Abstract

Polarization dependence of saturable absorption in Cr4+:YAG was investigated. We theoretically proposed its general analytical formula expressed in terms of the intensity and the polarization angle of the pump beam. We also derive transmission formulas for specific incident surfaces of (100)-, (110)-, and (111)-planes. In order to prove our model, we examined the polarization dependence in the transmittance of (110)-cut Cr4+:YAG. With the consideration of pump depletion in Cr4+:YAG, we succeeded to explain the polarization dependence that is consistent with past spectroscopic parameters of Cr4+:YAG.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Second-harmonic generation by Nd3+:YAG/Cr4+:YAG-laser pulses with changing state of polarization

Alexander V. Kir’yanov, Vicente Aboites, and Igor V. Mel’nikov
J. Opt. Soc. Am. B 17(10) 1657-1664 (2000)

Direct bleaching of a Cr4+:YAG saturable absorber in a passively Q-switched Nd:YAG laser

Baichao Zhang, Ying Chen, Pengyuan Wang, Yanchao Wang, Jinbo Liu, Shu Hu, Xusheng Xia, Youbao Sang, Hong Yuan, Xianglong Cai, Dong Liu, Baodong Gai, and Jingwei Guo
Appl. Opt. 57(16) 4595-4600 (2018)

> 6 MW peak power at 532 nm from passively Q-switched Nd:YAG/Cr4+:YAG microchip laser

Rakesh Bhandari and Takunori Taira
Opt. Express 19(20) 19135-19141 (2011)

References

  • View by:
  • |
  • |
  • |

  1. H. Sakai, H. Kan, and T. Taira, “>1 MW peak power single-mode high-brightness passively Q-switched Nd 3+:YAG microchip laser,” Opt. Express 16(24), 19891–19899 (2008).
    [Crossref] [PubMed]
  2. N. Pavel, M. Tsunekane, and T. Taira, “Composite, all-ceramics, high-peak power Nd:YAG/Cr4+:YAG monolithic micro-laser with multiple-beam output for engine ignition,” Opt. Express 19(10), 9378–9384 (2011).
    [Crossref] [PubMed]
  3. T. Taira, S. Morishima, K. Kanehara, N. Taguchi, A. Sugiura, and M. Tsunekane, “World first laser ignited gasoline engine vehicle,” The 1st Laser Ignition Conference (LIC’13), OPIC’13, Yokohama, Japan, April 23–25, LIC3–1 (2013).
  4. V. Yahia and T. Taira, “Development of a 0.3GW Microchip-seeded Amplifier,” The 4th. Laser Ignition Conference (LIC'16), OPIC'16, Yokohama, Japan, LIC3–3 (2016).
  5. H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
    [Crossref]
  6. Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
    [Crossref]
  7. A. Sennaroglu, U. Demirbas, S. Ozharar, and F. Yaman, “Accurate determination of saturation parameters for Cr4+-doped solid-state saturasble absorbers,” J. Opt. Soc. Am. B 23(2), 241–249 (2006).
    [Crossref]
  8. A. G. Okhrimchuk and A. V. Shestakov, “Absorption saturation mechanism for YAG:Cr4+ crystals,” Phys. Rev. B 61(2), 988–995 (2000).
    [Crossref]
  9. N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, “Model of passive Q switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres,” Quantum Electron. 28(2), 147–151 (1998).
    [Crossref]
  10. H. Sakai, A. Sone, H. Kan, and T. Taira, “Polarization stabilizing for diode-pumped passively Q-switched Nd:YAG microchip lasers,” Advanced-Solid-State Photonics 2006, MD2, USA (2006).
  11. H. Sakai, H. Kan, and T. Taira, “Passive Q switch laser device,” (2006), WO Patent App. PCT/JP2005/016,315.
  12. S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
    [Crossref] [PubMed]
  13. M. Tsunekane and T. Taira, “Direct Measurement of Temporal Transmission Distribution of a Saturable Absorber in a Passively Q-Switched Laser,” IEEE J. Quantum Electron. 52(5), 1–7 (2016).
    [Crossref]
  14. T. Hahn and A. Looijenga-Vos, “2.2 Contents and arrangement of the tables” in International Tables for Crystallography Brief Teaching Ed. Vol. A, T. Hahn ed. (Kluwer Academic Publishers, 2002).
  15. R. W. G. Wyckoff, Crystal Structures Ed. 2, Vol.3, (John Wiley & Sons, 1965) p.222.

2016 (1)

M. Tsunekane and T. Taira, “Direct Measurement of Temporal Transmission Distribution of a Saturable Absorber in a Passively Q-Switched Laser,” IEEE J. Quantum Electron. 52(5), 1–7 (2016).
[Crossref]

2014 (1)

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

2011 (1)

2008 (1)

2006 (1)

2000 (1)

A. G. Okhrimchuk and A. V. Shestakov, “Absorption saturation mechanism for YAG:Cr4+ crystals,” Phys. Rev. B 61(2), 988–995 (2000).
[Crossref]

1998 (2)

N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, “Model of passive Q switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres,” Quantum Electron. 28(2), 147–151 (1998).
[Crossref]

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

1992 (1)

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

Blau, P.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

Burshtein, Z.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

Demirbas, U.

Dennis, W. M.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

Eilers, H.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

Hayashi, S.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

Hoffman, K. R.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

Il’ichev, N. N.

N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, “Model of passive Q switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres,” Quantum Electron. 28(2), 147–151 (1998).
[Crossref]

Jacobsen, S. M.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

Kalisky, Y.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

Kan, H.

Kawase, K.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

Kikta, M. R.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

Kir’yanov, A. V.

N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, “Model of passive Q switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres,” Quantum Electron. 28(2), 147–151 (1998).
[Crossref]

Minamide, H.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

Nawata, K.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

Okhrimchuk, A. G.

A. G. Okhrimchuk and A. V. Shestakov, “Absorption saturation mechanism for YAG:Cr4+ crystals,” Phys. Rev. B 61(2), 988–995 (2000).
[Crossref]

Ozharar, S.

Pashinin, P. P.

N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, “Model of passive Q switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres,” Quantum Electron. 28(2), 147–151 (1998).
[Crossref]

Pavel, N.

Sakai, H.

Sennaroglu, A.

Shestakov, A. V.

A. G. Okhrimchuk and A. V. Shestakov, “Absorption saturation mechanism for YAG:Cr4+ crystals,” Phys. Rev. B 61(2), 988–995 (2000).
[Crossref]

Shikata, J.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

Shimony, Y.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

Taira, T.

M. Tsunekane and T. Taira, “Direct Measurement of Temporal Transmission Distribution of a Saturable Absorber in a Passively Q-Switched Laser,” IEEE J. Quantum Electron. 52(5), 1–7 (2016).
[Crossref]

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

N. Pavel, M. Tsunekane, and T. Taira, “Composite, all-ceramics, high-peak power Nd:YAG/Cr4+:YAG monolithic micro-laser with multiple-beam output for engine ignition,” Opt. Express 19(10), 9378–9384 (2011).
[Crossref] [PubMed]

H. Sakai, H. Kan, and T. Taira, “>1 MW peak power single-mode high-brightness passively Q-switched Nd 3+:YAG microchip laser,” Opt. Express 16(24), 19891–19899 (2008).
[Crossref] [PubMed]

Tsunekane, M.

M. Tsunekane and T. Taira, “Direct Measurement of Temporal Transmission Distribution of a Saturable Absorber in a Passively Q-Switched Laser,” IEEE J. Quantum Electron. 52(5), 1–7 (2016).
[Crossref]

N. Pavel, M. Tsunekane, and T. Taira, “Composite, all-ceramics, high-peak power Nd:YAG/Cr4+:YAG monolithic micro-laser with multiple-beam output for engine ignition,” Opt. Express 19(10), 9378–9384 (2011).
[Crossref] [PubMed]

Yaman, F.

Yen, W. M.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

Appl. Phys. Lett. (1)

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett. 61(25), 2958–2960 (1992).
[Crossref]

IEEE J. Quantum Electron. (2)

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kikta, “Excited-state absorption studies of Cr4+ ions in several garnets host materials,” IEEE J. Quantum Electron. 34(2), 292–299 (1998).
[Crossref]

M. Tsunekane and T. Taira, “Direct Measurement of Temporal Transmission Distribution of a Saturable Absorber in a Passively Q-Switched Laser,” IEEE J. Quantum Electron. 52(5), 1–7 (2016).
[Crossref]

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

Opt. Express (2)

Phys. Rev. B (1)

A. G. Okhrimchuk and A. V. Shestakov, “Absorption saturation mechanism for YAG:Cr4+ crystals,” Phys. Rev. B 61(2), 988–995 (2000).
[Crossref]

Quantum Electron. (1)

N. N. Il’ichev, A. V. Kir’yanov, and P. P. Pashinin, “Model of passive Q switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres,” Quantum Electron. 28(2), 147–151 (1998).
[Crossref]

Sci. Rep. (1)

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
[Crossref] [PubMed]

Other (6)

H. Sakai, A. Sone, H. Kan, and T. Taira, “Polarization stabilizing for diode-pumped passively Q-switched Nd:YAG microchip lasers,” Advanced-Solid-State Photonics 2006, MD2, USA (2006).

H. Sakai, H. Kan, and T. Taira, “Passive Q switch laser device,” (2006), WO Patent App. PCT/JP2005/016,315.

T. Hahn and A. Looijenga-Vos, “2.2 Contents and arrangement of the tables” in International Tables for Crystallography Brief Teaching Ed. Vol. A, T. Hahn ed. (Kluwer Academic Publishers, 2002).

R. W. G. Wyckoff, Crystal Structures Ed. 2, Vol.3, (John Wiley & Sons, 1965) p.222.

T. Taira, S. Morishima, K. Kanehara, N. Taguchi, A. Sugiura, and M. Tsunekane, “World first laser ignited gasoline engine vehicle,” The 1st Laser Ignition Conference (LIC’13), OPIC’13, Yokohama, Japan, April 23–25, LIC3–1 (2013).

V. Yahia and T. Taira, “Development of a 0.3GW Microchip-seeded Amplifier,” The 4th. Laser Ignition Conference (LIC'16), OPIC'16, Yokohama, Japan, LIC3–3 (2016).

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 (10)

Fig. 1
Fig. 1 Representation of the polarization by use of the polar coordinate with angles Θ and Φ.
Fig. 2
Fig. 2 Definition of θ for (100)-cut Cr4+:YAG crystals. (a) The relation between θ and crystal axes described with the view direction of the [100]-axis. The square and tetrahedrons indicate the unit cell of YAG crystal and S4 site in the unit cell, respectively. (b) The relation between θ, Θ, and Φ. The gray surface indicates the (100)-plane. r- axis and z-axis are parallel to the direction of the polarization and the direction of [ 1 ¯ 00 ], respectively.
Fig. 3
Fig. 3 Definition of θ for (110)-cut Cr4+:YAG crystals. (a) The relation between θ and crystal axes described with the view direction of the [110]-axis. The square and tetrahedrons indicate the unit cell of YAG crystal and S4 site in the unit cell, respectively. (b) The relation between θ, Θ, and Φ. The gray surface indicates the (110)-plane. r- axis and z-axis are parallel to the direction of the polarization and the direction of [ 1 ¯ 1 ¯ 0 ], respectively.
Fig. 4
Fig. 4 Definition of θ for (111)-cut Cr4+:YAG crystals. (a) The relation between θ and crystal axes described with the view direction of the [111]-axis. The square and tetrahedrons indicate the unit cell of YAG crystal and S4 site in the unit cell, respectively. (b) The relation between θ, Θ, and Φ. The gray surface indicates the (111)-plane. r- axis and z-axis are parallel to the direction of the polarization and the direction of [ 1 ¯ 1 ¯ 1 ¯ ], respectively.
Fig. 5
Fig. 5 Estimated polarized absorption coefficients of (100)-, (110)-, and (111)-cut Cr4+:YAG with α0 of 2.8 cm−1. β and the ratio between I and Is are assumed to be 0.28 and 27.6, respectively.
Fig. 6
Fig. 6 The schematic diagram of experimental setup.
Fig. 7
Fig. 7 Transmittance of a (110)-cut Cr4+:YAG with T0 of 75% under 1-W pumping focused into the spot with the radius of 25 μm. Black marker is the experimental value, and red line, blue line, and green lines are the calculation by use of Eq. (4) with β of 0.3, 0.4, and 0.5, respectively.
Fig. 8
Fig. 8 Transmittance of a (110)-cut Cr4+:YAG crystal with T0 of 75% unde 1-W pumping focused into the spot with the radius of 25 μm. Red marker is the experimental value, and blue line is the calculation by use of Eqs. (4) and (7) with β of 0.28.
Fig. 9
Fig. 9 Unit cell in the crystal structure of YAG. (a) The position of all ions in unit cell, which contains 24 Y3+-ions with site symmetry of D2 (gray spheres), 16 Al3+-ions with site symmetry of S6 (spheres in hexahedrons), 24 Al3+-ions with the site symmetry of S4 (spheres in tetrahedrons), and 96 O2--ions with the site symmetry of C1 (red spheres). (b) The projection of 24 Al3+-ions with site symmetry of S4 from the [100]-direction.
Fig. 10
Fig. 10 Energy diagram of Cr4+:YAG, where A, B, and E are irreducible representations under S4 symmetry. Related transitions with cross sections (σabs, σesa), radiative the decay time (τ), and the population density (n) are also indicated.

Equations (24)

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

α( I,Θ,Φ )= α 0 [ 1( 1β )( I cos 4 Φ sin 4 Θ I cos 2 Φ sin 2 Θ+ I s + I sin 4 Φ sin 4 Θ I sin 2 Φ sin 2 Θ+ I s + I cos 4 Θ I cos 2 Θ+ I s ) ].
β= σ esa σ abs ,
I s = E P σ abs τ ,
α 100 ( I,θ )= α 0 1+ I I s [ 1( 1β )( cos 4 θ+ sin 4 θ ) ]+β I 2 I s 2 sin 2 θ cos 2 θ ( 1+ I I s cos 2 θ )( 1+ I I s sin 2 θ ) .
α 110 ( I,θ )= α 0 1+ I I s ( β cos 4 θ+ 3 2 cos 2 θ sin 2 θ+ β 2 sin 4 θ )+ β I 2 2 I s 2 cos 2 θ sin 2 θ ( 1+ I I s cos 2 θ )( 1+ I 2 I s sin 2 θ ) .
Θ( θ )= cot 1 [ sinΦ( θ )+cosΦ( θ ) ],
Φ( θ )= tan 1 ( 3 tanθ )+ π 4 .
α 111 ( I,θ )= α 0 1+ 1 2 I I s ( 1+β )+ 1 36 I 2 I s 2 [ ( 1+8β )+( 1β )cos6θ ]+ 1 108 β( 1+cos6θ ) I 3 I s 3 ( 1+ 2 3 I I s cos 2 θ )[ 1+ 1 6 I I s ( 1+2 sin 2 θ+ 3 sin2θ ) ][ 1+ 1 6 I I s ( 1+2 sin 2 θ 3 sin2θ ) ] .
dP( z ) dz =P( z ) 0 1 α j [ 2kP( z ) π w 2 ,θ ]dk ,
ϕ( x,y,z )=ϕ( y,x,z )=ϕ( x,y,z )=ϕ( y,x,z ).
d n 2 i dt = 1 τ I i I s n tot 3 1 τ ( 1+ I i I s ) n 2 i ,
I [100] =I cos 2 Φ sin 2 Θ,
I [010] =I sin 2 Φ sin 2 Θ,
I [001] =I cos 2 Θ.
d I i dz =( n tot 3 n 2 i ) σ abs I i n 2 i σ esa I i = α 0 I i [ 1( 1β ) 3 n 2 i n tot ].
Τ 0 =exp( α 0 l )=exp( n tot 3 σ abs l ),
β= σ esa σ abs .
α( n 2 i , I i )= α 0 [ 1( 1β ) 3 n tot i n 2 i I i I ].
n 2 i = n tot 3 I i I i + I s .
I( z,r )= 2P( z ) π w 2 exp( 2 r 2 w 2 ).
dP( z ) dz = 0 2πr α j ( I,θ )I( z,r )dr ,
k=exp( 2 r 2 w 2 ).
0 l dz = P( 0 ) P( l ) dP P 0 1 dk α j ( 2kP π w 2 ,θ ) ,
l= T( P in ,θ ) P in P in dP P 0 1 α j ( 2kP π w 2 ,θ )dk .

Metrics