Abstract

We solve the coupled cw electric field differential equations for an hexagonal array of fiber gain elements all sharing a common monolithic Talbot cavity mirror. A threshold analysis shows that the lowest gains are nearly equal, within 10% of one another, and that one of these corresponds to an in-phase supermode. Above threshold we study the extraction characteristics as a function of the Talbot cavity length, and we also determine the optimum outcoupling reflectivity. These simulations show that the lasing mode is an in-phase solution. Lastly, we study extraction when random linear propagation phases are present by using Monte Carlo techniques. This shows that the coherence function decreases as exp(-σ 2), and that the near-field intensity decreases faster as the rms phase σ 2 increases. All of the above behaviors are strongly influenced by the hexagonal array rotational symmetry.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. P. Peterson, A. Gavrielides, M. P. Sharma, "Extraction characteristics of a one dimensional Talbot cavity with stochastic propagation phase," Opt. Express 8, 670-682 (2001), http://www.opticsexpress.org/oearchive/source/32913.htm
    [CrossRef] [PubMed]
  2. David Mehuys, William Streifer, Robert G. Waarts and Davie F. Welsh, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16 823-825 (1991).
    [CrossRef] [PubMed]
  3. V. P. Kandidov, A. V. Kondrat'ev, M. B. Surovitskii, "Collective modes of two-dimensional laser arrays in a Talbot cavity," Quant. Elect. 28, 692-696 (1998).
    [CrossRef]

Other

P. Peterson, A. Gavrielides, M. P. Sharma, "Extraction characteristics of a one dimensional Talbot cavity with stochastic propagation phase," Opt. Express 8, 670-682 (2001), http://www.opticsexpress.org/oearchive/source/32913.htm
[CrossRef] [PubMed]

David Mehuys, William Streifer, Robert G. Waarts and Davie F. Welsh, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16 823-825 (1991).
[CrossRef] [PubMed]

V. P. Kandidov, A. V. Kondrat'ev, M. B. Surovitskii, "Collective modes of two-dimensional laser arrays in a Talbot cavity," Quant. Elect. 28, 692-696 (1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Double hexagonal array and coordinate nomenclature

Fig. 2.
Fig. 2.

The three lowest threshold eigenvalue gains (colored) and the bounding largest threshold eigenvalue gain (black) as functions of the normalized Talbot length.

Fig. 3.
Fig. 3.

(a) the coherence function (green) and the threshold eigenvalue gain (black) for the 1/3 Talbot plane;(b), the coherence function and the threshold eigenvalue gain for the 2/3 Talbot plane. Both are functions of mode number.

Fig. 4.
Fig. 4.

(a), the far-field on-axis intensity; (b), the Talbot cavity effective reflectivity as functions of the normalized Talbot cavity length.

Fig. 5.
Fig. 5.

(a), the optimum far-field outcoupled on-axis intensity for the the 1/3 plane (red), and the 2/3 plane (black); (b) the forward recirculating power for the central emitter in the 1/3 plane (red), and in the 2/3 plane (black). All graphs are functions of the intensity reflectivity r 2.

Fig. 6.
Fig. 6.

(a), coherence function; (b) central emitter near-field intensity; (c), far-field on-axis intensity; (d) the locking probability. All are functions of the rms phase for the 2/3 Talbot plane.

Fig. 7.
Fig. 7.

I(x, y) contour plot for z=zt , z=1/3zt , z=2/3zt , from top to bottom. The maximum contour intervals are .0875–.1, .36–.4, .1225–.14, respectively.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

d A j ± d z = ± g j 1 + A j ± 2 + C j A j ± 2 A j ±
E j ± ( z ) = A j ± ( z ) exp ( ϕ j ± ( z ) ) .
ϕ j ± ( L j ) ϕ j ± ( 0 ) = ± k j L j
C j = A j + ( z ) A j ( z ) = A j + ( L j ) A j ( L j ) = A j + ( 0 ) A j ( 0 ) .
< E i + ( L ) > = r exp ( 2 g L ) [ R i , i < E i > + exp ( σ 2 ) j i N R i , j < E j + ( L ) > ] .
c = Σ E j ( 0 ) 2 Σ E j ( 0 ) 2
< c > = 1 N < i , j N exp [ i ( ϕ j ϕ i ) > = 1 N [ N + N ( N 1 ) exp ( σ 2 ) ] ,
E i + ( L ) r exp ( 2 g L ) j N R i , j E j + ( L ) = 0
E 0 ( x , y , z ) = j = 0 N E j exp [ i ( x x j ) 2 + ( y y j ) 2 w o 2 ] .
E P ( x , z ) = i exp ( i k z ) z E 0 ( x , y ) exp ( i k 2 z [ ( x x ' ) 2 + ( y y ' ) 2 ] d x ' d y ' .
E P ( x , y , z ) = exp ( i k z ) 1 1 + i z z 0 j = 0 N E j exp [ i k 2 ( z i z 0 ) ( ( x x j ) 2 + ( y y j ) 2 ) ]
R i , j = G i ( x , y , 0 ) * G j ( x , y , z ) d x d y G i ( x , y , 0 ) * G i ( x , y , 0 ) d x d y
G j ( x , y , z ) = exp ( i k z ) 1 1 + i z z 0 exp [ i k 2 ( z i z 0 ) ( ( x x j ) 2 + ( y y j ) 2 ) ] .
R i , j = exp ( i k z ) 1 1 + i z 2 z 0 exp [ i k 2 ( z i 2 z 0 ) [ ( x i x j ) 2 + ( y i y j ) 2 ] ] .

Metrics