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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25501–25508
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Curved Yb:YAG waveguide lasers, fabricated by femtosecond laser inscription

Thomas Calmano, Anna-Greta Paschke, Sebastian Müller, Christian Kränkel, and Günter Huber  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25501-25508 (2013)
http://dx.doi.org/10.1364/OE.21.025501


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Abstract

Straight and s-curve Yb(7%):YAG waveguides have been fabricated with the femtosecond laser writing technique. By employing a novel writing scheme an increase of the refractive index change could be achieved in comparison to waveguides written with the standard procedure. Straight waveguides, fabricated with this scheme, enabled highly efficient Ti:sapphire laser pumped waveguide lasers with slope efficiencies of 79% and output powers of more than 1 W. With slope efficiencies from 50% to 60% for the curved waveguide lasers with radii of curvature of R ≥ 20 mm the possibility of fs-laser written complex optical devices is demonstrated.

© 2013 OSA

1. Introduction

By focusing femtosecond (fs) laser radiation into dielectric media, material modifications leading to refractive index changes on a micrometer scale can be produced [1

1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

]. With a translation of the sample transversally to the focused laser beam, tracks of modified material can be fabricated. In combination with the resulting refractive index change, waveguiding structures are produced. Utilizing this technique, different passive and active micro-optical devices have been fabricated in various glasses and crystalline materials [2

2. R. G. Gatass and E. Mazur, “Femtosecond micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008). [CrossRef]

, 3

3. E. Cantelar, D. Jaque, and G. Lifante, “Waveguide lasers based on dielectric materials,” Opt. Mater. 34, 555–571 (2012). [CrossRef]

].

Particularly in rare earth doped crystals and ceramics highly efficient waveguide lasers with output powers above 2 W and slope efficiencies of more than 70% have been realized in neodymium and ytterbium doped garnets and vanadates [4

4. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG:Nd3+crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250 (2005). [CrossRef] [PubMed]

9

9. T. Calmano, J. Siebenmorgen, A.-G. Paschke, C. Fiebig, K. Paschke, G. Erbert, K. Petermann, and G. Huber, “Diode pumped high power operation of a femtosecond laser inscribed Yb:YAG waveguide laser [Invited],” Opt. Mater. Express 1, 428–433 (2011). [CrossRef]

]. Especially the approach of writing two parallel tracks of modified material with the waveguiding region in between is a well investigated technique for waveguide fabrication in crystals. The relative refractive index difference between cladding and core results from a refractive index decrease within the modified material itself. Additionally, in the surrounding of the modified regions stress induces a refractive index increase in the order of Δn ≈ 10−3 − 10−4 [7

7. J. Siebenmorgen, T. Calmano, K. Petermann, and G. Huber, “Highly efficient Yb:YAG channel waveguide laser written with a femtosecond-laser,” Opt. Express 18, 16035–16041 (2010). [CrossRef] [PubMed]

, 10

10. A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95, 85–96 (2009). [CrossRef]

]. Waveguide lasers inscribed with this writing geometry in Yb:YAG exhibit an excellent performance with slope efficiencies of 75% and output powers of 2.3 W [7

7. J. Siebenmorgen, T. Calmano, K. Petermann, and G. Huber, “Highly efficient Yb:YAG channel waveguide laser written with a femtosecond-laser,” Opt. Express 18, 16035–16041 (2010). [CrossRef] [PubMed]

, 9

9. T. Calmano, J. Siebenmorgen, A.-G. Paschke, C. Fiebig, K. Paschke, G. Erbert, K. Petermann, and G. Huber, “Diode pumped high power operation of a femtosecond laser inscribed Yb:YAG waveguide laser [Invited],” Opt. Mater. Express 1, 428–433 (2011). [CrossRef]

].

So far the fabrication of optical devices like directional couplers [11

11. W.-J. Chen, S. M. Eaton, H Zhang, and P. R. Herman, “Broadband directional couplers fabricated in bulk glass with high repetition rate femtosecond laser pulses,” Opt. Express 16, 11470–11480 (2008). [CrossRef] [PubMed]

], beam splitters [12

12. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: A new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003). [CrossRef]

], ring resonators [13

13. A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1062 (2005). [CrossRef] [PubMed]

], bragg gratings [14

14. G. D. Marshall, P. Dekker, M. Ams, J. A. Piper, and M. J. Withford, “Directly written monolithic waveguide laser incorporating a distributed feedback waveguide-Bragg grating,” Opt. Lett. 33, 956–958 (2008). [CrossRef] [PubMed]

] and lab-on-a-chip applications [15

15. L. Qiao, F. He, C. Wang, Y. Cheng, K. Sugioka, and K. Midorikawa, “A microfluidic chip integrated with a microoptical lens fabricated by femtosecond laser micromachining,” Appl. Phys. A 102, 179–183 (2011). [CrossRef]

] was mainly demonstrated in glasses as well as in LiNbO3 [16

16. J. Thomas, M. Heinrich, P. Zeil, V. Hilbert, K. Rademaker, R. Riedel, S. Ringleb, C. Dubs, J.-P. Ruske, S. Nolte, and A. Tünnermann, “Laser direct writing: Enabling monolithic and hybrid integrated solutions on the lithium niobate platform,” Phys. Stat. Sol. A 208, 276–283 (2011). [CrossRef]

].

In this paper we show for the first time to the best of our knowledge the fabrication and characterization of curved waveguiding structures and waveguide lasers in Yb:YAG crystals. These curved waveguides are the basic optical components for more complex optical devices. Yb:YAG exhibits excellent thermomechanical properties, which makes it an ideal material for high power applications as well as applications in integrated optics. By utilizing this crystal as substrate material the possible realization of so called lossless optical devices, in which the waveguide losses are compensated by gain, is demonstrated.

A novel writing scheme with a spatially oscillating translation movement was developed for this purpose. Within this scheme the stress, induced by the tracks, is increased. This results in a two times higher refractive index difference between the waveguide core and the surrounding regions. This allows for a reduced radius of curvature in curved waveguiding structures. Additionally, a stronger confinement of the guided mode can be achieved in waveguides with a larger refractive index contrast, resulting in waveguide lasers with lower laser thresholds.

2. Fabrication procedure

The waveguides were inscribed into an Yb(7%):YAG sample with dimensions of x × y × z = 10×3.5×9.5 mm3. For the waveguide writing a chirped pulse amplification (CPA) Ti:sapphire fs-laser system (Clark-MXR CPA-2010, 150 fs pulse duration, 775 nm center wavelength, 1 mJ maximum pulse energy) and a high precision three-axis positioning system (Aerotech ABL1000 axis) were employed. The laser beam was focused with different aspheric lenses or a microscope objective about 300 μm below the polished surface of the sample, while the crystal was moved transversally (xz-plane) to the incident laser pulses with different schemes as shown in Fig. 1. In the following those sets of parameters are indicated, which led to the best results for each writing scheme.

Fig. 1 Different writing schemes for the fabrication of waveguides (a). Definition of parameters for s-curve (b) and circularly curved (c) waveguides. The light incoupling direction is indicated by the red arrow.

For the fabrication of straight waveguides two different writing schemes A and B were employed, which are illustrated in Fig. 1(a). In scheme A the sample is moved linearly parallel to the z-axis with velocity v = 25 μm/s, while the laser beam is irradiated perpendicular to the translation direction and parallel to the y-axis. In this case a fully illuminated aspheric lens with a numerical aperture of NA = 0.55 and a focal length of f = 4.51 mm was employed for focusing. In scheme B this linear translation (v = 25 μm/s) is superimposed by a sine oscillation perpendicular to the translation direction with an oscillation amplitude of Aosc = 2 μm and an oscillation frequency of νosc = 70 Hz. In this case a fully illuminated microscope objective with a NA = 0.65 was used for focusing.

Additionally, s-curve waveguides were inscribed into the same crystal [Fig. 1(b)]. These structures consist of four different parts. Two parts, which are curved in opposite directions (marked with blue and purple dashed lines in Fig. 1(b)), are connected at one of each ends to straight parts (marked with black and orange solid lines in Fig. 1(b)). As shown in the right part of this figure the straight parts were written with scheme B. In order to increase the relative refractive index difference in the curved parts, these were written with a third approach (scheme C), in which the linear translation is superimposed by a zigzag-movement perpendicular to the translation direction. Detailed information about the different motion sequences of this writing scheme can be found in Fig. 1(a). In this case the sample is translated a small increment Δb = 0.357 μm of the total arc length b with the velocity vΔb. This movement is followed by a zigzag-movement in x-direction with amplitude Aosc at a velocity vΔx and is repeated until a curve with the whole arc length is written. The arc length and radius of curvature of the s-curve waveguides were b = 1.0 mm – 1.8 mm and R = 10 mm – 100 mm, respectively. The straight parts of these waveguides, which were written with scheme B and the same parameters as the straight waveguides described before, had a length of 2.95 mm. Sets of suitable writing parameters for the zigzag oscillation are summarized in Tab. 1.

Table 1. Set of suitable writing parameters for zigzag movement.

table-icon
View This Table

These parameters result in velocities along the direction of the curved path of vα = 13.6 μm/s (Aosc = 3.5 μm) and vα = 25 μm/s (Aosc = 5 μm), respectively. In this case a fully illuminated aspheric lens with a NA = 0.68 and f = 3.1 mm was used for focusing the fs-laser radiation. The pulse energy of the incident laser pulses was varied between 1 μJ and 1.8 μJ and the distance d between two tracks from d = 25 μm to d = 28 μm.

For basic investigations also circularly curved waveguides were written in undoped YAG samples. The radius of curvature was varied between 30 mm and 80 mm. In this case a fully illuminated aspheric lens with f = 4.51 mm and NA = 0.55 was used. No zigzag-movements or sine oscillations were employed and the track distance was kept constant at 25 μm. The corresponding writing scheme is shown in Fig. 1(c).

3. Characterization of the waveguides

Figure 2 (a) shows a polarization contrast microscope image of the cross section of a pair of tracks in a 60 μm thin YAG sample prepared from a scheme B waveguide written with 1.8 μJ pulse energy. Since YAG exhibits a cubic crystalline structure, the bright white areas in this picture result from a polarization change of the transmitted linear polarized illumination light due to stress induced birefringence. This stress originates from the fs-laser written structures and causes a refractive index increase in the surrounding area of the tracks.

Fig. 2 Polarization contrast images of the cross section of pairs of tracks in a 60 μm thin YAG disk prepared from waveguides written with scheme B (a) and scheme A (b) in the xy-plane. Bright field microscope image of an s-curve structure at the transition between the straight and the curved part (c). Polarization contrast image of an s-curve structure at the transition between the straight and the curved part (d) in the xz-plane.

For comparison the cross section of a pair of tracks in the same sample, written with scheme A and similar writing parameters, is shown in Fig. 2(b). In this picture, which was recorded with the same microscope and camera settings, much less birefringence can be observed than in Fig. 2(a). The lower birefringence points towards a smaller refractive index change.

Figure 2(c) shows a bright field microscope image of the transition between the straight and the bent part (R = 80 mm) of an s-curve structure in the xz-plane. The tracks in the straight part exhibit flat boundaries with a periodically modified inner part as result of the sinusoidal movement, whereas micro-cracks in the surrounding of the bent parts can be observed. These cracks are an indication of larger stress, which is induced into the surrounding material. This assumption is confirmed by Fig. 2(d), which shows a polarization contrast image of the same structure. In this case the curved parts show stronger birefringence, revealing the desired larger refractive index change in these segments of the s-curve.

The waveguiding properties of the fabricated structures were investigated at wavelengths of 633 nm and 1064 nm by coupling the linearly polarized light of a Helium-Neon laser and a Nd:YVO4 laser, respectively, into the waveguides with a lens (f = 25 mm). The near field of the guided modes was imaged with a 50× microscope objective on the sensor of a CCD camera. The maximum waveguide losses were determined with a transmission measurement considering the Fresnel reflection losses at both end-facets of the crystal.

Figures 3(a) and 3(b) show the mode profiles of straight waveguides at 1064 nm with a track distance of d = 25 μm written with schemes A and B, respectively. The waveguide in (a) exhibits a mode profile with an elliptically shaped cross section with mode field diameters of 2wx = 18.3 μm and 2wy = 28.3 μm, respectively. By employing scheme B for waveguide writing a stronger confinement in y-direction could be achieved resulting from the larger stress induced refractive index change [Fig. 3(b)]. In this case the mode profile is nearly circular with dimensions of 2wx × 2wy = 16.8 × 18.3 μm2. Furthermore, the mode profile is nearly Gaussian.

Fig. 3 Mode profiles at 1064 nm of straight waveguides (d = 25 μm) written with scheme A (a) and scheme B (b). Mode profiles at 633 nm of circularly curved waveguides (d = 25 μm) with different arc lenghts and radii of curvature (c) and (d). Mode profiles of straight (R = ∞, d = 25 μm, scheme B) and s-curve waveguides (d = 26 μm) at 633 nm for different R (e) – (i). The cross sections of the tracks written with scheme A are indicated with white ellipses. The cross sections of the tracks written with scheme B are marked with white rectangles.

The refractive index change was roughly estimated from the numerical aperture of the waveguides [7

7. J. Siebenmorgen, T. Calmano, K. Petermann, and G. Huber, “Highly efficient Yb:YAG channel waveguide laser written with a femtosecond-laser,” Opt. Express 18, 16035–16041 (2010). [CrossRef] [PubMed]

]. The NA was determined by measuring the mode field diameter in the far field at different distances from the waveguides end-facet. For the scheme A waveguide a Δn of approximately 1.6 · 10−4 was estimated, whereas the refractive index difference for the scheme B waveguide was twice as large with Δn ≈ 3.2 · 10−4.

Figures 3(c) and 3(d) show the mode profiles of circularly curved waveguides at 633 nm. These mode profiles are deformed and shifted to the outer track, which is located on the right side in this picture (compare Fig. 1(c)).

Figures 3(e)–3(i) show the mode profiles of straight (R = ∞, d = 25 μm) and s-curve waveguides (d = 26 μm) with different radii of curvature R at a wavelength of 633 nm. The s-curve waveguides were written with the parameters shown in the first line of Table 1. In contrast to the straight waveguides a shift of the mode profile to the outer track of the second curve (compare Fig. 1) can be observed. Furthermore, especially for waveguides with R ≤ 60 mm, higher order modes are excited.

In curved waveguides the effective refractive index is increased towards the outer part of the curve, which can be explained by the method of conformal transformation [17

17. M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Elect. 11, 75–83 (1975). [CrossRef]

]. Furthermore, assuming a perpendicular orientation of the stress lines to the curved tracks, a larger stress and consequently a larger refractive index change at the inner curve of the outer track is expected [Fig. 1(c)]. This supports the described refractive index increase towards the outer part of the waveguide and results in the observed mode shift to this region as well as the deformation. These effects become stronger with smaller R and can also be observed in bent fibers [18

18. R. W. Smink, B. P. de Hon, and A. G. Tijhuis, “Bending loss in optical fibers–a full-wave approach,” J. Opt. Soc. Am. B 24, 2610–2618 (2007). [CrossRef]

].

In consequence a mode mismatch between the curved and straight sections of the s-curve is present. Since the boundary conditions of the electric field at the transition between straight and curved parts have to be fulfilled, the excitation of higher order modes is necessary [19

19. B. M. A. Rahman, D. M. H. Leung, S. S. A. Obayya, and K. T. V. Grattan, “Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling,” Appl. Opt. 47, 2961–2970 (2008). [CrossRef] [PubMed]

]. Furthermore, the mode mismatch might lead to additional losses at the transition between straight and curved part in s-curve waveguides.

The damping of the straight and s-curve waveguides at 633 nm plotted against the radius of curvature is shown in Fig. 4. The losses decrease exponentially with increasing R for all waveguides from about 7 dB to the value of the straight waveguides (R = ∞, d = 27 μm, scheme B) of about 1 dB. For straight waveguides fabricated with scheme A nearly the same losses were measured. The minimum losses were 0.8 dB for an s-curve with a track distance of 28 μm and a radius of curvature of 100 mm.

Fig. 4 Damping of s-curve waveguides in dependency of the radius of curvature for waveguides with different track distances and oscillation amplitudes for the zigzag oscillation. The red dotted line indicates the losses of straight waveguides (R = ∞, d = 27 μm, scheme B).

4. Laser experiments

For the laser experiments a continuous wave (cw) Ti:sapphire laser emitting at a wavelength of 940 nm was utilized as pump source. The pump light was coupled into the waveguides with a lens (f = 25 mm). In waveguides the overlap between pump and laser mode is nearly perfect over the entire length of the gain medium. Due to this and the high gain, cw laser oscillation at 1030 nm could be achieved without any external mirrors in all waveguides utilizing only the Fresnel reflections of about RFresnel = 9% at each end-facet of the waveguides. According to the logarithmic outputcoupling losses [20

20. O. Svelto, Principles of Lasers (Plenum Press, New York, 1998), Chap. 7. [CrossRef]

] of γOC = − ln(1 − TOC) = γ1 + γ2, with the logarithmic outputcoupling losses to each side of the crystal of γ1 = γ2 = − ln(RFresnel), this corresponds to a total output coupling transmission of TOC = 99% per roundtrip.

Figure 5(a) shows exemplary input-output curves for the s-curve waveguides from Figs. 3(f)–3(i) with different R (d = 26 μm) and additionally of a waveguide with R = 80 mm. Furthermore, the laser characteristic of a straight waveguide laser (R = ∞, d = 27 μm) is plotted in this figure. For this waveguide laser a slope efficiency of 73% and a maximum output power of 1054 mW at 1587 mW incident pump power were achieved, corresponding to an optical to optical efficiency of ηopt = 66%. Pincident is defined as the measured power in front of the waveguide corrected by the Fresnel reflection losses at the incoupling end-facet of the crystal. Furthermore, the coupling efficiency of the Ti:sapphire laser into the waveguide was determined by calculating the overlap integral between waveguide and pump-laser mode at the incident facet [21

21. L. McCaughan and E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3Waveguide Insertion Loss at λ= 1.3 μm,” IEEE J. Quantum Electron. 19, 131–136 (1983). [CrossRef]

] to ηc = 92%. In this case the corrected slope efficiency with respect to launched pump power is as high as 79%.

Fig. 5 Input output characteristics of straight (R = ∞) and s-curve waveguide lasers with different radii of curvature (a). Laser threshold plotted against radius of curvature (b).

Also the s-curve waveguide lasers with R ≥ 60 mm are very efficient with slope efficiencies of about 60%. Even for R = 20 mm a slope efficiency of more than 50% was determined. However, for R = 10 mm the slope efficiency drops to 18%.

In Fig. 5(b) the laser threshold is plotted against the radius of curvature. As expected from the loss measurements [Fig. 4] and basic laser theory Pthr decreases linearly with the damping and thus exponentially with R leading to laser thresholds below 220 mW for all R ≥ 20 mm. However, the laser threshold for the s-curved waveguide lasers is larger than for the straight waveguide laser of Pthr = 141 mW, which is not directly expected from the loss measurements at 633 nm [Fig. 4]. For waveguide lasers one has to consider, that the laser mode will oscillate in the area with largest gain and lowest losses. The location of this area depends on the guiding properties of the s-curves at the pump wavelength of 940 nm as well as the laser wavelength of 1030 nm. However, neither the intensity distribution of the pump light nor the laser light throughout the entire length of the s-curve is known. Hence, it can only be supposed, that the overlap between pump and laser mode is larger in the straight waveguides than in the s-curves, which would explain the observed lower laser threshold as well as higher slope efficiency.

5. Summary and conclusion

Highly efficient s-curved and straight waveguide lasers have been fabricated by femtosecond laser writing in Yb(7%):YAG crystals. Slope efficiencies of more than 51% and laser thresholds of less than 220 mW have been demonstrated in waveguides with radii of curvature of R ≥ 20 mm. Furthermore, with these waveguide lasers maximum output powers exceeding 700 mW could be achieved. It is worth mentioning that the total length of the curved parts in the s-curve (b = 3.6 mm) is more than half of the total length of the straight parts (5.9 mm). Considering the low losses of the s-curve waveguides it can be assumed that also the curved parts contribute to the gain of the waveguide lasers and do not only introduce additional losses into the system, which would be compensated only by the gain of the straight parts. The realization of these curved waveguide lasers demonstrates the potential for the fabrication of more complex active optical devices like lossless beam splitters or ring lasers in crystalline materials with the fs-laser writing technique. The fabrication of half or quarter circle waveguides in Yb:YAG is planned and will be a further step towards a ring laser, fabricated by the fs-laser writing technique.

Acknowledgments

The Yb:YAG crystals were provided by FEE GmbH, Germany. This work was supported by the Deutsche Forschungsgemeinschaft (Graduate School 1355) and the Joachim Herz Stiftung.

References and links

1.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

2.

R. G. Gatass and E. Mazur, “Femtosecond micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008). [CrossRef]

3.

E. Cantelar, D. Jaque, and G. Lifante, “Waveguide lasers based on dielectric materials,” Opt. Mater. 34, 555–571 (2012). [CrossRef]

4.

A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG:Nd3+crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250 (2005). [CrossRef] [PubMed]

5.

G. A. Torchia, A. Ródenas, A. Benayas, E. Cantelar, L. Roso, and D. Jaque, “Highly efficient laser action in femtosecond-written Nd:yttrium aluminum garnet ceramic waveguides,” Appl. Phys. Lett. 92, 111103 (2008). [CrossRef]

6.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B 100, 131–135 (2010). [CrossRef]

7.

J. Siebenmorgen, T. Calmano, K. Petermann, and G. Huber, “Highly efficient Yb:YAG channel waveguide laser written with a femtosecond-laser,” Opt. Express 18, 16035–16041 (2010). [CrossRef] [PubMed]

8.

Y. Tan, A. Ródenas, F. Chen, R. R. Thomson, A. K. Kar, D. Jaque, and Q. Lu, “70% slope efficiency from an ultrafast laser-written Nd:GdVO4channel waveguide laser,” Opt. Express 18, 24994–24999 (2010). [CrossRef] [PubMed]

9.

T. Calmano, J. Siebenmorgen, A.-G. Paschke, C. Fiebig, K. Paschke, G. Erbert, K. Petermann, and G. Huber, “Diode pumped high power operation of a femtosecond laser inscribed Yb:YAG waveguide laser [Invited],” Opt. Mater. Express 1, 428–433 (2011). [CrossRef]

10.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95, 85–96 (2009). [CrossRef]

11.

W.-J. Chen, S. M. Eaton, H Zhang, and P. R. Herman, “Broadband directional couplers fabricated in bulk glass with high repetition rate femtosecond laser pulses,” Opt. Express 16, 11470–11480 (2008). [CrossRef] [PubMed]

12.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: A new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003). [CrossRef]

13.

A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1062 (2005). [CrossRef] [PubMed]

14.

G. D. Marshall, P. Dekker, M. Ams, J. A. Piper, and M. J. Withford, “Directly written monolithic waveguide laser incorporating a distributed feedback waveguide-Bragg grating,” Opt. Lett. 33, 956–958 (2008). [CrossRef] [PubMed]

15.

L. Qiao, F. He, C. Wang, Y. Cheng, K. Sugioka, and K. Midorikawa, “A microfluidic chip integrated with a microoptical lens fabricated by femtosecond laser micromachining,” Appl. Phys. A 102, 179–183 (2011). [CrossRef]

16.

J. Thomas, M. Heinrich, P. Zeil, V. Hilbert, K. Rademaker, R. Riedel, S. Ringleb, C. Dubs, J.-P. Ruske, S. Nolte, and A. Tünnermann, “Laser direct writing: Enabling monolithic and hybrid integrated solutions on the lithium niobate platform,” Phys. Stat. Sol. A 208, 276–283 (2011). [CrossRef]

17.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Elect. 11, 75–83 (1975). [CrossRef]

18.

R. W. Smink, B. P. de Hon, and A. G. Tijhuis, “Bending loss in optical fibers–a full-wave approach,” J. Opt. Soc. Am. B 24, 2610–2618 (2007). [CrossRef]

19.

B. M. A. Rahman, D. M. H. Leung, S. S. A. Obayya, and K. T. V. Grattan, “Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling,” Appl. Opt. 47, 2961–2970 (2008). [CrossRef] [PubMed]

20.

O. Svelto, Principles of Lasers (Plenum Press, New York, 1998), Chap. 7. [CrossRef]

21.

L. McCaughan and E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3Waveguide Insertion Loss at λ= 1.3 μm,” IEEE J. Quantum Electron. 19, 131–136 (1983). [CrossRef]

OCIS Codes
(230.7380) Optical devices : Waveguides, channeled
(140.3615) Lasers and laser optics : Lasers, ytterbium
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 6, 2013
Revised Manuscript: October 7, 2013
Manuscript Accepted: October 7, 2013
Published: October 17, 2013

Citation
Thomas Calmano, Anna-Greta Paschke, Sebastian Müller, Christian Kränkel, and Günter Huber, "Curved Yb:YAG waveguide lasers, fabricated by femtosecond laser inscription," Opt. Express 21, 25501-25508 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25501


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References

  1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett.21, 1729–1731 (1996). [CrossRef] [PubMed]
  2. R. G. Gatass and E. Mazur, “Femtosecond micromachining in transparent materials,” Nat. Photonics2, 219–225 (2008). [CrossRef]
  3. E. Cantelar, D. Jaque, and G. Lifante, “Waveguide lasers based on dielectric materials,” Opt. Mater.34, 555–571 (2012). [CrossRef]
  4. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG:Nd3+crystal by femtosecond laser writing,” Opt. Lett.30, 2248–2250 (2005). [CrossRef] [PubMed]
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