Ellipsometry with polarisation-entangled photons

doi:10.1364/OE.14.007037

Ellipsometry with polarisation-entangled photons

David J. L. Graham, A. Scott Parkins, and Lionel R. Watkins »View Author Affiliations

Optics Express, Vol. 14, Issue 16, pp. 7037-7045 (2006)
http://dx.doi.org/10.1364/OE.14.007037

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Abstract

Polarisation-entangled photon pairs from a two crystal, type-I spontaneous parametric down conversion source are used to make accurate measurements of the ellipsometric angles of a silicon dioxide film on silicon and of internal and external reflection from BK7 glass. Since our source produces an entangled state with some mixture, a novel technique based on quantum tomography was developed to estimate the components of the density matrix for the state before and after reflection from the samples. The ellipsometric angles are readily calculated from these components and experimental measurements made on the samples were found to be in good agreement with their expected values.

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(270.0270) Quantum optics : Quantum optics

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: May 9, 2006
Revised Manuscript: July 6, 2006
Manuscript Accepted: July 3, 2006
Published: August 7, 2006

Citation
David J. L. Graham, A. Scott Parkins, and Lionel R. Watkins, "Ellipsometry with polarisation-entangled photons," Opt. Express 14, 7037-7045 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-16-7037

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References

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, The Netherlands,1987).
D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3 - 13 (2004). [CrossRef]
K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1 - 9 (1998). [CrossRef]
T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D Appl. Phys. 32, R45 - R56 (1999). [CrossRef]
P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773 - R776 (1999). [CrossRef]
D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312(2001). [CrossRef]
A. Aspect, "Bell’s inequality test: more ideal than ever," Nature (London) 398, 189 - 190 (1999). [CrossRef]
J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum Controlled-NOT Gate," Nature (London) 426, 264 - 267 (2003). [CrossRef]
N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145 - 195 (2002). [CrossRef]
A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, andM. C. Teich, "Ellipsometric measurements by use of photon pairs generated by spontaneous parametric downconversion," Opt. Lett. 26, 1717 - 1719 (2001). [CrossRef]
A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Entangled-Photon Ellipsometry," J. Opt. Soc. Am. B 19, 656 - 662 (2002). [CrossRef]
A. V. Sergienko and G. S. Jaeger, "Quantum information processing and precise optical measurement with entangled-photon pairs," Contemp. Phys. 44, 341 - 356 (2003). [CrossRef]
K. C. Toussaint, G. D. Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Quantum ellipsometry using correlated-photon beams," Phys. Rev. A 70, 023801 (2004). [CrossRef]
A. F. Abouraddy, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Quantum entanglement and the two-photon Stokes parameters," Opt. Commun. 201, 93 - 98 (2002). [CrossRef]
A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally Entangled States: Production, Characterization and Utilization," Phys. Rev. Lett. 83, 3103-3107 (1999). [CrossRef]
T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Two-photon geometric optics," Phys. Rev. A 53, R2804 - R2815 (1996). [CrossRef]
D. Dehlinger and M. W. Mitchell, "Entangled photon apparatus for the undergraduate laboratory," Am. J. Phys. 70, 898 - 902 (2002). [CrossRef]
D. Dehlinger and M. W. Mitchell, "Entangled photons, nonlocality, and Bell inequalities in the under graduate laboratory," Am. J. Phys. 70, 903 - 910 (2002). [CrossRef]
W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239 - 1246 (2001).
T. S. Larchuk, M. C. Teich, and B. E. A. Saleh, "Statistics of Entangled-Photon Coincidences in Parametric Downconversion," Ann. NY Acad. Sci. 755, 680 - 686 (1995). [CrossRef]
E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic Press, San Diego, California, 1998).
J. Altepeter, E. Jeffrey, and P. Kwiat, "Phase-compensated ultra-bright source of entangled photons," Opt. Express 13, 8951 - 8959 (2005). [CrossRef] [PubMed]

Am. J. Phys.

D. Dehlinger and M. W. Mitchell, "Entangled photon apparatus for the undergraduate laboratory," Am. J. Phys. 70, 898 - 902 (2002). [CrossRef]
D. Dehlinger and M. W. Mitchell, "Entangled photons, nonlocality, and Bell inequalities in the under graduate laboratory," Am. J. Phys. 70, 903 - 910 (2002). [CrossRef]

Ann. NY Acad. Sci.

T. S. Larchuk, M. C. Teich, and B. E. A. Saleh, "Statistics of Entangled-Photon Coincidences in Parametric Downconversion," Ann. NY Acad. Sci. 755, 680 - 686 (1995). [CrossRef]

Contemp. Phys.

A. V. Sergienko and G. S. Jaeger, "Quantum information processing and precise optical measurement with entangled-photon pairs," Contemp. Phys. 44, 341 - 356 (2003). [CrossRef]

J. Mod. Opt.

W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239 - 1246 (2001).

J. Opt. Soc. Am. B

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Entangled-Photon Ellipsometry," J. Opt. Soc. Am. B 19, 656 - 662 (2002). [CrossRef]

J. Phys. D Appl. Phys.

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D Appl. Phys. 32, R45 - R56 (1999). [CrossRef]

Nature (London)

A. Aspect, "Bell’s inequality test: more ideal than ever," Nature (London) 398, 189 - 190 (1999). [CrossRef]
J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum Controlled-NOT Gate," Nature (London) 426, 264 - 267 (2003). [CrossRef]

Opt. Commun.

A. F. Abouraddy, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Quantum entanglement and the two-photon Stokes parameters," Opt. Commun. 201, 93 - 98 (2002). [CrossRef]

Opt. Express

J. Altepeter, E. Jeffrey, and P. Kwiat, "Phase-compensated ultra-bright source of entangled photons," Opt. Express 13, 8951 - 8959 (2005). [CrossRef] [PubMed]

Opt. Lett.

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, andM. C. Teich, "Ellipsometric measurements by use of photon pairs generated by spontaneous parametric downconversion," Opt. Lett. 26, 1717 - 1719 (2001). [CrossRef]

Phys. Rev. A

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773 - R776 (1999). [CrossRef]
D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312(2001). [CrossRef]
K. C. Toussaint, G. D. Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Quantum ellipsometry using correlated-photon beams," Phys. Rev. A 70, 023801 (2004). [CrossRef]

Phys. Rev. Lett.

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally Entangled States: Production, Characterization and Utilization," Phys. Rev. Lett. 83, 3103-3107 (1999). [CrossRef]

Rev. Mod. Phys.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145 - 195 (2002). [CrossRef]

Thin Solid Films

D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3 - 13 (2004). [CrossRef]
K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1 - 9 (1998). [CrossRef]

Other

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, The Netherlands,1987).
T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Two-photon geometric optics," Phys. Rev. A 53, R2804 - R2815 (1996). [CrossRef]
E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic Press, San Diego, California, 1998).

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[1] R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, The Netherlands,1987).

[2] D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3 - 13 (2004). [CrossRef]

[3] K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1 - 9 (1998). [CrossRef]

[4] T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D Appl. Phys. 32, R45 - R56 (1999). [CrossRef]

[5] P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773 - R776 (1999). [CrossRef]

[6] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312(2001). [CrossRef]

[7] A. Aspect, "Bell’s inequality test: more ideal than ever," Nature (London) 398, 189 - 190 (1999). [CrossRef]

[8] J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum Controlled-NOT Gate," Nature (London) 426, 264 - 267 (2003). [CrossRef]

[9] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145 - 195 (2002). [CrossRef]

[10] A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, andM. C. Teich, "Ellipsometric measurements by use of photon pairs generated by spontaneous parametric downconversion," Opt. Lett. 26, 1717 - 1719 (2001). [CrossRef]

[11] A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Entangled-Photon Ellipsometry," J. Opt. Soc. Am. B 19, 656 - 662 (2002). [CrossRef]

[12] A. V. Sergienko and G. S. Jaeger, "Quantum information processing and precise optical measurement with entangled-photon pairs," Contemp. Phys. 44, 341 - 356 (2003). [CrossRef]

[13] K. C. Toussaint, G. D. Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Quantum ellipsometry using correlated-photon beams," Phys. Rev. A 70, 023801 (2004). [CrossRef]

[14] A. F. Abouraddy, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Quantum entanglement and the two-photon Stokes parameters," Opt. Commun. 201, 93 - 98 (2002). [CrossRef]

[15] A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally Entangled States: Production, Characterization and Utilization," Phys. Rev. Lett. 83, 3103-3107 (1999). [CrossRef]

[16] T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Two-photon geometric optics," Phys. Rev. A 53, R2804 - R2815 (1996). [CrossRef]

[17] D. Dehlinger and M. W. Mitchell, "Entangled photon apparatus for the undergraduate laboratory," Am. J. Phys. 70, 898 - 902 (2002). [CrossRef]

[18] D. Dehlinger and M. W. Mitchell, "Entangled photons, nonlocality, and Bell inequalities in the under graduate laboratory," Am. J. Phys. 70, 903 - 910 (2002). [CrossRef]

[19] W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239 - 1246 (2001).

[20] T. S. Larchuk, M. C. Teich, and B. E. A. Saleh, "Statistics of Entangled-Photon Coincidences in Parametric Downconversion," Ann. NY Acad. Sci. 755, 680 - 686 (1995). [CrossRef]

[21] E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic Press, San Diego, California, 1998).

[22] J. Altepeter, E. Jeffrey, and P. Kwiat, "Phase-compensated ultra-bright source of entangled photons," Opt. Express 13, 8951 - 8959 (2005). [CrossRef] [PubMed]

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Ellipsometry with polarisation-entangled photons

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Abstract

References

Am. J. Phys.

Ann. NY Acad. Sci.

Contemp. Phys.

J. Mod. Opt.

J. Opt. Soc. Am. B

J. Phys. D Appl. Phys.

Nature (London)

Opt. Commun.

Opt. Express

Opt. Lett.

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Phys. Rev. Lett.

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Thin Solid Films

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