Abstract

The possibility of exciting laser modes such as Laguerre–Gaussian (LG) or Ince–Gaussian (IG) modes is discussed on the basis of a gain-matching integral. We reach the conclusion that, using tight pumping and away from degeneracy regions, only the IGn,ne modes can be excited. Furthermore, pure high-order modes with circular or elliptical nodal lines can never be excited. Only an approximation of such modes, which we call quasi-IG or quasi-LG modes, can be observed and only when the cavity is partially degenerate. We provide experimental results in perfect agreement with the theory and discuss the exact nature of the profiles observed at degeneracy in our experiments and elsewhere in the literature.

© 2014 Optical Society of America

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2013 (2)

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

2012 (2)

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

W. Kong, A. Sugita, and T. Taira, Opt. Lett. 37, 2661 (2012).
[CrossRef]

2010 (1)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

2009 (1)

2007 (3)

2004 (2)

2003 (1)

2002 (1)

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

2001 (1)

J. Dingjan, M. van Exter, and J. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

1997 (1)

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1990 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1979 (1)

K. Kubodera and K. Otsuka, J. Appl. Phys. 50, 653 (1979).
[CrossRef]

1977 (1)

M. Lax, J. Appl. Phys. 48, 3919 (1977).
[CrossRef]

Ait-Ameur, K.

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bandres, M. A.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bisson, J.-F.

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chen, C.-H.

Chen, Y. F.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

Chiang, P. Y.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chu, S.

Chu, S.-C.

Desyatnikov, A. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Dingjan, J.

J. Dingjan, M. van Exter, and J. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Fickler, R.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Flood, C. J.

Fromager, M.

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

Giuliani, G.

Gutiérrez-Vega, J. C.

Hsieh, W.-F.

Huang, K. F.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

Huang, T. M.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Kamikariya, K.

Kao, C. F.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

Kivshar, Y. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Kong, W.

Krenn, M.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Krolikowski, W.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Kubodera, K.

K. Kubodera and K. Otsuka, J. Appl. Phys. 50, 653 (1979).
[CrossRef]

Labbé, C.

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

Lax, M.

M. Lax, J. Appl. Phys. 48, 3919 (1977).
[CrossRef]

Li, J.

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Liang, H. C.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

Martel, G.

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Ohtomo, T.

Otsuka, K.

Plick, W. N.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Ramelow, S.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Rode, A. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Sanchez, F.

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

Schwarz, U. T.

Senatsky, Y.

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Shirakawa, A.

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Shvedov, V. G.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Sugita, A.

Tai, P.-T.

Taira, T.

Thirugnanasambandam, M.

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Tung, J. C.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

Ueda, K.-i.

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

van Driel, H. M.

van Exter, M.

J. Dingjan, M. van Exter, and J. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

Wang, C. L.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

Wang, S. C.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

Wei, M.-D.

Woerdman, J.

J. Dingjan, M. van Exter, and J. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Zeilinger, A.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Zhan, Q.

Adv. Opt. Photon. (1)

IEEE J. Quantum Electron. (1)

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, IEEE J. Quantum Electron. 33, 1025 (1997).
[CrossRef]

J. Appl. Phys. (2)

M. Lax, J. Appl. Phys. 48, 3919 (1977).
[CrossRef]

K. Kubodera and K. Otsuka, J. Appl. Phys. 50, 653 (1979).
[CrossRef]

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

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

Opt. Commun. (2)

G. Martel, C. Labbé, F. Sanchez, M. Fromager, and K. Ait-Ameur, Opt. Commun. 201, 117 (2002).
[CrossRef]

J. Dingjan, M. van Exter, and J. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Opt. Rev. (1)

Y. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.-i. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Phys. Rev. A (3)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, Phys. Rev. A 88, 013827 (2013).
[CrossRef]

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[CrossRef]

Phys. Rev. Lett. (3)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Hemispherical laser cavity configuration.

Fig. 2.
Fig. 2.

(a) Normalized intensity profiles of some LG modes, and Gaussian tight-pump profile fitting the central peak of the LG0,1 mode. (b) and (c) LG0,1 and LG0,0 overlap with the pump profile in the transverse plane.

Fig. 3.
Fig. 3.

Experimental and simulated intensity profiles, for different pump positions xp. Red circle: pump position.

Fig. 4.
Fig. 4.

Correlation between the Fox–Li mode and the GMI prediction when varying the cavity length in both (a) on-axis and (b) off-axis situations. Red curves: wp=0.75w0, blue: wp=0.50w0, green: wp=0.33w0.

Fig. 5.
Fig. 5.

Experimental and simulated near field (NF) and far field (FF) quasi-LG and quasi-IG modes intensity profiles, in both (a) on-axis and (b) off-axis situations. Mode expansion (a): 37.9% LG0,0, 51.7% LG0,2, 7.6% LG0,4, 1.7% LG0,6, 1.1% others. Mode expansion (b): 27.4% HG1,0, 65% IG5,3e(ϵ=1.5), 5.3% IG9,3e(ϵ=5), 2.3% others.

Equations (1)

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λfrei(p+1)ΨG(1+2d|f(x,y)|2f(x,y)2g0(x,y)dxdy),

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