## Investigations on the beam pointing stability of a pulsed optical parametric oscillator |

Optics Express, Vol. 21, Issue 9, pp. 10720-10730 (2013)

http://dx.doi.org/10.1364/OE.21.010720

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### Abstract

Although the beam pointing stability of optical parametric oscillators and amplifiers is important for various applications few results on this parameter have been published. Here, we investigate the beam pointing stability of an injection-seeded, nanosecond optical parametric oscillator, compare it to its pump laser, and measure correlations between them. Although correlation between both quantities are found, the beam pointing stability of the OPO is significantly better that the one of its pump. Furthermore, the concept of the Allan variance is applied to analyze the temporal components of the pointing stability.

© 2013 OSA

## 1. Introduction

2. M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. **8**(10), 1151–1161 (2007). [CrossRef]

4. A. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE **54**(2), 221–230 (1966). [CrossRef]

## 2. Set-up

### 2.1 Pump laser system

^{2}of the Nd:YAG laser was measured to be of the order of 1.7. To pump the OPO, a beam reduction telescope (1:2.6) was inserted into the pump beam.

### 2.2 Optical parametric oscillator

5. A. Fix, C. Büdenbender, M. Wirth, M. Quatrevalet, A. Amediek, C. Kiemle, and G. Ehret, “Optical parametric oscillators and amplifiers for airborne and spaceborne active remote sensing of CO2 and CH4,” Proc. SPIE **8182**, 818206, 818206-10 (2011). [CrossRef]

5. A. Fix, C. Büdenbender, M. Wirth, M. Quatrevalet, A. Amediek, C. Kiemle, and G. Ehret, “Optical parametric oscillators and amplifiers for airborne and spaceborne active remote sensing of CO2 and CH4,” Proc. SPIE **8182**, 818206, 818206-10 (2011). [CrossRef]

### 2.2 Camera systems

## 3. Analysis of beam angular stability

_{x}, δα

_{y}are defined to be twice the standard deviation of the measured angular movement. Often, it is helpful to relate the angular stability to the divergence angle of the beam. In this case, the

*relative*beam angular stability δα

_{rel,x}, δα

_{rel,y}is derived which is the beam angular stability divided by the divergence angle. Within the context of this investigation we do not perform a transformation into the beams’ coordinate systems (the directions parallel and orthogonal to the axis of maximum movement of the asymmetric centroid distribution) in order to better trace down the reasons for drifts and to derive correlations between pump and OPO in the same coordinate frame. The respective beam angular stabilities were derived

*including*the telescopes in the respective beam paths. Therefore the absolute stability of the Nd:YAG is a factor of 2 smaller upstream of the telescope whereas it is a factor of 2.6 larger in case of the OPO. We argue that the measured quantities correspond to those for pumping the OPO as well as after recollimating its beam. The relative angular stabilities are anyway not affected by the telescopes.

4. A. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE **54**(2), 221–230 (1966). [CrossRef]

6. P. Groß, L. Kleinschmidt, S. Beer, and C. Fallnich, “Beam position stabilization for a confocal multiphoton microscope,” Appl. Opt. **50**(28), 5361–5368 (2011). [CrossRef] [PubMed]

_{0}averaging, of an infinite time series y

_{i}of a random variable y with even temporal sampling τ

_{0}is given by:where m is the number of measurements. The Allan standard deviation is the square root of the Allan variance. The most common way to express the time domain stability of a measurement which we also adapt here is by means of sigma-tau plots that show the dependence of stability on averaging time. Log-sigma versus log-tau plots do not only show the dependence of stability but provide means to derive the type of noise since the power law of different noise contributions show specific slopes [7].

## 4. Results

### 4.1 Beam pointing stability

_{x}= (38.4 ± 5.2) µrad and δα

_{y}= (35.7 ± 11.0) µrad which is in-line with the specifications given by the manufacturer (< 50 µrad). The beam angular stability of the OPO was (4.7 ± 0.7) µrad in the x direction and (5.1 ± 1.3) µrad in the y direction, respectively. In relation to the divergence of the beams the relative angular beam stability of the OPO is 0.9% whereas the one of the pump laser is approximately 5 times higher. Table 2 gives an overview over the experimental results.

### 4.2 Correlations between pump and OPO

### 4.3 Differences between on- and off-line operation

_{1}= 1572.012 nm and λ

_{2}= 1571.893 nm were chosen, which were measured using a wavemeter (High Finesse, WS6 IR). Thus the frequency offset between both wavelengths is Δν~14.4 GHz. The wavelengths were alternatively switched to the OPO at its repetition frequency of the OPO, i.e. 100 Hz using a fiber switch (see Fig. 1). As the InGaAs camera is read out at 20-Hz frame rate, every second data acquisition corresponds to the same wavelength. However, which wavelength corresponds to the even and odd records is uncertain because it depends on which wavelength the series has started with.

_{x}= 5.5 µrad and δα

_{y}= 6.4 µrad. For the red distribution the numbers are slightly worse and amount to δα

_{x}= 7.0 µrad and δα

_{y}= 7.4 µrad, respectively.

## 5. Summary and conclusions

8. J. Caron, Y. Durand, J.-L. Bézy, and R. Meynart, “Performance modeling for A-SCOPE: a space-borne lidar measuring atmospheric CO2,” Proc. SPIE **7479**, 74790E, 74790E-15 (2009). [CrossRef]

9. C. Kiemle, M. Quatrevalet, G. Ehret, A. Amediek, A. Fix, and M. Wirth, “Sensitivity studies for a space-based methane lidar mission,” Atmos. Meas. Tech. **4**(10), 2195–2211 (2011). [CrossRef]

## Acknowledgments

## References and links

1. | A. Fix, “Tunable light sources for lidar applications,” in: |

2. | M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. |

3. | EN ISO 11670:2003, |

4. | A. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE |

5. | A. Fix, C. Büdenbender, M. Wirth, M. Quatrevalet, A. Amediek, C. Kiemle, and G. Ehret, “Optical parametric oscillators and amplifiers for airborne and spaceborne active remote sensing of CO2 and CH4,” Proc. SPIE |

6. | P. Groß, L. Kleinschmidt, S. Beer, and C. Fallnich, “Beam position stabilization for a confocal multiphoton microscope,” Appl. Opt. |

7. | W. J. Riley, |

8. | J. Caron, Y. Durand, J.-L. Bézy, and R. Meynart, “Performance modeling for A-SCOPE: a space-borne lidar measuring atmospheric CO2,” Proc. SPIE |

9. | C. Kiemle, M. Quatrevalet, G. Ehret, A. Amediek, A. Fix, and M. Wirth, “Sensitivity studies for a space-based methane lidar mission,” Atmos. Meas. Tech. |

**OCIS Codes**

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(140.3295) Lasers and laser optics : Laser beam characterization

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: February 8, 2013

Revised Manuscript: April 12, 2013

Manuscript Accepted: April 16, 2013

Published: April 25, 2013

**Citation**

Andreas Fix and Christian Stöckl, "Investigations on the beam pointing stability of a pulsed optical parametric oscillator," Opt. Express **21**, 10720-10730 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10720

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### References

- A. Fix, “Tunable light sources for lidar applications,” in: Atmospheric Physics U. Schumann, ed., Research Topics in Aerospace (Springer, 2012).
- M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys.8(10), 1151–1161 (2007). [CrossRef]
- EN ISO 11670:2003, Lasers and Laser-Related Equipment – Test Methods for Laser Beam Parameters – Beam Positional Stability (ISO, 2003).
- A. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE54(2), 221–230 (1966). [CrossRef]
- A. Fix, C. Büdenbender, M. Wirth, M. Quatrevalet, A. Amediek, C. Kiemle, and G. Ehret, “Optical parametric oscillators and amplifiers for airborne and spaceborne active remote sensing of CO2 and CH4,” Proc. SPIE8182, 818206, 818206-10 (2011). [CrossRef]
- P. Groß, L. Kleinschmidt, S. Beer, and C. Fallnich, “Beam position stabilization for a confocal multiphoton microscope,” Appl. Opt.50(28), 5361–5368 (2011). [CrossRef] [PubMed]
- W. J. Riley, Handbook of Frequency Stability Analysis NIST Special Publication 1065, (National Institute of Standards and Technology, Boulder, CO, 2008).
- J. Caron, Y. Durand, J.-L. Bézy, and R. Meynart, “Performance modeling for A-SCOPE: a space-borne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E, 74790E-15 (2009). [CrossRef]
- C. Kiemle, M. Quatrevalet, G. Ehret, A. Amediek, A. Fix, and M. Wirth, “Sensitivity studies for a space-based methane lidar mission,” Atmos. Meas. Tech.4(10), 2195–2211 (2011). [CrossRef]

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