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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26295–26307
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Coupled simulation of chemical lasers based on intracavity partially coherent light model and 3D CFD model

Kenan Wu, Ying Huai, Shuqin Jia, and Yuqi Jin  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26295-26307 (2011)
http://dx.doi.org/10.1364/OE.19.026295


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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

Both geometrical optics and wave optics models have been applied for the optical computation of COIL [9

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]

11

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 49, 1212–1219 (2006).

]. For the study of unstable cavities, numerous models faithfully preserve the cavity geometry [8

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.

10

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]

]. In cases of stable resonators, however, the Fabry-Perot cavity and the roof-top cavity are often used as the approximation model [3

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

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]

14

14. T. T. Yang, “Modeling of cw HF chemical lasers with rotational nonequilibrium,” J. Phys. C9, 51–57 (1980).

]. The Fabry-Perot model was successful in estimating the output power and the chemical efficiency with respect to the outcoupling rate and the flow condition. However, certain difficulty arises when using the Fabry-Perot model to predict the intensity pattern. The upstream-downstream optical coupling effect in COIL with stable cavity, known as the sugar scooping phenomenon, cannot be explained by the Fabry-Perot model [3

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

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]

-14

14. T. T. Yang, “Modeling of cw HF chemical lasers with rotational nonequilibrium,” J. Phys. C9, 51–57 (1980).

]. In order to simulate this phenomenon, Yang adopted the roof-top cavity model which forces the optical field to flip as it is reflected by one of the mirrors [14

14. T. T. Yang, “Modeling of cw HF chemical lasers with rotational nonequilibrium,” J. Phys. C9, 51–57 (1980).

]. Hence, both the Fabry-Perot model and the roof-top model change the geometry of cavity mirrors and obscure the optical mechanism of the device. Another model, namely the constant intracavity intensity model, assumes the intracavity intensity to be uniformly distributed over the resonator cross section [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]

]. Recently this model was coupled with 3D CFD model of the gas flow under various I2 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]

]. The predicted output power results were compared with experimental results to examine the I2 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]

] the constant intracavity intensity model predicts accurate value of the output power from a stable resonator. However, it neglects the optical propagating mechanism and therefore cannot give reliable information about the output intensity distribution and divergence angle.

It should be noted that many iterative methods based on Fourier optics, including the Fox-Li method [16

16. A. G. Fox and T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

], the Hermite-Gaussian expansion method [17

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]

] and the Fast Fourier transform method [18

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]

], work well for unstable resonators which oscillate only at the lowest transverse mode. However, if these methods are directly used on stable resonators with very large Fresnel numbers, the propagating wave expands and converges repetitively making the computational convergence difficult [19

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]

]. A stable cavity of COIL is often with large Fresnel number (>500) and many transverse modes oscillating simultaneously. Bhowmik noticed the partially coherent nature of the fields, and developed an improved Fox-Li type iteration by starting with a random noise distribution [20

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

]. The random noise distribution was supposed to represent the partially coherence field which could fill the cavity width during whole propagation inside the cavity. This method leads to a quasi-steady solution and the final optical intensity is statistically averaged among many rounds. Later Endo developed Bhowmik’s method to two-dimensional cases [19

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]

]. These studies demonstrate the partial coherent nature of the oscillating field and provide a better understanding of the oscillating process. Therefore, a more formalized representation of intracavity field of stable cavities with large Fresnel numbers based on the partially coherent theory, and the coupled computational study of the partially coherent optical field and the chemical reacting flow field are expected.

In this paper, the dynamic equation of the partially coherent intracavity field is established based on the partially coherent light theory [21

21. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

,22

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]

], a numerical method for solving the equation is given, and a numerical scheme for the optical-fluidic-chemical coupled computation is discussed. To our knowledge, a coupled simulation based on the intracavity partially coherent light model and a 3D CFD model is achieved for the first time. The coupled simulation provides critical information about COIL operation and reveals the influence of operational parameters on the formation of the partially coherent beam.

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

According to the partially coherent light theory [22

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]

], a stationary optical field of any state of coherence can be represented as an ensemble of monochromatic wave fields. Each member of the ensemble is in the form of
U(r)=nanϕn(r),
(1)
where ϕn(r) are eigenfunctions of the Helmholtz equation, r is the Cartesian coordinates of N dimension, n stands for N ordered positive integers (n1,n2,,nN), and an are some random variables obeying the relationship

an*am=|an|2δmn.
(2)

In this paper where loaded stable cavities are studied, three dimensional Cartesian coordinates are established with z axis along the optical axis. And the intracavity partially coherent field consists of the {U(ρ,z)} ensemble, where ρ=(x,y) denotes the transverse coordinates. U(ρ,z) is expanded in the transverse plane and expressed as
U(ρ,z)=nan(z)ϕn(ρ,z),
(3)
where ϕn(ρ,z) are chosen to be the Hermite-Gaussian modes of bare cavity so that they satisfy the orthonormalized relationship [17

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]

]

ϕn*(ρ,z)ϕn(ρ,z)dρ=δnn.
(4)

Intensity of the partially coherent field is expressed as the average intensity of the ensemble members, and by using Eq. (3) and Eq. (2), equals the uncorrelated superposition of the Hermite-Gaussian modes:

I(ρ,z)=|U(ρ,z)|2=nλn(z)|ϕn(ρ,z)|2.
(5)

Here λn(z)=an*(z)an(z). We will deduct the motion equation to which the expansion coefficients {λn(z)} yield for loaded stable cavities. In the following part of this paper, λn(z) of the forward propagating intracavity field, λn(z) of the backward propagating intracavity field and λn(z) of the output field are written as λn+(z), λn(z) and λnout(z), respectively, if discrimination among them is necessary.

Let us consider the forward propagating field U(ρ,z) along axis z in loaded cavities with gain distribution g(ρ,z). U(ρ,z) is governed by the paraxial wave equation
[ρ22ik(z12g(ρ,z))]U(ρ,z)=0,
(6)
where ρ2 is the transverse Laplacian and k is the wave number. Substituting Eq. (3) into Eq. (6) and using the orthogonality relationship [Eq. (4)], and noticing ϕn(ρ,z) which represents the bare cavity mode satisfies
[ρ22ikz]ϕn(ρ,z)=0,
(7)
the equations for the expansion coefficients an(z) are obtained as
zan(z)12nGnn(z)an(z)=0,
(8)
where Gnn(z) is given by
Gnn(z)=ϕn*(ρ,z)g(ρ,z)ϕn(ρ,z)dρ.
(9)
With some further algebra on Eq. (8) we obtain
z[an(z)an*(z)]12nRe[Gnn(z)an*(z)an(z)]=0,
(10)
where Re() denotes the real part of a complex. By having ensemble average on both sides of Eq. (10) and noticing that Gnn<<Gnn for all nn, the motion equation of the forward propagating partially coherent light inside the loaded stable cavity is given by

zλn+(z)λn+(z)Re(Gnn(z))=0.
(11)

We consider Gnn<<Gnn for all nn because in practical chemical lasers, the loaded gain is a slowly varying function with its value near the threshold gain [2

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

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]

]. And from the orthonormalized relationship [Eq. (4)] it can be seen that as the gain distribution g(ρ,z) tends to a uniform distribution the Gnn approaches to zero.

Similarly, the motion equation of the backward propagating partially coherent field is given by

zλn(z)+λn(z)Re(Gnn(z))=0.
(12)

Equations (11), (12) and (5) constitute the equations for describing the intracavity partially coherent fields of loaded stable cavities and are coupled with a 3D CFD based dynamic gain model in this study.

3. Numerical methods

3.1 Numerical scheme of the coupled simulation

The motion equations given in Sec. 2 are working together with a 3D CFD model to perform the coupled simulation of the operational mechanisms of COIL. The schematic of the computation process is shown in Fig. 1
Fig. 1 Schematic of the coupled computation process.
. The coupled numerical simulation of intracavity partially coherent light and supersonic flowing chemical reacting media is achieved with an iterative process with the optical computation and the CFD computation executed in turns and providing intermittent data to each other. The CFD computation provides the gain distribution for the optical computation, and the optical computation returns the optical intensity to the CFD codes. This process is repeated until both the gain and the intensity converge to a steady distribution.

3.2 Computation method of intracavity partially coherent fields

Assuming the cavity length is L. The outcoupling mirror M1 and the reflecting mirror M2 are located at plane z=z1 and plane z=z2, respectively. The radii of curvature of mirror M1 and M2 are R1 and R2, respectively. For solving Eqs. (11), (12), and (5), the Hermite-Gaussian modes {ϕn(ρ,z)} are firstly computed based on the following formulas [17

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]

]
ϕn(ρ,z)=ϕn1(x,z)ϕn2(y,z),
(13)
ϕn1(x,z)=[Q*(z)n1Q(z)]1/22xω(z)ϕn11(x,z)(n11n1)1/2Q*(z)Q(z)ϕn12(x,z),
(14)
ϕ0(x,z)=(2π)1/4[1ω0Q(z)]1/2exp[jkx22q(z)],
(15)
ϕ1(x,z)=[Q*(z)Q(z)]1/2[2xω(z)]ϕ0(x,z).
(16)
And ϕn2(y,z) has equations similar to Eqs. (14)-(16) but just replacing n1 with n2 and x with y. The complex radius of curvature q(z) and the Q(z) factor are given by
1q=1R(z)jλπω2(z),
(17)
q(z)=q(z0)+zz0,
(18)
Q(z)=q(z)/q(z0),
(19)
where R(z) and ω(z) are the wave front radius and spot radius at plane z, respectively. ω0=ω(z0) is the spot radius at the reference plane z=z0.

Generally, when the mode ϕn(ρ,z) given by Eqs. (13)-(19) is reflected by a spherical mirror, e.g. by M2, q(z) and Q(z) of the reflected mode will change into q(z) and Q(z), respectively, according to
1q(z2)=1q(z2)2R2,
(20)
q(z)=q(z2)z+z2,
(21)
and

Q(z)=q(z)q(z2)Q(z2).
(22)

Thus the reflected modes need to be computed again. However, by setting the reference plane z=z0and the q(z0) according to Eqs. (23)-(25), we have q(z)=q(z) and Q(z)=Q(z). Under this condition, the modes satisfy the self-consistency criteria of the cavity. It means that the forward and backward propagating modes have exactly the same profile and can both be expressed by Eqs. (13)-(19). It provides convenience for numerical realization since these modes keep unchanged after reflection and therefore need to be computed only once:

ω02=λπ[(R1L)(R2L)(R1+R2L)L(R1+R22L)2]1/2
(23)
z0=zM1+(R2L)LR1+R22L
(24)
q(z0)=jπω02λ
(25)

After the modes {ϕn(ρ,z)} are calculated, computation of intracavity fields can be accomplished by simulating the back and forth propagating, like the Fox-Li method. However, since the field of interest is partially coherent, the propagating should start with a randomly chosen set of λn+(z0) at the reference plane z=z0. From Eq. (5) we know that this set contains information about the intensity of each mode contained in the initializing field. Expansion coefficients {λn+(z)} of the forward propagating field are computed by solving the motion equation [Eq. (11)]. When the field is reflected by the mirror M2, the expansion coefficients will keep unchanged, as

λn(z2)=λn+(z2).
(26)

Expansion coefficients {λn(z)} of the backward propagating field are computed by solving Eq. (12). And when the field arrives at the outcoupling mirror M1 with transmissivity α, the expansion coefficients of the reflected field is
λn+(z1)=(1α)λn(z1),
(27)
while the expansion coefficients of the output field is

λnout(z1)=αλn(z1).
(28)

Note that in solving Eq. (11) and Eq. (12), the gain distribution g(ρ,z) is needed for calculating Gnn(z), and this is supported by the CFD computation. When the expansion coefficients {λn+(z)}, {λn(z)} and {λnout(z1)} are obtained, the corresponding forward propagating, backward propagating and output field intensity can be computed via Eq. (5). The two-way intracavity intensity (summation of forward and backward intensity) is then given back to the CFD codes to update the gain data g(ρ,z) and therefore forms a close-loop coupled simulation.

4. Calculation and discussion

From Eqs. (15)-(17) we know that the spot size of the fundamental Hermite-Gaussian mode on the reference plane is ω0=0.0997 mm. And the reference plane is located at the output plane z=z1=0 . A practical question is how many modes are needed in computation. We determine the minimum amount of modes by ensuring the expansion basis {ϕn(ρ,z)} cover the whole aperture region. For the nxth order 1D Hermite-Gaussian mode, its plot exhibits a quasi-periodic behavior with nx zero crossings, and the function amplitude falls to zero very rapidly outside the point x=nxω [17

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]

]. Therefore, the number of modes that must be involved in computation is estimated by
nxmaxω0ax.
(29)
And for the same reason we have

nymaxω0ay.
(30)

Results of the proposed model are compared with results of the Fabry-Perot approximation model, the roof-top model, and the experiment. The calculated output power of the proposed model, the Fabry-Perot model and the roof-top model are 1516 W, 1490 W and 1551 W, respectively. The experimentally measured output power is 1530 W. The calculated output power of the proposed model is in good agreement with the experimental result. And all three models predict close values of the output power.

The calculated intensity distributions of the Fabry-Perot model and the roof-top model are displayed in Fig. 7
Fig. 7 Calculated intensity distribution by (a) the Fabry-Perot model and (b) the roof-top model.
. In our experiment, the output intensity was measured by the moving-pinhole method. Because the lasing lasts just a few seconds, only 1D measurement was made. The measured output intensity along x axis is shown in Fig. 8
Fig. 8 Comparison of intensity distribution along x axis. (a) The experimental result. (b) The proposed model. (c) The Fabry-Perot model. (d) The roof-top model.
together with computational results obtained by the proposed model, the Fabry-Perot model and the roof-top model. Generally, the Fabry-Perot model cannot express the downstream peak phenomenon, and the roof-top model leads to a result with too high intensity value at the upstream and downstream edges. The filled factor, defined as the average intensity divided by the maximum intensity, is adopted to give a quantitative assessment of the intensity uniformity. The filled factors predicted by the proposed model, the Fabry-Perot model and the roof-top model are 0.304, 0.110 and 0.232, respectively. The experimental measured filled factor is 0.327. Therefore, the filled factor predicted by the proposed model is in good agreement with the experimental result.

5. Conclusion

Acknowledgments

This work is supported by National Nature Science Foundation of China with the project “Numerical investigation of the coupled flow-optics interaction in supersonic gas chemical lasers” (20903087).

References and links

1.

E. A. Duff and K. A. Truesdell, “Chemical oxygen iodine laser (COIL) technology and development,” Proc. SPIE 5414, 52–68 (2004). [CrossRef]

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]

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T. J. Madden, “Aspects of 3D chemical oxygen-iodine laser simulation,” Proc. SPIE 5120, 363–375 (2003). [CrossRef]

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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.

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. 45(1), 90–97 (2007). [CrossRef]

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. 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]

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 49, 1212–1219 (2006).

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]

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]

14.

T. T. Yang, “Modeling of cw HF chemical lasers with rotational nonequilibrium,” J. Phys. C9, 51–57 (1980).

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]

16.

A. G. Fox and T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

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]

21.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

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]

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.

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25.

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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]

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30.

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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 5, 389–393 (1993) (In Chinese).

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

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