Abstract

Laser beam quality metrics like M2 can be used to describe the spot sizes and propagation behavior of a wide variety of non-ideal laser beams. However, for beams that have been diffracted by limiting apertures in the near-field, or those with unusual near-field profiles, the conventional metrics can lead to an inconsistent or incomplete description of far-field performance. This paper motivates an alternative laser beam quality definition that can be used with any beam. The approach uses a consideration of the intrinsic ability of a laser beam profile to heat a material. Comparisons are made with conventional beam quality metrics. An analysis on an asymmetric Gaussian beam is used to establish a connection with the invariant beam propagation ratio.

© 2012 OSA

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Errata

Harold C. Miller, "A laser beam quality definition based on induced temperature rise: erratum," Opt. Express 21, 5635-5635 (2013)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-5-5635

References

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  1. A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., 17, OSA Trends in Optics and Photonics (OSA, 1998), paper MQ1.
  2. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett.36(14), 2686–2688 (2011).
    [CrossRef] [PubMed]
  3. J. M. Slater and B. Edwards, “Characterization of high power lasers,” Proc. SPIE7686, 76860W, 76860W-12 (2010).
    [CrossRef]
  4. M. Lax, “Temperature rise induced by a laser beam,” J. Appl. Phys.48(9), 3919–3924 (1977).
    [CrossRef]
  5. M. Lax, “Temperature rise induced by a laser beam II. the nonlinear case,” Appl. Phys. Lett.33(8), 786–788 (1978).
    [CrossRef]
  6. Y. Lu, “Square-shaped temperature distribution induced by a Gaussian-shaped laser beam,” Appl. Surf. Sci.81(3), 357–364 (1994).
    [CrossRef]
  7. Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
    [CrossRef]
  8. J. E. Moody and R. H. Hendel, “Temperature profiles induced by a scanning cw laser beam,” J. Appl. Phys.53(6), 4364–4371 (1982).
    [CrossRef]
  9. International Standards Organization, “Lasers and laser-related equipment-test methods for laser beam widths, divergence angles and beam propagation ratios. part 2: general astigmatic beams,” Ref. ISO 11146–2:2005(E) (2005).

2011

2010

J. M. Slater and B. Edwards, “Characterization of high power lasers,” Proc. SPIE7686, 76860W, 76860W-12 (2010).
[CrossRef]

1994

Y. Lu, “Square-shaped temperature distribution induced by a Gaussian-shaped laser beam,” Appl. Surf. Sci.81(3), 357–364 (1994).
[CrossRef]

1982

J. E. Moody and R. H. Hendel, “Temperature profiles induced by a scanning cw laser beam,” J. Appl. Phys.53(6), 4364–4371 (1982).
[CrossRef]

1980

Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
[CrossRef]

1978

M. Lax, “Temperature rise induced by a laser beam II. the nonlinear case,” Appl. Phys. Lett.33(8), 786–788 (1978).
[CrossRef]

1977

M. Lax, “Temperature rise induced by a laser beam,” J. Appl. Phys.48(9), 3919–3924 (1977).
[CrossRef]

Augst, S. J.

Edwards, B.

J. M. Slater and B. Edwards, “Characterization of high power lasers,” Proc. SPIE7686, 76860W, 76860W-12 (2010).
[CrossRef]

Fan, T. Y.

Gibbons, J. F.

Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
[CrossRef]

Gold, R. B.

Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
[CrossRef]

Goldizen, K. C.

Hendel, R. H.

J. E. Moody and R. H. Hendel, “Temperature profiles induced by a scanning cw laser beam,” J. Appl. Phys.53(6), 4364–4371 (1982).
[CrossRef]

Lax, M.

M. Lax, “Temperature rise induced by a laser beam II. the nonlinear case,” Appl. Phys. Lett.33(8), 786–788 (1978).
[CrossRef]

M. Lax, “Temperature rise induced by a laser beam,” J. Appl. Phys.48(9), 3919–3924 (1977).
[CrossRef]

Lietoila, A.

Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
[CrossRef]

Lu, Y.

Y. Lu, “Square-shaped temperature distribution induced by a Gaussian-shaped laser beam,” Appl. Surf. Sci.81(3), 357–364 (1994).
[CrossRef]

Moody, J. E.

J. E. Moody and R. H. Hendel, “Temperature profiles induced by a scanning cw laser beam,” J. Appl. Phys.53(6), 4364–4371 (1982).
[CrossRef]

Murphy, D. V.

Nissim, Y. I.

Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
[CrossRef]

Redmond, S. M.

Sanchez, A.

Slater, J. M.

J. M. Slater and B. Edwards, “Characterization of high power lasers,” Proc. SPIE7686, 76860W, 76860W-12 (2010).
[CrossRef]

Yu, C. X.

Appl. Phys. Lett.

M. Lax, “Temperature rise induced by a laser beam II. the nonlinear case,” Appl. Phys. Lett.33(8), 786–788 (1978).
[CrossRef]

Appl. Surf. Sci.

Y. Lu, “Square-shaped temperature distribution induced by a Gaussian-shaped laser beam,” Appl. Surf. Sci.81(3), 357–364 (1994).
[CrossRef]

J. Appl. Phys.

Y. I. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, “Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam,” J. Appl. Phys.51(1), 274–279 (1980).
[CrossRef]

J. E. Moody and R. H. Hendel, “Temperature profiles induced by a scanning cw laser beam,” J. Appl. Phys.53(6), 4364–4371 (1982).
[CrossRef]

M. Lax, “Temperature rise induced by a laser beam,” J. Appl. Phys.48(9), 3919–3924 (1977).
[CrossRef]

Opt. Lett.

Proc. SPIE

J. M. Slater and B. Edwards, “Characterization of high power lasers,” Proc. SPIE7686, 76860W, 76860W-12 (2010).
[CrossRef]

Other

A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., 17, OSA Trends in Optics and Photonics (OSA, 1998), paper MQ1.

International Standards Organization, “Lasers and laser-related equipment-test methods for laser beam widths, divergence angles and beam propagation ratios. part 2: general astigmatic beams,” Ref. ISO 11146–2:2005(E) (2005).

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Figures (2)

Fig. 1
Fig. 1

Calculated PIB curves. The upper curve is for an ideal Airy pattern with its first zero at 1.22λ/D. The lower curve is the PIB of a core-pedestal beam approximated using two Gaussian beams with widths of 0.85 λ/D and 12.2 λ/D. In this example, 25% of the power is in the narrower core beam.

Fig. 2
Fig. 2

Comparison of beam quality definitions versus far-field beam profile. The ideal beam is a Gaussian with a width of 1.0 (in arbitrary units), while the test beam is a core-pedestal beam formed using the sum of two Gaussians with widths of 1.0 (core) and 10.0 (pedestal). The horizontal axis is the fractional power in the core lobe of the test beam. The HBQ threshold power level is 50% and the VBQ bucket radius is arbitrarily set at 1.22. The BQ curve is calculated using Eq. (19).

Equations (28)

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PIB(θ)= 0 2π 0 θ I(θ',φ)θ'dθ'dφ =2π 0 θ I ave (θ')θ'dθ' ,
θ(r)= r f = 2rλ π w 0 D ,
θ(r)= 1.22rλ r 0 D ,
I ave (θ)= 1 2π 0 2π I(θ,φ)dφ .
I ave (θ)= 1 2πθ dPIB(θ) dθ .
ΔT(R,Z,W)=Δ T max N(R,Z,W),
dΔT(R,0,W) dz =0,
N(0,0,)=1.
Δ T max = P 2πκ 1 r ,
1 r = 0 ( 1 r )f(R)rdr ( 0 f(R)rdr ) 1 .
Δ T max = 1 κ 0 I(r)dr ,
2 ΔT(x,y,z)= S(x,y,z) κ ,
ΔT(x,y,z)= 1 2πκ V S(x',y',z')dx'dy'dz' (xx') 2 + (yy') 2 + (zz') 2 ,
S(x',y',z')=αI(x',y',0)exp(αz'),
S(x',y',z')=I(x',y',0)δ(z').
Δ T max =ΔT(0,0,0)= 1 2πκ 0 0 I(x',y')dx'dy' x ' 2 +y ' 2 .
Δ T max = 1 2πκ 0 0 2π I(r,φ)rdrdφ r = 1 κ 0 I ave (r)dr .
BQ= Δ T maxideal Δ T maxmeasured .
BQ= 0 dPIB (θ) ideal θ 0 dPIB (θ) measured θ .
VBQ= PIB ( θ 0 ) ideal PIB ( θ 0 ) meas 0.84 0.26 1.8.
HBQ= θ meas (PI B th ) θ ideal (PI B th ) 5.5 0.5 11.
M eff 2 = M x 2 M y 2 ,
I(x,y)= 2P π x 0 y 0 exp( 2 x 2 x 0 2 )exp( 2 y 2 y 0 2 ),
Δ T max = 2 P π 3 2 κ y 0 K( 1 β 2 ),
BQ= π 2 1 M y 2 K( 1 ( M x 2 M y 2 ) 2 ) ,
η= Δ T maxcircular Δ T maxelliptical = ( π 2 ) β K( 1 β 2 ) ,
BQ=η M x 2 M y 2 .
η= β ideal K( 1 β ideal 2 ) β meas K( 1 β meas 2 ) ,

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