Abstract

Using a simple optical setup to detect and characterize transmission gratings in the far field, we demonstrate that going beyond the diffraction limit is not possible using linear interaction of nonclassical illumination with the target grating. We also confirm that nonlinear optical interactions with the target grating, or with the optical medium around it, do allow improvement in resolution.

© 2013 Optical Society of America

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    [CrossRef]
  36. H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
    [CrossRef]
  37. G. Cerullo and S. De Silvetri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (1)

C. Cremer and B. R. Masters, “Resolution enhancement techniques in microscopy,” Eur. Phys. J. A 38, 281–344 (2013).

2012 (1)

2011 (1)

2010 (2)

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[CrossRef]

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef]

2009 (2)

H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
[CrossRef]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).

2008 (3)

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[CrossRef]

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

L. N. Guo, Z. L. Tang, and D. Xing, “Imaging theory of nonlinear Raman confocal microscopy,” J. Mod. Opt. 55, 375–386 (2008).
[CrossRef]

2007 (3)

2006 (3)

J. B. Ashcom, R. R. Gattass, C. B. Schaffer, and E. Mazur, “Numerical aperture dependence of damage and supercontinuum generation from femtosecond laser pulses in bulk fused silica,” J. Opt. Soc. Am. B 23, 2317–2322 (2006).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

M. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
[CrossRef]

2004 (1)

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

2003 (1)

G. Cerullo and S. De Silvetri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003).
[CrossRef]

2002 (1)

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B 4, 176–183 (2002).

2001 (1)

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

1999 (2)

R. Heintzmann and C. Cremer, “Lateral modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).

A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. G. Martinez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245–7251 (1999).
[CrossRef]

1998 (2)

1997 (2)

A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
[CrossRef]

M. C. Teich and B. E. A. Saleh, “Entangled-photon microscopy,” translation of Mikroskopie s kvantove’ provazanymi fotony, Ceskoslovensky casopis pro fyziku 47, 3–8 (1997).

1995 (1)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef]

1994 (1)

1969 (1)

H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1967 (4)

1966 (1)

1963 (1)

W. Lukosz and M. Marchand, “Optischen Abbildung Unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Optica Acta 10, 241–255 (1963).
[CrossRef]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmum,” Archiv für Mikroskopische Anatomie IX, 413–468 (1873).

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmum,” Archiv für Mikroskopische Anatomie IX, 413–468 (1873).

Afek, I.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable, and J. P. Dowling, “Quantum states of light produced by a high-gain optical parametric amplifier for use in quantum lithography,” J. Opt. Soc. Am. B 24, 270–274 (2007).
[CrossRef]

S. J. Bentley, R. W. Boyd, E. M. Nagasako, and G. S. Agarwal, “Quantum entanglement for optical lithography and microscopy beyond the Rayleigh limit,” in Quantum Electronics and Laser Science Conference (The Optical Society, 2001), paper QTuD2.

Ambar, O.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef]

Ashcom, J. B.

Bachl, A.

Barsi, C.

C. Barsi and J. W. Fleischer, “Increased field of view via nonlinear digital holography,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMCC4.

Bates, M.

M. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
[CrossRef]

Bentley, S. J.

S. J. Bentley, R. W. Boyd, E. M. Nagasako, and G. S. Agarwal, “Quantum entanglement for optical lithography and microscopy beyond the Rayleigh limit,” in Quantum Electronics and Laser Science Conference (The Optical Society, 2001), paper QTuD2.

Björk, G.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1997).

Boyd, R. W.

G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable, and J. P. Dowling, “Quantum states of light produced by a high-gain optical parametric amplifier for use in quantum lithography,” J. Opt. Soc. Am. B 24, 270–274 (2007).
[CrossRef]

S. J. Bentley, R. W. Boyd, E. M. Nagasako, and G. S. Agarwal, “Quantum entanglement for optical lithography and microscopy beyond the Rayleigh limit,” in Quantum Electronics and Laser Science Conference (The Optical Society, 2001), paper QTuD2.

Brambilla, E.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B 4, 176–183 (2002).

Bryant, G. W.

Cable, H.

H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
[CrossRef]

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable, and J. P. Dowling, “Quantum states of light produced by a high-gain optical parametric amplifier for use in quantum lithography,” J. Opt. Soc. Am. B 24, 270–274 (2007).
[CrossRef]

Cao, W.

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

Cerullo, G.

G. Cerullo and S. De Silvetri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003).
[CrossRef]

Chan, K. W.

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Cho, P.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

Choi, S.-K.

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef]

Cremer, C.

C. Cremer and B. R. Masters, “Resolution enhancement techniques in microscopy,” Eur. Phys. J. A 38, 281–344 (2013).

R. Heintzmann and C. Cremer, “Lateral modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).

Crimmins, T. F.

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

De Silvetri, S.

G. Cerullo and S. De Silvetri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003).
[CrossRef]

DeMartini, F.

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

den Dekker, A. J.

di Francia, G. T.

G. T. di Francia, “Super-gain antennas and optical resolving power,” Supplemento AL Volume IX, Series IX DEL NUOVO CIMENTO, N. 3 (1952), pp. 426–438.

Dowling, J. P.

H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
[CrossRef]

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[CrossRef]

G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable, and J. P. Dowling, “Quantum states of light produced by a high-gain optical parametric amplifier for use in quantum lithography,” J. Opt. Soc. Am. B 24, 270–274 (2007).
[CrossRef]

Edamatsu, K.

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

Fleischer, J. W.

C. Barsi and J. W. Fleischer, “Increased field of view via nonlinear digital holography,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMCC4.

Fujita, K.

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Fujiwara, H.

Garcia, J.

Gattass, R. R.

Gatti, A.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B 4, 176–183 (2002).

Gerry, C. C.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004), Section 6.2.

Giovannetti, V.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).

Glasser, R.

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Glauber, R. J.

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. I,” Phys. Rev. 160, 1076–1096 (1967).
[CrossRef]

Goldhar, J.

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), p. 162.

Guo, L. N.

L. N. Guo, Z. L. Tang, and D. Xing, “Imaging theory of nonlinear Raman confocal microscopy,” J. Mod. Opt. 55, 375–386 (2008).
[CrossRef]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

Haus, H.

H. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).

Heintzmann, R.

R. Heintzmann and C. Cremer, “Lateral modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).

Hell, B. W.

Herman, W. N.

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

Itoh, T.

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef]

Kawabe, Y.

Kawano, S.

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Kawata, S.

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Kim, H.

Kim, Y.-H.

Kim, Y.-S.

Knight, P. L.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004), Section 6.2.

Kobayashi, M.

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kwon, O.

Lee, C. H.

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

Lee, J.-C.

Lee, S. M.

Leng, Y.

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

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V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).

Lugiato, L.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B 4, 176–183 (2002).

Lukosz, W.

Maccone, L.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).

Marchand, M.

W. Lukosz and M. Marchand, “Optischen Abbildung Unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Optica Acta 10, 241–255 (1963).
[CrossRef]

Martinez, P. G.

Masters, B. R.

C. Cremer and B. R. Masters, “Resolution enhancement techniques in microscopy,” Eur. Phys. J. A 38, 281–344 (2013).

Maznev, A. A.

Mazur, E.

McCutchen, C. W.

Mendlovic, D.

Mollow, B. R.

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. I,” Phys. Rev. 160, 1076–1096 (1967).
[CrossRef]

Muthukrishnan, A.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

Nagasako, E. M.

S. J. Bentley, R. W. Boyd, E. M. Nagasako, and G. S. Agarwal, “Quantum entanglement for optical lithography and microscopy beyond the Rayleigh limit,” in Quantum Electronics and Laser Science Conference (The Optical Society, 2001), paper QTuD2.

Nelson, K. A.

Novotny, L.

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[CrossRef]

Okamoto, R.

Park, D. H.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

Park, H. S.

Peng, Y.-H.

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

Quidant, R.

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[CrossRef]

Renger, J.

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[CrossRef]

Rogers, J. A.

Rust, M.

M. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
[CrossRef]

Saleh, B. E. A.

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Schaffer, C. B.

Sciarrino, F.

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Scully, M. O.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

Shapiro, J. H.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).

Shemer, A.

Shih, Y.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

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R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

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I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef]

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H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
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L. N. Guo, Z. L. Tang, and D. Xing, “Imaging theory of nonlinear Raman confocal microscopy,” J. Mod. Opt. 55, 375–386 (2008).
[CrossRef]

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M. C. Teich and B. E. A. Saleh, “Entangled-photon microscopy,” translation of Mikroskopie s kvantove’ provazanymi fotony, Ceskoslovensky casopis pro fyziku 47, 3–8 (1997).

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van Hulst, N.

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[CrossRef]

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F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

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H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
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M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1997).

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L. N. Guo, Z. L. Tang, and D. Xing, “Imaging theory of nonlinear Raman confocal microscopy,” J. Mod. Opt. 55, 375–386 (2008).
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J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
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K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Yun, V.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

Zalevsky, Z.

Zhuang, X.

M. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
[CrossRef]

Zubairy, M. S.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

Appl. Opt. (1)

Archiv für Mikroskopische Anatomie (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmum,” Archiv für Mikroskopische Anatomie IX, 413–468 (1873).

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H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Contemp. Phys. (1)

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[CrossRef]

Eur. Phys. J. A (1)

C. Cremer and B. R. Masters, “Resolution enhancement techniques in microscopy,” Eur. Phys. J. A 38, 281–344 (2013).

J. Microsc. (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

J. Mod. Opt. (1)

L. N. Guo, Z. L. Tang, and D. Xing, “Imaging theory of nonlinear Raman confocal microscopy,” J. Mod. Opt. 55, 375–386 (2008).
[CrossRef]

J. Opt. B (2)

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B 4, 176–183 (2002).

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Mikroskopie s kvantove’ provazanymi fotony (1)

M. C. Teich and B. E. A. Saleh, “Entangled-photon microscopy,” translation of Mikroskopie s kvantove’ provazanymi fotony, Ceskoslovensky casopis pro fyziku 47, 3–8 (1997).

Nat. Methods (1)

M. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
[CrossRef]

New J. Phys. (1)

H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Optica Acta (1)

W. Lukosz and M. Marchand, “Optischen Abbildung Unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Optica Acta 10, 241–255 (1963).
[CrossRef]

Phys. Rev. (1)

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. I,” Phys. Rev. 160, 1076–1096 (1967).
[CrossRef]

Phys. Rev. A (3)

F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).

Phys. Rev. Lett. (4)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[CrossRef]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Proc. SPIE (1)

R. Heintzmann and C. Cremer, “Lateral modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).

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[CrossRef]

Science (1)

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef]

Other (10)

W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004), Section 6.2.

H. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).

S. J. Bentley, R. W. Boyd, E. M. Nagasako, and G. S. Agarwal, “Quantum entanglement for optical lithography and microscopy beyond the Rayleigh limit,” in Quantum Electronics and Laser Science Conference (The Optical Society, 2001), paper QTuD2.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), p. 162.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1997).

G. T. di Francia, “Super-gain antennas and optical resolving power,” Supplemento AL Volume IX, Series IX DEL NUOVO CIMENTO, N. 3 (1952), pp. 426–438.

C. Barsi and J. W. Fleischer, “Increased field of view via nonlinear digital holography,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMCC4.

Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.

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Figures (13)

Fig. 1.
Fig. 1.

(a) Classical coherent light imaged grating interferometer. (b) Nonclassical interferometer of the type used in Ref. [36]. (c) Imaged grating squeezed vacuum interferometer used in this work, which is equivalent to (b).

Fig. 2.
Fig. 2.

Schematic of a setup for characterization of grating G 2 .

Fig. 3.
Fig. 3.

Plot of the outputs of two detectors at low intensity for a 10 μm period test grating G 2 .

Fig. 4.
Fig. 4.

Experimental setup for generation and characterization of two-photon spatial interference pattern.

Fig. 5.
Fig. 5.

Propagation of quantum mechanical operators through a single slit in the Heisenberg picture corresponding to the experimental setup in Fig. 4.

Fig. 6.
Fig. 6.

(a) Interference pattern with coherent light; the intensity (lower trace) is modulated and the degree of second-order correlation (upper trace) remains constant. (b) With squeezed vacuum, the degree of second-order correlation is modulated and the intensity is not. The spatial period of modulation differs by a factor of two.

Fig. 7.
Fig. 7.

Propagation of the beams through a grating can be modeled as a multiport device.

Fig. 8.
Fig. 8.

(a) Interaction of coherent light with 32 μm period target grating; intensity in each detector (lower traces) is modulated and the degree of second-order correlation (upper trace) remains constant. (b) Interaction of squeezed vacuum beams with 32 μm grating. The degree of second-order correlation (upper two traces are g 11 ( 2 ) , g 22 ( 2 ) , and the middle one is cross correlation g 12 ( 2 ) ) is modulated with twice the spatial frequency (period of 16 μm). The lowest two traces are the intensity measured by the two detectors, and there is no modulation. (c) There is no observable modulation in the degree of second-order correlation for grating G 2 with Λ g = 16 μm interacting with squeezed vacuum beams.

Fig. 9.
Fig. 9.

Schematic showing optical beams used for calculation of nonlinear grating characterization.

Fig. 10.
Fig. 10.

(a) Schematic of the experimental setup of the robust nonlinear interferometer for the sub-diffraction-limited grating structure characterization ( G 2 with a period of 5 μm). (b) Photodiode outputs from the two probing beams. (c) and (d) are the Fourier frequency components of the individual photodiode output. (e) Fourier frequency components of the difference of the two photodiode outputs.

Fig. 11.
Fig. 11.

Modulation depths versus incident laser intensity. Red asterisks are experiment results and solid line is numerical simulation.

Fig. 12.
Fig. 12.

Schematic of experiment setup of Ref. [10] for obtaining super resolution. OP, object plane; IP, image plane; I P , another image plane; L 1 and L 2 , lenses; M and M , grating masks. Green lines illustrate rays for image formation without, and red is with gratings inserted into the optical path.

Fig. 13.
Fig. 13.

Numerical simulation of modulation depth versus period of the target grating.

Equations (25)

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

T ( x ) e i m 2 sin K g ( x x 0 ) A 0 + n = 1 [ A n e i n K g ( x x 0 ) + A n e i n K g ( x x 0 ) ] ,
E i n ( x , z ) = E 1 e i ( k x x + k z z ) + E 2 e i ( k x x + k z z ) ,
E out ( x ) = T ( x ) E in ( x , 0 ) = E 1 A 0 e i K 2 x + E 2 A 0 e i K 2 x + n = 1 [ E 1 A n e i ( n K g x 0 ) e i ( K 2 + n K g ) x + E 1 A n e i ( n K g x 0 ) e i ( K 2 n K g ) x ] + n = 1 [ E 2 A n e i ( n K g x 0 ) e i ( K 2 + n K g ) x + E 2 A n e i ( n K g x 0 ) e i ( K 2 n K g ) x ] .
( E 1 E 2 ) out = ( τ 11 τ 12 τ 21 τ 22 ) ( E 1 E 2 ) in .
( τ 11 τ 12 τ 21 τ 22 ) = ( A 0 A 1 e i K g x 0 A 1 e i K g x 0 A 0 ) .
I 1 = | E 0 | 2 | A 0 + A 1 e i K g x 0 e i ϕ | 2 = | E 0 | 2 [ A 0 2 + A 1 2 + 2 A 0 A 1 cos K g ( x d x 0 ) ] ,
I 2 = | E 0 | 2 | A 0 + A 1 e i K g x 0 e i ϕ | 2 = | E 0 | 2 [ A 0 2 + A 1 2 2 A 0 A 1 cos K g ( x d x 0 ) ] .
K max = 2 k x = 4 π λ sin θ max ,
Λ g = 2 π K max = λ 2 sin θ max = λ 0 2 NA ,
| Ψ in = | ζ 1 | ζ 2 n > 2 | 0 n ,
ζ | a ^ a ^ | ζ = n 0 = sinh 2 ( s ) .
b ^ m = n = 1 , 2 τ m n a ^ n + k = 1 , 2 ρ m k c ^ k ,
Ψ in | b ^ 0 b ^ 0 | Ψ in = 2 ζ | 1 ζ | b ^ 0 b ^ 0 | ζ 1 | ζ 2 = ( | τ 01 | 2 + | τ 02 | 2 ) n 0 .
Ψ in | b ^ 0 b ^ 0 b ^ 0 b ^ 0 | Ψ in = 2 | τ 01 | 4 n 0 [ ( 5 n 0 + 1 ) + ( n 0 + 1 ) cos 2 ϕ ] .
g b b ( 2 ) = b ^ 0 b ^ 0 b ^ 0 b ^ 0 b ^ 0 b ^ 0 2 = 1 2 n 0 [ 5 n 0 + 1 ( n 0 + 1 ) cos 2 ϕ ] n 0 2 .
b ^ 1 = τ 11 a ^ 1 + τ 12 a ^ 2 + n > 2 τ 1 n a ^ n + m τ 1 m c ^ m ,
g b 1 b 1 ( 2 ) = b ^ 1 b ^ 1 b ^ 1 b ^ 1 b ^ 1 b ^ 1 2 = 1 2 n 0 [ 5 n 0 + 1 ( n 0 + 1 ) cos ( 2 ϕ ) ] n 0 2 ,
g b 1 b 2 ( 2 ) = b ^ 1 b ^ 2 b ^ 1 b ^ 2 b ^ 1 b ^ 1 b ^ 2 b ^ 2 = 1 2 n 0 [ 3 n 0 + 1 + ( n 0 + 1 ) cos ( 2 ϕ ) ] n 0 2 ,
( τ 11 τ 12 τ 21 τ 22 ) = ( A 0 0 0 A 0 ) .
k⃗ ± 1 = ± k x x ^ + k 1 z z ^ , k 1 z = k 2 k x 2 .
k⃗ ± 3 = ± 3 k x x ^ + k 3 z z ^ , k 3 z = k 2 ( 3 k x ) 2 , k⃗ ± 5 = ± 5 k x x ^ + k 5 z z ^ , k 5 z = k 2 ( 5 k x ) 2 .
E ( x , z = 0 ) = E 0 cos ( K g 2 x ) T ( x ) .
E ( x , z = 0 ) = E 0 ( A 1 e i K g 2 x + i K g x d + A 1 e i K g 2 x i K g x d + A 3 e i 3 K g 2 x i K g x d + A 3 e i 3 K g 2 x i K g x d + A 5 e i 5 K g 2 x + i K g x d + A 5 e i 5 K g 2 x i K g x d ) ,
z E ( x , z ) = 1 2 i k 0 2 E ( x , z ) i k 0 n 2 | E ( x , z ) | 2 E ( x , z ) .
d 2 i n 2 k 0 d z E 1 = ( | E 1 | 2 2 + | E 1 | 2 + | E 3 | 2 + | E 3 | 2 + | E 5 | 2 + | E 5 | 2 ) E 1 + E 3 E 1 * E 1 e i Δ 31 z + E 3 E 3 * E 5 e i Δ 51 z + E 1 2 2 E 3 * e i Δ 13 z + E 3 E 3 E 1 * e 2 i Δ 31 z + E 3 2 E 5 * 2 e i ( Δ 31 + Δ 35 ) z + E 5 E 1 * E 5 e 2 i Δ 51 z + E 1 E 3 * E 5 e i Δ 53 z + E 1 E 3 E 5 * e i Δ 35 z + E 3 E 1 * E 5 e i ( Δ 31 + Δ 51 ) z ,

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