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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 13 — Jun. 23, 2008
  • pp: 9507–9512

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High-power linearly-polarized operation of a cladding-pumped Yb fibre laser using a volume Bragg grating for wavelength selection

P. Jelger, P. Wang, J. K. Sahu, F. Laurell, and W. A. Clarkson  »View Author Affiliations


Optics Express, Vol. 16, Issue 13, pp. 9507-9512 (2008)
http://dx.doi.org/10.1364/OE.16.009507


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Abstract

In this work a volume Bragg grating is used as a wavelength selective element in a high-power cladding-pumped Yb-doped silica fiber laser. The laser produced 138 W of linearly-polarized single-spatial-mode output at 1066 nm with a relatively narrow linewidth of 0.2 nm for ~202 W of launched pump power at 976 nm. The beam propagation factor (M2) for the output beam was determined to be 1.07. Thermal limitations of volume Bragg gratings are discussed in the context of power scaling for fiber lasers.

© 2008 Optical Society of America

1. Introduction

High-power narrow linewidth lasers are used in a wide range of areas such as stand-off measurements and Raman spectroscopy, as well as pump sources for Raman lasers and continuous wave optical parametric oscillators. They can also potentially be used to reach multiple kW of continuous-wave emission through spectral beam combination, a technique which requires the individual lasers to have a well defined narrow spectral width [1

A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, “Efficient power scaling of laser radiation by spectral beam combining,” Opt. Lett. 33, 384–386 (2008). [CrossRef] [PubMed]

].

There are several feedback techniques available to yield a narrow linewidth laser emission. For fiber lasers, the use of fiber Bragg gratings (FBGs), written holographically by exposing photosensitive fibers to UV radiation or via a direct-writing with a femtosecond laser [2

N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Stable high-power continuous-wave Yb˄ 3+-doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating,” Opt. Lett. 32, 1486–1488 (2007). [CrossRef] [PubMed]

] is the standard approach. Recently, stable output power in the multi-hundred-watt regime has been attained with this approach [3

C. H. Liu, A. Galvanauskas, V. Khitrov, B. Samson, U. Manyam, K. Tankala, D. Machewirth, and S. Heinemann, “High-power single-polarization and single-transverse-mode fiber laser with an all-fiber cavity and fiber-grating stabilized spectrum,” Opt. Lett. 31, 17–19 (2006). [CrossRef] [PubMed]

]. Nonetheless, FBGs have the disadvantage that it is difficult to achieve linewidths <1 nm with slightly multi-mode fiber laser configurations. Thus, scaling to large core sizes to facilitate further power scaling whilst retaining a relatively narrow linewidth output is problematic. The use of a reflective surface diffraction grating in an external feedback cavity is an alternative approach, but this suffers from the drawback that a large collimated beam size must be incident on the grating for narrow-linewidth operation making the external cavity quite cumbersome and difficult to align. Recently, volume Bragg gratings (VBGs) have attracted a great deal of interest for wavelength selection in laser diodes [4

B. L. Volodin, S. V. Dolgy, E. D. Melnik, E. Downs, J. Shaw, and V. S. Ban, “Wavelength stabilization and spectrum narrowing of high-power multimode laser diodes and arrays by use of volume Bragg gratings,” Opt. Lett. 29, 1891–1893 (2004). [CrossRef] [PubMed]

], solid state lasers [5

B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Tunable single-longitudinal-mode ErYb:glass laser locked by a bulk glass Bragg grating,” Opt. Lett. 31, 1663–1665 (2006). [CrossRef] [PubMed]

], optical parametric oscillators [6

B. Jacobsson, M. Tiihonen, V. Pasiskevicius, and F. Laurell, “Narrowband bulk Bragg grating optical parametric oscillator,” Opt. Lett. 30, 2281–2283 (2005). [CrossRef] [PubMed]

] and fiber lasers [7

P. Jelger and F. Laurell, “Efficient skew-angle cladding-pumped tunable narrow-linewidth Yb-doped fiber laser,” Opt. Lett. 32, 3501–3503 (2007). [CrossRef] [PubMed]

]. VBGs are generally fabricated from holographically exposed photo-thermo-refractive (PTR) glass doped with silver, cerium and fluorine. PTR-glass [8

O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, “High-efficiency Bragg gratings in photothermorefractive glass,” Appl. Opt. 38, 619–627 (1999). [CrossRef]

] has a large transparency window (350-2700 nm), low thermal variations in refractive index (dn/dT=5×10-8K-1), high damage threshold [9

L. B. Glebov, L. N. Glebova, V. I. Smirnov, M. Dubinskii, L. D. Merkle, S. Papernov, and A. W. Schmid, “Laser damage resistance of photo-thermo-refractive glass Bragg gratings,” Proceedings of Solid State and Diode Lasers Technical Review. Albuquerque (2004).

] and they can be designed with high reflectivity (>99.9 %) and bandwidths from tens of pm up to ~0.5 nm. These properties make VBGs highly interesting for high power applications. Even more recently, we reported on an Er,Yb-doped fiber laser and the benefits of locking it with a VBG compared to a dielectric mirror or a replica diffraction grating [10

J. W. Kim, P. Jelger, J. K. Sahu, F. Laurell, and W. A. Clarkson, “High-power and wavelength-tunable operation of an Er,Yb fiber laser using a volume Bragg grating,” Opt. Lett. 33, 1204–1206 (2008). [CrossRef] [PubMed]

]. A higher slope efficiency was achieved together with a higher output power thanks to the narrow reflection bandwidth.

In this work we evaluate the behavior of a VBG in a high power fiber laser set-up. The previously reported output power from a VBG locked Yb-fiber laser [7

P. Jelger and F. Laurell, “Efficient skew-angle cladding-pumped tunable narrow-linewidth Yb-doped fiber laser,” Opt. Lett. 32, 3501–3503 (2007). [CrossRef] [PubMed]

] has been scaled almost two orders-of-magnitude to 138 W of continuous-wave output (limited by pump power). The output was nearly diffraction-limited with a linewidth of 0.2 nm. In addition, a polarization extinction ratio (PER) of 15 dB was achieved. To the authors’ knowledge, this is the first operation of a VBG-locked high power fiber laser with a highly polarized output. Additionally, as the laser peak was found to shift at high powers, the power handling capabilities of the VBG in a fiber laser cavity are discussed which. In the context of this discussion, it is also shown that the experimental results did not show any signs of a degradation of the diffraction efficiency of the VBG.

2. Setup and results

The fiber laser set-up is depicted in Fig. 1. An ytterbium-doped polarization-maintaining double-clad silica fiber was used in the experiments. The fiber had a core diameter of 20 µm and a cladding diameter of 400 µm with corresponding numerical apertures of 0.06 and 0.46. The stress rods in the circular outer-cladding helped to increase the pump absorption along the fiber, which was determined to be 2 dB/m at 976 nm. A fiber length of 6 m was chosen as this provided the best gain around 1066 nm, which corresponded to the design wavelength of the VBG. The fiber was coiled (15 cm) to increase the losses for the higher order modes and promote single-mode lasing. The intracavity fiber-end adjacent to the external cavity was angle-polished to 8 degrees to help prevent parasitic lasing between the fiber ends. The fiber was pumped by a two polarization-combined laser diode-stacks emitting at 976 nm with a maximum output power of 250 W. The pump launch efficiency was measured by using a short piece of gain fiber and it was found to be 81%. A dicroic mirror was used to separate the laser emission from the pump.

Fig. 1. Experimental set-up. L1 and L2 are collimating lenses.

The VBG used in our experiments was 5 mm thick, had a clear aperture of 3×5 mm and was anti-reflection coated for 1.06 µm. The focal length of the intracavity lens L2 was chosen to be 8 mm, giving a beam diameter of 0.9 mm maximizing the use of the VBG aperture. The glass surfaces were tilted 2 degrees relative to the grating planes to further reduce any parasitic feedback due to Fresnel reflections. The reflectivity of the grating was 99% and the bandwidth was 0.22 nm FWHM as measured with a Ti:Sapphire laser (see Fig. 2). The VBG was installed in a passively-cooled aluminum heat-sink to enable monitoring of the temperature of the VBG as well as allow for active cooling if it would become necessary. Although the residual absorption in PTR-glass is low (<1%) [11

J. Lumeau, L. Glebova, and L. B. Glebov, “Influence of UV-exposure on the crystallization and optical properties of photo-thermo-refractive glass,” J. Non-Cryst. Solids (2007).

], a small shift in emission wavelength was noticed due to heating of the glass. At low powers, the laser operated at 1065.9 while at high powers it was shifted 0.1 nm to 1066 nm. Despite this, there was no noticeable degradation in spectral shape once the grating had reached its new thermal equilibrium. As scattering can be high (several precent) [11

J. Lumeau, L. Glebova, and L. B. Glebov, “Influence of UV-exposure on the crystallization and optical properties of photo-thermo-refractive glass,” J. Non-Cryst. Solids (2007).

], the heating might in part be attributed to scattered light being absorbed in the mount.

Fig. 2. Measured reflectivity of VBG.

Many applications require radiation with a high degree of polarization (e.g. nonlinear parametric processes). As the fiber was polarization-maintaining, a half-wave plate and a thin-film polarizer were inserted between the fiber and the VBG. The degree of polarization was measured with an additional λ/2-plate and a polarizing prism at the output. The beam was attenuated with the help of a highly reflective mirror, in order not to destroy the polarizing prism. By rotating the intra-cavity λ/2-plate, a polarization extinction ratio (PER) of 15 dB was determined.

The output power was measured with a water-cooled power meter and a maximum output power of 138 W was recorded with a slope efficiency of 76 %, and a threshold of roughly 4 W. This was compared to an identical set-up with a conventional broadband mirror used to provide feedback in place of the VBG, but no discernable difference in slope efficiency or output power could be seen. In both cases, Fresnel reflections from the perpendicularly-cleaved output end of the fiber provided the necessary feedback for lasing. At the highest power, the FWHM emission spectrum was measured to be below 0.2 nm. The output power versus pump power and the emission spectrum are shown in Fig. 3(a) and Fig. 3(b), respectively.

Fig 3. (a). Output power versus launched pump power. b) Typical spectral output from free-running laser compared to VBG-locked laser.

3. Discussion and conclusion

As was mentioned in the results section, the emission wavelength was shifted 0.1 nm due to heating of the VBG. This raises the important question of how the VBG will perform at much higher power levels. Although PTR-glass has a high damage threshold [9

L. B. Glebov, L. N. Glebova, V. I. Smirnov, M. Dubinskii, L. D. Merkle, S. Papernov, and A. W. Schmid, “Laser damage resistance of photo-thermo-refractive glass Bragg gratings,” Proceedings of Solid State and Diode Lasers Technical Review. Albuquerque (2004).

], it may fail even earlier in its function as a Bragg grating due to non-uniform heating and hence distortion.

When a grating is subjected to a high power laser beam the grating will be distorted via differential thermal expansion, governed by the expansion coefficient, α=8.4 ppm/K [12

J. W. Zwanziger, U. Werner-Zwanziger, E. D. Zanotto, E. Rotari, L. N. Glebova, L. B. Glebov, and J. F. Schneider, “Residual internal stress in partially crystallized photothermorefractive glass: Evaluation by nuclear magnetic resonance spectroscopy and first principles calculations,” J. Appl. Phys. 99, 083511 (2006). [CrossRef]

], and via thermally-induced change in refractive index, governed by the thermal dispersion coefficient, dn/dT=0.05 ppm/K [13

G. B. Venus, A. Sevian, V. I. Smirnov, and L. B. Glebov, “High-brightness narrow-line laser diode source with volume Bragg-grating feedback,” Proc. SPIE 5711, 166–276 (2005). [CrossRef]

]. Additionally, the beam incident on the VBG will be refracted by the thermal lens caused by the refractive index change and non-uniform expansion. It is important to note that the thermal lens will actually counteract the effect of the grating distortion.

The impact of a temperature change in the VBG can also be understood from the derivative of the Bragg condition at normal incidence λB =2n0Λ, where λB is the Bragg wavelength, n0 is the refractive index of the glass and Λ is the grating period [14

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Finite Beams in Reflective Volume Bragg Gratings: Theory and Experiments,” IEEE J. Quantum Electron. 44, 81–89 (2008). [CrossRef]

]:

d λB dT= 2 d n0 dTΛ+2 dΛ dT · n0= λB ( 1 n0 d n0 dT+α)
(1)

In the above expression, we can see that the temperature dependence of the Bragg wavelength λ B is proportional to both dn/dT and α. As we can see from the numbers above however, the thermal expansion will be the dominant effect as it is two orders-of-magnitude larger than thermal dispersion. Direct measurements show that the Bragg wavelength temperature dependence is roughly 8.8 pm/K at 1.066 µm, which corresponds well with our experimental data. In our experiment, the wavelength shift corresponds to an overall temperature increase of roughly 15 degrees.

In a recent paper by Shu et al [15

H. Shu and M. Bass, “Modeling the reflection of a laser beam by a deformed highly reflective volume bragg grating,” Appl. Opt. 46, 2930–2938 (2007). [CrossRef] [PubMed]

], the effect of uniform grating distortion was numerically simulated and it was shown that even for small distortions, i.e. a few µm along the optic axis, the reflectivity of the grating was considerably reduced. The model however assumed that the grating distortion only varied radially with a Gaussian distortion profile, which generally is not the case. For a strong grating, the light intensity inside the VBG is not uniform along the optical axis and, for plane waves, it can easily be shown that the normalized averaged intensity distribution as a function of position z along the optical axis is given by [16

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

]:

I (z)= 1 cosh⁡ ( tanh⁡ −1 ( R)) · cosh⁡ (2 tanh⁡ −1 ( R) · ( d−z))
(2)

In Eq. (2) above, R is the peak reflectivity and d is the thickness of the grating. A normalized plot of the intensity distribution for various reflectivities is shown in Fig. 4(a). The exponential intensity drop will induce a temperature gradient along the optical axis leading to ‘chirping’ of the grating. In fact, there is also a radial variation in temperature which arises due to the edge-cooled heat-sinking arrangement. The net effect is broadening of the reflectivity bandwidth as well as a reduction of the effective grating length, and consequently a reduction in reflectivity.

Fig 4. (a). Intensity distribution in VBGs with different grating strengths b), Simulated axial temperature drop for a VBG with a 1 kW incident beam and R=99%

The thermal lens in the VBG can be estimated with the following simplified expression [17

W. Koechner, Solid-State Laser Engineering , 6th ed. (Springer, 2006).

]:

fth= πK ωp2 Pabsχ
(3)

Here K is the thermal conductivity, ωp is the 1/e 2 beam radius, Pabs is absorbed optical power and χ is the thermo-optic coefficient given by χ=dn/dT+(n0 -1)(1+υ)·α, where υ and α are the Poisson’s ratio and thermal expansion coefficient, respectively. This model for thermal lensing assumes a cylindrical geometry (i.e. radial heat flow) in addition to uniform thermal loading density along the optical axis and hence can only be used as a rough guide in our situation. If we assume that a Gaussian beam is incident on the VBG with an average power of 1 kW and assuming an absorption of ~10-3 cm-1, the thermal lens would have a focal length on the order of 500 mm. In our setup the refractive power would be an order weaker as the power was an order lower but it still goes to show that the thermally induced aberrations will become increasingly important at higher powers.

The same data was used to numerically simulate the heat flow in a VBG with the same dimensions as the one used in this experiment, 3×5×5 mm. The VBG was assumed to maintain a temperature of 300 K on the boundaries parallel to the optical axis. Additionally, a heat transfer coefficient of 100 W/mK was associated with the boundaries perpendicular to the optical axis. This was intended to mimic the behavior of a VBG beam placed in temperature controlled heat-sink. The steady-state temperature distribution is plotted in Fig. 4(b). The simulation shows that although the temperature increase is not severe, the chirping can be significant as the temperature drop of 55 K corresponds to almost 0.5 nm chirp.

Throughout our experiments, no degradation of the VBG performance could be seen even at the highest output powers. The shift in emission wavelength at high power is therefore attributed to a more or less uniform heating of the VBG, either from direct absorption or by scattered light absorbed by the holder (or a combination thereof). A power meter placed behind the VBG monitored how much of the laser emission was transmitted. A non-uniform heating of the VBG would, as was discussed above, have lead to broadening of the reflection spectrum and a reduction of the reflectivity leading to a reduction in the output power, as well as an increase of the transmitted power through the grating, neither of which were seen.

In low gain solid state lasers, high finesse cavities are needed to achieve a high overall efficiency. This essentially means that a much higher power will be oscillating inside the cavity than is extracted. As a result, even a small fraction of the intracavity power absorbed in the VBG can pose serious problems for power scaling as reported by Hellström et al. [18

J. E. Hellström, B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Quasi-two-level Yb: KYW laser with a volume Bragg grating,” Opt. Express 15, 13930–13935 (2007). [CrossRef] [PubMed]

]. In fiber lasers, on the other hand, relatively low finesse resonators are employed (due to the high gain) and hence the intracavity power at the output end of the fiber is typically only 1.04-1.2 times higher than the output power. In addition, the power at the opposite end of the fiber is typically 2–5 times smaller (depending on the resonator configuration) hence the power absorbed in the VBG is much smaller than for a conventional bulk solid-state laser with the same output power.

In conclusion, an Yb-fiber laser has been demonstrated with an output power of 138 W, a narrow linewidth of 0.2 nm and a high PER of 15 dB. A volume Bragg grating was used to select the lasing wavelength and narrow the linewidth. It was shown that the grating can stand this high power without degradation and it offers easy alignment and a small footprint in combination with a high degree of flexibility. It is evident that absorption and scattering in VBGs will become increasingly important at higher powers; a thorough analysis of how the grating will behave in a high power laser set-up near the breaking limit is currently under investigation.

Acknowledgments

This work was partially supported by the Engineering and Physical Sciences Research Council (UK) and the Carl Trygger foundation and the Göran Gustafsson foundation in Sweden.

References and links

1.

A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, “Efficient power scaling of laser radiation by spectral beam combining,” Opt. Lett. 33, 384–386 (2008). [CrossRef] [PubMed]

2.

N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Stable high-power continuous-wave Yb˄ 3+-doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating,” Opt. Lett. 32, 1486–1488 (2007). [CrossRef] [PubMed]

3.

C. H. Liu, A. Galvanauskas, V. Khitrov, B. Samson, U. Manyam, K. Tankala, D. Machewirth, and S. Heinemann, “High-power single-polarization and single-transverse-mode fiber laser with an all-fiber cavity and fiber-grating stabilized spectrum,” Opt. Lett. 31, 17–19 (2006). [CrossRef] [PubMed]

4.

B. L. Volodin, S. V. Dolgy, E. D. Melnik, E. Downs, J. Shaw, and V. S. Ban, “Wavelength stabilization and spectrum narrowing of high-power multimode laser diodes and arrays by use of volume Bragg gratings,” Opt. Lett. 29, 1891–1893 (2004). [CrossRef] [PubMed]

5.

B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Tunable single-longitudinal-mode ErYb:glass laser locked by a bulk glass Bragg grating,” Opt. Lett. 31, 1663–1665 (2006). [CrossRef] [PubMed]

6.

B. Jacobsson, M. Tiihonen, V. Pasiskevicius, and F. Laurell, “Narrowband bulk Bragg grating optical parametric oscillator,” Opt. Lett. 30, 2281–2283 (2005). [CrossRef] [PubMed]

7.

P. Jelger and F. Laurell, “Efficient skew-angle cladding-pumped tunable narrow-linewidth Yb-doped fiber laser,” Opt. Lett. 32, 3501–3503 (2007). [CrossRef] [PubMed]

8.

O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, “High-efficiency Bragg gratings in photothermorefractive glass,” Appl. Opt. 38, 619–627 (1999). [CrossRef]

9.

L. B. Glebov, L. N. Glebova, V. I. Smirnov, M. Dubinskii, L. D. Merkle, S. Papernov, and A. W. Schmid, “Laser damage resistance of photo-thermo-refractive glass Bragg gratings,” Proceedings of Solid State and Diode Lasers Technical Review. Albuquerque (2004).

10.

J. W. Kim, P. Jelger, J. K. Sahu, F. Laurell, and W. A. Clarkson, “High-power and wavelength-tunable operation of an Er,Yb fiber laser using a volume Bragg grating,” Opt. Lett. 33, 1204–1206 (2008). [CrossRef] [PubMed]

11.

J. Lumeau, L. Glebova, and L. B. Glebov, “Influence of UV-exposure on the crystallization and optical properties of photo-thermo-refractive glass,” J. Non-Cryst. Solids (2007).

12.

J. W. Zwanziger, U. Werner-Zwanziger, E. D. Zanotto, E. Rotari, L. N. Glebova, L. B. Glebov, and J. F. Schneider, “Residual internal stress in partially crystallized photothermorefractive glass: Evaluation by nuclear magnetic resonance spectroscopy and first principles calculations,” J. Appl. Phys. 99, 083511 (2006). [CrossRef]

13.

G. B. Venus, A. Sevian, V. I. Smirnov, and L. B. Glebov, “High-brightness narrow-line laser diode source with volume Bragg-grating feedback,” Proc. SPIE 5711, 166–276 (2005). [CrossRef]

14.

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Finite Beams in Reflective Volume Bragg Gratings: Theory and Experiments,” IEEE J. Quantum Electron. 44, 81–89 (2008). [CrossRef]

15.

H. Shu and M. Bass, “Modeling the reflection of a laser beam by a deformed highly reflective volume bragg grating,” Appl. Opt. 46, 2930–2938 (2007). [CrossRef] [PubMed]

16.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

17.

W. Koechner, Solid-State Laser Engineering , 6th ed. (Springer, 2006).

18.

J. E. Hellström, B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Quasi-two-level Yb: KYW laser with a volume Bragg grating,” Opt. Express 15, 13930–13935 (2007). [CrossRef] [PubMed]

OCIS Codes
(050.7330) Diffraction and gratings : Volume gratings
(140.3510) Lasers and laser optics : Lasers, fiber

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 23, 2008
Revised Manuscript: June 9, 2008
Manuscript Accepted: June 9, 2008
Published: June 12, 2008

Citation
P. Jelger, P. Wang, J. K. Sahu, F. Laurell, and W. A. Clarkson, "High-power linearly-polarized operation of a cladding-pumped Yb fibre laser using a volume Bragg grating for wavelength selection," Opt. Express 16, 9507-9512 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9507


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References

  1. A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, "Efficient power scaling of laser radiation by spectral beam combining," Opt. Lett. 33, 384-386 (2008). [CrossRef] [PubMed]
  2. N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, "Stable high-power continuous-wave Yb^ 3+-doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating," Opt. Lett. 32, 1486-1488 (2007). [CrossRef] [PubMed]
  3. C. H. Liu, A. Galvanauskas, V. Khitrov, B. Samson, U. Manyam, K. Tankala, D. Machewirth, and S. Heinemann, "High-power single-polarization and single-transverse-mode fiber laser with an all-fiber cavity and fiber-grating stabilized spectrum," Opt. Lett. 31, 17-19 (2006). [CrossRef] [PubMed]
  4. B. L. Volodin, S. V. Dolgy, E. D. Melnik, E. Downs, J. Shaw, and V. S. Ban, "Wavelength stabilization and spectrum narrowing of high-power multimode laser diodes and arrays by use of volume Bragg gratings," Opt. Lett. 29, 1891-1893 (2004). [CrossRef] [PubMed]
  5. B. Jacobsson, V. Pasiskevicius, and F. Laurell, "Tunable single-longitudinal-mode ErYb:glass laser locked by a bulk glass Bragg grating," Opt. Lett. 31, 1663-1665 (2006). [CrossRef] [PubMed]
  6. B. Jacobsson, M. Tiihonen, V. Pasiskevicius, and F. Laurell, "Narrowband bulk Bragg grating optical parametric oscillator," Opt. Lett. 30, 2281-2283 (2005). [CrossRef] [PubMed]
  7. P. Jelger and F. Laurell, "Efficient skew-angle cladding-pumped tunable narrow-linewidth Yb-doped fiber laser," Opt. Lett. 32, 3501-3503 (2007). [CrossRef] [PubMed]
  8. O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, "High-efficiency Bragg gratings in photothermorefractive glass," Appl. Opt. 38, 619-627 (1999). [CrossRef]
  9. L. B. Glebov, L. N. Glebova, V. I. Smirnov, M. Dubinskii, L. D. Merkle, S. Papernov, and A. W. Schmid, "Laser damage resistance of photo-thermo-refractive glass Bragg gratings," Proceedings of Solid State and Diode Lasers Technical Review, Albuquerque (2004).
  10. J. W. Kim, P. Jelger, J. K. Sahu, F. Laurell, and W. A. Clarkson, "High-power and wavelength-tunable operation of an Er,Yb fiber laser using a volume Bragg grating," Opt. Lett. 33, 1204-1206 (2008). [CrossRef] [PubMed]
  11. J. Lumeau, L. Glebova, and L. B. Glebov, "Influence of UV-exposure on the crystallization and optical properties of photo-thermo-refractive glass," J. Non-Cryst. Solids (2007).
  12. J. W. Zwanziger, U. Werner-Zwanziger, E. D. Zanotto, E. Rotari, L. N. Glebova, L. B. Glebov, and J. F. Schneider, "Residual internal stress in partially crystallized photothermorefractive glass: Evaluation by nuclear magnetic resonance spectroscopy and first principles calculations," J. Appl. Phys. 99, 083511 (2006). [CrossRef]
  13. G. B. Venus, A. Sevian, V. I. Smirnov, and L. B. Glebov, "High-brightness narrow-line laser diode source with volume Bragg-grating feedback," Proc. SPIE 5711, 166(2005). [CrossRef]
  14. J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, "Finite Beams in Reflective Volume Bragg Gratings: Theory and Experiments," IEEE J. Quantum Electron. 44, 81-89 (2008). [CrossRef]
  15. H. Shu and M. Bass, "Modeling the reflection of a laser beam by a deformed highly reflective volume bragg grating," Appl. Opt. 46, 2930-2938 (2007). [CrossRef] [PubMed]
  16. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  17. W. Koechner, Solid-State Laser Engineering, 6th ed. (Springer, 2006).
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