## Enhanced 2D-image upconversion using solid-state lasers

Optics Express, Vol. 17, Issue 23, pp. 20885-20890 (2009)

http://dx.doi.org/10.1364/OE.17.020885

Acrobat PDF (237 KB)

### Abstract

Based on enhanced upconversion, we demonstrate a highly efficient method for converting a full image from one part of the electromagnetic spectrum into a new desired wavelength region. By illuminating a metal transmission mask with a 765 nm Gaussian beam to create an image and subsequently focusing the image inside a nonlinear PPKTP crystal located in the high intra-cavity field of a 1342 nm solid-state Nd:YVO_{4} laser, an upconverted image at 488 nm is generated. We have experimentally achieved an upconversion efficiency of 40% under CW conditions. The proposed technique can be further adapted for high efficiency mid-infrared image upconversion where direct and fast detection is difficult or impossible to perform with existing detector technologies.

© 2009 OSA

## 1. Introduction

1. R. A. Andrews, “Wide angular aperture image up-conversion,” J. Quantum Electron. **5**(11), 548–550 (
1969). [CrossRef]

7. F. Devaux, A. Mosset, E. Lantz, S. Monneret, and H. Le Gall, “Image upconversion from the visible to the UV domain: application to dynamic UV microstereolithography,” Appl. Opt. **40**(28), 4953–4957 (
2001), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-28-4953. [CrossRef] [PubMed]

4. J. Falk and Y. C. See, “Internal CW parametric upconversion,” Appl. Phys. Lett. **32**(2), 100–101 (
1978). [CrossRef]

_{4}(PPKTP) crystal. The power conversion efficiency from 765 nm to 488 nm was 32% [8

8. E. Karamehmedović, C. Pedersen, M. T. Andersen, and P. Tidemand-Lichtenberg, “Efficient visible light generation by mixing of a solid-state laser and a tapered diode laser,” Opt. Express **15**(19), 12240–12245 (
2007), http://www.opticsinfobase.org/abstract.cfm?id=141313. [CrossRef] [PubMed]

9. E. Karamehmedović, C. Pedersen, O. B. Jensen, and P. Tidemand-Lichtenberg, “Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing,” Appl. Phys. B **96**(2-3), 409–413 (
2009). [CrossRef]

10. D. J. Stothard, M. H. Dunn, and C. F. Rae, “Hyperspectral imaging of gases with a continuous-wave pump-enhanced optical parametric oscillator,” Opt. Express **12**(5), 947–955 (
2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-5-947. [CrossRef] [PubMed]

## 2. Theory

*E*=

_{object}*E*(

_{object}*x,y*) will be derived, where

*x*and

*y*denote the transverse coordinates of the field. The upconverted image,

*E*=

_{up}*E*(

_{up}*x,y*), is the result of the upconversion process between

*E*and a Gaussian intra-cavity field,

_{object}*U*=

_{Gauss}*U*(

_{Gauss}*u,v*), where

*u*and

*v*are the transverse coordinates at the Fourier plane. The specific system under consideration is shown in Fig. 1 .

*E*and

_{object}*U*can be approximated as being constant throughout the entire interaction length of the nonlinear crystal. Further, a plane wave approximation is used, and finally, the length of the crystal is considered to be short compared to the confocal length of the interacting beams. All these assumptions are not strictly necessary, but allow derivation of a simple relation between the light from the object and the corresponding upconverted image at the image plane. Using the mentioned assumptions,

_{Gauss}*E*can be calculated as:

_{up}*λ*is determined by the energy conservation law:

_{3}*λ*is the wavelength of the intra-cavity Gaussian beam and

_{2}*λ*is the wavelength of light emitted from the object.

_{1}*n*,

_{1}*n*and

_{2}*n*are the refractive indices of the non-linear crystal corresponding to

_{3}*λ*and

_{1}, λ_{2}*λ*.

_{3}*f*and

*f*are the focal lengths of the Fourier transforming lenses,

_{1}*P*is the power of the intra-cavity Gaussian field,

_{Gauss}*c*is the speed of light in vacuum,

*w*is the radius of the intra-cavity beam at the beam waist,

_{0}*d*is the effective second order nonlinearity of the crystal and

_{eff}*L*is the length of the crystal. From Eq. (1), the intensity profile of the upconverted light

*I*can be calculated as:

_{up}12. G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light beams,” J. Appl. Phys. **39**(8), 3597–3640 (
1968). [CrossRef]

*w*of the intra-cavity Gaussian field becomes sufficiently large (effectively transforming the normalized convolution function into a delta-function), a perfect upconverted replica of the original image, in the new spectral region can be obtained, scaled with a factor

_{0}*P*(

*x,y,x*) can be expressed as:

_{0},y_{0}*E*is a delta function positioned at the coordinates (

_{object}*x*). From Eq. (4), it can be seen that the size of the Gaussian beam defines the shape of the point spread function, and thus the resolution of the imaging process. The cost of increasing the beam size to improve the resolution is a reduced intensity (assuming constant power), therefore the conversion efficiency reduces accordingly. However, another important and limiting parameter in the image upconversion is the acceptance bandwidth of the nonlinear process. The angular acceptance parameter of the SFG process acts as a filter limiting the maximum size of

_{0},y_{0}*E*to be converted. Similarly, the spectral acceptance parameter defines the spectral width of frequencies that can be upconverted in a specific set-up.

_{object}## 3. Setup

8. E. Karamehmedović, C. Pedersen, M. T. Andersen, and P. Tidemand-Lichtenberg, “Efficient visible light generation by mixing of a solid-state laser and a tapered diode laser,” Opt. Express **15**(19), 12240–12245 (
2007), http://www.opticsinfobase.org/abstract.cfm?id=141313. [CrossRef] [PubMed]

9. E. Karamehmedović, C. Pedersen, O. B. Jensen, and P. Tidemand-Lichtenberg, “Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing,” Appl. Phys. B **96**(2-3), 409–413 (
2009). [CrossRef]

*E*). The two slits forming the cross are 1 mm by 5 mm in width. (Some minor diffraction effects appear in the transmitted image). The 765 nm object is transformed by a lens L2 (f = 100 mm) in combination with curved mirror M2 (f = −200 mm) to the Fourier plane inside the PPKTP crystal. The PPKTP crystal is placed at the beam waist in the 1342 nm cavity.

_{object}## 4. Results

*E*and is shown in Fig. 3(b). The Fourier transform of the object field (

_{object}*E*) is performed using the lens L2 (f = 100 mm) placed 80 mm from the object plane and 62 mm from mirror M2 (acting as a negative lens with f = −200 mm). At the position of the beam waist inside the PPKTP crystal, the high intra-cavity field of the 1342 nm laser and the Fourier transformed object field interact through SFG to generate a blue, 488 nm upconverted image. This is shown in Fig. 3(d). Figure 3(c) shows the calculated upconverted image using the simple theory outlined in section 2 with some additional stretching (18% on the horizontal axis and 3% on the vertical axis) originating from imaging/upconverting through the Brewster cut surfaces. The additional stretching along the horizontal axis from Brewster-cut surfaces can be calculated to be

_{object}*x*- and

*x*-

*y*axes, respectively. Figures 4(a) -4(c) demonstrate that a misalignment of the transverse position of the Gaussian 1342 nm beam favors the higher spatial frequency components of the object, as expected from Fourier optics theory [11].

*x*-

*y*plane. Also here we note a good correspondence between the predicted and measured results.

## 5. Discussion

*E*that can be converted is reduced. Thus, a trade-off is encountered, allowing for optimization of one of the two parameters only at the expense of the other.

_{object}## 6. Conclusion

## Acknowledgments

## References and Links

1. | R. A. Andrews, “Wide angular aperture image up-conversion,” J. Quantum Electron. |

2. | A. H. Firester, “Image upconversion: Part III*,” J. Appl. Phys. |

3. | W. Chiou, “Geometric Optics Theory of Parametric Image Upconversion,” J. Appl. Phys. |

4. | J. Falk and Y. C. See, “Internal CW parametric upconversion,” Appl. Phys. Lett. |

5. | J. E. Midwinter, “Infrared up conversion in lithium-niobate with large bandwidth and solid acceptance angle,” Appl. Phys. Lett. |

6. | S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric up converter,” J. Appl. Phys. |

7. | F. Devaux, A. Mosset, E. Lantz, S. Monneret, and H. Le Gall, “Image upconversion from the visible to the UV domain: application to dynamic UV microstereolithography,” Appl. Opt. |

8. | E. Karamehmedović, C. Pedersen, M. T. Andersen, and P. Tidemand-Lichtenberg, “Efficient visible light generation by mixing of a solid-state laser and a tapered diode laser,” Opt. Express |

9. | E. Karamehmedović, C. Pedersen, O. B. Jensen, and P. Tidemand-Lichtenberg, “Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing,” Appl. Phys. B |

10. | D. J. Stothard, M. H. Dunn, and C. F. Rae, “Hyperspectral imaging of gases with a continuous-wave pump-enhanced optical parametric oscillator,” Opt. Express |

11. | J. W. Goodman, “Introduction to Fourier Optics” (Third edition), Robers & Company Publishers (2005). |

12. | G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light beams,” J. Appl. Phys. |

**OCIS Codes**

(110.3080) Imaging systems : Infrared imaging

(140.3480) Lasers and laser optics : Lasers, diode-pumped

(140.3580) Lasers and laser optics : Lasers, solid-state

(140.7300) Lasers and laser optics : Visible lasers

(190.7220) Nonlinear optics : Upconversion

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: August 26, 2009

Revised Manuscript: October 28, 2009

Manuscript Accepted: October 28, 2009

Published: October 30, 2009

**Citation**

Christian Pedersen, Emir Karamehmedović, Jeppe Seidelin Dam, and Peter Tidemand-Lichtenberg, "Enhanced 2D-image upconversion using solid-state lasers," Opt. Express **17**, 20885-20890 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-23-20885

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### References

- R. A. Andrews, “Wide angular aperture image up-conversion,” J. Quantum Electron. 5(11), 548–550 (1969). [CrossRef]
- A. H. Firester, “Image upconversion: Part III*,” J. Appl. Phys. 41(2), 703–709 (1970). [CrossRef]
- W. Chiou, “Geometric Optics Theory of Parametric Image Upconversion,” J. Appl. Phys. 42(5), 1985–1993 (1971). [CrossRef]
- J. Falk and Y. C. See, “Internal CW parametric upconversion,” Appl. Phys. Lett. 32(2), 100–101 (1978). [CrossRef]
- J. E. Midwinter, “Infrared up conversion in lithium-niobate with large bandwidth and solid acceptance angle,” Appl. Phys. Lett. 14(1), 29–32 (1969). [CrossRef]
- S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric up converter,” J. Appl. Phys. 51(1), 50–60 (1980). [CrossRef]
- F. Devaux, A. Mosset, E. Lantz, S. Monneret, and H. Le Gall, “Image upconversion from the visible to the UV domain: application to dynamic UV microstereolithography,” Appl. Opt. 40(28), 4953–4957 (2001), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-28-4953 . [CrossRef] [PubMed]
- E. Karamehmedović, C. Pedersen, M. T. Andersen, and P. Tidemand-Lichtenberg, “Efficient visible light generation by mixing of a solid-state laser and a tapered diode laser,” Opt. Express 15(19), 12240–12245 (2007), http://www.opticsinfobase.org/abstract.cfm?id=141313 . [CrossRef] [PubMed]
- E. Karamehmedović, C. Pedersen, O. B. Jensen, and P. Tidemand-Lichtenberg, “Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing,” Appl. Phys. B 96(2-3), 409–413 (2009). [CrossRef]
- D. J. Stothard, M. H. Dunn, and C. F. Rae, “Hyperspectral imaging of gases with a continuous-wave pump-enhanced optical parametric oscillator,” Opt. Express 12(5), 947–955 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-5-947 . [CrossRef] [PubMed]
- J. W. Goodman, “Introduction to Fourier Optics” (Third edition), Robers & Company Publishers (2005).
- G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light beams,” J. Appl. Phys. 39(8), 3597–3640 (1968). [CrossRef]

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