Abstract

We propose a new technique for laser beam shaping into a desirable beam profile by using a laser amplifier with a pump beam that has a modified intensity profile. We developed the analytical formula, which describes the transformation of the seed beam into the desired beam profile in a four level amplifiers small signal regime. We propose a numerically method to obtain the required pump intensity profile in the case where high pump power saturated the laser crystal or for three level materials. The theory was experimentally verified by one dimensionally shaping a Gaussian shaped seed into a Flat-Top beam in a Ho:YLF amplifier pumped by a Tm:YLF laser with a HG01 intensity profile.

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References

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  1. F. M. Dickey and S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, Inc., 2000).
  2. I. A. Litvin, “Implementation of intra-cavity beam shaping technique to enhance pump efficiency,” J. Mod. Opt. 59(3), 241–244 (2012).
    [Crossref]
  3. I. A. Litvin and A. Forbes, “Gaussian mode selection with intracavity diffractive optics,” Opt. Lett. 34(19), 2991–2993 (2009).
    [Crossref] [PubMed]
  4. H. J. Strauss, D. Preussler, M. J. D. Esser, W. Koen, C. Jacobs, O. J. P. Collett, and C. Bollig, “330 mJ single-frequency Ho:YLF slab amplifier,” Opt. Lett. 38(7), 1022–1024 (2013).
    [Crossref] [PubMed]
  5. Z. Xiang, D. Wang, S. Pan, Y. Dong, Z. Zhao, T. Li, J. Ge, C. Liu, and J. Chen, “Beam quality improvement by gain guiding effect in end-pumped Nd:YVO₄ laser amplifiers,” Opt. Express 19(21), 21060–21073 (2011).
    [Crossref] [PubMed]
  6. A. E. Siegman, Lasers (University Science Books, 1986), pp. 292–293.
  7. I. A. Litvin and O. J. P. Collett, “Beam shaping with a laser amplifier,” Proc. SPIE 8960, 89601N (2014).
    [Crossref]
  8. C. Czeranowsky, “Resonatorinterne Frequenzverdopplung von diodengepumpten Neodym-Lasern mit hohen Ausgangsleistungen im blauen Spektralbereich,” PhD thesis, University of Hamburg (2002).
  9. B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772 (1998).
    [Crossref]
  10. M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B 93(2-3), 269–316 (2008).
    [Crossref]
  11. W. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988).
    [Crossref]
  12. S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, “The digital laser,” arXiv:1301.4760.
  13. D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
    [Crossref]
  14. H. J. Strauss, M. J. D. Esser, G. King, and L. Maweza, “Tm:YLF slab wavelength-selected laser,” Opt. Mater. Express 2(8), 1165–1170 (2012).
    [Crossref]

2014 (1)

I. A. Litvin and O. J. P. Collett, “Beam shaping with a laser amplifier,” Proc. SPIE 8960, 89601N (2014).
[Crossref]

2013 (1)

2012 (2)

I. A. Litvin, “Implementation of intra-cavity beam shaping technique to enhance pump efficiency,” J. Mod. Opt. 59(3), 241–244 (2012).
[Crossref]

H. J. Strauss, M. J. D. Esser, G. King, and L. Maweza, “Tm:YLF slab wavelength-selected laser,” Opt. Mater. Express 2(8), 1165–1170 (2012).
[Crossref]

2011 (2)

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Z. Xiang, D. Wang, S. Pan, Y. Dong, Z. Zhao, T. Li, J. Ge, C. Liu, and J. Chen, “Beam quality improvement by gain guiding effect in end-pumped Nd:YVO₄ laser amplifiers,” Opt. Express 19(21), 21060–21073 (2011).
[Crossref] [PubMed]

2009 (1)

2008 (1)

M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B 93(2-3), 269–316 (2008).
[Crossref]

1998 (1)

B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772 (1998).
[Crossref]

1988 (1)

Aït-Ameur, K.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Barnes, N. P.

B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772 (1998).
[Crossref]

Bollig, C.

Cagniot, E.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Chen, J.

Collett, O. J. P.

Di Bartolo, B.

B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772 (1998).
[Crossref]

Dong, Y.

Eichhorn, M.

M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B 93(2-3), 269–316 (2008).
[Crossref]

Esser, M. J. D.

Forbes, A.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

I. A. Litvin and A. Forbes, “Gaussian mode selection with intracavity diffractive optics,” Opt. Lett. 34(19), 2991–2993 (2009).
[Crossref] [PubMed]

Fromager, M.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Ge, J.

Godin, T.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Jacobs, C.

King, G.

Koen, W.

Li, T.

Litvin, I. A.

I. A. Litvin and O. J. P. Collett, “Beam shaping with a laser amplifier,” Proc. SPIE 8960, 89601N (2014).
[Crossref]

I. A. Litvin, “Implementation of intra-cavity beam shaping technique to enhance pump efficiency,” J. Mod. Opt. 59(3), 241–244 (2012).
[Crossref]

I. A. Litvin and A. Forbes, “Gaussian mode selection with intracavity diffractive optics,” Opt. Lett. 34(19), 2991–2993 (2009).
[Crossref] [PubMed]

Liu, C.

Maweza, L.

Naidoo, D.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Pan, S.

Passilly, N.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Preussler, D.

Risk, W.

Strauss, H. J.

Walsh, B. M.

B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772 (1998).
[Crossref]

Wang, D.

Xiang, Z.

Zhao, Z.

Appl. Phys. B (1)

M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B 93(2-3), 269–316 (2008).
[Crossref]

J. Appl. Phys. (1)

B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772 (1998).
[Crossref]

J. Mod. Opt. (1)

I. A. Litvin, “Implementation of intra-cavity beam shaping technique to enhance pump efficiency,” J. Mod. Opt. 59(3), 241–244 (2012).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284(23), 5475–5479 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Opt. Mater. Express (1)

Proc. SPIE (1)

I. A. Litvin and O. J. P. Collett, “Beam shaping with a laser amplifier,” Proc. SPIE 8960, 89601N (2014).
[Crossref]

Other (4)

C. Czeranowsky, “Resonatorinterne Frequenzverdopplung von diodengepumpten Neodym-Lasern mit hohen Ausgangsleistungen im blauen Spektralbereich,” PhD thesis, University of Hamburg (2002).

F. M. Dickey and S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, Inc., 2000).

A. E. Siegman, Lasers (University Science Books, 1986), pp. 292–293.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, “The digital laser,” arXiv:1301.4760.

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Figures (10)

Fig. 1
Fig. 1 Energy levels diagram of Nd:YVO4 (four level system) [5].
Fig. 2
Fig. 2 (a) A schematic of beam shaping by a laser amplifier where 1 is the seed beam profile, 2 is the output beam profile and 3 is the pump beam profile. (b) The simulated upper laser level population density (n2) along the z-axis of an 0.2% Nd:YVO4 amplifier for different pump powers and pump and seed beam radii of 1.5 mm. For 20 W incident pump, the zero order solution (red dashed) as well as the solution of Eq. (2) without assumption on the population density (solid lines) are shown. For 40 W incident pump, both the zero (black dashed) and the first order (green dashed) solutions are shown.
Fig. 3
Fig. 3 The analytical and numerically simulated outputs of a 0.2% Nd:YVO4 amplifier pumped with a super-Gaussian pump profile and seeded with a Gaussian seed profile.
Fig. 4
Fig. 4 Conversion of a Gaussian seed beam (red dashed) to a super-Gaussian beam of order 6 (black dashed). The required pump beam (green dashed) was calculated using Eq. (5). The actual shaped-output beam (solid red trace) was calculated with a standard algorithm [11] for the solution of Eqs. (1a)–(1c).
Fig. 5
Fig. 5 (a) Improvement of the output beam contrast by increased amplification of the seed (calculated using the numerical technique). (b) The efficiency of the amplification and transformation of the Gaussian beam into a Super-Gaussian beam of order 6 for different powers of the seed beam. The red point corresponds to the amplification presented in the Fig. 5(a). (c) Beam shaping of a Gaussian beam using an LG03 pump beam in an amplifier.
Fig. 6
Fig. 6 The numerical result (a) and 3rd order polynomial fit (b) of the amplification with a 5 cm, 0.2% doped Ho:YLF gain medium.
Fig. 7
Fig. 7 (a) The numerical result of the amplification and reshaping of a Gaussian seed beam into a 6th order Super–Gaussian by a (a) 5 cm (0.5%) Yb:YAG rod and (b) a 5 cm (0.2%) Ho:YLF rod by implementing a 3rd order polynomial emulator.
Fig. 8
Fig. 8 The schematic of beam quality improving in the slab laser where OC is the output coupler; CLV is the cylindrical lens which effect on vertical direction; HR is the high reflection mirror.
Fig. 9
Fig. 9 (a-c) The experimentally obtained intensity profiles of the beam emitted by corresponding laser crystals (see a1-c1 (photos of the mounted corresponding laser crystals)). (d) Experimental setup of a Tm:YLF(c1) beam shaping laser (1.885 μm) pumping a Ho:LiLuF seed laser (b1) with 45W and an Ho:YLF (a1) amplifier with 35W and the seed co-aligned to the 1.885 μm beam into the amplifier ; where (1) laser diode 0.808 μm, (2) polarizing beam splitter, (3) beam dump, (4) beam shaping lens for pump, (5) beam splitter HT for pump (0.808 μm) and HR for 1.885 μm, (6) lens, (7) HR mirror for 1.885 μm, (8) 85% output coupler, (9) HR mirror for 2.073 μm, (10) fold mirror HT for 1.885 μm and HR for 2.073 μm, (11) 95% output coupler for 2.073μm, (12) HR mirror for 2.073 μm, (13) f = 200 mm lens and (14) f = 105 mm lens.
Fig. 10
Fig. 10 (a) Measured 2D beam profiles of the transformation of a Gaussian seed beam (red) into a Flat-Top beam (blue) in an amplifier being pumped by a lobe shaped pump beam (black). (b) The 1D numerical simulation of such a transformation and (c) the centroid profile of the experimental results as shown in Fig. 10(a).

Tables (1)

Tables Icon

Table 1 Some of the optical properties of Nd:YVO4, Ho:YLF and Yb:YAG [8–10].

Equations (7)

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I p ( r,z ) z =- σ a n 1 ( r,z ) I p ( r,z ),
I s ( r,z ) z = σ e n 2 ( r,z ) I S ( r,z ),
n 2 ( r,z ) t = σ a n 1 ( r,z ) I p ( r,z ) h ν p - σ e n 2 ( r,z ) I S ( r,z ) h ν p - n 2 ( r,z ) τ 2 ,
σ a I p ( r,z ) h ν p ( n tot n 2 ( r,z ) )= n 2 ( r,z ) τ 2 ,
n 2 0 ( z )= I p ( z 0 ) n tot σ a τ 2 h ν p e σ a n tot z + σ a τ 2 I p ( z 0 ) .
I s ( r,L )= I s ( r,z 0 )+ I s ( r,z 0 ) σ e σ a ( L n tot σ a +log[ h ν p + τ 2 σ a I p ( r, z 0 ) h ν p e L n tot σ a + τ 2 σ a I p ( r, z 0 ) ] ),
I p ( r, z 0 )= e L n tot σ a + σ a σ e + e L n tot σ a + σ a I s ( r,L ) σ e I s ( r,z 0 ) e L n tot σ a + σ a σ e e σ a I s ( r,L ) σ e I s ( r,z 0 ) h ν p τ 2 σ a .

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