Abstract

A novel fly’s eye homogenizer for single mode laser diodes is presented. This technology overcomes the speckle problem that has been unavoidable for fly’s eye homogenizers used with coherent light sources such as single mode laser diodes. Temporal and spatial coherence are reduced simultaneously by introducing short pulse driving of the injection current and a staircase element. Speckle has been dramatically reduced to 5% from 87% compared to a conventional system and a uniform laser line illumination was obtained by the proposed fly’s eye homogenizer with a single mode UV-blue laser diode for the first time. A new spatial coherence function was mathematically formulated to model the proposed system and was applied to a partially coherent intensity formula that was newly developed in this study from Wolf’s theory to account for the results.

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References

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  1. L. Erdmann, M. Burkhardt, and R. Brunner, “Coherence management for microlens laser beam homogenizers,” Proc. SPIE 4775, 145–154 (2002).
    [Crossref]
  2. M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).
  3. F. Wippermann, U. Zeitner, P. Dannberg, A. Bräuer, and S. Sinzinger, “Beam homogenizers based on chirped microlens arrays,” Opt. Express 15(10), 6218–6231 (2007).
    [Crossref] [PubMed]
  4. P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
    [Crossref]
  5. F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).
  6. K. Petermann, Laser Diode Modulation and Noise (Kluwer, 1988).
    [Crossref]
  7. J. W. Goodman, Statistical Optics (John Wiley & Sons, 2000).
  8. R. A. Shore, B. J. Thompson, and R. E. Whitney, “Diffraction by apertures illuminated with partially coherent light,” J. Opt. Soc. Am. 56(6), 733–738 (1966).
    [Crossref]
  9. A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15(1), 187–188 (1967).
    [Crossref]
  10. M. Born and E. Wolf, Principles of Optics, 7th ed. (McGraw-Hill, 1968).
  11. Y. Mizuyama, R. Leto, and N. Harrison, “A new fly’s eye homogenizer for single mode laser,” Proc. SPIE 8429, 842915 (2012).
    [Crossref]
  12. A. Büttner and U. D. Zeitner, “Wave optical analysis of light-emitting diode beam shaping using microlens arrays,” Opt. Eng. 41(10), 2393–2401 (2002).
    [Crossref]

2012 (1)

Y. Mizuyama, R. Leto, and N. Harrison, “A new fly’s eye homogenizer for single mode laser,” Proc. SPIE 8429, 842915 (2012).
[Crossref]

2010 (1)

M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).

2007 (1)

2005 (1)

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

2002 (2)

A. Büttner and U. D. Zeitner, “Wave optical analysis of light-emitting diode beam shaping using microlens arrays,” Opt. Eng. 41(10), 2393–2401 (2002).
[Crossref]

L. Erdmann, M. Burkhardt, and R. Brunner, “Coherence management for microlens laser beam homogenizers,” Proc. SPIE 4775, 145–154 (2002).
[Crossref]

1967 (1)

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15(1), 187–188 (1967).
[Crossref]

1966 (1)

Bollanti, S.

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (McGraw-Hill, 1968).

Bräuer, A.

Brunner, R.

L. Erdmann, M. Burkhardt, and R. Brunner, “Coherence management for microlens laser beam homogenizers,” Proc. SPIE 4775, 145–154 (2002).
[Crossref]

Burkhardt, M.

L. Erdmann, M. Burkhardt, and R. Brunner, “Coherence management for microlens laser beam homogenizers,” Proc. SPIE 4775, 145–154 (2002).
[Crossref]

Büttner, A.

A. Büttner and U. D. Zeitner, “Wave optical analysis of light-emitting diode beam shaping using microlens arrays,” Opt. Eng. 41(10), 2393–2401 (2002).
[Crossref]

Dannberg, P.

Di Lazzaro, P.

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

Dickey, F. M.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

Erdmann, L.

L. Erdmann, M. Burkhardt, and R. Brunner, “Coherence management for microlens laser beam homogenizers,” Proc. SPIE 4775, 145–154 (2002).
[Crossref]

Felici, G.

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

Goodman, J. W.

J. W. Goodman, Statistical Optics (John Wiley & Sons, 2000).

Harrison, N.

Y. Mizuyama, R. Leto, and N. Harrison, “A new fly’s eye homogenizer for single mode laser,” Proc. SPIE 8429, 842915 (2012).
[Crossref]

Holswade, S. C.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

Leto, R.

Y. Mizuyama, R. Leto, and N. Harrison, “A new fly’s eye homogenizer for single mode laser,” Proc. SPIE 8429, 842915 (2012).
[Crossref]

Lindlein, N.

M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).

Mizuyama, Y.

Y. Mizuyama, R. Leto, and N. Harrison, “A new fly’s eye homogenizer for single mode laser,” Proc. SPIE 8429, 842915 (2012).
[Crossref]

Murra, D.

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

Petermann, K.

K. Petermann, Laser Diode Modulation and Noise (Kluwer, 1988).
[Crossref]

Schell, A. C.

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15(1), 187–188 (1967).
[Crossref]

Shealy, D. L.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

Shore, R. A.

Sinzinger, S.

Tefouet Kana, E.

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

Thompson, B. J.

Voelkel, R.

M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).

Weible, K.

M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).

Whitney, R. E.

Wippermann, F.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (McGraw-Hill, 1968).

Zeitner, U.

Zeitner, U. D.

A. Büttner and U. D. Zeitner, “Wave optical analysis of light-emitting diode beam shaping using microlens arrays,” Opt. Eng. 41(10), 2393–2401 (2002).
[Crossref]

Zimmermann, M.

M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).

IEEE Trans. Antennas Propag. (1)

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15(1), 187–188 (1967).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

A. Büttner and U. D. Zeitner, “Wave optical analysis of light-emitting diode beam shaping using microlens arrays,” Opt. Eng. 41(10), 2393–2401 (2002).
[Crossref]

Opt. Express (1)

Proc. SPIE (4)

P. Di Lazzaro, S. Bollanti, D. Murra, E. Tefouet Kana, and G. Felici, “Flat-top shaped laser beams: reliability of standard parameters,” Proc. SPIE 5777, 705–710 (2005).
[Crossref]

L. Erdmann, M. Burkhardt, and R. Brunner, “Coherence management for microlens laser beam homogenizers,” Proc. SPIE 4775, 145–154 (2002).
[Crossref]

M. Zimmermann, N. Lindlein, R. Voelkel, and K. Weible, “Microlens laser beam homogenizer - from theory to application,” Proc. SPIE 6663, 1–13 (2010).

Y. Mizuyama, R. Leto, and N. Harrison, “A new fly’s eye homogenizer for single mode laser,” Proc. SPIE 8429, 842915 (2012).
[Crossref]

Other (4)

M. Born and E. Wolf, Principles of Optics, 7th ed. (McGraw-Hill, 1968).

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

K. Petermann, Laser Diode Modulation and Noise (Kluwer, 1988).
[Crossref]

J. W. Goodman, Statistical Optics (John Wiley & Sons, 2000).

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Figures (7)

Fig. 1
Fig. 1

Optical layout of proposed despeckling fly’s eye homogenizer. The system has a single mode (TEM00) laser diode, two fly’s eye lenses with N (=4) microlenses with aperture size d and focal length fML, a staircase element with four steps of height h and a field lens with focal length fFL. The laser beam is homogenized in the fast axis (top) and is focused in the slow axis (bottom).

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Fig. 2
Fig. 2

(a) Measured power spectra and (b) computed fringe visibilities for various pulse widths (blue: 1 ns, green: 10 ns,yellow: 100 ns) compared to CW operation (red). Fringe visibility revives at the multiple of 2nLDL = 5.5 mm optical path difference corresponding to the measured free spectral range of c/(2nLDL)= 55 GHz. Here nLD and L are the refractive index of the laser diode material and the laser cavity length, respectively.

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Fig. 3
Fig. 3

Logarithmic close-up plot of Fig. 2(b). The abscissa is normalized by the unit optical path difference corresponding to a single step height. Circles show the degree of coherence corresponding to each step difference.

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Fig. 4
Fig. 4

Far field intensity of the input beam measured by a CCD camera and cross section plots showing the Gaussian mode for both axes. The fast axis was used for homogenization while the slow axis was focused by the field lens.

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Fig. 5
Fig. 5

CCD camera images and the integral row data. (a) 1 ns driving without staircase element, (b) CW driving without staircase, (c) – (f) CW, 100 ns, 10 ns and 1 ns with staircase. The insets are magnified images showing the detail structure of the speckle. The numbers in the figure denote the average local speckle contrasts.

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Fig. 6
Fig. 6

Spatial coherence functions γ(y′, y″) at the second microlens array for proposed despeckling fly’s eye system versus normalized coordinate of y″.

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Fig. 7
Fig. 7

(a) Computational results of the intensity at the image plane z = z2 for the proposed despeckling fly’s eye homogenizer with various laser driving conditions (1, 10, 100 ns and CW) versus coherent intensity indicated as Dirichlet2. Horizontal axis is normalized by the flat-top width dfFL / fML, (b) Close-up plot versus relative position normalized by the speckle period λfFL / d. The numbers in the legend are the local speckle contrast in the center.

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Equations (12)

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𝒟 N ( y ) = sin ( N y π / p ) / sin ( y π / p ) ,
𝒫 ( ν ) = ∑ m = 0 N 0 − 1 I m π δ ν / 2 ( ν − ν 0 + m d ν ) 2 + ( δ ν / 2 ) 2
𝒱 ( τ ) = A exp [ − π δ ν | τ | ] ∑ m = 0 N 0 − 1 I m exp [ − 2 π i ( ν 0 − m d ν ) τ ]
γ ( y ′ , y ″ ) = { γ 1 ( y ″ ) , 0 < y ′ / d < 1 γ 2 ( y ″ ) , 1 < y ′ / d < 2 γ 3 ( y ″ ) , 2 < y ′ / d < 3 γ 4 ( y ″ ) , 3 < y ′ / d < 4
( γ 1 , γ 2 , γ 3 , γ 4 ) = { ( g 0 , g 1 , g 2 , g 3 ) , 0 < y ″ / d < 1 ( g 1 , g 0 , g 1 , g 2 ) , 1 < y ″ / d < 2 ( g 2 , g 1 , g 0 , g 1 ) , 2 < y ″ / d < 3 ( g 3 , g 2 , g 1 , g 0 ) , 3 < y ″ / d < 4
g m = { 1 , m = 0 𝒱 ( ( n ST − 1 ) m h ) , m = 1 , ⋯ , 3 .
I pc ( y ; z ) = 1 λ z ∫ 𝒜 u ( y ′ ) u * ( y ″ ) γ ( y ′ , y ″ ) e − i k ( y ′ − y ″ ) y / z d y ′ d y ″
I pc ( y 2 ; z 2 ) = 1 λ f FL ∫ 0 d u ( y 1 ′ ; z 1 ) e − i k y 1 ′ y 2 / f FL d y 1 ′ ∫ − ∞ ∞ u * ( y 1 ″ , z 1 ) γ 1 ( y 1 ″ ) e i k y 1 ″ y 2 / f FL d y 1 ″ + ⋯ = 1 λ f FL ∫ − ∞ ∞ u ( y 1 ′ , z 1 ) rect ( y 1 ′ − d 2 d ) e − i k y 1 ′ y 2 / f FL d y 1 ′ ∫ − ∞ ∞ u * ( y 1 ″ , z 1 ) γ 1 ( y 1 ″ ) e i k y 1 ″ y 2 / f FL d y 1 ″ + ⋯ = 1 λ f FL ∑ m = 1 N ℱ f FL [ u ( y 1 ′ , z 1 ) rect ( y 1 ′ − ( m − 1 2 ) d d ) ] ( ℱ f FL [ u ( y 1 ″ , z 1 ) γ m ( y 1 ″ ) ] ) * ,
rect ( ξ ) = { 1 , | ξ | < 1 / 2 1 / 2 , | ξ | = 1 / 2 0 , otherwise
T ML ( y ) = ∑ m = 1 N rect ( y − ( m − 1 2 ) d d ) e − i k { y − ( m − 1 2 ) d } 2 / ( 2 f ML ) .
u 0 − ( y 0 ) = A e − ( y 0 − 2 d ) 2 / σ 2 u 0 + ( y 0 ) = u 0 − ( y 0 ) T ML y 0 u 1 − ( y 1 ) = e i k y 1 2 / ( 2 f ML ) ℱ f ML [ u 0 + ( y 0 ) T ML ( y 0 ) e i k y 0 2 / ( 2 f ML ) ] u 1 + ( y 1 ) = u 1 − ( y 1 ) T ML ( y 1 )
u ( y 1 , z 1 ) = u 1 + ( y 1 ) e i k y 1 2 / ( 2 f FL ) .

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