Abstract

A processing technique for the determination of the average refractive index and thickness of a two-layer system is presented. It is based on a single measurement with a standard terahertz time-domain spectrometer and the multilayer system thickness. The technique relies on the interference caused by the main pulse with the echoes produced in each material. This approach allows noninvasive inspection of double-layer compound products.

© 2014 Optical Society of America

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References

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  1. B. M. Fischer, H. Helm, and P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007) .
    [CrossRef]
  2. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging—modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
    [CrossRef]
  3. H. G. Tompkins and E. A. Irene, eds., Handbook of Ellipsometry, (Springer, 2005).
  4. A. Yu. Nikulin and P. V. Petrashen, “Practical applications of optical inverse problem technique to characterization of multilayers,” in Proceedings of Advances in X-ray Analysis (AXA), Denver X-ray Conference (1997), Vol. 41, pp. 155–164.
  5. S. E. Ralph, S. Perkowitz, N. Katzenellenbogen, and D. Grischkowsky, “Terahertz spectroscopy of optically thick multilayered semiconductor structures,” J. Opt. Soc. Am. B 11, 2528–2532 (1994).
    [CrossRef]
  6. R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
    [CrossRef]
  7. J. A. Hejase, E. J. Rothwell, and P. Chahal, “A multiple angle method for THz time-domain material characterization,” IEEE Trans. THz Sci. Technol. 3, 656–665 (2013).
    [CrossRef]
  8. A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.
  9. F. Sanjuan and B. Vidal, “Refractive index calculation from echo interference in pulsed terahertz spectroscopy,” Electron. Lett. 50, 308–309 (2014).
    [CrossRef]
  10. F. Sanjuan, A. Bockelt, and B. Vidal, “Birefringence measurement in the THz range based on double Fourier analysis,” Opt. Lett. 39, 809–812 (2014).
    [CrossRef]

2014 (2)

F. Sanjuan and B. Vidal, “Refractive index calculation from echo interference in pulsed terahertz spectroscopy,” Electron. Lett. 50, 308–309 (2014).
[CrossRef]

F. Sanjuan, A. Bockelt, and B. Vidal, “Birefringence measurement in the THz range based on double Fourier analysis,” Opt. Lett. 39, 809–812 (2014).
[CrossRef]

2013 (1)

J. A. Hejase, E. J. Rothwell, and P. Chahal, “A multiple angle method for THz time-domain material characterization,” IEEE Trans. THz Sci. Technol. 3, 656–665 (2013).
[CrossRef]

2011 (1)

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

2008 (1)

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[CrossRef]

2007 (1)

B. M. Fischer, H. Helm, and P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007) .
[CrossRef]

1994 (1)

Bockelt, A.

Brahm, A.

A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.

Cernat, R.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[CrossRef]

Chahal, P.

J. A. Hejase, E. J. Rothwell, and P. Chahal, “A multiple angle method for THz time-domain material characterization,” IEEE Trans. THz Sci. Technol. 3, 656–665 (2013).
[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, 124–166 (2011).
[CrossRef]

Fischer, B. M.

B. M. Fischer, H. Helm, and P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007) .
[CrossRef]

Grischkowsky, D.

Hejase, J. A.

J. A. Hejase, E. J. Rothwell, and P. Chahal, “A multiple angle method for THz time-domain material characterization,” IEEE Trans. THz Sci. Technol. 3, 656–665 (2013).
[CrossRef]

Helm, H.

B. M. Fischer, H. Helm, and P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007) .
[CrossRef]

Jepsen, P. U.

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

B. M. Fischer, H. Helm, and P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007) .
[CrossRef]

Katzenellenbogen, N.

Koch, M.

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

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[CrossRef]

Nikulin, A. Yu.

A. Yu. Nikulin and P. V. Petrashen, “Practical applications of optical inverse problem technique to characterization of multilayers,” in Proceedings of Advances in X-ray Analysis (AXA), Denver X-ray Conference (1997), Vol. 41, pp. 155–164.

Notni, G.

A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.

Perkowitz, S.

Petrashen, P. V.

A. Yu. Nikulin and P. V. Petrashen, “Practical applications of optical inverse problem technique to characterization of multilayers,” in Proceedings of Advances in X-ray Analysis (AXA), Denver X-ray Conference (1997), Vol. 41, pp. 155–164.

Pupeza, I.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[CrossRef]

Ralph, S. E.

Riehemann, S.

A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.

Rothwell, E. J.

J. A. Hejase, E. J. Rothwell, and P. Chahal, “A multiple angle method for THz time-domain material characterization,” IEEE Trans. THz Sci. Technol. 3, 656–665 (2013).
[CrossRef]

Sanjuan, F.

F. Sanjuan, A. Bockelt, and B. Vidal, “Birefringence measurement in the THz range based on double Fourier analysis,” Opt. Lett. 39, 809–812 (2014).
[CrossRef]

F. Sanjuan and B. Vidal, “Refractive index calculation from echo interference in pulsed terahertz spectroscopy,” Electron. Lett. 50, 308–309 (2014).
[CrossRef]

Tünnermann, A.

A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.

Vidal, B.

F. Sanjuan, A. Bockelt, and B. Vidal, “Birefringence measurement in the THz range based on double Fourier analysis,” Opt. Lett. 39, 809–812 (2014).
[CrossRef]

F. Sanjuan and B. Vidal, “Refractive index calculation from echo interference in pulsed terahertz spectroscopy,” Electron. Lett. 50, 308–309 (2014).
[CrossRef]

Weigel, A.

A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.

Wilk, R.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[CrossRef]

Electron. Lett. (1)

F. Sanjuan and B. Vidal, “Refractive index calculation from echo interference in pulsed terahertz spectroscopy,” Electron. Lett. 50, 308–309 (2014).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate THz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[CrossRef]

IEEE Trans. THz Sci. Technol. (1)

J. A. Hejase, E. J. Rothwell, and P. Chahal, “A multiple angle method for THz time-domain material characterization,” IEEE Trans. THz Sci. Technol. 3, 656–665 (2013).
[CrossRef]

J. Opt. Soc. Am. B (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, 124–166 (2011).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

B. M. Fischer, H. Helm, and P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007) .
[CrossRef]

Other (3)

H. G. Tompkins and E. A. Irene, eds., Handbook of Ellipsometry, (Springer, 2005).

A. Yu. Nikulin and P. V. Petrashen, “Practical applications of optical inverse problem technique to characterization of multilayers,” in Proceedings of Advances in X-ray Analysis (AXA), Denver X-ray Conference (1997), Vol. 41, pp. 155–164.

A. Brahm, A. Weigel, S. Riehemann, G. Notni, and A. Tünnermann, “Highly precise parameter extraction of thin multi-layers in THz transmission and reflection geometry,” in Proceedings of IEEE Conference on Infrared, Millimeter and Terahertz Waves, Houston, 2011, pp. 1–2.

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Figures (3)

Fig. 1.
Fig. 1.

Electric-field ray tracing in a system made up of two layers with two different thicknesses and refraction indices.

Fig. 2.
Fig. 2.

Numerical simulation of the discrete Fourier transform (DFT) applied to Eq. (3).

Fig. 3.
Fig. 3.

(a) Time-domain measurement from the THz spectrometer. (b) Outcome of double Fourier processing of the temporal trace shown in (a).

Equations (11)

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Et1(ω)=Ei(ω)τ1(ω)P1(ω)(1+r12(ω)r1airP12(ω)),
τ1(ω)=2n1(ω)n1(ω)+n2(ω),r12(ω)=n1(ω)n2(ω)n1(ω)+n2(ω),r1air(ω)=n1(ω)1n1(ω)+1,andP1(ω)=ejn1ωd1c
Et2(ω)=Et1(ω)τ2(ω)P2(ω)(1+r21(ω)r2air(ω)P22(ω))=Ei(ω)τ1(ω)P1(ω)τ2(ω)P2(ω)+Ei(ω)τ1(ω)r12(ω)r1airP13(ω)τ2(ω)P2(ω)+Ei(ω)τ1(ω)P1(ω)τ2(ω)r21(ω)r2air(ω)P23(ω)+Ei(ω)τ1(ω)r12(ω)r1airP13(ω)τ2(ω)r21(ω)r2air(ω)P23(ω),
|Et2(ω)|2=H1(n1,n2)+H2(n1,n2)cos(2n1ωd0c)+H3(n1,n2)cos(2n2ωd2c)+H4(n1,n2)cos(2wc(n1d1n2d2)).
H1=C12+C22+C32,H2=2C1C2,H3=2C2C3,H4=2C1C3.
I(t)=FT(|Et2(ω)|2)=H1(n1,n2)δ(t)+H2(n1,n2)2δ(t2n1d1c)+H3(n1,n2)2δ(t2n2d2c)+H4(n1,n2)2δ(2wc|n1d1n2d2|).
T1=2n1d1c,
T2=2n2d2c,
H2(n1,n2)H3(n1,n2)=r1air(ω)r2air(ω)=(n11)(n2+1)(n1+1)(n21),
d=d1+d2.
T1=15.4ps,T2=18.9ps,H1/H2=1.9,d=2220μm.

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