Abstract

Diffractive resonators have already been successfully applied to improve the transverse modal properties of solid-state lasers, gas lasers, external-cavity diode lasers, and diode-laser arrays. We discuss the possibility of designing monolithic diffractive broad-area lasers with a Gaussian fundamental mode and high modal discrimination. Using an empty resonator model, we demonstrate by numerical calculations that it is possible to achieve high-brightness diffractive broad-area waveguide lasers despite the large extent of the structures and fewer geometrical degrees of freedom. Owing to the diffraction of the fields inside the waveguide structures, the shape of the diffractive structures becomes important and needs to be considered in the design.

© 2005 Optical Society of America

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References

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1999 (1)

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).

1997 (1)

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, "Numerical simulation of broad-area high-power semiconductor laser amplifiers," IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

1995 (2)

G. Mowry and J. R. Leger, "Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output," Appl. Phys. Lett. 66, 1614-1616 (1995).
[CrossRef]

J. R. Leger, D. Chen, and G. Mowry, "Design and performance of diffractive optics for custom laser resonators," Appl. Opt. 34, 2498-2508 (1995).
[CrossRef] [PubMed]

1994 (3)

1993 (3)

1992 (1)

1991 (2)

1989 (1)

S. Nakatsuka and K. Tatsuno, "Fundamental lateral-mode operation in broad-area lasers having built-in lenslike refractive index distributions," Jpn. J. Appl. Phys. 28, L1003-L1005 (1989).
[CrossRef]

1961 (1)

T. Li and A. Fox, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).
[CrossRef]

Abraham, E.

Adachihara, H.

Bélanger, P. A.

Bélanger , P. A.

Brenner, K. H.

Chen, D.

Dai, K.

Dai, Z.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, "Numerical simulation of broad-area high-power semiconductor laser amplifiers," IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Ebeling, K. J.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, "Numerical simulation of broad-area high-power semiconductor laser amplifiers," IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Fox, A.

T. Li and A. Fox, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).
[CrossRef]

Hess, O.

Huttunen, J.

Lachance, R.

Leger, J. R.

Li , T.

T. Li and A. Fox, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).
[CrossRef]

Michalzik, R.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, "Numerical simulation of broad-area high-power semiconductor laser amplifiers," IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Moloney, J. V.

Mowry, G.

Mowry , G.

G. Mowry and J. R. Leger, "Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output," Appl. Phys. Lett. 66, 1614-1616 (1995).
[CrossRef]

G. Mowry and J. R. Leger, "External diode-laser-array cavity with mode-selecting mirror," Appl. Phys. Lett. 63, 2884-2886 (1993).
[CrossRef]

Nakatsuka , S.

S. Nakatsuka and K. Tatsuno, "Fundamental lateral-mode operation in broad-area lasers having built-in lenslike refractive index distributions," Jpn. J. Appl. Phys. 28, L1003-L1005 (1989).
[CrossRef]

Paré, C.

Ru, P.

Saarinen, J.

Singer , W.

Tatsuno, K.

S. Nakatsuka and K. Tatsuno, "Fundamental lateral-mode operation in broad-area lasers having built-in lenslike refractive index distributions," Jpn. J. Appl. Phys. 28, L1003-L1005 (1989).
[CrossRef]

Turunen, J.

Unger, P.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, "Numerical simulation of broad-area high-power semiconductor laser amplifiers," IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Wang, Z.

Wyrowski, F.

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).

Zeitner , U. D.

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).

Appl. Opt. (3)

Appl. Phys. Lett. (2)

G. Mowry and J. R. Leger, "External diode-laser-array cavity with mode-selecting mirror," Appl. Phys. Lett. 63, 2884-2886 (1993).
[CrossRef]

G. Mowry and J. R. Leger, "Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output," Appl. Phys. Lett. 66, 1614-1616 (1995).
[CrossRef]

Bell Syst. Tech. J. (1)

T. Li and A. Fox, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).
[CrossRef]

IEEE J. Quantum Electron. (1)

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, "Numerical simulation of broad-area high-power semiconductor laser amplifiers," IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

J. Mod. Opt. (1)

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).

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

Jpn. J. Appl. Phys. (1)

S. Nakatsuka and K. Tatsuno, "Fundamental lateral-mode operation in broad-area lasers having built-in lenslike refractive index distributions," Jpn. J. Appl. Phys. 28, L1003-L1005 (1989).
[CrossRef]

Opt. Lett. (5)

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. Mueller and W. Karthe, Integrierte Optik (Akademische Verlagsgesellschaft, Leipzig, 1991).

U. D. Zeitner and R. Guether, "Laser resonators comprising mode-selective phase structures," world patent WO01/97349A1 (December 20, 2001).

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Figures (12)

Fig. 1
Fig. 1

Scheme of a diffractive broad-area laser. W, the width; L, the length of the resonator; Z1, the distance of the first structure to the outcoupling mirror. The laterally varying thicknesses of the first and second structures are denoted d1(x) and d2(x).

Fig. 2
Fig. 2

Results of Fox–Li calculations for diffractive waveguide resonators with three different Fresnel numbers N, varying the location of the grating Z1/L and the number of periods within the resonator width P. Only configurations leading to a fundamental-mode beam quality factor of M2<1.6 are displayed (in the thin-element case). In the left column the results for the thin-element case (Δn=) are shown, and the gray levels denote the modal discrimination. In the right column the results for the thick-element case (Δn=-0.03) are shown for broad-area lasers with λ0=808 nm, n=3.45, ne=3.42, W=200 µm, and L=4, 2, and 1 mm. The gray levels denote the lowest round-trip loss of the fundamental mode.

Fig. 3
Fig. 3

(a) Top view of the amplitude distribution in the resonator for the first design example. The phase distributions of (b) structure 1 (P=25 mm-1, Z1=2.5 mm) and (c) structure 2.

Fig. 4
Fig. 4

Comparison of the fundamental modes calculated by the Fox–Li algorithm with (Δn=-0.03, lower row) and without (Δn=, upper row) considering diffraction of the field inside the structures for the first design example.

Fig. 5
Fig. 5

(a) Top view of the amplitude distribution in the resonator for the second design example. The phase distributions of (b) structure 1 (P=10 mm-1, Z1=0.725 mm) and (c) structure 2.

Fig. 6
Fig. 6

Comparison of the fundamental modes calculated by the Fox–Li algorithm with (Δn=-0.03, lower row) and without (Δn=, upper row) considering diffraction of the field inside the structures for the second design example.

Fig. 7
Fig. 7

Effect of the offset-phase value of the second structure on the modal behavior when diffraction of the field within the structures is considered, calculated for the second design example.

Fig. 8
Fig. 8

(a) and (b) Influence of the shape of the second structure on the impinging field U(x; zc). The field U(x; zc) results from our applying the design algorithm in Section 2 [see Eq. (4)] to the second design example. The amplitude distribution |U(x; zb)| and phase distribution arg[U(x; zb)] of the field U(x; zb) in the plane of the back mirror, resulting from propagating the field U(x; zc) through the different structures, are displayed in the second and third rows of the diagram, respectively. The resulting modal behavior is shown in Fig. 7.

Fig. 9
Fig. 9

(a) Top view of the amplitude distribution in the resonator for the third design example. The phase distributions of (b) structure 1 (P=10 mm-1, Z1=1.0 mm, and p=20 µm) and (c) structure 2.

Fig. 10
Fig. 10

Dependence of the round-trip losses of the third design example on the grating period of the outer regions of the first structure. Both results for the case of thin elements (curves without symbols) and thick elements (curves with symbols) are displayed.

Fig. 11
Fig. 11

Comparison of the fundamental modes calculated by the Fox–Li algorithm with (Δn=-0.03, lower row) and without (Δn=, upper row) considering diffraction of the field inside the structures for the third design example.

Fig. 12
Fig. 12

Dependence of the round-trip loss of the first- (straight lines) and second-order modes (dashed lines) on the tilt angle of the structures against the mirrors for the three design examples. Both results for the case of thin elements (curves without symbols) and thick elements (curves with symbols) are displayed.

Tables (2)

Tables Icon

Table 1 Comparison of the Resonator Configurations Leading to the Highest Modal Discrimination with M2<1.6 in the Case of Thin Elements (Δn=) with the Lowest Loss of the Fundamental Mode Obtained for the Broad-Area Laser Design Example (Δn=-0.03)a

Tables Icon

Table 2 Modal Properties of the Design Examples with Thin Elements (Δn=) and Thick Elements (Δn=-0.03), Compared with Those of a Planar Fabry–Perot Resonator Having the Same Fresnel Number N=10.7a

Equations (7)

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N=W2/4λL.
U(x; zo)=exp[-(x/w0)2],
T1(x; zg)=exp{2πj[1+cos(2πPx)]},
U(x; zc)=A(x)exp[jϕ(x, zc)],
T2(x; zc)=exp[-jϕ(x, zc)]
d1,2(x)=λ02π|Δn|{arg[T1,2(x)]+Φ1,2}.
T1(x; zg)=exp{2πj[1+cos(2πPx)]}:|x|0.24Wexp[2πjΦ1+2πj|x|sin β/λ]:0.24W<|x|0.5W,

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