Abstract

This study report a first systematic approach to the selective excitations of all Ince-Gaussian modes (IGMs) in end-pumped solid-state lasers. The proposed Ince-Gaussian mode excitation mechanism is based on the “mode-gain control” concept. This study classifies IGMs into three categories, explores and verifies approach to excite each IGM category using numerical simulation.

© 2007 Optical Society of America

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  1. M. A. Bandres and JulioC. Gutiérrez-Vega, "Ince-Gaussian beams," Opt. Lett. 29144 (2004).
    [CrossRef] [PubMed]
  2. M. A. Bandres and J. C. Gutiérrez-Vega, "Ince-Gaussian modes of the paraxial wave equation and stable resonators," J. Opt. Soc. Am. A 21, 873 (2004).
    [CrossRef]
  3. MiguelA. Bandres, "Elegant Ince-Gaussian beams," Opt. Lett.  29, 1724-1726, August 2004.
    [CrossRef] [PubMed]
  4. Julio C. Gutiérrez-Vega and Miguel A. Bandres, "Ince-Gaussian beam in quadratic index medium," J. Opt. Soc. Am. A,  22, 306, February 2005.
    [CrossRef]
  5. Miguel A. Bandres and J. C. Gutiérrez-Vega, "Ince-Gaussian series representation of the two-dimensional fractional Fourier transform," Opt. Lett. 30, 540, March 2005.
    [CrossRef] [PubMed]
  6. T. Xu and S. Wang, "Propagation of Ince-Gaussian beams in a thermal lens medium," Opt. Commun. 265,1-5 (2006).
    [CrossRef]
  7. U. T. Schwarz, M. A. Bandres and J. C. Gutiérrez-Vega, "Observation of Ince-Gaussian modes in stable resonators," Opt. Lett. 291870 (2004).
    [CrossRef] [PubMed]
  8. K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
    [CrossRef]
  9. T. Ohtomo, K. Kamikariya, K. Otsuka and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15, 10705 (2007).
    [CrossRef] [PubMed]
  10. The Language of Technical Computing, See http://www.mathworks.com/.
  11. 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, 3298 (1999).
    [CrossRef]
  12. M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical Simulation of the W-Axicon type Optical Resonator for Coaxial Slab CO2 Lasers," J. Phys. D 34, 68 (2001).
    [CrossRef]
  13. M. Endo, "Numerical simulation of an optical resonator for generation of a doughnut-like laser beam," Opt. Express 12, 1959 (2004).http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1959
    [CrossRef] [PubMed]
  14. A. Bhowmik, "Closed-cavity solutions with partially coherent fields in the space-frequency domain," Appl. Opt. 22, 3338 (1983).
    [CrossRef] [PubMed]
  15. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004), Chap. 4.
  16. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004) pp.97-101.
  17. A. E. Siegman, Lasers (University Science Books, 1986), pp.295.
  18. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  19. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
    [CrossRef]
  20. W. H. Press, A. S. Teukolsky, W. T. Vetterling and B. P. Flannery, NUMERCAL RECIPES in C++ (Cambridge, 2002), Chap. 10.

2007

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
[CrossRef]

T. Ohtomo, K. Kamikariya, K. Otsuka and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15, 10705 (2007).
[CrossRef] [PubMed]

2006

T. Xu and S. Wang, "Propagation of Ince-Gaussian beams in a thermal lens medium," Opt. Commun. 265,1-5 (2006).
[CrossRef]

2005

2004

2001

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical Simulation of the W-Axicon type Optical Resonator for Coaxial Slab CO2 Lasers," J. Phys. D 34, 68 (2001).
[CrossRef]

1999

1993

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1983

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Bandres, M. A.

Bandres, Miguel A.

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Bhowmik, A.

Chu, S.-C.

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
[CrossRef]

T. Ohtomo, K. Kamikariya, K. Otsuka and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15, 10705 (2007).
[CrossRef] [PubMed]

Endo, M.

Fujioka, T.

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical Simulation of the W-Axicon type Optical Resonator for Coaxial Slab CO2 Lasers," J. Phys. D 34, 68 (2001).
[CrossRef]

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, 3298 (1999).
[CrossRef]

Gutiérrez-Vega, J. C.

Gutiérrez-Vega, Julio C.

Julio, M. A.

Kamikariya, K.

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
[CrossRef]

T. Ohtomo, K. Kamikariya, K. Otsuka and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15, 10705 (2007).
[CrossRef] [PubMed]

Kawakami, M.

Nanri, K.

Nemoto, K.

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
[CrossRef]

Ohtomo, T.

Otsuka, K.

T. Ohtomo, K. Kamikariya, K. Otsuka and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15, 10705 (2007).
[CrossRef] [PubMed]

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
[CrossRef]

Schwarz, U. T.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Takeda, S.

Uchiyama, T.

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical Simulation of the W-Axicon type Optical Resonator for Coaxial Slab CO2 Lasers," J. Phys. D 34, 68 (2001).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
[CrossRef]

Wang, S.

T. Xu and S. Wang, "Propagation of Ince-Gaussian beams in a thermal lens medium," Opt. Commun. 265,1-5 (2006).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Xu, T.

T. Xu and S. Wang, "Propagation of Ince-Gaussian beams in a thermal lens medium," Opt. Commun. 265,1-5 (2006).
[CrossRef]

Yamaguchi, S.

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical Simulation of the W-Axicon type Optical Resonator for Coaxial Slab CO2 Lasers," J. Phys. D 34, 68 (2001).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

J. Phys. D

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical Simulation of the W-Axicon type Optical Resonator for Coaxial Slab CO2 Lasers," J. Phys. D 34, 68 (2001).
[CrossRef]

Jpn. J. Appl. Phys.

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. 46, 5865 (2007).
[CrossRef]

Opt. Commun.

T. Xu and S. Wang, "Propagation of Ince-Gaussian beams in a thermal lens medium," Opt. Commun. 265,1-5 (2006).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Other

W. H. Press, A. S. Teukolsky, W. T. Vetterling and B. P. Flannery, NUMERCAL RECIPES in C++ (Cambridge, 2002), Chap. 10.

MiguelA. Bandres, "Elegant Ince-Gaussian beams," Opt. Lett.  29, 1724-1726, August 2004.
[CrossRef] [PubMed]

The Language of Technical Computing, See http://www.mathworks.com/.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004), Chap. 4.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004) pp.97-101.

A. E. Siegman, Lasers (University Science Books, 1986), pp.295.

Supplementary Material (3)

» Media 1: MOV (169 KB)     
» Media 2: MOV (206 KB)     
» Media 3: MOV (290 KB)     

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Figures (13)

Fig. 1.
Fig. 1.

Some analytical amplitude distributions of the Ince-Gaussian modes

Fig. 2.
Fig. 2.

Diagram of the simulation model of a half-symmetric cavity

Fig. 3.
Fig. 3.

Analytical amplitude distribution of the three categories of IGMs: (a) IGe p,m modes (p≥m>0), (b) IGo p,m modes (p≥m>1) and (c) IGe p,0 and IGo p,1 modes. (Here, the ellipticity parameter ε is 4)

Fig. 4.
Fig. 4.

(a) Relative effective gain region to excite IGe p,m modes with p≥m>0 (b) Transverse phase distribution of these modes

Fig. 5.
Fig. 5.

The resulting stable amplitude distribution in the cavity from simulations with the effective gain region situated according to the parameters in Table 1

Fig. 6.
Fig. 6.

(a) Relative gain region to excite IGo p,m modes with p≥m>1 (b) Transverse phase distribution of these modes

Fig. 7.
Fig. 7.

The resulting stable amplitude distribution in the bar-inserted cavity from simulations with the effective gain region situated according to the parameters of Table 2

Fig. 8.
Fig. 8.

(a) Relative gain region to excite IGe p,0 and IGo p,1 modes (b) Transverse phase distribution of these modes

Fig. 9.
Fig. 9.

The resulting stable amplitude distribution from simulations with the effective gain region controlled according to the parameters of Table 3

Fig. 10.
Fig. 10.

Demonstration of resulting progress of stable amplitude distribution of (a) IGe p,m modes (p≥m>0), (b) IGo p,m modes (p≥m>1) and (c) IGe p,0 modes and IGo p,1 modes. The left-hand side images are simulated spontaneous emissions with partially coherent random fields.

Fig. 11.
Fig. 11.

Movie of resulting progress of stable amplitude distribution of (a) IGe 6,6 mode (122 KB) [Media 1], (b) IGo 7,5 mode (1107 KB) [Media 2] and (c) IGo 5,1 mode(1667 KB) [Media 3]

Fig. 12.
Fig. 12.

Resulting IGMs’ amplitude distribution from simulations while effective gain region are at same off-axis position x=0.8 w0 but different spot sizes: (a) 0.6 w0, (b) 0.4 w0 and (c) 0.2 w0

Fig. 13.
Fig. 13.

The matching factor, MF , of several IGMs to a gain region for IGe 6,2 modes excitation

Tables (3)

Tables Icon

Table 1. Estimated off-axis distance x and size of effective gain region to IGe p,m modes at the crystal in the half-symmetric cavity

Tables Icon

Table 2. Estimated off-axis distance x, y and size of effective gain region to IGo p,m modes at the crystal in the half-symmetric cavity

Tables Icon

Table 3. Estimated off-axis distance y and size of effective gain region to IGe p,0 and IGo p,1 modes at the crystal in the half-symmetric cavity

Equations (10)

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I G e p , m ( r , ε ) = C [ w 0 w ( z ) ] C p m ( i ξ , ε ) C p m ( η , ε ) exp [ r 2 w 2 ( z ) ]
× exp i [ k z + { k r 2 2 R ( z ) } ( p + 1 ) ψ z ( z ) ] ,
I G o p , m ( r , ε ) = S [ w 0 w ( z ) ] S p m ( i ξ , ε ) S p m ( η , ε ) exp [ r 2 w 2 ( z ) ]
× exp i [ k z + { k r 2 2 R ( z ) } ( p + 1 ) ψ z ( z ) ] ,
g i ( x , y ) = g i 0 ( x , y ) ( 1 + I ˜ i + ( x , y ) + I ˜ i ( x , y ) I s ( x , y ) ) ,
I ˜ i + ( x , y ) = ( 1 α ) i = 0 q α i I i + ( q i ) ,
I ˜ i ( x , y ) = ( 1 α ) i = 0 q α i I i ( q i ) .
E i out ( x , y ) = E i in ( x , y ) exp [ 1 2 g i ( x , y ) d ] ,
E q + 1 ( x , y ) E q ( x , y ) .
M F ( ε ) = g , u pm ( ε ) = g × u pm ( ε ) d A ,

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