Abstract

We describe a novel scheme of detecting rotational anisotropy-second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RASHG apparatus. The method directly measures the nth harmonics of the scanning frequency corresponding to SHG signal components of Cn symmetry that appear in a Fourier series expansion of a general RA-SHG signal. GaAs was used as a test sample allowing comparison of point-by-point averaging with the lock-in based method. When divided by the C∞ signal component, the lock-in detected data allowed for both self-referenced determination of ratios of Cn components of up to 1 part in 104 and significantly more sensitive measurement of the relative amount of different Cn components when compared with conventional methods.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. M. Fiebig, V. V. Pavlov, and R. V. Pisarev, “Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals,” JOSA B 22, 96–118 (2005).
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    [Crossref]
  3. J. McGilp, “Probing surface and interface structure using optics,” J. Physics: Condens. Matter 22, 084018 (2010).
  4. S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
    [Crossref]
  5. D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
    [Crossref]
  6. J. Harter, L. Niu, A. Woss, and D. Hsieh, “High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection,” Opt. Lett. 40, 4671–4674 (2015).
    [Crossref] [PubMed]
  7. D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
    [Crossref]
  8. L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
    [Crossref]
  9. J. Harter, Z. Zhao, J.-Q. Yan, D. Mandrus, and D. Hsieh, “A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7,” Science 356, 295–299 (2017).
    [Crossref] [PubMed]
  10. L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
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    [Crossref] [PubMed]
  23. A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett.  114, 183902 (2015).
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    [Crossref]
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    [Crossref]

2017 (2)

J. Harter, Z. Zhao, J.-Q. Yan, D. Mandrus, and D. Hsieh, “A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7,” Science 356, 295–299 (2017).
[Crossref] [PubMed]

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

2016 (1)

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

2015 (3)

J. Harter, L. Niu, A. Woss, and D. Hsieh, “High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection,” Opt. Lett. 40, 4671–4674 (2015).
[Crossref] [PubMed]

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett.  114, 183902 (2015).
[Crossref] [PubMed]

2014 (2)

D. E. Wilcox, M. E. Sykes, A. Niedringhaus, M. Shtein, and J. P. Ogilvie, “Heterodyne-detected and ultrafast time-resolved second-harmonic generation for sensitive measurements of charge transfer,” Opt. Lett. 39, 4274–4277 (2014).
[Crossref] [PubMed]

D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
[Crossref]

2012 (1)

2011 (1)

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
[Crossref]

2010 (1)

J. McGilp, “Probing surface and interface structure using optics,” J. Physics: Condens. Matter 22, 084018 (2010).

2005 (2)

M. Fiebig, V. V. Pavlov, and R. V. Pisarev, “Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals,” JOSA B 22, 96–118 (2005).
[Crossref]

A. Kirilyuk and T. Rasing, “Magnetization-induced-second-harmonic generation from surfaces and interfaces,” JOSA B 22, 148–167 (2005).
[Crossref]

2004 (1)

1997 (2)

T. A. Germer, K. W. Kołasin-Acuteski, J. C. Stephenson, and L. J. Richter, “Depletion-electric-field-induced second-harmonic generation near oxidized GaAs (001) surfaces,” Phys. Rev. B 55, 10694 (1997).
[Crossref]

Y. Chang, L. Xu, and H. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[Crossref]

1995 (1)

M. Feldstein, P. Vöhringer, and N. Scherer, “Rapid-scan pump–probe spectroscopy with high time and wave-number resolution: Optical-kerr-effect measurements of neat liquids,” JOSA B 12, 1500–1510 (1995).
[Crossref]

1991 (1)

D. Edelstein, R. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instruments 62, 579–583 (1991).
[Crossref]

1987 (1)

1983 (1)

C. Shank, R. Yen, and C. Hirlimann, “Femtosecond time resolved surface structural dynamics of optically excited silicon,” MRS Online Proc. Libr. Arch.  23, 53 (1983).
[Crossref]

Aguilar, R. V.

Apostol, T. M.

T. M. Apostol, Mathematical analysis(Addison Wesley Publishing Company, 1974).

Armitage, N.

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

Armitage, N. P.

Barnes, E.

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
[Crossref]

Belvin, C.

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

Birss, R. R.

R. R. Birss, Symmetry and magnetism(North-Holland Publishing Company, 1964).

Bonn, D.

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

Cao, G.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
[Crossref]

Chang, Y.

Y. Chang, L. Xu, and H. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[Crossref]

Chu, H.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
[Crossref]

Denev, S. A.

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
[Crossref]

Edelstein, D.

D. Edelstein, R. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instruments 62, 579–583 (1991).
[Crossref]

Elzinga, P. A.

Feldstein, M.

M. Feldstein, P. Vöhringer, and N. Scherer, “Rapid-scan pump–probe spectroscopy with high time and wave-number resolution: Optical-kerr-effect measurements of neat liquids,” JOSA B 12, 1500–1510 (1995).
[Crossref]

Fiebig, M.

M. Fiebig, V. V. Pavlov, and R. V. Pisarev, “Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals,” JOSA B 22, 96–118 (2005).
[Crossref]

Flint, R.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

Germer, T. A.

T. A. Germer, K. W. Kołasin-Acuteski, J. C. Stephenson, and L. J. Richter, “Depletion-electric-field-induced second-harmonic generation near oxidized GaAs (001) surfaces,” Phys. Rev. B 55, 10694 (1997).
[Crossref]

Goodman, A. J.

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett.  114, 183902 (2015).
[Crossref] [PubMed]

Gopalan, V.

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
[Crossref]

Hardy, W.

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

Harter, J.

J. Harter, Z. Zhao, J.-Q. Yan, D. Mandrus, and D. Hsieh, “A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7,” Science 356, 295–299 (2017).
[Crossref] [PubMed]

J. Harter, L. Niu, A. Woss, and D. Hsieh, “High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection,” Opt. Lett. 40, 4671–4674 (2015).
[Crossref] [PubMed]

Hirlimann, C.

C. Shank, R. Yen, and C. Hirlimann, “Femtosecond time resolved surface structural dynamics of optically excited silicon,” MRS Online Proc. Libr. Arch.  23, 53 (1983).
[Crossref]

Hsieh, D.

J. Harter, Z. Zhao, J.-Q. Yan, D. Mandrus, and D. Hsieh, “A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7,” Science 356, 295–299 (2017).
[Crossref] [PubMed]

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

J. Harter, L. Niu, A. Woss, and D. Hsieh, “High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection,” Opt. Lett. 40, 4671–4674 (2015).
[Crossref] [PubMed]

D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
[Crossref]

Ivanov, V.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

Jian, Y.

King, G. B.

Kirilyuk, A.

A. Kirilyuk and T. Rasing, “Magnetization-induced-second-harmonic generation from surfaces and interfaces,” JOSA B 22, 148–167 (2005).
[Crossref]

Kolasin-Acuteski, K. W.

T. A. Germer, K. W. Kołasin-Acuteski, J. C. Stephenson, and L. J. Richter, “Depletion-electric-field-induced second-harmonic generation near oxidized GaAs (001) surfaces,” Phys. Rev. B 55, 10694 (1997).
[Crossref]

Kumar, A.

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
[Crossref]

Laiho, L. H.

Laurendeau, N. M.

Liang, R.

L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

Lifshitz, R.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

Lu, B.

B. Lu, J. D. Tran, and D. H. Torchinsky, “Fast reflective optic based fast rotational-anistropy nonlinear harmonic generation spectrometer,” ar”Xiv:1811.01862 (2018).

Lummen, T. T.

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
[Crossref]

Lytle, F. E.

Mandrus, D.

J. Harter, Z. Zhao, J.-Q. Yan, D. Mandrus, and D. Hsieh, “A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7,” Science 356, 295–299 (2017).
[Crossref] [PubMed]

McGilp, J.

J. McGilp, “Probing surface and interface structure using optics,” J. Physics: Condens. Matter 22, 084018 (2010).

Morris, C. M.

Niedringhaus, A.

Niu, L.

Ogilvie, J. P.

Pavlov, V. V.

M. Fiebig, V. V. Pavlov, and R. V. Pisarev, “Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals,” JOSA B 22, 96–118 (2005).
[Crossref]

Perkins, N.

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

Pisarev, R. V.

M. Fiebig, V. V. Pavlov, and R. V. Pisarev, “Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals,” JOSA B 22, 96–118 (2005).
[Crossref]

Qi, T.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
[Crossref]

Rasing, T.

A. Kirilyuk and T. Rasing, “Magnetization-induced-second-harmonic generation from surfaces and interfaces,” JOSA B 22, 148–167 (2005).
[Crossref]

Richter, L. J.

T. A. Germer, K. W. Kołasin-Acuteski, J. C. Stephenson, and L. J. Richter, “Depletion-electric-field-induced second-harmonic generation near oxidized GaAs (001) surfaces,” Phys. Rev. B 55, 10694 (1997).
[Crossref]

Romney, R.

D. Edelstein, R. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instruments 62, 579–583 (1991).
[Crossref]

Scherer, N.

M. Feldstein, P. Vöhringer, and N. Scherer, “Rapid-scan pump–probe spectroscopy with high time and wave-number resolution: Optical-kerr-effect measurements of neat liquids,” JOSA B 12, 1500–1510 (1995).
[Crossref]

Scheuermann, M.

D. Edelstein, R. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal-averaging system for ultrafast measurements,” Rev. Sci. Instruments 62, 579–583 (1991).
[Crossref]

Shank, C.

C. Shank, R. Yen, and C. Hirlimann, “Femtosecond time resolved surface structural dynamics of optically excited silicon,” MRS Online Proc. Libr. Arch.  23, 53 (1983).
[Crossref]

Shtein, M.

Sizyuk, Y.

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

So, P. T.

Stephenson, J. C.

T. A. Germer, K. W. Kołasin-Acuteski, J. C. Stephenson, and L. J. Richter, “Depletion-electric-field-induced second-harmonic generation near oxidized GaAs (001) surfaces,” Phys. Rev. B 55, 10694 (1997).
[Crossref]

Stier, A. V.

Sykes, M. E.

Tisdale, W. A.

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett.  114, 183902 (2015).
[Crossref] [PubMed]

Tom, H.

Y. Chang, L. Xu, and H. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[Crossref]

Torchinsky, A.

A. Torchinsky, Private Communication (2018).

Torchinsky, D.

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
[Crossref]

D. Torchinsky, H. Chu, L. Zhao, N. Perkins, Y. Sizyuk, T. Qi, G. Cao, and D. Hsieh, “Structural distortion-induced magnetoelastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation,” Phys. Rev. Lett.  114, 096404 (2015).
[Crossref]

Torchinsky, D. H.

D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
[Crossref]

B. Lu, J. D. Tran, and D. H. Torchinsky, “Fast reflective optic based fast rotational-anistropy nonlinear harmonic generation spectrometer,” ar”Xiv:1811.01862 (2018).

Tran, J. D.

B. Lu, J. D. Tran, and D. H. Torchinsky, “Fast reflective optic based fast rotational-anistropy nonlinear harmonic generation spectrometer,” ar”Xiv:1811.01862 (2018).

Vöhringer, P.

M. Feldstein, P. Vöhringer, and N. Scherer, “Rapid-scan pump–probe spectroscopy with high time and wave-number resolution: Optical-kerr-effect measurements of neat liquids,” JOSA B 12, 1500–1510 (1995).
[Crossref]

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J. Harter, Z. Zhao, J.-Q. Yan, D. Mandrus, and D. Hsieh, “A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7,” Science 356, 295–299 (2017).
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L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
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Appl. Spectrosc. (1)

J. Am. Ceram. Soc. (1)

S. A. Denev, T. T. Lummen, E. Barnes, A. Kumar, and V. Gopalan, “Probing ferroelectrics using optical second harmonic generation,” J. Am. Ceram. Soc. 94, 2699–2727 (2011).
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J. McGilp, “Probing surface and interface structure using optics,” J. Physics: Condens. Matter 22, 084018 (2010).

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[Crossref]

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[Crossref]

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L. Zhao, C. Belvin, R. Liang, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nat. Phys. 13, 250–254 (2017).
[Crossref]

L. Zhao, D. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, “Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate,” Nat. Phys. 12, 32–36 (2016).
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T. A. Germer, K. W. Kołasin-Acuteski, J. C. Stephenson, and L. J. Richter, “Depletion-electric-field-induced second-harmonic generation near oxidized GaAs (001) surfaces,” Phys. Rev. B 55, 10694 (1997).
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Y. Chang, L. Xu, and H. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
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D. H. Torchinsky, H. Chu, T. Qi, G. Cao, and D. Hsieh, “A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries,” Rev. Sci. Instruments 85, 083102 (2014).
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Figures (3)

Fig. 1
Fig. 1 Raw data from the RA-SHG spectrometer. (a) On the timescale of one revolution of the kinetic optics, the four-fold symmetry of the GaAs response is observable through the four equally tall peaks over the 100 ms period of the experiment at frequency 4 fr . This frequency may be demodulated to yield A4. (b) At short times, the 50% duty cycle output of the sample-and-hold hardware is evident, accounting for the “filled-in” appearance of the data in panel (a). This fl = 5 kHz carrier frequency can be demodulated to yield A0. The sampling rate of the data are not sufficiently fast enough to see the effect of glitching.

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Fig. 2
Fig. 2 RA-SHG data as acquired by the lock-in amplifier and from the DAC. (a)-(c) show the the lock-in amplifier amplitudes of A0 and A4 as a function of time for 20τ in various circumstances including: (a) well-aligned with good SNR, (b) poorly aligned with moderate SNR, (c) well-aligned with low SNR and (d) at the limit of experimental detection (on average ≲ 1 photon/shot at maximum). The variation of the corresponding ratio A4/A0 is shown in panels (e)-(h). The DAC acquired traces are shown below the ratios in panels (i)-(l). Depicted in these panels are overlap of the DAC acquired raw RA-SHG data (blue), a reconstruction of the lockin data (red) and a line of best fit to the DAC data using the minimal model (green). The vertical scale is given in terms of a voltage output by the detection electronics with ∼ 260 µV corresponding to the output voltage pulse equivalent to a single 3.0 eV photon.

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Fig. 3
Fig. 3 Comparison of lock-in with “data-sparse” traces representative of most currently used RA-SHG detection schemes for signals at the threshold of experimental detection. The data from Fig. 2(i) are either (a) averaged over a window every 5° or (b) sampled every 5°. Also shown are fits to each data acquisition scheme and the reconstructed lock-in signal using the data of Table 1.

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Tables (1)

Tables Icon

Table 1 Comparison between fitted values and lock-in amplifier measured values for the various configurations discussed in the text. An are the magnitudes of the demodulated signals, ψ4 is the angle of the C4 component signal, and r(A0, A4) is the Pearson correlation coefficient between the A0 and A4 components. Uncertainties are reported as the standard deviation of the data or 67% confidence interval for both sets of values.

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Equations (8)

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P i ( 2 ω ) = χ i j k ( 2 ) E j ( ω ) E k ( ω )
a i j = [ cos ( ϕ ) − sin ( ϕ ) 0 sin ( ϕ ) cos ( ϕ ) 0 0 0 1 ]
χ i j k ′ ( 2 ) = a i l a j m a k n χ i j k ( 2 ) .
I 2 ω M N ( ϕ ) = | ∑ r = 0 3 ∑ s = 0 r b r s cos r − s ( ϕ ) sin s ( ϕ ) | 2 ,
I 2 ω M N ( ϕ ) = X 0 + X 2 cos ( 2 ϕ ) + X 4 cos ( 4 ϕ ) + X 6 cos ( 6 ϕ ) + Y 2 sin ( 2 ϕ ) + Y 4 sin ( 4 ϕ ) + Y 6 sin ( 6 ϕ )
I 2 ω M N ( ϕ ) = A 0 + A 2 cos ( 2 ϕ + ψ 2 ) + A 4 cos ( 4 ϕ + ψ 4 ) + A 6 cos ( 6 ϕ + ψ 6 ) ,
s ( t ) = I 2 ω M N ( 2 π f r t ) × { 1 2 + ∑ k = 1 ∞ 2 k π sin ( k π 2 ) cos ( 2 π k f l t ) } ,
I 2 ω S S ( ϕ ) = 0 I 2 ω P S ( ϕ ) = 2 χ x y z 2 ( 1 + cos ( 4 ϕ ) ) I 2 ω S P ( ϕ ) = χ x y z 2 / 2 ( 1 − cos ( 4 ϕ ) ) I 2 ω P P ( ϕ ) = χ x y z 2 / 2 ( 1 − cos ( 4 ϕ ) )

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