3), 910–928 (2002).
[Crossref]

Sim, E.

Song, H.-J.

H.-J. Song and T. Nagatsuma, ““Present and future of terahertz communications,” IEEE Trans. THz Sci. Technol. 1(1), 256–263 (2011).

Spinelli, N.

B. Apicella, A. Bruno, X. Wang, and N. Spinelli, “Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra,” Int. J. Mass Spectrom. 338, 30–38 (2013).
[Crossref]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

Vasilyev, A.

Verghese, S.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

Wada, O.

Wang, L. J.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

Wang, X.

B. Apicella, A. Bruno, X. Wang, and N. Spinelli, “Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra,” Int. J. Mass Spectrom. 338, 30–38 (2013).
[Crossref]

Watanabe, Y.

Xu, S.

Yang, C.-S.

Yariv, A.

Yee, D.-S.

Yoon, Y.-J.

Yoshimoto, N.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

Yu, P.

C.-S. Yang, C.-H. Chang, M.-H. Lin, P. Yu, O. Wada, and C.-L. Pan, “THz conductivities of indium-tin-oxide nanowhiskers as a graded-refractive-index structure,” Opt. Express 20(S4Suppl 4), A441 (2012).
[Crossref] [PubMed]

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (2)

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2–3), 395–399 (2007).
[Crossref]

G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, A. Cuisset, J. F. Lampin, K. Blary, and D. Lippens, “THz media characterization by means of coherent homodyne detection, results and potential applications,” Appl. Phys. B 89(2-3), 395–399 (2007).
[Crossref]

Appl. Phys. Lett. (4)

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997).
[Crossref]

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96(15), 151112 (2010).
[Crossref]

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8-THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
[Crossref]

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998).
[Crossref]

ETRI J. (1)

N. Kim, Y. A. Leem, H. Ko, M. Y. Jeon, C. W. Lee, S.-P. Han, D. Lee, and K. H. Park, “Widely tunable 1.55-μm detuned dual-mode laser diode for compact continuous-wave THz emitter,” ETRI J. 33(5), 810–813 (2011).
[Crossref]

IEEE J. Quantum Electron. (1)

C.-W. Chen, Y.-C. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, and C.-L. Pan, “Frequency-Dependent Complex Conductivities and Dielectric Responses of Indium Tin Oxide Thin Films from the Visible to the Far-Infrared,” IEEE J. Quantum Electron. 46(12), 1746–1754 (2010).
[Crossref]

IEEE Sens. J. (1)

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive sensitive terahertz self-homodyne system based on photodiode and low-temperature-grown GaAs photoconductor at 1.55 μm,” IEEE Sens. J. 13(1), 31–36 (2013).
[Crossref]

IEEE T. Microw. Theory (1)

P. H. Siegel, “Terahertz technology,” IEEE T. Microw. Theory 50(3), 910–928 (2002).
[Crossref]

IEEE Trans. THz Sci. Technol. (1)

H.-J. Song and T. Nagatsuma, ““Present and future of terahertz communications,” IEEE Trans. THz Sci. Technol. 1(1), 256–263 (2011).

Int. J. Mass Spectrom. (1)

B. Apicella, A. Bruno, X. Wang, and N. Spinelli, “Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra,” Int. J. Mass Spectrom. 338, 30–38 (2013).
[Crossref]

J. Appl. Phys. (1)

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011).
[Crossref]

J. Infrared Milli. Thz Waves (1)

M. Scheller, T. Kinder, O. Peters, T. Müller-Wirts, and M. Koch, “Single sampling point detection of frequency modulated terahertz waves,” J. Infrared Milli. Thz Waves 33(1), 36–42 (2012).
[Crossref]

J. Korean Phys. Soc. (1)

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49(2), 513–517 (2006).

J. Lightwave Technol. (1)

Laser Photon. Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Laser Phys. Lett. (1)

N. Kim, H.-C. Ryu, D. Lee, S.-P. Han, H. Ko, K. Moon, J.-W. Park, M. Y. Jeon, and K. H. Park, “Monolithically integrated optical beat sources toward a single-chip broadband terahertz emitter,” Laser Phys. Lett. 10(8), 085805 (2013).
[Crossref]

Nat. Photonics (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

New J. Phys. (1)

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12(4), 043017 (2010).
[Crossref]

Opt. Express (6)

Other (3)

D. Havelock, S. Kuwano, and M. Vorländer, Handbook of Signal Processing in Acoustics (Springer, 2008), Chap. 3.

K. Petermann, Laser Diode Modulation and Noise (Kluwer, 1991).

J. Zheng, Optical Frequency-Modulated Continuous-Wave (FMCW) Interferometry (Springer, 2005).

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic diagram of 1.3μm DML with its constitutional parts; two λ/4 phase-shifted DFB laser sections, a phase section, and two integrated μ-heaters. (b) Optical spectrum of the DML used in this study when the μ-heaters are not biased.
Fig. 2
Fig. 2 Schematic diagram of the proposed FM-based CW THz homodyne system. A sample of which thickness to be measured is inserted between Tx and Rx modules. Instead of using a mechanical delay line, the beating frequency from DML is repeatedly modulated by the bias pattern fed by a function generator.
Fig. 3
Fig. 3 A linearization of frequency sweeping profile for the driving voltage of μ-heater. (a) The dependence of the beating frequency of DML to the applied voltage. (b) Time-dependent voltage output from a function generator for 100GHz saw-tooth waveform modulation.
Fig. 4
Fig. 4 Relations between the frequency profiles of the modulated waves passed through the two paths in Fig. 2. The cases are (a) τ0 < 0 and s < |τ0 |/T, (b) τ0 < 0 and s ≥ |τ0 |/T, (c) τ0 ≥ 0 and s ≥ τ0 /T, and (d) τ0 ≥ 0 and s < τ0 /T. The shaded regions stand for the time interval that corresponds to the signal pulse from the previous (p = −1, (a) and (b)), or from the next (p = 1, (c) and (d)) period. For all other time between (−1, 1) and outside of the shaded region, p = 0.
Fig. 5
Fig. 5 Measured optical spectra of DML for the cases of (a) static (μ-heater 1 is DC biased and μ-heater 2 is unbiased) and (b) μ-heater 2 is modulated with 20 Hz waveform.
Fig. 6
Fig. 6 (a) Delay position dependent beating frequencies obtained by peak counting method. The curve for number of counted peaks is depicted with rectangular markers and that of the calculated beating frequencies is depicted with circular markers. (b)-(c) Examples of the obtained beating signals for several delay positions of A, B, and C are shown in, respectively.
Fig. 7
Fig. 7 (a) Amount of frequency shift dependent on delay position obtained by autocorrelation method is depicted in a curve with triangular markers. For the comparison of the linearity, the beating frequency curve obtained in Fig. 6(a) is plotted in the same panel. (b) The autocorrelation functions for several delay positions. In these data, an inverse of the second autocorrelation peak corresponds to its beating frequency.
Fig. 8
Fig. 8 (a) Autocorrelation results for Teflon disks. (b) Sample-dependent frequencies for the correlation peaks. In (b), the zero-th sample is free space as a reference. The data was obtained at the delay position of 100 ps.

Tables (2)

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Table 1 Parameters used in the experiments

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Table 2 Measured thickness of Teflon disk

Equations (16)

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E( t )= E 1 ( t )exp[ j ϕ 1 ( t ) ]+ E 2 ( t )exp[ j ϕ 2 ( t ) ],
ϕ i ( t )= 0 t ω i ( t ) dt+ ϕ i0 ,
ω 2 ( t )=a( tsT ) + ω 20 ,
α={ 00t'/T<s, Δ ω 2 ( 1s )T st'/T<1.
E( t )= E 0 exp[ j( ω 1 t'+ ϕ 10 ) ]+ E 0 exp{ j[ 1 2 αt ' 2 +( ω 20 αsT )t'+ ϕ 02 ] }.
E η = E 0 2 exp{ j[ ω 1 ( t' τ η )+ ϕ 10 ] }+ E 0 2 exp{ j[ α ( t' τ η ) 2 2 +( ω 20 αsT )( t' τ η )+ ϕ 02 ] },
E Tx | E 0 | 2 2 { 1+cos[ α p ( t' τ 0 +pT ) 2 2 +( ω 20 ω 1 α p sT )( t' τ 0 +pT )+( ϕ 20 ϕ 10 ) ] },
E THz cos[ 1 2 α p ( t' τ 0 +pT ) 2 +( ω 0 α p sT )( t' τ 0 +pT )+ ϕ 0 ],
I Rx E THz { 1+cos[ 1 2 αt ' 2 +( ω 0 αsT )t'+ ϕ 0 ] }.
I Rx cos[ 1 2 αt ' 2 +( ω α α τ p )t'+ 1 2 τ p 2 ω α τ p + ϕ 0 ] + 1 2 cos[ 1 2 ( α p +α )t ' 2 ( α p τ p 2 ω α )t'+ 1 2 α p τ p 2 τ p +2 ϕ 0 ] + 1 2 cos[ 1 2 ( α p α )t ' 2 α p τ p t'+ 1 2 α p τ p 2 ω α τ p ].
I Rx = I 0 { 1+Mcos[ 1 2 ( α p α )t ' 2 α p τ p t'+ 1 2 α p τ p 2 ω α τ p ] },
ω b =| ( α p α )t' α p τ p |={ αt' α p =0, α| τ p | α p =α.
τ s = τ 0 + n1 c 0 d.
Δ ω b =α n1 c 0 d.
Δ ϕ b = ω α n1 c 0 d.
f b = 1 | t 2 t 1 |/( N peaks /2 ) = N peaks 2| t 2 t 1 | .

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