Abstract

Performing reliable measurements in optical metrology, such as those needed in ellipsometry, requires a calibrated source and detector, or a well-characterized reference sample. We present a novel interferometric technique to perform reliable ellipsometric measurements. This technique relies on the use of a nonclassical optical source, namely, polarization-entangled twin photons generated by spontaneous parametric downconversion from a nonlinear crystal, in conjunction with a coincidence-detection scheme. Ellipsometric measurements acquired with this scheme are absolute, i.e., they require neither source nor detector calibration, nor do they require a reference.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  35. B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
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2002 (1)

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

2001 (2)

2000 (4)

D. Branning, A. L. Migdall, and A. V. Sergienko, “Simultaneous measurement of group and phase delay between two photons,” Phys. Rev. A 62, 063808 (2000).
[CrossRef]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[CrossRef] [PubMed]

M. Mansuripur, “Ellipsometry,” Opt. Photon. News 11(4), 52–56 (2000).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

1999 (2)

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

1998 (1)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

1995 (3)

A. Migdall, R. Datla, A. V. Sergienko, and Y. H. Shih, “Absolute detector quantum efficiency measurements using correlated photons,” Metrologia 32, 479–483 (1995).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental evaluation of a two-photon wave packet in type-II parametric downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[CrossRef]

1992 (1)

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef] [PubMed]

1990 (1)

M. C. Teich and B. E. A. Saleh, “Squeezed and antibunched light,” Phys. Today 43(6), 26–34 (1990).
[CrossRef]

1989 (1)

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

1988 (2)

M. C. Teich and B. E. A. Saleh, “Photon bunching and antibunching,” Prog. Opt. 26, 1–104 (1988).
[CrossRef]

D. N. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle,” Usp. Fiz. Nauk 154, 133–152 (1988) [Sov. Phys. Usp. 31(1), 74–85 (1988)].
[CrossRef]

1985 (1)

1977 (1)

D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Kvant. Elektron. (Moscow) 4, 1056–1062 (1977) [Sov. J. Quantum Electron. 7, 591–595 (1977)].
[CrossRef]

1974 (1)

1968 (2)

T. G. Giallorenzi and C. L. Tang, “Quantum theory of spontaneous parametric scattering of intense light,” Phys. Rev. 166, 225–233 (1968).
[CrossRef]

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
[CrossRef]

1967 (2)

D. N. Klyshko, “Coherent decay of photons in a nonlinear medium,” Pis'ma Zh. Eksp. Teor. Fiz. 6, 490–492 (1967) [Sov. Phys. JETP Lett. 6, 23–25 (1967)].

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18, 732–735 (1967).
[CrossRef]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

1957 (1)

U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957).
[CrossRef]

1946 (1)

A. B. Winterbottom, “Optical methods of studying films on reflecting bases depending on polarisation and interference phenomena,” Trans. Faraday Soc. 42, 487–495 (1946).
[CrossRef]

1945 (1)

A. Rothen, “The ellipsometer, an apparatus to measure thicknesses of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

1890 (1)

P. Drude, “Bestimmung optischer Konstanten der Metalle,” Ann. Physik Chemie 39, 481–554 (1890).
[CrossRef]

Abouraddy, A. F.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050101(R) (2001).
[CrossRef]

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

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Atatüre, M.

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

Bashara, N. M.

Booth, M. C.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Branca, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Branning, D.

D. Branning, A. L. Migdall, and A. V. Sergienko, “Simultaneous measurement of group and phase delay between two photons,” Phys. Rev. A 62, 063808 (2000).
[CrossRef]

Byer, R. L.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18, 732–735 (1967).
[CrossRef]

Campos, R. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

Datla, R.

A. Migdall, R. Datla, A. V. Sergienko, and Y. H. Shih, “Absolute detector quantum efficiency measurements using correlated photons,” Metrologia 32, 479–483 (1995).
[CrossRef]

De Martini, F.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Drude, P.

P. Drude, “Bestimmung optischer Konstanten der Metalle,” Ann. Physik Chemie 39, 481–554 (1890).
[CrossRef]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Ekert, A. K.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957).
[CrossRef]

Giallorenzi, T. G.

T. G. Giallorenzi and C. L. Tang, “Quantum theory of spontaneous parametric scattering of intense light,” Phys. Rev. 166, 225–233 (1968).
[CrossRef]

Glauber, R. J.

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Hardy, L.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Harris, S. E.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18, 732–735 (1967).
[CrossRef]

Jaeger, G.

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

Jennewein, T.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[CrossRef] [PubMed]

Kempe, M.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

Kleinman, D. A.

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
[CrossRef]

Klyshko, D. N.

D. N. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle,” Usp. Fiz. Nauk 154, 133–152 (1988) [Sov. Phys. Usp. 31(1), 74–85 (1988)].
[CrossRef]

D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Kvant. Elektron. (Moscow) 4, 1056–1062 (1977) [Sov. J. Quantum Electron. 7, 591–595 (1977)].
[CrossRef]

D. N. Klyshko, “Coherent decay of photons in a nonlinear medium,” Pis'ma Zh. Eksp. Teor. Fiz. 6, 490–492 (1967) [Sov. Phys. JETP Lett. 6, 23–25 (1967)].

Kohles, R. B.

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Mansuripur, M.

M. Mansuripur, “Ellipsometry,” Opt. Photon. News 11(4), 52–56 (2000).
[CrossRef]

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Migdall, A.

A. Migdall, R. Datla, A. V. Sergienko, and Y. H. Shih, “Absolute detector quantum efficiency measurements using correlated photons,” Metrologia 32, 479–483 (1995).
[CrossRef]

Migdall, A. L.

D. Branning, A. L. Migdall, and A. V. Sergienko, “Simultaneous measurement of group and phase delay between two photons,” Phys. Rev. A 62, 063808 (2000).
[CrossRef]

Nasr, M. B.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

Oshman, M. K.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18, 732–735 (1967).
[CrossRef]

Palma, G. M.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef] [PubMed]

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Popescu, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Rarity, J. G.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef] [PubMed]

Rothen, A.

A. Rothen, “The ellipsometer, an apparatus to measure thicknesses of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

Rubin, M. H.

Saleh, B. E.

Saleh, B. E. A.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050101(R) (2001).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

M. C. Teich and B. E. A. Saleh, “Squeezed and antibunched light,” Phys. Today 43(6), 26–34 (1990).
[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

M. C. Teich and B. E. A. Saleh, “Photon bunching and antibunching,” Prog. Opt. 26, 1–104 (1988).
[CrossRef]

M. C. Teich and B. E. A. Saleh, “Observation of sub-Poisson Franck–Hertz light at 253.7 nm,” J. Opt. Soc. Am. B 2, 275–282 (1985).
[CrossRef]

Sergienko, A. V.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050101(R) (2001).
[CrossRef]

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

D. Branning, A. L. Migdall, and A. V. Sergienko, “Simultaneous measurement of group and phase delay between two photons,” Phys. Rev. A 62, 063808 (2000).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

A. Migdall, R. Datla, A. V. Sergienko, and Y. H. Shih, “Absolute detector quantum efficiency measurements using correlated photons,” Metrologia 32, 479–483 (1995).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental evaluation of a two-photon wave packet in type-II parametric downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[CrossRef]

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P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental evaluation of a two-photon wave packet in type-II parametric downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[CrossRef]

A. Migdall, R. Datla, A. V. Sergienko, and Y. H. Shih, “Absolute detector quantum efficiency measurements using correlated photons,” Metrologia 32, 479–483 (1995).
[CrossRef]

Simon, C.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[CrossRef] [PubMed]

Tang, C. L.

T. G. Giallorenzi and C. L. Tang, “Quantum theory of spontaneous parametric scattering of intense light,” Phys. Rev. 166, 225–233 (1968).
[CrossRef]

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[CrossRef] [PubMed]

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M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050101(R) (2001).
[CrossRef]

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

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

M. C. Teich and B. E. A. Saleh, “Squeezed and antibunched light,” Phys. Today 43(6), 26–34 (1990).
[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

Toussaint Jr., K. C.

Walton, Z.

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

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T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[CrossRef] [PubMed]

Weinfurter, H.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[CrossRef] [PubMed]

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[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

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A. B. Winterbottom, “Optical methods of studying films on reflecting bases depending on polarisation and interference phenomena,” Trans. Faraday Soc. 42, 487–495 (1946).
[CrossRef]

Wollenschensky, R.

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

Zeidler, J. R.

Zeilinger, A.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
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A. Migdall, R. Datla, A. V. Sergienko, and Y. H. Shih, “Absolute detector quantum efficiency measurements using correlated photons,” Metrologia 32, 479–483 (1995).
[CrossRef]

Nature (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

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M. Mansuripur, “Ellipsometry,” Opt. Photon. News 11(4), 52–56 (2000).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

A. V. Sergienko, M. Atatüre, Z. Walton, G. Jaeger, B. E. A. Saleh, and M. C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622–R2625 (1999).
[CrossRef]

M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, M. Kempe, and R. Wollenschensky, “Biphoton focusing for two-photon excitation,” Phys. Rev. A 65, 023816 (2002).
[CrossRef]

D. Branning, A. L. Migdall, and A. V. Sergienko, “Simultaneous measurement of group and phase delay between two photons,” Phys. Rev. A 62, 063808 (2000).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050101(R) (2001).
[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

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A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef] [PubMed]

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[CrossRef]

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M. C. Teich and B. E. A. Saleh, “Squeezed and antibunched light,” Phys. Today 43(6), 26–34 (1990).
[CrossRef]

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M. C. Teich and B. E. A. Saleh, “Photon bunching and antibunching,” Prog. Opt. 26, 1–104 (1988).
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[CrossRef]

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H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry (Wiley, New York, 1999).

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B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B (to be published).

B. E. A. Saleh, S. Popescu, and M. C. Teich, “Generalized entangled-photon imaging,” in Proceedings of the Ninth Annual Meeting of the IEEE Lasers and Electro-Optics Society, P. Zory, ed. (IEEE, Piscataway, N.J., 1996), Vol. 1, pp. 362–363.

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Figures (4)

Fig. 1
Fig. 1

Null ellipsometer: S is an optical source, P is a linear polarizer, λ/4 is a quarter-wave plate (compensator), A is a linear polarization analyzer, and D is an optical detector; θi is the angle of incidence. The sample is characterized by the ellipsometric parameters ψ and Δ defined in the text.

Fig. 2
Fig. 2

Unentangled twin-photon ellipsometer: NLC stands for nonlinear crystal; BS is a nonpolarizing beam splitter; A1 and A2 are linear polarization analyzers; D1 and D2 are single-photon detectors; and Nc is the coincidence rate.

Fig. 3
Fig. 3

Entangled twin-photon ellipsometer.

Fig. 4
Fig. 4

Unfolded version of the entangled twin-photon ellipsometer displayed in Fig. 3.

Equations (21)

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|Ψ=12(|HV+|VH),
|Ψ=|HV.
Jˆ1=j{-Aˆs(ω)+Aˆi(ω)}Aˆs(ω)+Aˆi(ω),
T=T11T12T21T22,
Tp=P(-θ1)00P(θ2),
P(θ)=cos2 θcos θ sin θcos θ sin θsin2 θ,
Jˆ2=TpJˆ1=jP(-θ1){-Aˆs(ω)+Aˆi(ω)}P(θ2){Aˆs(ω)+Aˆi(ω)}=j{-cos θ1aˆs(ω)+sin θ1aˆi(ω)}cos θ1-sin θ1{cos θ2aˆs(ω)+sin θ2aˆi(ω)}cos θ2sin θ2.
Eˆ1+(t)=j-cos θ1dω exp(-jωt)aˆs(ω)+sin θ1dω exp(-jωt)aˆi(ω)cos θ1-sin θ1,
Eˆ2+(t)=cos θ2dω exp(-jωt)aˆs(ω)+sin θ2dω exp(-jωt)aˆi(ω)cos θ2sin θ2,
Ts=R00I,
R=r˜100r˜2
Jˆ3=TpTsJˆ1=j{-r˜1 cos θ1aˆs(ω)+r˜2 sin θ1aˆi(ω)}cos θ1-sin θ1{cos θ2aˆs(ω)+sin θ2aˆi(ω)}cos θ2sin θ2,
Eˆ1+(t)=j-r˜1 cos θ1dω exp(-jωt)aˆs(ω)+r˜2 sin θ1dω exp(-jωt)aˆi(ω)cos θ1-sin θ1,
Nc=C[tan2 ψ cos2 θ1 sin2 θ2+sin2 θ1 cos2 θ2-2 tan ψ cos Δ cos θ1 cos θ2 sin θ1 sin θ2],
Nc=C[tan2 ψ cos2 θ1 sin2 θ2+sin2 θ1 cos2 θ2-2 tan ψ cos Δ cos θ1 cos θ2 sin θ1 ×sin θ2Φ(τ)cos(ω0τ)].
Nc=C[tan2 ψ cos2 θ1 sin2 θ2+sin2 θ1 cos2 θ2+2 tan ψ cos Δ cos θ1 cos θ2 sin θ1 sin θ2].
bˆ1=jr˜aˆ1+t˜aˆv,bˆv=t˜aˆ1+jr˜aˆv,
G(t1, t2)=Ψ|Eˆ1(-)(t1)Eˆ2(-)(t2)Eˆ2(+)(t2)Eˆ1(+)(t1)|Ψ,
|Ψ=dωφ(ω, ωp-ω)|1ω, 1ωp-ω, 0ω.
n1,n2,n3|n1, n2, n3n1, n2, n3|
G(t1, t2)=n1,n2,n3Ψ|Eˆ1(-)(t1)Eˆ2(-)(t2)|n1, n2, n3×n1, n2, n3|Eˆ2(+)(t2)Eˆ1(+)(t1)|Ψ=n1,n2,n3|n1, n2, n3|Eˆ2(+)(t2)Eˆ1(+)(t1)|Ψ|2.

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