Abstract

A new type of diffractive optical element for detecting and measuring the power distribution of transverse modes emanating from radially symmetric laser resonators is presented. It is based on a relatively simple straightforward design of a phase-only diffractive optical element that serves as a matched filter, which correlates between specific prerecorded transverse modes with a certain azimuthal mode order and those in the incident laser light. Computer simulations supported by experimental results demonstrate how such elements can accurately detect modes with spiral phases and provide quantitative results on the modal power distribution.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006

M. R. Duparre, B. Luedge, and S. Schroeter, "Etalons for pure and composite transversal modes," Proc. SPIE 6101, 61011C (2006).
[CrossRef] [PubMed]

2005

2004

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).
[PubMed]

2003

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, "Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser," IEEE J. Quantum Electron. 39, 74-82 (2003).
[CrossRef] [PubMed]

2002

G. Machavariani, N. Davidson, E. Hasman, S. Blit, and A. A. Friesem, "Efficient conversion of Gaussian beam to a high purity helical mode," Opt. Commun. 209, 265-271 (2002).
[CrossRef]

2001

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

S. Makki and J. Leger, "Mode shaping of a graded-reflectivity-mirror unstable resonator with an intracavity phase element," IEEE J. Quantum Electron. 37, 80-86 (2001).
[CrossRef] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, "Transverse mode shaping and selection in laser resonators," Prog. Opt. 42, 325-386 (2001).
[CrossRef] [PubMed]

2000

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, "Gaussian-Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element," Opt. Commun. 175, 301-308 (2000).
[CrossRef] [PubMed]

M. R. Duparre, V. S. Pavelyev, V. A. Soifer, and B. Luedge, "Laser beam characterization by means of diffractive optical correlation filters," Proc. SPIE 4095, 40-48 (2000).
[CrossRef] [PubMed]

C. M. Warnky, B. L. Anderson, and C. A. Klein, "Determining spatial modes of lasers with spatial coherence measurements," Appl. Opt. 39, 6109-6117 (2000).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, "Continuous phase elements can improve laser beam quality," Opt. Lett. 25, 939-941 (2000).
[CrossRef]

1999

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, "Discontinuous phase elements for transverse mode selection in laser resonators," Appl. Phys. Lett. 74, 1373-1374 (1999).
[CrossRef]

1997

1996

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soifer, and G. V. Uspleniev, "Experimental investigation of a multibeam holographic optical element matched to Gaussian-Laguerre modes," Quantum Electron. 26, 184-186 (1996).
[CrossRef] [PubMed]

1992

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, "Computer generated diffractive multi-focal lens," J. Mod. Opt. 39, 1245-1251 (1992).
[CrossRef] [PubMed]

R. L. Morrison, "Symmetries that simplify the design of spot array phase gratings," J. Opt. Soc. Am. A 9, 464-471 (1992).
[CrossRef]

D. Prongue, H. P. Herzig, R. Dandliker, and M. T. Gale, "Optimized kinoform structures for highly efficient fan-out elements," Appl. Opt. 31, 5706-5711 (1992).
[CrossRef] [PubMed]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef] [PubMed]

1991

L. L. Doskolovich, V. V. Kotlyar, and V. A. Soifer, "Phase gratings with a prescribed intensity distribution among the diffraction orders," Sov. Tech. Phys. Lett. 17, 771-772 [P. Zh. Tekh. Fizi. 17, 54-57 (1991)].
[PubMed]

M. A. Golub, I. N. Sissakian, V. A. Soifer, and G. V. Uvarov, "Mode-selective fiber sensors operating with computer generated optical elements," Proc. SPIE 1572, 101-106 (1991).
[CrossRef] [PubMed]

1990

1983

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, "Mode analysis of optical fibers using computer-generated matched filters," Electron. Lett. 19, 247-249 (1983).
[CrossRef] [PubMed]

1982

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, "Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation," Quantum Electron. 12, 1208-1209 (1982).
[CrossRef]

1979

K. I. Kitayama, M. Tateda, S. Seikai, and N. Uchida, "Determination of mode power distribution in a parabolic index optical fibers," IEEE J. Quantum Electron. QE-15, 1161-1165 (1979).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, "Discontinuous phase elements for transverse mode selection in laser resonators," Appl. Phys. Lett. 74, 1373-1374 (1999).
[CrossRef]

Electron. Lett.

H. O. Bartelt, A. W. Lohmann, W. Freude, and G. K. Grau, "Mode analysis of optical fibers using computer-generated matched filters," Electron. Lett. 19, 247-249 (1983).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

K. I. Kitayama, M. Tateda, S. Seikai, and N. Uchida, "Determination of mode power distribution in a parabolic index optical fibers," IEEE J. Quantum Electron. QE-15, 1161-1165 (1979).
[CrossRef] [PubMed]

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, "Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser," IEEE J. Quantum Electron. 39, 74-82 (2003).
[CrossRef] [PubMed]

S. Makki and J. Leger, "Mode shaping of a graded-reflectivity-mirror unstable resonator with an intracavity phase element," IEEE J. Quantum Electron. 37, 80-86 (2001).
[CrossRef] [PubMed]

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).
[PubMed]

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, "Computer generated diffractive multi-focal lens," J. Mod. Opt. 39, 1245-1251 (1992).
[CrossRef] [PubMed]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Opt. Technol.

Opt. Commun.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, and A. A. Friesem, "Efficient conversion of Gaussian beam to a high purity helical mode," Opt. Commun. 209, 265-271 (2002).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, "Gaussian-Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element," Opt. Commun. 175, 301-308 (2000).
[CrossRef] [PubMed]

Opt. Lett.

Proc. SPIE

M. A. Golub, I. N. Sissakian, V. A. Soifer, and G. V. Uvarov, "Mode-selective fiber sensors operating with computer generated optical elements," Proc. SPIE 1572, 101-106 (1991).
[CrossRef] [PubMed]

M. R. Duparre, V. S. Pavelyev, V. A. Soifer, and B. Luedge, "Laser beam characterization by means of diffractive optical correlation filters," Proc. SPIE 4095, 40-48 (2000).
[CrossRef] [PubMed]

M. R. Duparre, B. Luedge, and S. Schroeter, "Etalons for pure and composite transversal modes," Proc. SPIE 6101, 61011C (2006).
[CrossRef] [PubMed]

Prog. Opt.

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, "Transverse mode shaping and selection in laser resonators," Prog. Opt. 42, 325-386 (2001).
[CrossRef] [PubMed]

Quantum Electron.

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, "Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation," Quantum Electron. 12, 1208-1209 (1982).
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soifer, and G. V. Uspleniev, "Experimental investigation of a multibeam holographic optical element matched to Gaussian-Laguerre modes," Quantum Electron. 26, 184-186 (1996).
[CrossRef] [PubMed]

Sov. Tech. Phys. Lett.

L. L. Doskolovich, V. V. Kotlyar, and V. A. Soifer, "Phase gratings with a prescribed intensity distribution among the diffraction orders," Sov. Tech. Phys. Lett. 17, 771-772 [P. Zh. Tekh. Fizi. 17, 54-57 (1991)].
[PubMed]

Other

V. A. Soifer and M. A. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Basic optical arrangement for mode detection and measurements.

Fig. 2
Fig. 2

Typical mode-matched DOE that has five diffraction orders of equal intensities and a carrier spatial frequency of 5 lines / mm : (a) nonlinearity function Q ( φ c ) for each groove; and (b) central part of the gray level mask of the desired phase function.

Fig. 3
Fig. 3

Calculated far field intensity distributions of the input modes and corresponding correlation results. (a)–(f) Input mode distributions; (g)–(l) correlation results after passing through the mode-matched DOE; white ruler shows expected locations of the correlation peaks according to λ F ν ( l ) .

Fig. 4
Fig. 4

(Color online) Experimental far field intensity distributions of the input modes and corresponding correlation results. (a)–(f) Input mode distributions along with phase elements for forming these modes as essentially single TEM* or TEM modes, (g)–(l) correlation results after passing through the mode-matched DOE; white ruler shows expected locations of the correlation peaks according to λ F ν ( l ) .

Tables (1)

Tables Icon

Table 1 Experimental Modal Power Distribution: Normalized Experimental Correlation Intensities at the Output Locations According to λ F ν( l ) for Each of the Six Input Modal Distributions

Equations (7)

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ψ p , l ( r , φ ) = R p , l ( r )   cos ( l φ ) ,   degenerate ,
ψ p , l ( r , φ ) = R p , l ( r )   exp ( i l φ ) ,   nondegenerate ,
T = l t l   exp [ i ( l φ + 2 π ν ( l ) x ) ] ,
φ c = φ + 2 π ν ( 1 ) x ,
T = exp [ i Q ( φ c ) ] = l = t l   exp ( i l φ c ) = l = t l   exp ( i l φ + i 2 π l ν ( 1 ) x ) ,
t l = 1 2 π 0 2 π exp [ i Q ( φ c ) i l φ c ] d φ c .
ν ( l ) = l ν ( 1 ) .

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