Abstract

In this paper we present a model to investigate the thermal limitations of volume Bragg gratings (VBGs) used in lasers for spectral control. Also presented are the limiting optical powers, to which intracavity VBGs of different length could be subjected, before the laser operation rapidly deteriorates. The results revealed that the power limit of a VBG-locked laser is highly dependent on the length of the employed VBG. Furthermore, the power limit expressed in incident power related linearly to the radius of the laser beam irradiating the VBG.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2013

2011

T. Waritanant and T.-Y. Chung, “Influence of minute self-absorption of a volume Bragg grating used as a laser mirror,” IEEE J. Quantum Electron. 47, 390–397 (2011).
[CrossRef]

2009

2008

2007

2006

2005

2004

1999

1995

Andrusyak, O.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

Ban, V. S.

Bass, M.

Cheng, M.-Y.

Chung, T.-Y.

T. Waritanant and T.-Y. Chung, “Influence of minute self-absorption of a volume Bragg grating used as a laser mirror,” IEEE J. Quantum Electron. 47, 390–397 (2011).
[CrossRef]

T.-y. Chung, A. Rapaport, V. Smirnov, L. B. Glebov, M. C. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
[CrossRef]

Clarkson, W. A.

Dolgy, S. V.

Downs, E.

Efimov, O. M.

Flecher, E.

Galvanauskas, A.

Glebov, L.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

Glebov, L. B.

Glebova, L. N.

Jacobsson, B.

Jelger, P.

Kim, J. W.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” in The Bell System Technical Journal, Vol. 48 (American Telephone and Telegraph Company, 1969), pp. 2909–2947.

Laurell, F.

Liao, K.-H.

Melnik, E. D.

Mitsas, C.

Mokhov, S.

Pasiskevicius, V.

Rapaport, A.

Richardson, K. C.

Richardson, M. C.

Rotar, V.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

Sahu, J. K.

Shaw, J.

Shu, H.

Siapkas, D.

Smirnov, V.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

T.-y. Chung, A. Rapaport, V. Smirnov, L. B. Glebov, M. C. Richardson, and M. Bass, “Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror,” Opt. Lett. 31, 229–231 (2006).
[CrossRef]

Smirnov, V. I.

Tiihonen, M.

Tjörnhammar, S.

Venus, G.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

Volodin, B. L.

Wang, P.

Waritanant, T.

T. Waritanant and T.-Y. Chung, “Influence of minute self-absorption of a volume Bragg grating used as a laser mirror,” IEEE J. Quantum Electron. 47, 390–397 (2011).
[CrossRef]

Zeldovich, B. Y.

Appl. Opt.

IEEE J. Quantum Electron.

T. Waritanant and T.-Y. Chung, “Influence of minute self-absorption of a volume Bragg grating used as a laser mirror,” IEEE J. Quantum Electron. 47, 390–397 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” in The Bell System Technical Journal, Vol. 48 (American Telephone and Telegraph Company, 1969), pp. 2909–2947.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the simulation process. The simulation finds steady state solutions of DE(λ), I(z)) and T(z) for incremental values of αabsI0,inc. For each αabsI0,inc value, the simulation model iterates between the two parts until the solutions converge. Input parameters when creating the VBG are the grating period Λ, the length of the VBG L, and the refractive index modulation amplitude n1.

Fig. 2.
Fig. 2.

Schematic of a three-layer stack of dielectrics. Here, Eij is the electric field of the propagating light, where the subscripts indicate the position in the stack and the + and the − signs denote right- and left-traveling waves, respectively.

Fig. 3.
Fig. 3.

Bar chart illustrating the modeling of a sinusoidal refractive index modulation.

Fig. 4.
Fig. 4.

Derivative of DEmax with respect to αabsI0,inc. The lines shows the results for VBGs of length, in order from the left to the right, 10, 8, 6, 5, 4, 3, and 2 mm, respectively. The radius of the beam irradiating the VBGs was constant at 250 μm.

Fig. 5.
Fig. 5.

(a) Power limit expressed in the absorbed power. (b) Power limit as expressed in the product of the absorption coefficient and the incident power. The radius of the beam irradiating the VBGs was constant at 250 μm. The solid lines are used to guide the eye.

Fig. 6.
Fig. 6.

Power limit expressed in the product of the absorption coefficient and the incident power as a function of the reflected beam radius. Results for the 2 mm and the 10 mm long VBG are shown in (a) and (b), respectively.

Fig. 7.
Fig. 7.

Power limit expressed in the product of the absorption coefficient and the incident intensity as a function of the reflected beam radius. Results for the 2 mm and the 10 mm long VBG are shown in (a) and (b), respectively. The solid lines are used to guide the eye.

Tables (1)

Tables Icon

Table 1. Refractive Index Modulation Amplitude, n1, and the Zero-to-Zero Spectral Width, Δλ, for the Simulated VBGs of Different Length, L

Equations (15)

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

[E12+E12]=12[1+n1n21n1n21n1n21+n1n2][E11+E11]=B2,1[E11+E11].
[E11+E11]=12[1+n2n11n2n11n2n11+n2n1][E12+E12]=B1,2[E12+E12].
[E22+E22]=[exp{ik2d}00exp{ik2d}][E12+E12]
[E12+E12]=[exp{ik2d}00exp{ik2d}][E22+E22]=P2[E22+E22].
[E11+E11]=B1,2P2B2,3[E23+E23]=M[E23+E23].
M=B0,1P1B1,2P2B2,3P3BN1,NPNBN,N+1=[m11m12m21m22],
[E0+E0]=[m11m12m21m22][EN+1+0]=[m11EN+1+m21EN+1+].
r=E0E0+=m21m11.
DE=|r|2.
λB=2n0Λ.
n1=λBπLtanh1(DEmax).
I(z)=(1+DE)n(0)|E(0)|2n(z)|E(z)|2,
·(k·T)=Q.
Cp(T)=9.36×109T31.54×105T2+8.22×103T0.637,
Q(x,y,z)=αabsI0,incexp{2x2+y2ω2}I(z).

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