An alternative differential method of femtosecond pump-probe examination of materials

R. Ivanov; Jesús Villa; Ismael de la Rosa; E. Marín

doi:10.1364/OE.19.011290

An alternative differential method of femtosecond pump-probe examination of materials

R. Ivanov, Jesús Villa, Ismael de la Rosa, and E. Marín

Optics Express
Vol. 19,
Issue 12,
pp. 11290-11298
(2011)
•https://doi.org/10.1364/OE.19.011290

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R. Ivanov, Jesús Villa, Ismael de la Rosa, and E. Marín, "An alternative differential method of femtosecond pump-probe examination of materials," Opt. Express 19, 11290-11298 (2011)

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Abstract

We describe an alternative method for femtosecond pump-probe beam examination of energy transport properties of materials. All already reported techniques have several drawbacks which limit precise measurements of reflection coefficient as function of time. A typical problem is present when rough samples are being studied. In this case the pump-beam polarization changes randomly which may produce a spurious signal, drastically reducing the signal to noise ratio. Some proposals to alleviate such problem have been reported, however, they have not been totally satisfactory. The method presented here consists on measuring the difference between the two delays’ signals of the probe-beam. As will be explained, our proposal is free of typical drawbacks. We also propose a numerical method to recover the ΔR(t)/R curve from the measured data. Numerical simulations show that our proposal is a viable alternative.

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References

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P. M. Norris, A. P. Caffrey, R. J. Stevens, J. M. Klopf, J. T. McLeskey, and A. N. Smith, “Femtosecond pump-probe nondestructive examination of materials,” Rev. Sci. Instrum. 74, 400–406 (2003).
[Crossref]
G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]
K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump-probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. 17, 874–876 (1992).
[Crossref] [PubMed]
K. Yokoyama, C. Silva, D. H. Son, P. K. Walhout, and P. F. Barbara, “Detailed investigation of the femtosecond pump-probe spectroscopy of the hydrated electron,” J. Phys. Chem. A 102, 6957–6966 (1998).
[Crossref]
H.C Wang, Y. C. Lu, C. Y. Chen, C. Y. Chi, S. C. Chin, and C. C. Yang, “Non-degenerate fs pump-probe study on InGaN with multi-wavelength second-harmonic generation,” Opt. Express 13, 5245–5251 (2005).
[Crossref] [PubMed]
J. Zhang, A. Belousov, J. Karpinski, B. Batlogg, and R. Sobolewski, “Femtosecond optical spectroscopy studies of high-pressuregrown (Al,Ga)N single crystals,” Appl. Phys. B: Lasers Opt. 29, 135–138 (1982).
Illingworth and I. S. Ruddock, “The analysis of excite and probe measurements of relaxation times with fluctuating pulse duration,” Appl. Opt. 43, 6139–6146 (2004).
S. V. Rao, D. Swain, and S. P. Tewari, “Pump-probe experiments with sub-100 femtosecond pulses for characterizing the excited state dynamics of phthalocyanine thin films,” Proc. SPIE 7599, 75991P (2010).
[Crossref]
A. Yu, X. Ye, D. Ionascu, W. Cao, and P. M. Champion, “Two-color pump-probe laser spectroscopy instrument with picosecond time-resolved electronic delay and extended scan range,” Rev. Sci. Instrum. 76, 114301 (2005).
[Crossref]
K. Kang, Y. K. Koh, C. Chiritescu, X. Zheng, and D. G. Cahill, “Two-tint pump-probe measurements using a femtosecond laser oscillator and sharp-edged optical filters,” Rev. Sci. Instrum. 79, 114901 (2008).
[Crossref] [PubMed]
B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

2010 (1)

S. V. Rao, D. Swain, and S. P. Tewari, “Pump-probe experiments with sub-100 femtosecond pulses for characterizing the excited state dynamics of phthalocyanine thin films,” Proc. SPIE 7599, 75991P (2010).
[Crossref]

2008 (1)

K. Kang, Y. K. Koh, C. Chiritescu, X. Zheng, and D. G. Cahill, “Two-tint pump-probe measurements using a femtosecond laser oscillator and sharp-edged optical filters,” Rev. Sci. Instrum. 79, 114901 (2008).
[Crossref] [PubMed]

2006 (1)

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]

2005 (2)

A. Yu, X. Ye, D. Ionascu, W. Cao, and P. M. Champion, “Two-color pump-probe laser spectroscopy instrument with picosecond time-resolved electronic delay and extended scan range,” Rev. Sci. Instrum. 76, 114301 (2005).
[Crossref]

H.C Wang, Y. C. Lu, C. Y. Chen, C. Y. Chi, S. C. Chin, and C. C. Yang, “Non-degenerate fs pump-probe study on InGaN with multi-wavelength second-harmonic generation,” Opt. Express 13, 5245–5251 (2005).
[Crossref] [PubMed]

2004 (1)

Illingworth and I. S. Ruddock, “The analysis of excite and probe measurements of relaxation times with fluctuating pulse duration,” Appl. Opt. 43, 6139–6146 (2004).

2003 (1)

P. M. Norris, A. P. Caffrey, R. J. Stevens, J. M. Klopf, J. T. McLeskey, and A. N. Smith, “Femtosecond pump-probe nondestructive examination of materials,” Rev. Sci. Instrum. 74, 400–406 (2003).
[Crossref]

1999 (1)

B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

1998 (1)

K. Yokoyama, C. Silva, D. H. Son, P. K. Walhout, and P. F. Barbara, “Detailed investigation of the femtosecond pump-probe spectroscopy of the hydrated electron,” J. Phys. Chem. A 102, 6957–6966 (1998).
[Crossref]

1992 (1)

K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump-probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. 17, 874–876 (1992).
[Crossref] [PubMed]

1982 (1)

J. Zhang, A. Belousov, J. Karpinski, B. Batlogg, and R. Sobolewski, “Femtosecond optical spectroscopy studies of high-pressuregrown (Al,Ga)N single crystals,” Appl. Phys. B: Lasers Opt. 29, 135–138 (1982).

Antonelli, G. A.

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]

Barbara, P. F.

Batlogg, B.

Belousov, A.

Bousquet, B.

B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

Caffrey, A. P.

Cahill, D. G.

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]

Canioni, L.

B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

Cao, W.

Champion, P. M.

Chen, C. Y.

Chi, C. Y.

Chin, S. C.

Chiritescu, C.

Daly, B. C.

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]

Hall, K. L.

Illingworth,

Illingworth and I. S. Ruddock, “The analysis of excite and probe measurements of relaxation times with fluctuating pulse duration,” Appl. Opt. 43, 6139–6146 (2004).

Ionascu, D.

Ippen, E. P.

Kang, K.

Karpinski, J.

Klopf, J. M.

Koh, Y. K.

Lenz, G.

Lu, Y. C.

McLeskey, J. T.

Norris, P. M.

Perrin, B.

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]

Plantard, J.

B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

Rao, S. V.

Raybon, G.

Ruddock, I. S.

Illingworth and I. S. Ruddock, “The analysis of excite and probe measurements of relaxation times with fluctuating pulse duration,” Appl. Opt. 43, 6139–6146 (2004).

Sarger, L.

B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

Silva, C.

Smith, A. N.

Sobolewski, R.

Son, D. H.

Stevens, R. J.

Swain, D.

Tewari, S. P.

Walhout, P. K.

Wang, H.C

Yang, C. C.

Ye, X.

Yokoyama, K.

Yu, A.

Zhang, J.

Zheng, X.

Appl. Opt. (1)

Illingworth and I. S. Ruddock, “The analysis of excite and probe measurements of relaxation times with fluctuating pulse duration,” Appl. Opt. 43, 6139–6146 (2004).

Appl. Phys. B: Lasers Opt. (2)

B. Bousquet, L. Canioni, J. Plantard, and L. Sarger, “Collinear pump probe experiment, novel approach to ultra-fast spectroscopy,” Appl. Phys. B: Lasers Opt. 68, 689–692 (1999).
[Crossref]

J. Phys. Chem. A (1)

MRS Bull. (1)

G. A. Antonelli, B. Perrin, B. C. Daly, and D. G. Cahill, “Characterization of mechanical and thermal properties using ultrafast optical metrology,” MRS Bull. 31, 607–613 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

Rev. Sci. Instrum. (3)

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Fig. 1

Time dependent Δ(t)/R function (29 nm Pt/Si sample, photon wavelenght= 757 nm).

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Fig. 2

Experimental setup for the proposed transient thermoreflectance and transient thermotransmission technique.

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Fig. 3

The total probe-beam delay as a function of the time.

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Fig. 4

Reflection coefficient ΔR(t)/R and the probe-beam for delays t_i ₊₁ and t_i as a time function (data were taken from Fig. (4) in Ref. [1]).

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Fig. 5

Reflection coefficient ΔR(t)/R and the probe-beam for delays t_i ₊₁ and t_i as a time function (data were taken from Fig. (4) in Ref. [1]).

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Fig. 6

(a) Theoretical graph of A(t_i ) and the graph of B(t_i ) computed with equation (10) for m = 201. (b) Graphs of the theoretical and recovered A(t_i ) for L = 21.

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Fig. 7

(a) Graphs of the NRMSE of A(t_i ) and B(t_i ) for different L values. (b) NRMSE of A(t_i ) vs NRMSE of B(t_i ) for different L values.

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Equations (18)

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

I (t) = A \cdot exp [- \frac{{(t - t_{0})}^{2}}{2 σ^{2}}],

I_{R, i} (t) = [R + Δ R (t)] \cdot I (t, t_{i}) = R \cdot I (t, t_{i}) + Δ R (t) I (t, t_{i}),

I_{R, i + 1} (t) = [R + Δ R (t)] \cdot I (t, t_{i + 1}) = R \cdot I (t, t_{i + 1}) + Δ R (t) I (t, t_{i + 1}) .

V (t) = k \cdot I (t)

\bar{V_{R, i}} = k \cdot [R \cdot \bar{I (t, t_{i})} + \bar{Δ R (t) I (t, t_{i})}],

\bar{V_{R, i + 1}} = k \cdot [R \cdot \bar{I (t, t_{i + 1})} + \bar{Δ R (t) I (t, t_{i + 1})}] .

\begin{array}{l} Ampl (V_{DP}) & = & \bar{V_{R, i + 1}} - \bar{V_{R, i}} \\ = & k \cdot [\bar{Δ R (t) I (t, t_{i + 1})} - \bar{Δ R (t) I (t, t_{i})}] \\ = & k \cdot \bar{Δ R (t) [I (t, t_{i + 1}) - Δ R (t) I (t, t_{i})]} . \end{array}

V_{LI, i, i + 1} = \frac{BkA}{T} \int_{0}^{T} (exp [- \frac{{(t - t_{i + 1})}^{2}}{2 σ^{2}}] - exp [- \frac{{(t - t_{i})}^{2}}{2 σ^{2}}]) Δ R (t) d t .

V_{LI, i, i + 1} = \frac{BkA}{t} \int_{- \infty}^{+ \infty} (exp [- \frac{{(t - t_{i + 1})}^{2}}{2 σ^{2}}] - exp [- \frac{{(t - t_{i})}^{2}}{2 σ^{2}}]) Δ R (t) dt .

B (t_{i + 1}) \approx \int_{t_{i} - 5 σ}^{t_{i + 1} + 5 σ} G_{i + 1} (t) A (t) dt, i = 1, 2, \dots, m,

G_{i + 1} (t) = exp [- \frac{{(t - t_{i + 1})}^{2}}{2 σ^{2}}] - exp [- \frac{{(t - t_{i})}^{2}}{2 σ^{2}}] .

A (t) \approx \sum_{k = 0}^{L} a_{k} t^{k} .

B (t_{i + 1}) \approx \sum_{k = 0}^{L} a_{k} \int_{t_{i} - 5 σ}^{t_{i + 1} + 5 σ} G_{i + 1} (t) t^{k} dt .

U (a_{0}, a_{1}, \dots, a_{L}) = \sum_{i = 1}^{m} {[\sum_{k = 0}^{L} a_{k} \int_{t_{i} - 5 σ}^{t_{i + 1} + 5 σ} G_{i + 1} (t) t^{k} dt - B (t_{i + 1})]}^{2} .

\frac{\partial U}{\partial a_{j}} = 2 \sum_{i = 1}^{m} [\sum_{k = 0}^{L} a_{k} \int_{t_{i} - 5 σ}^{t_{i + 1} + 5 σ} G_{i + 1} (t) t^{k} dt - B (t_{i + 1})] \int_{t_{i} - 5 σ}^{t_{i + 1} + 5 σ} G_{i + 1} (t) t^{j} dt = 0,

\sum_{i = 1}^{m} [\sum_{k = 0}^{L} a_{k} ψ_{i, k}] ψ_{i, j} - \sum_{i = 1}^{m} B (t_{i + 1}) ψ_{i, j} = 0.

\sum_{k = 0}^{L} [\sum_{i = 1}^{m} ψ_{i, k} ψ_{i, j}] a_{k} = \sum_{i = 1}^{m} B (t_{i + 1}) ψ_{i, j}, j = 0, 1, \dots, L,

NRMSE = \sqrt{\frac{Σ {| f_{t} - f_{c} |}^{2}}{Σ {| f_{t} |}^{2}}} \times 100,

Abstract

References

2010 (1)

2008 (1)

2006 (1)

2005 (2)

2004 (1)

2003 (1)

1999 (1)

1998 (1)

1992 (1)

1982 (1)

Antonelli, G. A.

Barbara, P. F.

Batlogg, B.

Belousov, A.

Bousquet, B.

Caffrey, A. P.

Cahill, D. G.

Canioni, L.

Cao, W.

Champion, P. M.

Chen, C. Y.

Chi, C. Y.

Chin, S. C.

Chiritescu, C.

Daly, B. C.

Hall, K. L.

Illingworth,

Ionascu, D.

Ippen, E. P.

Kang, K.

Karpinski, J.

Klopf, J. M.

Koh, Y. K.

Lenz, G.

Lu, Y. C.

McLeskey, J. T.

Norris, P. M.

Perrin, B.

Plantard, J.

Rao, S. V.

Raybon, G.

Ruddock, I. S.

Sarger, L.

Silva, C.

Smith, A. N.

Sobolewski, R.

Son, D. H.

Stevens, R. J.

Swain, D.

Tewari, S. P.

Walhout, P. K.

Wang, H.C

Yang, C. C.

Ye, X.

Yokoyama, K.

Yu, A.

Zhang, J.

Zheng, X.

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (2)

J. Phys. Chem. A (1)

MRS Bull. (1)

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

Rev. Sci. Instrum. (3)

Cited By

Figures (7)

Equations (18)

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