Abstract

Two dimensional mid-infrared upconversion imaging provides unique spectral and spatial information showing good potential for mid-infrared spectroscopy and hyperspectral imaging. However, to extract spectral or spatial information from the upconverted images an elaborate model is needed, which includes non-collinear interaction. We derive here a general theory providing the far field of the upconverted light when two arbitrary fields interact inside a nonlinear crystal. Theoretical predictions are experimentally verified for incoherent radiation and subsequently applied to previously published data with good agreement.

© 2014 Optical Society of America

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References

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  • Publication
  1. P. R. Griffiths and J. A. de Haseth, Fourier Transform infrared Spectrometry 2nd Ed (Wiley, 2007).
  2. S. Wartewig and R. H. H. Neubert, “Pharmaceutical applications of mid-IR and raman spectroscopy,” Adv. Drug Deliver. Rev. 57(8), 1144–1170 (2005). http://www.sciencedirect.com/science/article/pii/S0165993602012086
  3. N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy 3rd ed. (Academic 1990).
  4. T. L. Williams, Thermal Imaging Cameras (CRC, 2009).
  5. J. E. Midwinter, “Image conversion from 1.6um to the visible in lithium niobate,” Appl. Phys. Lett. 12(3), 68–71 (1968), doi:.
    [Crossref]
  6. J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “Room-temperature mid-infrared single-photon spectral imaging,” Nature Photon. 6, 788 (2012). http://www.nature.com/doifinder/10.1038/nphoton.2012.231
  7. Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
    [Crossref]
  8. J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “High-resolution two-dimensional image upconversion of incoherent light,” Opt. Lett. 35(22), 3796–3798 (2010), doi:.
    [Crossref] [PubMed]
  9. C. Pedersen, E. Karamehmedović, J. S. Dam, and P. Tidemand-Lichtenberg, “Enhanced 2D-image upconversion using solid-state lasers,” Opt. Express 17(23), 20885–20890 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-23-20885 .
    [Crossref] [PubMed]
  10. J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “Theory for upconversion of incoherent images,” Opt. Express 20(2), 1475–1482 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1475 .
    [Crossref] [PubMed]
  11. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962), http://prola.aps.org/abstract/PR/v128/i2/p606_1 .
    [Crossref]
  12. D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174(3), 1027–1041 (1968), http://prola.aps.org/abstract/PR/v174/i3/p1027_1 .
    [Crossref]
  13. A. H. Firester, “Upconversion: Part III,” J. Appl. Phys. 41(2), 703–709 (1970).
    [Crossref]
  14. A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
    [Crossref]
  15. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics 2nd Ed (Wiley, 2007).
  16. J. W. Goodman, Introduction to Fourier Optics 3rd Ed (Roberts & Company, 2005).
  17. Q. Hu, J. Seidelin Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “High-resolution mid-IR spectrometer based on frequency upconversion,” Opt. Lett. 37(24), 5232–5234 (2012), http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-24-5232 .
    [Crossref] [PubMed]
  18. L. Høgstedt, O. B. Jensen, J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “500 nm continuous wave tunable single-frequency mid-IR light source for C-H spectroscopy,” Laser Phys. 22(11), 1676–1681 (2012), doi:.
    [Crossref]
  19. The commercial HITEMP database from “Spectral calculator - high resolution gas spectra,” http://www.spectralcalc.com/

2013 (1)

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

2012 (3)

2010 (1)

2009 (1)

1987 (1)

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[Crossref]

1970 (1)

A. H. Firester, “Upconversion: Part III,” J. Appl. Phys. 41(2), 703–709 (1970).
[Crossref]

1968 (2)

J. E. Midwinter, “Image conversion from 1.6um to the visible in lithium niobate,” Appl. Phys. Lett. 12(3), 68–71 (1968), doi:.
[Crossref]

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174(3), 1027–1041 (1968), http://prola.aps.org/abstract/PR/v174/i3/p1027_1 .
[Crossref]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962), http://prola.aps.org/abstract/PR/v128/i2/p606_1 .
[Crossref]

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962), http://prola.aps.org/abstract/PR/v128/i2/p606_1 .
[Crossref]

Cardimona, D.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[Crossref]

Dam, J. S.

Firester, A. H.

A. H. Firester, “Upconversion: Part III,” J. Appl. Phys. 41(2), 703–709 (1970).
[Crossref]

Gavrielides, A.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[Crossref]

Høgstedt, L.

L. Høgstedt, O. B. Jensen, J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “500 nm continuous wave tunable single-frequency mid-IR light source for C-H spectroscopy,” Laser Phys. 22(11), 1676–1681 (2012), doi:.
[Crossref]

Hu, Q.

Huang, K.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

Jensen, O. B.

L. Høgstedt, O. B. Jensen, J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “500 nm continuous wave tunable single-frequency mid-IR light source for C-H spectroscopy,” Laser Phys. 22(11), 1676–1681 (2012), doi:.
[Crossref]

Karamehmedovic, E.

Kleinman, D. A.

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174(3), 1027–1041 (1968), http://prola.aps.org/abstract/PR/v174/i3/p1027_1 .
[Crossref]

Midwinter, J. E.

J. E. Midwinter, “Image conversion from 1.6um to the visible in lithium niobate,” Appl. Phys. Lett. 12(3), 68–71 (1968), doi:.
[Crossref]

Pan, H.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

Pedersen, C.

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962), http://prola.aps.org/abstract/PR/v128/i2/p606_1 .
[Crossref]

Peterson, P.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[Crossref]

Seidelin Dam, J.

Tidemand-Lichtenberg, P.

Wu, E.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

Zheng, H.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

Zhou, Q.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

Appl. Phys. Lett. (2)

J. E. Midwinter, “Image conversion from 1.6um to the visible in lithium niobate,” Appl. Phys. Lett. 12(3), 68–71 (1968), doi:.
[Crossref]

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zheng, “Ultrasensitive mid-infrared up-conversion imaging af few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013), doi:.
[Crossref]

J. Appl. Phys. (2)

A. H. Firester, “Upconversion: Part III,” J. Appl. Phys. 41(2), 703–709 (1970).
[Crossref]

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[Crossref]

Laser Phys. (1)

L. Høgstedt, O. B. Jensen, J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “500 nm continuous wave tunable single-frequency mid-IR light source for C-H spectroscopy,” Laser Phys. 22(11), 1676–1681 (2012), doi:.
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (2)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962), http://prola.aps.org/abstract/PR/v128/i2/p606_1 .
[Crossref]

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174(3), 1027–1041 (1968), http://prola.aps.org/abstract/PR/v174/i3/p1027_1 .
[Crossref]

Other (8)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics 2nd Ed (Wiley, 2007).

J. W. Goodman, Introduction to Fourier Optics 3rd Ed (Roberts & Company, 2005).

J. S. Dam, C. Pedersen, and P. Tidemand-Lichtenberg, “Room-temperature mid-infrared single-photon spectral imaging,” Nature Photon. 6, 788 (2012). http://www.nature.com/doifinder/10.1038/nphoton.2012.231

P. R. Griffiths and J. A. de Haseth, Fourier Transform infrared Spectrometry 2nd Ed (Wiley, 2007).

S. Wartewig and R. H. H. Neubert, “Pharmaceutical applications of mid-IR and raman spectroscopy,” Adv. Drug Deliver. Rev. 57(8), 1144–1170 (2005). http://www.sciencedirect.com/science/article/pii/S0165993602012086

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy 3rd ed. (Academic 1990).

T. L. Williams, Thermal Imaging Cameras (CRC, 2009).

The commercial HITEMP database from “Spectral calculator - high resolution gas spectra,” http://www.spectralcalc.com/

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Figures (7)
Fig. 1
Fig. 1 General layout of sum frequency generation illustrating two arbitrary input fields inside a second order nonlinear material, V, generating a plane wave at the sum frequency in the far field.

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Fig. 2
Fig. 2 Illustration of the non-linear crystal, the object and image planes respectively and the three wave-vectors involved in the non-collinear interaction.

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Fig. 3
Fig. 3 Theoretical calculation of of non-collinear upconversion of monochromatic incoherent light. a) The blue curves shows the normalized intensity curves for a very large laser beam diameter for a selection of phase matched angles; θ u = 0.046, 0.187, 0.262, 0.318, 0.365, 0.406, 0.444, 0.478, 0.509, 0.538, and 0.565 degrees respectively. The red curves shows a similar set of curves using a pump beam radius of 180 µm. b) This curve shows the decreased peak intensity values caused by the finite size of the mixing beam as a function of non-collinear upconverted angle.

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Fig. 4
Fig. 4 Plot of spectral acceptance for the same angles θ u used in Fig. 4a. The highest curve shows the situation for the smallest angle, i.e. θ u . As in Fig. 3, the absolute intensity peaks decrease for increasing θ u . For easy comparison, the calculation uses the same phase matched wavelength. It is apparent that the decrease in peak intensity is accompanied with a corresponding increase in wavelength acceptance.

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Fig. 5
Fig. 5 System for detection of incoherent, monochromatic light using frequency up-conversion and a NIR/VIS CCD camera.

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Fig. 6
Fig. 6 Experimental comparison to theoretical prediction. a) Raw data recorded by the CCD camera for two different temperatures of the nonlinear crystal. b) Cross sections of the ring patterns as function of θ u for different crystal temperatures (blue curves) plotted with theoretical predictions (red curves). The input wavelength was 2.937 µm throughout the measurement series. c) The correlation coefficient of the 11 data series comparing collinear theory (red dots) and non-collinear theory (blue dots).

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Fig. 7
Fig. 7 The green curve shows the raw data from [17]. Post processing the green curve using the presented theory for non-collinear upconversion provides the red curve. The spectra are compared to a modelled spectra using [19] shown as black curve (0.2 nm resolution) and blue curve (0.4 nm resolution). The red curve resembles the modelled spectrum better as expected.

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Equations (8)

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E 3 ( r u → ) ≡ E 3 ( r u , k 3 → ) = exp ( − i k 3 ⋅ r u ) 4 π r u ∫ V S 3 ( r ' → ) exp ( i k 3 → ⋅ r ' → ) d r '
S 3 ( r ′ → ) = − ∂ 2 P ∂ 2 t = − 2 d e f f ω 3 2 c 2 E 1 ( r ′ → ) E 2 ( r ′ → ) e − i ( k → 1 + k → 2 ) ⋅ r → ′
E 3 ( r u , k 3 → ) = − 2 d e f f ω 3 2 c 2 e − i k 3 r u 4 π r u F { E 1 ( r → ) } ⊗ F { E 2 ( r → ) }
E 2 ( r → ) exp ( − i k 2 z z ) = a 2 1 + i z z R exp ( − i k 2 z z ) exp ( − x 2 + y 2 w 0 2 ( 1 + i z z R ) ) ,
E 1 ( r → ) exp ( − i k 1 → ⋅ r → ) = a 1 exp ( − i k 1 → ⋅ r → ) ,
E ( r u , Δ k x , Δ k y , Δ k z ) = 2 d e f f ω 3 2 π w 0 2 l c 2 e − i k 3 r u 4 π r u a 1 a 2 e − ( Δ k x 2 + Δ k y 2 ) w 0 2 4 Sin c ( l 2 ( Δ k z − ( Δ k x 2 + Δ k y 2 ) 2 k 2 z ) )
I i m a g e ( r u → , λ 3 ) = 8 π 2 d e f f 2 l 2 P G a u s s n 1 n 2 n 3 ε 0 c λ 3 2 f 2 × ∫ L o b j e c t ( r ″ → , λ 1 ) ( w 0 2 k 3 2 2 π n 3 2 f 1 2 e − w 0 2 k 3 2 | r u → − r ″ → | 2 2 n 3 2 f 1 2 sin c 2 ( l 2 ( Δ k z ( r ″ , r u ) − k 3 2 2 k 2 | r u → − r ″ → | 2 n 3 2 f 1 2 ) ) ) d r ″ → ,
C = ∫ I m e a s ( θ u ) I t h e o r y ( θ u ) θ u d θ u ∫ I m e a s ( θ u ) I m e a s ( θ u ) θ u d θ u ∫ I t h e o r y ( θ u ) I t h e o r y ( θ u ) θ u d θ u

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