Abstract

we show for the first time that biaxial crystals exhibit continua of directions of propagation where the absorption coefficient is the same for the two associated polarization modes. This statement is supported by both calculations and experimental data obtained in Nd:YCOB.

© 2009 Optical Society of America

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References

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  1. Born and Wolf, Principles of Optics (Oxford Pergamon Press, 1965).
  2. Y. Petit, B. Boulanger, P. Segonds, C. Félix, B. Ménaert, J. Zaccaro, and G. Aka, "Absorption and fluorescence anisotropies of monoclinic crystals: the case of Nd:YCOB," Opt. Express 16(11), 7997 (2008).
  3. P. Segonds, B. Boulanger, J. P. Fève, B. Ménaert, J. Zaccaro, G. Aka, and D. Pelenc, "Linear and nonlinear optical properties of the monoclinic Ca4YO(BO3)3 crystal," J. Opt. Soc. Am. B 21(4), 765 (2004).
    [CrossRef]
  4. Landau and Lifchitz, Theory of Elasticity (MIR Editions, Moscow, 1967).
  5. M. Vacha and M. Kotaki, "Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy," J. Chem. Phys. 118(12), 5279 (2003).
    [CrossRef]
  6. M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
    [CrossRef]
  7. A. Shumelyuk, A. Volkov, A. Selinger, M. Imlau, and S. Odoulov, "Frequency-degenerate nonlinear light scattering in low-symmetry crystals," Opt. Lett. 33, 150 (2008).
    [CrossRef] [PubMed]

2008

2004

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

P. Segonds, B. Boulanger, J. P. Fève, B. Ménaert, J. Zaccaro, G. Aka, and D. Pelenc, "Linear and nonlinear optical properties of the monoclinic Ca4YO(BO3)3 crystal," J. Opt. Soc. Am. B 21(4), 765 (2004).
[CrossRef]

2003

M. Vacha and M. Kotaki, "Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy," J. Chem. Phys. 118(12), 5279 (2003).
[CrossRef]

Aka, G.

Boulanger, B.

Félix, C.

Fève, J. P.

Gâcon, J.-C.

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

Guyot, Y.

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

Imlau, M.

Joubert, M.-F.

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

Kazanskii, S. A.

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

Kotaki, M.

M. Vacha and M. Kotaki, "Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy," J. Chem. Phys. 118(12), 5279 (2003).
[CrossRef]

Ménaert, B.

Odoulov, S.

Pédrini, C.

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

Pelenc, D.

Petit, Y.

Segonds, P.

Selinger, A.

Shumelyuk, A.

Vacha, M.

M. Vacha and M. Kotaki, "Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy," J. Chem. Phys. 118(12), 5279 (2003).
[CrossRef]

Volkov, A.

Zaccaro, J.

J. Chem. Phys.

M. Vacha and M. Kotaki, "Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy," J. Chem. Phys. 118(12), 5279 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. B

M.-F. Joubert, S. A. Kazanskii, Y. Guyot, J.-C. Gâcon, and C. Pédrini, "Microwave study of photoconductivity induced by laser pulses in rare-earth-doped dielectric crystals," Phys. Rev. B 69(16), 165217 (2004).
[CrossRef]

Other

Born and Wolf, Principles of Optics (Oxford Pergamon Press, 1965).

Landau and Lifchitz, Theory of Elasticity (MIR Editions, Moscow, 1967).

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Figures (3)

Fig. 1.
Fig. 1.

Polar representation in the dielectric frame (x, y, z) as a function of the θ angle of the absorption coefficients α+(θ,φ) and α-(θ,φ) relative to the two polarization modes at 0.812 µm in four planes containing the z-axis at different φ angles. The circles stand for the data recorded in a 7.44-mm-diameter Nd:YCOB sphere ; the continuous lines are calculated curves. The concentric circles stand for the polar scale in 2, 4 and 6 cm-1 giving the magnitude of the absorption coefficients

Fig. 2.
Fig. 2.

Spherical coordinates of the direction of propagation for which the magnitude of the absorption coefficient is the same for the two polarization modes. The circles correspond to the experimental data recorded in a 7.44-mm-diameter Nd:YCOB sphere, the black ones corresponding to the intersection dots Ai and Bi, with i=1, 2, 3 and 4, defined in Fig.1. The continuous lines are calculated curves.

Fig. 3.
Fig. 3.

(a). Calculated absorption angular distribution of Nd:YCOB at 0.812 µm, and (b) calculated index surface of a fictive monoclinic crystal with nx=1, ny=3 and nz=6 in one quarter of the space.

Equations (6)

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α+,(θ,φ)=1Lln(T+,(θ,φ)T+,F(θ,φ))
α+,(θ,φ)=4πλn+,(θ,φ)
{((εxx+jεxx)ε0n̂2(uy2+uz2))Ex+((εxy+jεxy)ε0+n̂2uxuy)Ey+((εxz+jεxz)ε0+n̂2uxuz)Ez=0((εyx+jεyx)ε0+n̂2uyux)Ex+((εyy+jεyy)ε0n̂2(ux2+uz2))Ey+((εyz+jεyz)ε0+n̂2uyuz)Ez=0((εzx+jεzx)ε0+n̂2uzux)Ex+((εzy+jεzy)ε0+n̂2uzuy)Ey+((εzz+jεzz)ε0n̂2(ux2+uy2))Ez=0
εxx=ε0nx2εyy=ε0ny2εzz=ε0nz2
εxx=2ε0n1nxεyy=2ε0n2nyεzz=2ε0n3nz
εxz=ε0n4(nx+nz)=εzx=ε0n4 (nz+nx)

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