Abstract

The Cr3+- and Ti3+-doped crystals of chrysoberyl (BeAl2O4) and beryllium hexaaluminate (BeAl6O10) are very attractive for generation of near-IR ultrashort laser pulses in a few-optical-cycle regime from mode-locked oscillators. This work presents a detailed study of dispersive properties of both crystals, which is necessary for optimal dispersion control in such lasers. Sellmeier equations for the chrysoberyl (Cr:BeAl2O4 – Alexandrite) and BeAl6O10 crystals were derived and second- and third-order dispersive properties (GVD and TOD, respectively) were analyzed. Position of the optical axes and conicity angle were also predicted for these biaxial crystals which is of practical importance for their applications as conerefringent elements in lasers and laser beam shapers.

© 2016 Optical Society of America

1. Introduction

Over the past two decades generation of ultrashort laser pulses using cubic Ti3+:α-Al2O3 (Ti:Sapphire) crystal has become a well-established approach [1]. Such process strongly depends on the value of intracavity dispersion. In soliton mode-locking regime, the shortest pulses can be produced when the net intracavity dispersion is slightly negative [2]. Since laser materials typically display positive group velocity dispersion (GVD) in the near-IR spectral range, its proper compensation requires introduction of a certain amount of negative dispersion. Thus, the dispersion management relies on detailed knowledge of the dispersive properties of the laser crystal. This becomes even more critical when generation of a few-optical-cycle pulses is needed which have spectra spanning over hundreds of nm [3–5]. In this case, the spectral behavior of the dispersion also should be taken into account and plays a central role in determining the optimum design of dispersion compensating elements such as chirped mirrors [3–5]. Moreover, in the few-cycle regime, higher-order dispersive properties of materials, such as third-order dispersion (TOD), become increasingly important in pulse forming process and cannot be ignored [6].

Alongside the well-studied Ti3+:α-Al2O3 crystal, there are several other attractive candidates for generation of ultrashort laser pulses at around ~800 nm based on the Ti3+ and Cr3+ ions. Among them are the orthorhombic crystals of chrysoberyl, BeAl2O4 (Cr:BeAl2O4 – Alexandrite) and beryllium hexaaluminate, BeAl6O10. While Alexandrite is a well-known laser material [7,8], the other one was studied only recently [9]. Both crystals possess broad vibronic emission bands, they provide naturally polarized emission and have high thermal conductivity (~23 and 12 Wm−1K−1, respectively) [8,10]. Strong absorption in the blue-red spectral region opens the way for efficient pumping with visible laser diodes [11–13].

Recently, the first femtosecond mode-locked operation of Alexandrite laser was demonstrated producing pulses as short as 170 fs [14]. Considering a smooth wavelength tuning range of ~85 nm achieved in the continuous wave regime [15], the pulse duration can be reduced by at least one order of magnitude thus entering the few-optical-cycle regime where careful dispersion management is a must. Unfortunately, there was no detailed study of dispersive properties of BeAl2O4 to date and, for example, Sellmeier equations for its refractive indices are not available. In case of BeAl6O10, very limited information is available as well [10]. In addition, knowledge of Sellmeier equations is not only the necessary prerequisite for dispersive studies but it is also essential to predict refractive properties of crystals. Since both discussed crystals are optically biaxial, they exhibit internal conical refraction (CR) [16] and therefore can be used as passive (or active) conerefringent elements, e.g. in CR lasers [17,18] or beam shapers [19,20].

In the present work, we report on a detailed study of dispersive properties of Alexandrite and beryllium hexaaluminate, provide Sellmeier equations using enhanced four-parameter fitting model for both crystals and make initial analysis of their refractive properties.

2. Physical model

There are several known crystals in the xBeO–yAl2O3zSiO2 series, called in general beryllium aluminates [9,10]. In the present work, we will consider two compounds, BeAl2O4 (chrysoberyl, Cr:BeAl2O4 – Alexandrite) and BeAl6O10 (beryllium hexaaluminate). Both of them are orthorhombic (sp. gr. Pnma and Pcam, respectively). The unit cell of these crystals is characterized as abc and α = β = γ = 90°. In particular, the lattice parameters are a = 9.404 Å, b = 5.476 Å and c = 4.727 Å (for BeAl2O4) a = 9.553 Å, b = 13.816 Å and c = 8.929 Å (for BeAl6O10) [10,21].

Both crystals are biaxial. Their optical properties are thus described within the frame of the optical indicatrix with the mutually orthogonal principal axes Np, Nm and Ng (the corresponding refractive indices are np < nm < ng) [22]. These three axes are strictly linked to the crystal-physical frame, as follows: Np = [001], Nm = [100] and Ng = [010]. The two optical axes (OA) are located in the NpNg (or, equivalently, bc) plane. The angle between the Ng-axis and each of the OA is called the optical axis angle, Vg.

The data on the principal refractive indices of BeAl2O4 and BeAl6O10 in the spectral range covering visible and near-IR were taken from [8] and [10], respectively. The following four-parameter equation for the Sellmeier fit was used:

ni2=Ai+Bi1Ci/λ2+Diλ2.
Here, Ai, Bi, Ci and Di (i = p, m or g) are the Sellmeier coefficients and light wavelength λ is expressed in μm. The coefficients Ai and Bi should be positive for ni > 0. The coefficient Ci has the meaning of λ'g2 where λ'g is the wavelength corresponding to the “effective” bandgap E'g and thus Ci should be also positive. The coefficient Di describes dispersion in the mid-IR and it should be negative for the majority of dielectric crystals (which is supported by the experimental data for Alexandrite, as the decrease of refractive index is enhanced in the mid-IR [8]).

Using the obtained dispersion curves, we calculated dispersion of the optical axis angle Vg [16]:

sin2Vg=1/nm21/np21/ng21/np2.
For CR applications of a biaxial crystal, an important parameter is the full angle of a cone of internal conical refraction, 2ACR, that is also called conicity. It is defined as following [16]:

tan22ACR=nm2np2np2ng2nm2ng2.

Beryllium aluminates when doped with Cr3+ ions show very broad emission band in the red and near-IR spectral region spanning from ~0.65 up to 0.8 μm (for Alexandrite) or even up to ~1 μm (for BeAl6O10) [9] which is related to the 4T24A2 transition of the Cr3+ ions. For the Ti3+ ions (2E → 2T2 transition) in these crystals, the emission ranges are 0.65 – 1.05 μm and 0.62 – 1.15 μm, respectively [9]. This makes the Cr3+- and Ti3+-doped BeAl2O4 and BeAl6O10 crystals very attractive for generation of ultrashort laser pulses. The information about dispersion characteristics of both laser hosts is thus crucial for proper design of mode-locked oscillators. The important parameters for dispersion compensation are the group velocity dispersion (GVD) and third-order dispersion (TOD) which can be calculated as [23]:

GVDi=λ32πc2d2nidλ2,
TODi=(λ2πc)21c[3λ2d2nidλ2+λ3d3nidλ3].
Here, c is the speed of light, d2n/dλ2 and d3n/dλ3 are the second-order and third-order derivatives of the refractive index calculated at the particular wavelength.

For the description of refraction in dielectric crystals, a useful parameter is the molar polarizability αm. It can be determined from the Clausius–Mossotti relation. Strictly speaking, the latter can be applied only for homogeneous and isotropic dielectric. However, for particular classes of anisotropic materials (including orthorhombic crystals) for which optical indicatrix frame is linked to the crystal-physical one, it can be generalized for the principal αim values along the optical indicatrix axes [24]:

εi1εi+2Mρ=4πNAαmi3.
Here, εi = ni2 is the dielectric constant, M is the molar mass of the compound, ρ is its density and NA is the Avogadro number. In this way, the principal values αim take into account both the anisotropy of individual particles, as well as their arrangement in the lattice [24].

3. Results and discussion

Doping of the considered crystals with laser-active Cr3+ and Ti3+ ions results in the emission in the near-IR spectral region. For Alexandrite (Cr:BeAl2O4), the typical emission wavelength is 755 nm. For Cr:BeAl6O10, it is ~830 nm. As Alexandrite and BeAl6O10 crystals are optically biaxial, they exhibit internal conical refraction and if cut along one of the OA they can be used as passive or active conerefringent elements for visible and near-IR light. Thus, we discuss dispersive and refractive properties of these materials in the spectral range from ~0.25 to ~1 μm. Both BeAl2O4 and BeAl6O10 have relatively large optical bandgaps, Eg ~5.5 eV and thus they are transparent up to λg ~0.23 μm [10,21].

Data on the principal refractive indices ni as well as best-fitting Sellmeier curves for Alexandrite and BeAl6O10 crystals at room temperature are shown in Fig. 1. As one can see, the proposed Sellmeier fits describe perfectly the dispersion of the refractive indices (within an error of Δn ~10−5...10−4). The corresponding set of Sellmeier coefficients Ai, Bi, Ci and Di is compiled in Table 1. Due to the availability of ni for Alexandrite crystal, the derived Sellmeier equations are valid up to at least 2.5 μm. For Alexandrite, np = 1.734(5), nm = 1.736(4) and ng = 1.741(9) at the wavelength of 755 nm. For BeAl6O10, np = 1.731(2), nm = 1.733(0) and ng = 1.737(5) at 830 nm. Thus, the refractive indices of BeAl6O10 are slightly lower than those of Alexandrite. No change of the attribution of the optical indicatrix axes with respect to the crystal-physical frame is observed in the visible and near-IR. It should be noted that dispersion of BeAl6O10 was previously described with a simple three-term Sellmeier equation [10] which is less precise in the near-IR spectral range.

 figure: Fig. 1

Fig. 1 Dispersion of the principal refractive indices ni (i = p, m, g) for Alexandrite (a) and BeAl6O10 (b) crystals. Symbols: experimental data adopted from [8,10], curves: Sellmeier fits in accordance with Eq. (1), insets: relative size of the unit-cell and orientation of optical indicatrix axes (Np, Nm and Ng) with respect to the crystallographic ones.

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Tables Icon

Table 1. Sellmeier Coefficients in Eq. (1) for BeAl2O4 and BeAl6O10 Crystals

In Fig. 2(a), we have analyzed dispersion of the optical axis angle Vg for both crystals which is relevant for their potential CR-based applications. For this, Eq. (2) has been used. For Alexandrite Vg = 30°31′ at 755 nm and for BeAl6O10 Vg = 33°05′ at 830 nm. For Alexandrite, Vg is minimized in the visible and it further increases in the near-IR. For BeAl6O10, Vg decreases monotonously with the wavelength. For rays with any polarization propagating along the OA in the considered crystals, the refractive index will be the same, nOA = nm. The results on the full angle of the cone of CR, 2ACR, are shown in Fig. 2(b). For Alexandrite 2ACR = 12'44” (3.70 mrad) at 755 nm and for BeAl6O10 2ACR = 11'23” (3.31 mrad) at 830 nm.

 figure: Fig. 2

Fig. 2 (a) Positive biaxial Alexandrite and BeAl6O10 crystals: (a) dispersion of the optical axis angle Vg, as calculated with Eq. (2); inset: orientation of the optical axes with respect to the optical indicatrix and crystal-physical frames; (b) dispersion of the full angle of the cone of CR, 2ACR, as calculated with Eq. (3), inset: scheme explaining definition of this angle.

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Optically biaxial crystals are classified as positive and negative [22]. If the intermediate principal refractive index (nm) is closer to the minimum one (np) than to the maximum one (ng), the crystal is classified as positive. In our case OAs are located closer to the Ng-axis, i.e. Vg < 45°. In other words, the acute angle 2Vg between the two OAs is bisected by the Ng-axis. Both Alexandrite and BeAl6O10 crystals are thus positive biaxial.

Results on the GVD and TOD are shown in Fig. 3. For this, Eq. (4) has been used. Their anisotropy for the principal light polarizations is very weak. Due to the anisotropy of absorption and stimulated emission cross-sections, the polarization of interest for Alexandrite is E || b (b = Ng) and it is E || a (a = Nm) for Cr3+ doped BeAl6O10. GVD for both crystals is positive and relatively small in the visible and near-IR spectral regions. For Alexandrite, GVD = 60.7 fs2/mm (at 755 nm, for E || b) and for BeAl6O10 it is slightly lower, 53.1 fs2/mm (at 830 nm, E || a). These values can be compared to GVD of 56.6 fs2/mm for Ti:α-Al2O3 at 800 nm [23]. For both studied crystals, GVD decreases monotonously with the wavelength which is typical for dielectric crystals. TOD is also positive. It reaches minimum in the red spectral region and further increases in the near-IR. For Alexandrite, TOD = 39.5 fs3/mm and for BeAl6O10 it is larger, 45.2 fs3/mm (for the respective light wavelengths and polarizations). These values are also similar to 41.4 fs3/mm of TOD at 800 nm for Ti:α-Al2O3 [23].

 figure: Fig. 3

Fig. 3 (a,b) Group velocity dispersion (GVD) and (c,d) third-order dispersion (TOD) versus light wavelength for Alexandrite (BeAl2O4) (a,c) and BeAl6O10 (b,d) crystals, as calculated with Eq. (4).

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Finally, the analysis of anisotropy of polarizability is needed for further description of temperature variation of the refractive index expressed by the dn/dT coefficient. In order to determine molar polarizability of Alexandrite and BeAl6O10 crystals, we have used Eq. (5) with the following material parameters: M = 126.97 and 330.89 g/mol, ρ = 3.70 and 3.74 g/cm3, respectively. The results are shown in Fig. 4.

 figure: Fig. 4

Fig. 4 Dispersion of molecular polarizability αm for Alexandrite (a) and BeAl6O10 (b) crystals, as calculated with Eq. (5).

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The anisotropy of the principal αim values is weak which justifies the use of the “generalized” Clausius-Mossotti relation. Molecular polarizability decreases monotonously with the wavelength. At ~1 μm, polarization-averaged value is ‹αm› = 5.44 Å3 for Alexandrite and ‹αm› = 14.0 Å3 for BeAl6O10. This value can be taken as a long-wavelength one due to the weak dispersion of αm in the near-IR. Big difference in ‹αm› for two crystals is mainly attributed to the different number of O2- ions in one formula unit. It is known that ionic polarizability of O2- depends strongly on the compound and can vary as 0.5–3.2 Å3 [25]. The actual value of α(O2-) can be estimated by subtracting ionic polarizabilities of cations which are less sensitive to the crystal structure from the molecular one. The assumption of simple additivity for polarizabilities is reasonable for many crystals [25]. In our case, α(Be2+) = 0.04 Å3 and α(Al2+) = 0.067 Å3, so ‹α(O2-)› = 1.32 Å3 for BeAl2O4 and 1.36 Å3 for BeAl6O10. These two values are in close agreement with each other and they are also very close to the value for beryllium oxide BeO, α(O2-) = 1.29 Å3 [25]. Thus, the additivity approximation can explain the variation of polarizability in beryllium-containing simple and complex oxides.

4. Conclusion

We presented a detailed comparative analysis of dispersive properties for orthorhombic beryllium aluminates, namely chrysoberyl, BeAl2O4 (Cr:BeAl2O4 - Alexandrite) and BeAl6O10 (beryllium hexaaluminate), focusing on the parameters relevant for applications of these Cr3+-and Ti3+-doped crystals in ultrafast mode-locked oscillators. Sellmeier equations were derived for both materials based on the previously reported refractive indices. GVD and TOD values were calculated, yielding very similar and reasonably low values for both hosts in the red spectral region, ~60 fs2/mm and ~40 fs3/mm, respectively. Position of the optical axes and conicity angles were also predicted for these biaxial crystals which is of practical importance for their applications as CR-elements in lasers and laser beam shapers. Further work on BeAl2O4 and BeAl6O10 crystals will be focused on description of their thermo-optic properties. As a prerequisite for this, molecular polarizability of both compounds has been calculated.

Acknowledgments

The authors acknowledge funding from the Natural Sciences and Engineering Research Council of Canada.

References and links

1. D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16(1), 42–44 (1991). [CrossRef]   [PubMed]  

2. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000). [CrossRef]  

3. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24(6), 411–413 (1999). [CrossRef]   [PubMed]  

4. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24(9), 631–633 (1999). [CrossRef]   [PubMed]  

5. T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003). [CrossRef]  

6. C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994). [CrossRef]  

7. J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985). [CrossRef]  

8. J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980). [CrossRef]  

9. E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001). [CrossRef]  

10. E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997). [CrossRef]  

11. S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990). [CrossRef]  

12. E. Beyatli, I. Baali, B. Sumpf, G. Erbert, A. Leitenstorfer, A. Sennaroglu, and U. Demirbas, “Tapered diode-pumped continuous-wave alexandrite laser,” J. Opt. Soc. Am. B 30(12), 3184–3192 (2013). [CrossRef]  

13. A. Teppitaksak, A. Minassian, G. M. Thomas, and M. J. Damzen, “High efficiency >26 W diode end-pumped Alexandrite laser,” Opt. Express 22(13), 16386–16392 (2014). [CrossRef]   [PubMed]  

14. S. Ghanbari, R. Akbari, and A. Major, “Femtosecond Kerr-lens mode-locked Alexandrite laser,” in CLEO:2016, OSA Technical Digest Series (Optical Society of America, 2016), P. JTu5A.77.

15. S. Ghanbari and A. Major, “High power continuous-wave Alexandrite laser with green pump,” in CLEO:2014, OSA Technical Digest Series (Optical Society of America, 2014), P. JTu4A.126. [CrossRef]  

16. J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994). [CrossRef]  

17. J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007). [CrossRef]   [PubMed]  

18. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010). [CrossRef]   [PubMed]  

19. G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, “Conical Refraction: new observations and a dual cone model,” Opt. Express 21(9), 11125–11131 (2013). [CrossRef]   [PubMed]  

20. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010). [CrossRef]  

21. C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

22. A. J. F. Nye, Physical Properties of Crystals (Clarendon Press, 1957).

23. X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996). [CrossRef]  

24. H. E. J. Neugebauer, “Clausius-Mosotti equation for certain types of anisotropic crystals,” Can. J. Phys. 32(1), 1–8 (1954). [CrossRef]  

25. J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953). [CrossRef]  

References

  • View by:

  1. D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16(1), 42–44 (1991).
    [Crossref] [PubMed]
  2. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
    [Crossref]
  3. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24(6), 411–413 (1999).
    [Crossref] [PubMed]
  4. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24(9), 631–633 (1999).
    [Crossref] [PubMed]
  5. T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
    [Crossref]
  6. C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
    [Crossref]
  7. J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
    [Crossref]
  8. J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
    [Crossref]
  9. E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001).
    [Crossref]
  10. E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
    [Crossref]
  11. S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
    [Crossref]
  12. E. Beyatli, I. Baali, B. Sumpf, G. Erbert, A. Leitenstorfer, A. Sennaroglu, and U. Demirbas, “Tapered diode-pumped continuous-wave alexandrite laser,” J. Opt. Soc. Am. B 30(12), 3184–3192 (2013).
    [Crossref]
  13. A. Teppitaksak, A. Minassian, G. M. Thomas, and M. J. Damzen, “High efficiency >26 W diode end-pumped Alexandrite laser,” Opt. Express 22(13), 16386–16392 (2014).
    [Crossref] [PubMed]
  14. S. Ghanbari, R. Akbari, and A. Major, “Femtosecond Kerr-lens mode-locked Alexandrite laser,” in CLEO:2016, OSA Technical Digest Series (Optical Society of America, 2016), P. JTu5A.77.
  15. S. Ghanbari and A. Major, “High power continuous-wave Alexandrite laser with green pump,” in CLEO:2014, OSA Technical Digest Series (Optical Society of America, 2014), P. JTu4A.126.
    [Crossref]
  16. J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994).
    [Crossref]
  17. J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
    [Crossref] [PubMed]
  18. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
    [Crossref] [PubMed]
  19. G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, “Conical Refraction: new observations and a dual cone model,” Opt. Express 21(9), 11125–11131 (2013).
    [Crossref] [PubMed]
  20. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
    [Crossref]
  21. C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).
  22. A. J. F. Nye, Physical Properties of Crystals (Clarendon Press, 1957).
  23. X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996).
    [Crossref]
  24. H. E. J. Neugebauer, “Clausius-Mosotti equation for certain types of anisotropic crystals,” Can. J. Phys. 32(1), 1–8 (1954).
    [Crossref]
  25. J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953).
    [Crossref]

2014 (1)

2013 (2)

2010 (2)

2007 (1)

2003 (1)

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

2001 (1)

E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001).
[Crossref]

2000 (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
[Crossref]

1999 (2)

1997 (1)

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

1996 (1)

X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996).
[Crossref]

1994 (2)

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
[Crossref]

J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994).
[Crossref]

1991 (1)

1990 (1)

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

1985 (1)

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

1980 (1)

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

1979 (1)

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

1954 (1)

H. E. J. Neugebauer, “Clausius-Mosotti equation for certain types of anisotropic crystals,” Can. J. Phys. 32(1), 1–8 (1954).
[Crossref]

1953 (1)

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953).
[Crossref]

Abdolvand, A.

Alimpiev, A. I.

E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001).
[Crossref]

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Angelow, G.

Baali, I.

Beyatli, E.

Boulanger, B.

J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994).
[Crossref]

Brabec, T.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
[Crossref]

Bünting, U.

Carnegie, D. J.

Chen, Y.

Cho, S. H.

Cline, C. F.

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

Cormier, J.-F.

X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996).
[Crossref]

Curley, P. F.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
[Crossref]

Damzen, M. J.

Demirbas, U.

Donald, F. H.

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

Drexler, W.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Dutoit, M.

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

Erbert, G.

Féve, J. P.

J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994).
[Crossref]

Fuji, T.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Fujimoto, J. G.

Gallmann, L.

Gately, B. M.

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

Harget, P. J.

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

Harter, D. J.

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

Haus, H. A.

Haussmann, D.

Heller, D. F.

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

Hellström, J.

Henricsson, H.

Ippen, E. P.

Jenssen, H. P.

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

Kahn, A. H.

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953).
[Crossref]

Kalkandjiev, T. K.

Kärtner, F. X.

Kean, P. N.

Keller, U.

Kirpichnikov, A. V.

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Krasinski, J. S.

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

Krausz, F.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
[Crossref]

Leitenstorfer, A.

Marnier, G.

J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994).
[Crossref]

Matrosov, V. N.

E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001).
[Crossref]

Matuschek, N.

Minassian, A.

Morgner, U.

Morier-Genoud, F.

Morris, R. C.

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

Myers, J. F.

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

Neugebauer, H. E. J.

H. E. J. Neugebauer, “Clausius-Mosotti equation for certain types of anisotropic crystals,” Can. J. Phys. 32(1), 1–8 (1954).
[Crossref]

O’Dell, E. W.

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

Pasiskevicius, V.

Peet, V.

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

Pestryakov, E. V.

E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001).
[Crossref]

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Pete, J.

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

Peterson, O. G.

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

Petrov, V. V.

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Piché, M.

X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996).
[Crossref]

Rafailov, E. U.

Samelson, H.

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

Scheps, S. R.

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

Scheuer, V.

Semenov, V. I.

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Sennaroglu, A.

Shockley, W.

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953).
[Crossref]

Sibbett, W.

Sokolovskii, G. S.

Spence, D. E.

Spielmann, C.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
[Crossref]

Steinmeyer, G.

Stingl, A.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Sumpf, B.

Sutter, D. H.

Tempea, G.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Teppitaksak, A.

Tessman, J. R.

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953).
[Crossref]

Thomas, G. M.

Trunov, V. I.

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Tschudi, T.

Unterhuber, A.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Walling, J.

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

Walling, J. C.

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

Wilcox, K. G.

Yakovlev, V. S.

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Zhu, X.

X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996).
[Crossref]

Zubrinov, I. I.

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

Appl. Phys. B (1)

T. Fuji, A. Unterhuber, V. S. Yakovlev, G. Tempea, A. Stingl, F. Krausz, and W. Drexler, “Generation of smooth, ultra-broadband spectra directly from a prism-less Ti:sapphire laser,” Appl. Phys. B 77(1), 125–128 (2003).
[Crossref]

Appl. Phys. Lett. (1)

S. R. Scheps, B. M. Gately, J. F. Myers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor lasers,” Appl. Phys. Lett. 56(23), 2288–2290 (1990).
[Crossref]

Can. J. Phys. (1)

H. E. J. Neugebauer, “Clausius-Mosotti equation for certain types of anisotropic crystals,” Can. J. Phys. 32(1), 1–8 (1954).
[Crossref]

IEEE J. Quantum Electron. (3)

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30(4), 1100–1114 (1994).
[Crossref]

J. Walling, F. H. Donald, H. Samelson, D. J. Harter, J. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21(10), 1568–1581 (1985).
[Crossref]

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
[Crossref]

J. Appl. Phys. (1)

E. V. Pestryakov, V. V. Petrov, I. I. Zubrinov, V. I. Semenov, V. I. Trunov, A. V. Kirpichnikov, and A. I. Alimpiev, “Physical properties of BeAl6O10 single crystals,” J. Appl. Phys. 82(8), 3661–3666 (1997).
[Crossref]

J. Mater. Sci. (1)

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical properties of BeAl2O4 single crystals,” J. Mater. Sci. 14, 941–944 (1979).

J. Mod. Opt. (1)

X. Zhu, J.-F. Cormier, and M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43(8), 1701–1721 (1996).
[Crossref]

J. Opt. (1)

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

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

Opt. Commun. (1)

J. P. Féve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refractions in KTP,” Opt. Commun. 105(3-4), 243–252 (1994).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. (1)

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92(4), 890–895 (1953).
[Crossref]

Quantum Electron. (1)

E. V. Pestryakov, A. I. Alimpiev, and V. N. Matrosov, “Prospects for the development of femtosecond laser systems based on beryllium aluminate crystals doped with chromium and titanium ions,” Quantum Electron. 31(8), 689–696 (2001).
[Crossref]

Other (3)

S. Ghanbari, R. Akbari, and A. Major, “Femtosecond Kerr-lens mode-locked Alexandrite laser,” in CLEO:2016, OSA Technical Digest Series (Optical Society of America, 2016), P. JTu5A.77.

S. Ghanbari and A. Major, “High power continuous-wave Alexandrite laser with green pump,” in CLEO:2014, OSA Technical Digest Series (Optical Society of America, 2014), P. JTu4A.126.
[Crossref]

A. J. F. Nye, Physical Properties of Crystals (Clarendon Press, 1957).

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Figures (4)

Fig. 1
Fig. 1 Dispersion of the principal refractive indices ni (i = p, m, g) for Alexandrite (a) and BeAl6O10 (b) crystals. Symbols: experimental data adopted from [8,10], curves: Sellmeier fits in accordance with Eq. (1), insets: relative size of the unit-cell and orientation of optical indicatrix axes (Np, Nm and Ng) with respect to the crystallographic ones.
Fig. 2
Fig. 2 (a) Positive biaxial Alexandrite and BeAl6O10 crystals: (a) dispersion of the optical axis angle Vg, as calculated with Eq. (2); inset: orientation of the optical axes with respect to the optical indicatrix and crystal-physical frames; (b) dispersion of the full angle of the cone of CR, 2ACR, as calculated with Eq. (3), inset: scheme explaining definition of this angle.
Fig. 3
Fig. 3 (a,b) Group velocity dispersion (GVD) and (c,d) third-order dispersion (TOD) versus light wavelength for Alexandrite (BeAl2O4) (a,c) and BeAl6O10 (b,d) crystals, as calculated with Eq. (4).
Fig. 4
Fig. 4 Dispersion of molecular polarizability αm for Alexandrite (a) and BeAl6O10 (b) crystals, as calculated with Eq. (5).

Tables (1)

Tables Icon

Table 1 Sellmeier Coefficients in Eq. (1) for BeAl2O4 and BeAl6O10 Crystals

Equations (6)

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

n i 2 = A i + B i 1 C i / λ 2 + D i λ 2 .
sin 2 V g = 1 / n m 2 1 / n p 2 1 / n g 2 1 / n p 2 .
tan 2 2 A C R = n m 2 n p 2 n p 2 n g 2 n m 2 n g 2 .
G V D i = λ 3 2 π c 2 d 2 n i d λ 2 ,
T O D i = ( λ 2 π c ) 2 1 c [ 3 λ 2 d 2 n i d λ 2 + λ 3 d 3 n i d λ 3 ] .
ε i 1 ε i + 2 M ρ = 4 π N A α m i 3 .

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