## Narrow-band coherent Rayleigh scattering in a flame

Optics Express, Vol. 14, Issue 8, pp. 3461-3466 (2006)

http://dx.doi.org/10.1364/OE.14.003461

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### Abstract

We report on the application of coherent Rayleigh scattering (CRS) to the measurement of temperature in a flame using narrow bandwidth pump and probe fields. High resolution measurements of the line shape were used to derive flame temperature based on fits to the line shape. An uncertainty in the temperature of 3 % was determined utilizing a CRS model that includes scattering from a multi-component gas for the first time. This model was validated at room temperature for a mixture of atomic and molecular species.

© 2006 Optical Society of America

## 1. Introduction

## 2. Coherent Rayleigh scattering

*E*

_{1}(

*x*,

*t*) and

*E*

_{2}(

*x*,

*t*) and frequencies

*ω*

_{1}and

*ω*

_{2}interfere within the sample to produce an interference pattern. The interaction of the periodic intensity profile with the polarizability of the gas species gives rise to a periodic electrostrictive force that perturbs the spatial velocity distribution of particles moving close to the velocity

*υ*= Ω/q. The beat frequency of the electric field is given by Ω =

*ω*

_{1}-

*ω*

_{2}, and q=∣

**k**

_{1}-

**k**

_{2}∣ is the wave vector of the induced grating, where

**k**

_{1}and

**k**

_{2}are the wave vectors of pump beam 1 and 2, respectively. The CRS signal is produced by phase-matched scattering from this volume density grating that moves at the same speed. The magnitude of the perturbation at each beat frequency (velocity) is proportional to the square of the density at that frequency (velocity) in the distribution function. The intensity of the scattered CRS signal is proportional to [5

5. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. **85**, 1222–1225 (2000). [CrossRef] [PubMed]

*L*is the interaction length,

*I*

_{1},

*I*

_{2}and

*I*

_{3}are the intensities of pump beam 1, pump beam 2 and the probe beam respectively. In CRS, we operate in a regime where essentially no collisions occur during the interaction. In this limit the perturbation to the velocity distribution function to each species in a mixture is independent and thus the total induced density perturbation for

*n*species is given by

*δf*is the perturbation to the velocity distribution function

_{i}*f*

_{0,i}for each species density

*ρ*. The variation of

_{i}*δρ*with velocity, and therefore beat frequency, determines the spectral profile of the scattered light. In this work, the importance of collisions to the spectral profile is quantified by the

*y*parameter, which compares the molecular collision time with the grating vector and is defined as [7

7. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh Brillouin scattering,” Phys. Rev. Lett. **89**(18), 183001(4) (2002) [CrossRef] [PubMed]

*k*is the Boltzmann constant and τ is the molecular collision time at temperature

_{b}*T*. In the collisionless limit where

*y*≪ 1, the perturbation for each species is calculated from the one-dimensional, collisionless Boltzmann equation [6

6. X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. **27**, 161–163 (2002). [CrossRef]

*f*=

*δf*+

*f*. When

_{0}*δf*≪

_{i}*f*

_{0,i}, the perturbation for each species is given by [5

5. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. **85**, 1222–1225 (2000). [CrossRef] [PubMed]

*α*is the polarizability of each species and

_{i}*E*

_{1}and

*E*

_{2}are the amplitudes of the pump fields. Using Eq. (1), (2) and (4) the spectral profile of CRS can be modeled for multi-component gases. This enables CRS to be applied to more complex environments, such as flames, when the main constituents and their respective mass and polarizabilities are known.

## 3. Experiment and analysis

*y*parameter of approximately 0.02. We show results in Fig. 2 for mixtures of nitrogen and xenon. Although pure Xe and N

_{2}have near-Gaussian spectral profiles, the line shape of the mixtures cannot be approximated by a simple Gaussian because they have very different masses. For these and other mixtures, very good agreement with the model was found [9]. This allows us to model CRS spectral profiles from a flame when the major species fractions are known.

_{2}.

## 4. Conclusions

_{2}mixtures allowing temperature measurement of a butane flame modeled as a three species high temperature gas. Although the collisionless approximation is valid for y ≪ 1 there is not a clear physical interpretation for the exact y value in which the model will no longer accurately predict the spectral profile. For our experiments there was no measurable difference between our spectra and the simulations which assume collisionless conditions for y < 0.035. However, we stress that this is not an upper limit and further work is required to establish this limit for the spectral resolution of our experiments. We have found that, providing the major species are known and

*y*< 0.035, this technique can be applied to multi-component flows and to flames where the stoichiometry is not well known. The use of narrowband laser sources for the pump and probe beams has been demonstrated for the first time. For typical energies used in CRS, the use of narrowband pumps creates larger density perturbations for a particular velocity group and therefore we have found higher signal-to-noise ratios when compared to broadband CRS [5–7

5. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. **85**, 1222–1225 (2000). [CrossRef] [PubMed]

10. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh Brillouin scattering in molecular gases.” Phys. Rev. A **69**, 033814 (2004). [CrossRef]

11. P. Ewart, “A modeless, variable bandwidth, tuneable laser,” Opt. Commun. **55**, 124–126 (1985). [CrossRef]

## Acknowledgments

## References and links

1. | R. B. Miles and W. R. Lempert “Quantitative flow visualization in unseeded flows,” Annu. Rev. Fluid Mech. |

2. | R. W. Pitz, R. Cattolica, F. Robben, and L. Talbot, “Temperature and density in a hydrogen-air flame from Rayleigh scattering,” Comb. Flame |

3. | G. S. Elliot and T. J. Beutner, “Molecular filter based Doppler velocimetry,” Prog. Aero. Sci. |

4. | J. N. Forkey, W. R. Lempert, and R. B. Miles, “Accuracy limits for planar measurements of flow field velocity, temperature and density using filtered Rayleigh scattering.,” Exp. Fluids |

5. | J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. |

6. | X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. |

7. | X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh Brillouin scattering,” Phys. Rev. Lett. |

8. | M. N. Shneider, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 (personal communication, 2005). |

9. | H. T. Bookey, A. I. Bishop, M. N. Shneider, and P. F. Barker, School of Engineering and Physical Sciences, David Brewster Building, Heriot Watt University, Edinburgh are preparing a manuscript to be called “Narrow-band coherent Rayleigh scattering.” |

10. | X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh Brillouin scattering in molecular gases.” Phys. Rev. A |

11. | P. Ewart, “A modeless, variable bandwidth, tuneable laser,” Opt. Commun. |

**OCIS Codes**

(120.6780) Instrumentation, measurement, and metrology : Temperature

(190.1900) Nonlinear optics : Diagnostic applications of nonlinear optics

(280.2470) Remote sensing and sensors : Flames

(290.5870) Scattering : Scattering, Rayleigh

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 23, 2005

Revised Manuscript: April 6, 2006

Manuscript Accepted: April 10, 2006

Published: April 17, 2006

**Citation**

Henry T. Bookey, Alexis I. Bishop, and P. F. Barker, "Narrow-band coherent Rayleigh scattering in a flame," Opt. Express **14**, 3461-3466 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3461

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### References

- K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966). [CrossRef]
- S. D. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD Lattice," IEEE Trans. Antennas Propag. 44, 1630-1639 (1996), and references therein. [CrossRef]
- M. Okoniewski, M. Mrozowski, and M. A. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microwave Guid. Wave Lett. 7, 121-123 (1997), and references therein. [CrossRef]
- A. S. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1998). [CrossRef]
- Y. Huang, "Simulation of semiconductor material using FDTD method," Master Thesis, Northwestern University, June 2002. https://depot.northwestern.edu/yhu234/publish/YYHMS.pdf [CrossRef] [PubMed]
- S. Chang, Y. Huang, G. Chang, and S. T. Ho, "THz all-optical shutter based on semiconductor transparency switching by two optical π-pulses," OSA Annual Meeting, TuY3, Long Beach, CA, 2001. [CrossRef]
- S. T. Ho, research notes, 1998-1999. [CrossRef] [PubMed]
- Y. Huang, "Simulation of semiconductor structure using FDTD method", presented to the Physics Department at Northwestern University, 15 Jan. 2002.
- W. W. Chow, S. Koch, and M. SargentIII, Semiconductor-Laser Physics, (Springer Verlag, Berlin, 1994).
- J. Piprek, Optoelectronic Devices: Advanced Simulation and Analysis, (Springer Verlag, New York, 2005). [CrossRef]
- S. Park, "Development of InGaAsP/InP single-mode lasers using microring resonators for photonic integrated circuits," PhD Thesis, Northwestern University, Dec. 2000, and references therein. [CrossRef]
- Y. Huang and S. T. Ho, "A numerically efficient semiconductor model with Fermi-Dirac thermalization dynamics (band-filling) for FDTD simulation of optoelectronic and photonic devices," 2005 Technical Digest of the Annual Conference on Lasers and Electro-Optics, Paper QTuD7, Baltimore, MD, May 2005.
- S. T. Ho, P. Kumar, and J. H. Shapiro, "Quantum theory of nondegenerate multiwave mixing (I) - General formulation," Phys. Rev. A 37, 2017-2032 (1988).
- S. T. Ho and P. Kumar, "Quantum optics in a dielectric: Macroscopic electromagnetic-field and medium operators for a linear dispersive Lossy medium-A microscopic derivation of the operators and their commutation relations," J. Opt. Soc. Am. B 10, 1620-1636 (1993).
- S. T. Ho, P. Kumar, and J. H. Shapiro, "Vector-field quantum model of degenerate four-wave mixing," Phys. Rev. A 34, 293-303 (July 1986).
- J. J. Sakurai, Advanced Quantum Mechanics, (Addison Wesley, 1967).
- in semiconductor corresponds to the spatially localized operator.
- W. H. Louisell, Quantum Statistical Properties of Radiation, (Wiley-Interscience, New York, 1990).
- For example, if three upper levels can decay to a single ground level, then each upper level will be associated with a transition dipole so that the total number of dipoles involved will be three, which is equal to the number of the upper levels.
- R. F. Kazarinov, C. H. Henry, and R. A. Logan, "Longitudinal mode self-stabilization in semicondcutor lasers," J. Appl. Phys. 53, 4631-4644 (1982).
- S. Marrin, B. Deveaud, F. Clerot, K. Fuliwara, and K. Mitsunaga, "Capture of photoexcited carriers in a single quantum well with different confinement structures," IEEE J. Quantum Electron. 27, 1669-1675 (1991).
- L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, (Wiley, John & Sons. 1995).
- J. L. Oudar, D. Hulin, A. Migus, A. Antonetti, and F. Alexandre, "Subpicosecond spectral hole burning due to nonthermalized photoexcited carriers in GaAs," Phys. Rev. Lett. 55, 2074-2077 (1985).
- D. Y. Chu, M. K. Chin, S. Z. Xu, T. Y. Chang, and S. T. Ho, "1.5 µm InGaAs/InAlGaAs Quantum-well microdisk lasers," IEEE Photon. Technol. Lett. 5, 1353-1355 (1993).
- W. Fang, J. Y. Xu, A. Yamilov, H. Cao, Y. Ma, S. T. Ho, and G. S. Solomon, "Large enhancement of spontaneous emission rates of InAs quantum dots in GaAs microdisks," Opt. Lett. 27, 948-950 (2002).
- J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, "Photonic-wire laser," Phys. Rev. Lett. 75, 2678-2681 (1995).

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