## Coupled simulation of chemical lasers based on intracavity partially coherent light model and 3D CFD model |

Optics Express, Vol. 19, Issue 27, pp. 26295-26307 (2011)

http://dx.doi.org/10.1364/OE.19.026295

Acrobat PDF (1306 KB)

### Abstract

Coupled simulation based on intracavity partially coherent light model and 3D CFD model is firstly achieved in this paper. The dynamic equation of partially coherent intracavity field is derived based on partially coherent light theory. A numerical scheme for the coupled simulation as well as a method for computing the intracavity partially coherent field is given. The presented model explains the formation of the sugar scooping phenomenon, and enables studies on the dependence of the spatial mode spectrum on physical parameters of laser cavity and gain medium. Computational results show that as the flow rate of iodine increases, higher order mode components dominate in the partially coherent field. Results obtained by the proposed model are in good agreement with experimental results.

© 2011 OSA

## 1. Introduction

9. B. D. Barmashenko, “Analysis of lasing in chemical oxygen-iodine lasers with unstable resonators using a geometric-optics model,” Appl. Opt. **48**(13), 2542–2550 (2009). [CrossRef] [PubMed]

10. D. Yu, F. Sang, Y. Jin, and Y. Sun, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. **41**(10), 2668–2674 (2002). [CrossRef]

3. G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, and P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. **32**(9), 1525–1536 (1996). [CrossRef]

12. D. A. Copeland and A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. **29**(9), 2525–2539 (1993). [CrossRef]

3. G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, and P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. **32**(9), 1525–1536 (1996). [CrossRef]

13. B. Barmashenko, D. Furman, and S. Rosenwaks, “Analysis of lasing in gas-flow lasers with stable resonators,” Appl. Opt. **37**(24), 5697–5705 (1998). [CrossRef] [PubMed]

13. B. Barmashenko, D. Furman, and S. Rosenwaks, “Analysis of lasing in gas-flow lasers with stable resonators,” Appl. Opt. **37**(24), 5697–5705 (1998). [CrossRef] [PubMed]

_{2}dissociation mechanism assumptions [15

15. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Comparing modeling and measurements of the output power in chemical oxygen-iodine lasers: a stringent test of I2 dissociation mechanisms,” J. Chem. Phys. **133**(8), 084301 (2010). [CrossRef] [PubMed]

_{2}dissociation mechanism assumptions. As shown in [13

13. B. Barmashenko, D. Furman, and S. Rosenwaks, “Analysis of lasing in gas-flow lasers with stable resonators,” Appl. Opt. **37**(24), 5697–5705 (1998). [CrossRef] [PubMed]

17. A. E. Siegman and E. A. Sziklas, “Mode calculations in unstable resonators with flowing saturable gain. 1:hermite-gaussian expansion,” Appl. Opt. **13**(12), 2775–2791 (1974). [CrossRef] [PubMed]

18. E. A. Sziklas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt. **14**(8), 1874–1889 (1975). [CrossRef] [PubMed]

19. M. Endo, M. Kawakami, K. Nanri, S. Takeda, and T. Fujioka, “Two-dimensional simulation of an unstable resonator with a stable core,” Appl. Opt. **38**(15), 3298–3307 (1999). [CrossRef] [PubMed]

20. A. Bhowmik, “Closed-cavity solutions with partially coherent fields in the space-frequency domain,” Appl. Opt. **22**(21), 3338–3346 (1983). [CrossRef] [PubMed]

19. M. Endo, M. Kawakami, K. Nanri, S. Takeda, and T. Fujioka, “Two-dimensional simulation of an unstable resonator with a stable core,” Appl. Opt. **38**(15), 3298–3307 (1999). [CrossRef] [PubMed]

22. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A **3**(1), 76–85 (1986). [CrossRef]

## 2. Motion equation of partially coherent light inside loaded stable cavity

22. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A **3**(1), 76–85 (1986). [CrossRef]

*N*dimension,

*n*stands for

*N*ordered positive integers

17. A. E. Siegman and E. A. Sziklas, “Mode calculations in unstable resonators with flowing saturable gain. 1:hermite-gaussian expansion,” Appl. Opt. **13**(12), 2775–2791 (1974). [CrossRef] [PubMed]

2. D. A. Copeland, C. Warner, and A. H. Bauer, “Simple model for optical extraction from a flowing oxygen-iodine medium using a Fabry-Perot resonator,” Proc. SPIE **1224**, 474–499 (1990). [CrossRef]

3. G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, and P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. **32**(9), 1525–1536 (1996). [CrossRef]

## 3. Numerical methods

### 3.1 Numerical scheme of the coupled simulation

### 3.2 Computation method of intracavity partially coherent fields

_{1}and the reflecting mirror M

_{2}are located at plane

_{1}and M

_{2}are

17. A. E. Siegman and E. A. Sziklas, “Mode calculations in unstable resonators with flowing saturable gain. 1:hermite-gaussian expansion,” Appl. Opt. **13**(12), 2775–2791 (1974). [CrossRef] [PubMed]

_{2},

_{2}, the expansion coefficients will keep unchanged, as

_{1}with transmissivity

## 4. Calculation and discussion

_{1}and a spherical total reflector M

_{2}. The cavity length is

_{1}is

_{2}is 10.0 m. The aperture is a rectangle with side lengths of

*x*axis. Flow conditions for CFD calculation are listed in Table 1 . And the chemical reactions used in simulation can be found in [7

7. M. Endo, T. Masuda, and T. Uchiyama, “Development of hybrid simulation for supersonic chemical oxygen-iodine laser,” AIAA J. **45**(1), 90–97 (2007). [CrossRef]

**13**(12), 2775–2791 (1974). [CrossRef] [PubMed]

2. D. A. Copeland, C. Warner, and A. H. Bauer, “Simple model for optical extraction from a flowing oxygen-iodine medium using a Fabry-Perot resonator,” Proc. SPIE **1224**, 474–499 (1990). [CrossRef]

**32**(9), 1525–1536 (1996). [CrossRef]

26. G. F. Calvo, A. Picon, and R. Zambrini, “Measuring the complete transverse spatial mode spectrum of a wave field,” Phys. Rev. Lett. **100**(17), 173902 (2008). [CrossRef] [PubMed]

27. F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes,” Opt. Lett. **23**(13), 989–991 (1998). [CrossRef] [PubMed]

^{−5}rad and 8.7 × 10

^{−5}rad, respectively. Divergence angle (in the y direction) predicted by the proposed model is 9 mrad. Such a huge difference among the models is caused by the following reason. In the Fabry-Perot model and the roof-top model, curvatures of the cavity mirrors are neglected. Divergence of the beam is mainly caused by the diffraction of the aperture and the ununiformity of the active media. The diffraction limited divergence angle is characterized by

28. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-Cavity laser,” IEEE J. Quantum Electron. **29**(4), 1212–1217 (1993). [CrossRef]

28. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-Cavity laser,” IEEE J. Quantum Electron. **29**(4), 1212–1217 (1993). [CrossRef]

19. M. Endo, M. Kawakami, K. Nanri, S. Takeda, and T. Fujioka, “Two-dimensional simulation of an unstable resonator with a stable core,” Appl. Opt. **38**(15), 3298–3307 (1999). [CrossRef] [PubMed]

20. A. Bhowmik, “Closed-cavity solutions with partially coherent fields in the space-frequency domain,” Appl. Opt. **22**(21), 3338–3346 (1983). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgments

## References and links

1. | E. A. Duff and K. A. Truesdell, “Chemical oxygen iodine laser (COIL) technology and development,” Proc. SPIE |

2. | D. A. Copeland, C. Warner, and A. H. Bauer, “Simple model for optical extraction from a flowing oxygen-iodine medium using a Fabry-Perot resonator,” Proc. SPIE |

3. | G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, and P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. |

4. | T. J. Madden, “Aspects of 3D chemical oxygen-iodine laser simulation,” Proc. SPIE |

5. | R. C. Buggeln, S. Shamroth, A. Lampson, and P. G. Crowell, “Three-dimensional (3-D) Navier-Stokes analysis of the mixing and power extraction in a supersonic chemical oxygen iodine laser (COIL) with transverse I |

6. | J. Paschkewitz, J. Shang, J. Miller, and T. Madden, “An assessment of COIL physical property and chemical kinetic modeling methodologies,” presented at 31st AIAA Plasmadynamics and Lasers Conference, Denver, CO, 19–22 June, 2000. |

7. | M. Endo, T. Masuda, and T. Uchiyama, “Development of hybrid simulation for supersonic chemical oxygen-iodine laser,” AIAA J. |

8. | A. I. Lampson, D. N. Plummer, J. Erkkila, and P. G. Crowell, “Chemical oxygen iodine laser (COIL) beam quality predictions using 3-d Navier-Stokes (MINT) and wave optics (OCELOT) codes,” presented at 29th AIAA Plasmadynamics and Lasers Conference, Albuquerque, NM, 15–18 June, 1998. |

9. | B. D. Barmashenko, “Analysis of lasing in chemical oxygen-iodine lasers with unstable resonators using a geometric-optics model,” Appl. Opt. |

10. | D. Yu, F. Sang, Y. Jin, and Y. Sun, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. |

11. | M. Suzuki, H. Matsueda, and W. Masuda, “Numerical simulation of Q-switched supersonic flow chemical oxygen-iodine laser by solving time-dependent paraxial wave equation,” JSME Int. J. Ser. B |

12. | D. A. Copeland and A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. |

13. | B. Barmashenko, D. Furman, and S. Rosenwaks, “Analysis of lasing in gas-flow lasers with stable resonators,” Appl. Opt. |

14. | T. T. Yang, “Modeling of cw HF chemical lasers with rotational nonequilibrium,” J. Phys. |

15. | K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Comparing modeling and measurements of the output power in chemical oxygen-iodine lasers: a stringent test of I2 dissociation mechanisms,” J. Chem. Phys. |

16. | A. G. Fox and T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. |

17. | A. E. Siegman and E. A. Sziklas, “Mode calculations in unstable resonators with flowing saturable gain. 1:hermite-gaussian expansion,” Appl. Opt. |

18. | E. A. Sziklas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt. |

19. | M. Endo, M. Kawakami, K. Nanri, S. Takeda, and T. Fujioka, “Two-dimensional simulation of an unstable resonator with a stable core,” Appl. Opt. |

20. | A. Bhowmik, “Closed-cavity solutions with partially coherent fields in the space-frequency domain,” Appl. Opt. |

21. | L. Mandel and E. Wolf, |

22. | E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A |

23. | M. Hishida, N. Azami, K. Iwamoto, W. Masuda, H. Fujii, T. Atsutu, and M. Muro, “Flow and optical fields in a supersonic flow chemical oxygen-iodine laser,” presented at 28th Plasmadynamics and Lasers Conference, Atlanta, GA, 23–25 June, 1997. |

24. | Y. Huai, S. Jia, and Y. Jin, “Analysis and optimization of mixing process with large eddy simulation: An application to SCOIL,” presented at 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, TX, 22–25 June, 2009. |

25. | M. Guizar-Sicairos and J. C. Gutiérrez-Vera, “Coupled mode competition in unstable resonators using the exact cavity equations of motion with dynamic gain,” J. Opt. B Quantum Semiclassical Opt. |

26. | G. F. Calvo, A. Picon, and R. Zambrini, “Measuring the complete transverse spatial mode spectrum of a wave field,” Phys. Rev. Lett. |

27. | F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes,” Opt. Lett. |

28. | A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-Cavity laser,” IEEE J. Quantum Electron. |

29. | K. Shimizu and S. Yoshida, “High power chemical oxygen-iodine laser of good beam quality,” in |

30. | J. Bachar and S. Rosenwaks, “An efficient, small scale chemical oxygen-iodine laser,” Appl. Phys. Lett. |

31. | F. Sang, C. Gu, J. Pang, M. Li, F. Li, Y. Sun, Y. Jin, and Q. Zhuang, “Experimental study of a cw chemical oxygen-iodine laser,” High Power Laser Part. Beams |

**OCIS Codes**

(140.0140) Lasers and laser optics : Lasers and laser optics

(140.1550) Lasers and laser optics : Chemical lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: September 26, 2011

Revised Manuscript: November 11, 2011

Manuscript Accepted: November 11, 2011

Published: December 9, 2011

**Citation**

Kenan Wu, Ying Huai, Shuqin Jia, and Yuqi Jin, "Coupled simulation of chemical lasers based on intracavity partially coherent light model and 3D CFD model," Opt. Express **19**, 26295-26307 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26295

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### References

- E. A. Duff and K. A. Truesdell, “Chemical oxygen iodine laser (COIL) technology and development,” Proc. SPIE5414, 52–68 (2004). [CrossRef]
- D. A. Copeland, C. Warner, and A. H. Bauer, “Simple model for optical extraction from a flowing oxygen-iodine medium using a Fabry-Perot resonator,” Proc. SPIE1224, 474–499 (1990). [CrossRef]
- G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, and P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron.32(9), 1525–1536 (1996). [CrossRef]
- T. J. Madden, “Aspects of 3D chemical oxygen-iodine laser simulation,” Proc. SPIE5120, 363–375 (2003). [CrossRef]
- R. C. Buggeln, S. Shamroth, A. Lampson, and P. G. Crowell, “Three-dimensional (3-D) Navier-Stokes analysis of the mixing and power extraction in a supersonic chemical oxygen iodine laser (COIL) with transverse I2 injection,” presented at 25th AIAA Plasmadynamics and Lasers Conference, Colorado Springs, CO, 20–23 June, 1994.
- J. Paschkewitz, J. Shang, J. Miller, and T. Madden, “An assessment of COIL physical property and chemical kinetic modeling methodologies,” presented at 31st AIAA Plasmadynamics and Lasers Conference, Denver, CO, 19–22 June, 2000.
- M. Endo, T. Masuda, and T. Uchiyama, “Development of hybrid simulation for supersonic chemical oxygen-iodine laser,” AIAA J.45(1), 90–97 (2007). [CrossRef]
- A. I. Lampson, D. N. Plummer, J. Erkkila, and P. G. Crowell, “Chemical oxygen iodine laser (COIL) beam quality predictions using 3-d Navier-Stokes (MINT) and wave optics (OCELOT) codes,” presented at 29th AIAA Plasmadynamics and Lasers Conference, Albuquerque, NM, 15–18 June, 1998.
- B. D. Barmashenko, “Analysis of lasing in chemical oxygen-iodine lasers with unstable resonators using a geometric-optics model,” Appl. Opt.48(13), 2542–2550 (2009). [CrossRef] [PubMed]
- D. Yu, F. Sang, Y. Jin, and Y. Sun, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng.41(10), 2668–2674 (2002). [CrossRef]
- M. Suzuki, H. Matsueda, and W. Masuda, “Numerical simulation of Q-switched supersonic flow chemical oxygen-iodine laser by solving time-dependent paraxial wave equation,” JSME Int. J. Ser. B49, 1212–1219 (2006).
- D. A. Copeland and A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron.29(9), 2525–2539 (1993). [CrossRef]
- B. Barmashenko, D. Furman, and S. Rosenwaks, “Analysis of lasing in gas-flow lasers with stable resonators,” Appl. Opt.37(24), 5697–5705 (1998). [CrossRef] [PubMed]
- T. T. Yang, “Modeling of cw HF chemical lasers with rotational nonequilibrium,” J. Phys.C9, 51–57 (1980).
- K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Comparing modeling and measurements of the output power in chemical oxygen-iodine lasers: a stringent test of I2 dissociation mechanisms,” J. Chem. Phys.133(8), 084301 (2010). [CrossRef] [PubMed]
- A. G. Fox and T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J.40, 453–488 (1961).
- A. E. Siegman and E. A. Sziklas, “Mode calculations in unstable resonators with flowing saturable gain. 1:hermite-gaussian expansion,” Appl. Opt.13(12), 2775–2791 (1974). [CrossRef] [PubMed]
- E. A. Sziklas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt.14(8), 1874–1889 (1975). [CrossRef] [PubMed]
- M. Endo, M. Kawakami, K. Nanri, S. Takeda, and T. Fujioka, “Two-dimensional simulation of an unstable resonator with a stable core,” Appl. Opt.38(15), 3298–3307 (1999). [CrossRef] [PubMed]
- A. Bhowmik, “Closed-cavity solutions with partially coherent fields in the space-frequency domain,” Appl. Opt.22(21), 3338–3346 (1983). [CrossRef] [PubMed]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A3(1), 76–85 (1986). [CrossRef]
- M. Hishida, N. Azami, K. Iwamoto, W. Masuda, H. Fujii, T. Atsutu, and M. Muro, “Flow and optical fields in a supersonic flow chemical oxygen-iodine laser,” presented at 28th Plasmadynamics and Lasers Conference, Atlanta, GA, 23–25 June, 1997.
- Y. Huai, S. Jia, and Y. Jin, “Analysis and optimization of mixing process with large eddy simulation: An application to SCOIL,” presented at 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, TX, 22–25 June, 2009.
- M. Guizar-Sicairos and J. C. Gutiérrez-Vera, “Coupled mode competition in unstable resonators using the exact cavity equations of motion with dynamic gain,” J. Opt. B Quantum Semiclassical Opt.7(9), 253–263 (2005). [CrossRef]
- G. F. Calvo, A. Picon, and R. Zambrini, “Measuring the complete transverse spatial mode spectrum of a wave field,” Phys. Rev. Lett.100(17), 173902 (2008). [CrossRef] [PubMed]
- F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes,” Opt. Lett.23(13), 989–991 (1998). [CrossRef] [PubMed]
- A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-Cavity laser,” IEEE J. Quantum Electron.29(4), 1212–1217 (1993). [CrossRef]
- K. Shimizu and S. Yoshida, “High power chemical oxygen-iodine laser of good beam quality,” in Lasers '89; Proceedings of the International Conference (STS Press, 1990), pp. 218—222.
- J. Bachar and S. Rosenwaks, “An efficient, small scale chemical oxygen-iodine laser,” Appl. Phys. Lett.41(1), 16–17 (1982). [CrossRef]
- F. Sang, C. Gu, J. Pang, M. Li, F. Li, Y. Sun, Y. Jin, and Q. Zhuang, “Experimental study of a cw chemical oxygen-iodine laser,” High Power Laser Part. Beams5, 389–393 (1993) (In Chinese).

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