Abstract

A single-layer resonant-waveguide grating consisting of a sub-wavelength grating coupler etched into a waveguide is proposed in order to achieve high polarization and high spectral selectivity inside an Yb:YAG thin-disk laser resonator. The designed structure was fabricated with the help of a Lloyd’s-mirror interference lithography setup followed by reactive ion beam etching down to the desired grating groove depth. The wavelength and polarization dependent reflectivity is measured and compared to the design results. The behaviour of the device at higher temperatures is also investigated in the present work. The device is introduced as the end mirror of an Yb:YAG thin-disk laser cavity. Output powers of up to 123 W with a spectral bandwidth of about 0.5 nm (FWHM) is demonstrated in a multimode configuration (M2~6). In fundamental-mode operation (TEM00 with M2~1.1) 70 W of power with a spectral bandwidth of about 20 pm have been obtained. Moreover, the degree of linear polarization was measured to be higher than 99% for both multimode and fundamental mode operation.

© 2012 OSA

1. Introduction

Resonant waveguide gratings (RWG) exhibit very specific properties which make them attractive for many applications in the field of optics, laser physics and biochemistry [1]. This is due to their unique resonance properties either in reflection or transmission which can be achieved for a given polarization, wavelength and angle of incidence. RWG structures result from the combination of a single or multilayer planar waveguide and a sub-wavelength grating. The latter can be an index-modulation [24] or a physical corrugation [5, 6] within the waveguide structure. The sub-wavelength structures can be defined in one or more layers of the optical waveguide. The pioneering work of Sychugov et al [58], Vincent et al. [9], and Popov et al. [10] led to a deep phenomenological and theoretical understanding of the physical behavior of these structures. This attracted the attention of several scientific groups in further investigating such structures theoretically [1113] and experimentally [5, 6, 1416]. The application of RWG in different fields like telecommunication [17], biology [1820], and lasers [2126] has been demonstrated.

In the present paper we report on the application of RWG composed of a single thin-film waveguide and a sub-wavelength grating for selecting the polarization and the spectral bandwidth of the emitted beam from an Yb:YAG thin-disk laser. The design, the fabrication as well as the spectroscopic and the laser characterization are discussed in the following.

2. Design, fabrication and spectroscopic characterization of the RWG structures

A schematic of the RWG cross-section which was designed and investigated here is shown in the inset of Fig. 1 . It is composed of a 300 nm thick Ta2O5 layer with a refractive index of 2.185 (given by the supplier) at 1030 nm and a grating with a period of 545 nm and a groove-depth of 50 nm. The layer was deposited onto a fused silica substrate with a refractive index of 1.45 at 1030 nm wavelength. The structure was designed, using commercial codes, to be operated under normal incidence. It is intended to be used as the end mirror of an Yb:YAG thin-disk laser resonator, as will be shown in the following. The calculated reflectivities for both TE (electrical field parallel to the grating lines) and TM (electrical field perpendicular to the grating lines) polarization are shown in Fig. 1. As expected, the structure exhibits a polarization- and wavelength-dependent reflectivity. Under normal incidence, the reflectivity for the TE polarization reaches a maximum of 100% at the laser wavelength of λ = 1030 nm, whereas the TM polarization experiences only 8% of reflection close to the reflection from an uncorrugated Ta2O5-layer. The calculated spectral linewidth of the TE resonance peak is 5 nm (FWHM). The spectral width of the peak at the 90% reflection level is only 1.75 nm. In addition to the polarization selectivity this also leads to a strong wavelength (or spectral) selectivity when using such a device as a mirror of a laser cavity.

 

Fig. 1 Calculated TE and TM reflectivities versus wavelength for a resonant waveguide grating (RWG) with a period of 545 nm and a groove depth of 50 nm etched into a 300 nm thick Ta2O5 layer. A cross section of the RWG is shown in the inset.

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In order to verify the behavior of the described RWG, a number of structures were fabricated according to the design and with slightly different parameters, using the interference lithography setup described below.

For the photolithographic fabrication of the grating structures a Lloyd’s-mirror interference lithography setup was realized. This method was chosen in favor of a conventional two-beam interference setup because of its flexibility with respect to a varying interference fringe period and the fact that it offers a more compact setup. Thus it is less prone to environmental changes (i.e. air temperature, air pressure, humidity) which can cause interference fringe distortion and contrast reduction. A sketch of the setup is shown in Fig. 2a . The setup basically consists of an Ar + ion laser operating at 457.9 nm, a spatial filter that makes up the point source for the divergent beam (half angle approx. 5.6°) and the mirror assembly (Fig. 2b). After passing the spatial filter and propagating about one meter in free space, one part of the beam hits the substrate under an angle α. The other part hits the mirror that is mounted in an angle of 90° with respect to the substrate. Thus the reflected beam hits the substrate under an angle of αleading to a total interference angle of 2α. The period P of the interference fringes can then be expressed as follows: P=λ2sin(α). With our current setup which uses an exposure laser wavelength of 457.9 nm it is possible to realize grating periods within a range of 300nm – 1350nm.

 

Fig. 2 (a) Schematic of the Lloyd’s-mirror interference Lithography setup, (b) Photo of the Lloyd mirror assembly and (c) 3D AFM scan of the fabricated structure.

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The setup was calibrated by systematic measurements of the grating periods of different samples using a Littrow setup which allows for an absolute accuracy of better than 0.1 nm. The physical etching of the grating down to the desired groove-depth was performed with a Reactive Ion Beam Etching (RIBE) machine. Figure 2c shows a photo and a 3D scan of one of the fabricated structures. The AFM-scan shows the final structure in Ta2O5 which has a rectangular shape. This latter is a result of the highly nonlinear photochemical response of the photoresist (Shipley S1800) we used. Thus the sinusoidal intensity distribution of the interference pattern is transformed to a rectangular (or more precisely to a trapezoidal) structure. Additionally the slope angles of the grating profile are generally depending on the exposure contrast and the exposure dose.

A spectroscopic setup was built according to the DIN En ISO 13697 with a slight modification to measure the TE and TM reflectivity spectra of our RWG under normal incidence. The setup is described in details in [24]. Figure 3a shows the measurement results of the above described structure. At room temperature a peak with an amplitude of 99% ± 0.2% is measured for TE polarization at a wavelength of 1029.6 nm (black spheres). The measured reflectivity for TM polarization was very close to the designed value of about 8% (Fresnel reflection). A slight deviation of the resonance peak towards lower wavelengths is measured in comparison to the simulation results (red line). This is attributed to a slight deviation of the structure parameters (duty-cycle, groove depth and period) from the designed parameters. The measured spectral bandwidth of the TE resonance was about 2.9 nm FWHM and about 1 nm at 90% of the peak reflection. The latter case gives enough discrimination for high polarization and spectral selectivity when using this grating waveguide structure in a laser cavity.

 

Fig. 3 Spectroscopic measurements of the RWG. In (a) the measured reflectivities for TE and TM polarization are compared to the designed values. The temperature induced reflectivity shift to higher wavelengths is shown in (b).

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Since the resonance behavior of the structure is based on a waveguide coupling mechanism (a field accumulation over a certain propagation length in the thin-film waveguide), any absorption in the waveguide layer will lead to a certain amount of heating. This will influence the spectral position of the resonance because of the thermal expansion coefficients of Ta2O5 and of the thermal dispersion coefficient dn/dT. Therefore, the effect of the temperature on the resonance peak position of a similar resonant waveguide grating was analyzed. The parameters of the grating were set in order to observe a peak at a lower wavelength i.e. ~1023 nm. The sample was mounted on a Peltier element which was heated up. The temperature of the grating surface was measured using a thermo camera and the reflectivity spectrum was recorded at the desired temperature. Figure 3b depicts the reflectivity spectra at room temperature and at 156°C. A shift of the resonance peak of about 9 pm/K towards higher wavelengths was observed.

3. Intra-cavity characterization of the RWG structures

After the confirmation of the proper behavior of the fabricated structure by the above tests, the grating mirror was introduced as an end mirror in an Yb:YAG thin-disk laser resonator for a proof of principle although the reflectivity was slightly lower than expected. A fiber-coupled pump diode at a wavelength of 940 nm focused on to a spot diameter of 3.6 mm was used to pump a 215 µm thick Yb:YAG crystal (with a curvature of approx. 4 m concave at room temperature).

For the results presented here a plane output coupler with a transmittance of 10% was used in the resonator setups shown in Fig. 4 (the pump is not represented here). The comparatively high output coupling (for disk lasers) was chosen to reduce the thermal load on the RWG mirror by reducing the intra-cavity circulating power. This has the advantage to minimize the risk of damaging the RWG. The RWG mirror was tested in both a multimode (M2 ~6) and fundamental mode (M2 ~1.1) resonators as depicted in Figs. 4a and 4b, respectively.

 

Fig. 4 Schematics of the multi-mode (M2~6) and the single transverse mode (M2~1.1) Yb:YAG thin-disk laser resonator designs. The RWG replaces one-to-one the HR end mirror. The pump diode is not represented here.

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Power, polarization, M2, and spectrum of the beams from the resonators with the RGW structure were measured simultaneously and compared to that of the setups with a standard HR end mirror. Figure 5 shows the obtained power of the emitted beam as well as the spectra at full pump power for an HR mirror and for the RWG mirror described above. As can be seen in Fig. 5-a, only 123 W of output power with an optical efficiency of 35.9% was reached with the RWG in the multi-mode regime whereas 181 W (optical efficiency of 52.8%) has been obtained with the standard HR mirror.

 

Fig. 5 Power performances and spectral bandwidth measurements of the emitted beams. Pout, RWG and ηout, RWG are respectively the power and efficiency measured behind the output coupler. Pbehind, RWG and ηbehind, RWG are respectively the power and efficiency measured behind the RWG.

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The lower efficiency was expected since the RWG exhibits a lower reflectivity. For comparison we also measured the power transmitted through the RWG (as shown in the same figure) in order to evaluate the additional losses which are inflicted to the laser resonator by the RWG. Summing the power of these two output ports gives a total power of 146 W corresponding to an optical efficiency of about 42.7%. The power leakage through the RWG is attributed to the depolarization losses caused by the 215 µm thick Yb:YAG crystal [24] and to the residual transmission of the RWG. The drop in efficiency results mainly from absorption in the RWG caused by the long propagation length (which was estimated according to [1, 12] to be ~70 µm) of the excited waveguide mode as well as to the scattering losses due to the roughness (caused by the etching process) of the grating. This had the consequence of an increase of temperature of the RWG during laser operation up to 200°C which led (and was experimentally observed as can be seen in the spectra of Fig. 5) to a shift to longer wavelengths of the spectrum of the emitted beam. The measured spectra in both cases (RWG and HR) at the same pump power are shown in Fig. 5a (normalized). The spectral bandwidth of the laser emission is 4 times narrower in the case of the RWG mirror. It was estimated to be around 0.5 nm instead of the typical 2-3 nm in the case of a standard HR mirror.

In fundamental-mode operation (TEM00 with M2~1.1) an output power of 70 W could be extracted at the output coupler side with an efficiency of 24.3%. Behind the RWG mirror, 22 W were measured. The performances of the laser resonator with a RWG compared to that with a HR are plotted in Fig. 5b. A spectral bandwidth of about 20 pm (measurement limited by the resolution of the used optical spectrum analyzer (OSA)) was observed with the RWG, in comparison to 1.5 nm with a standard HR mirror. This corresponds to a reduction of the spectral bandwidth of almost 2 orders of magnitude. Figure 5b depicts the (normalized) emission spectra for the RWG and the standard HR mirror.

In both multimode and single transverse mode operation the degree of linear polarization (DOLP) was measured using a commercially available Stokes polarimeter to be higher than 99% over the whole power range performed in these experiments.

4. Conclusion

In conclusion we have shown that the combination of a single waveguide and a sub-wavelength grating can be used as a strongly polarization and wavelength selective mirror. For a proof of principle, the device was used within a Yb:YAG thin-disk laser resonator in multimode (M2~6) and single-mode (M2~1.1) operation. In multimode operation, an output power of up to 123 W with an optical efficiency of 35.9% and a spectral bandwidth of about 0.5 nm has been reached with the presented RWG. In fundamental mode operation, an output power of 70W with an optical efficiency of 24.3% was reached. The spectral bandwidth of the emitted beam was measured to be about 20 pm (limited by the optical spectrum analyzer resolution). In both cases the overall additional losses are attributed to the grating itself (transmission of about 1% and the absorption in the layer due to the wave-guiding) and to the depolarization loss introduced by the 215 µm thick laser crystal.

To increase the efficiency in order to use this concept in high average power lasers further improvements of the performance i.e. a higher reflectivity (> 99.5%) and a shorter propagation length (< 25µm) of the excited mode as well as narrower resonance peak (FWHM < 1nm), of such structures have to be achieved. Investigations are under progress which may enable the reflective resonant waveguide gratings to be used in high average power regimes where transmissive structures like etalons and Lyot filters suffer from strong thermal lensing.

Acknowledgments

This research project was financially supported by the Baden-Württemberg Stiftung within the project “PolGit”.

References and links

1. V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, “Waveguide coupling gratings for high-sensitivity biochemical sensors,” Sens. Actuators B Chem. 39(1-3), 360–364 (1997). [CrossRef]  

2. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef]   [PubMed]  

3. S. S. Wang and R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19(12), 919–921 (1994). [CrossRef]   [PubMed]  

4. S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617–1626 (1997). [CrossRef]  

5. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985). [CrossRef]  

6. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989). [CrossRef]  

7. V. A. Sychugov and A. V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Quantum Electron. 10, 326–331 (1980).

8. A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986). [CrossRef]  

9. P. Vincent and M. Nevière, “Corrugated Dielectric Waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979). [CrossRef]  

10. E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986). [CrossRef]  

11. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).

12. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11(11), 2816–2828 (1994). [CrossRef]  

13. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14(11), 2985–2993 (1997). [CrossRef]  

14. A. V. Tishchenko, “A generalised source method: new possibilities for waveguide and grating problems,” Opt. Quantum Electron. 32, 971–980 (2000). [CrossRef]  

15. L. B. Mashev and E. G. Loewen, “Anomalies of all-dielectric multilayer coated reflection gratings as a function of groove profile: an experimental study,” Appl. Opt. 27(1), 31–32 (1988). [CrossRef]   [PubMed]  

16. O. Boyko, F. Lemarchand, A. Talneau, A.-L. Fehrembach, and A. Sentenac, “Experimental demonstration of ultrasharp unpolarized filtering by resonant gratings at oblique incidence,” J. Opt. Soc. Am. A 26(3), 676–679 (2009). [CrossRef]  

17. F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23(15), 1149–1151 (1998). [CrossRef]   [PubMed]  

18. O. Parriaux and G. J. Veldhuis, “Normalized analysis for the sensitivity optimization of integrated optical evanescent-wave sensors,” J. Lightwave Technol. 16(4), 573–582 (1998). [CrossRef]  

19. S. Soria, T. Katchalski, E. Teitelbaum, A. A. Friesem, and G. Marowsky, “Enhanced two-photon fluorescence excitation by resonant grating waveguide structures,” Opt. Lett. 29(17), 1989–1991 (2004). [CrossRef]   [PubMed]  

20. V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004). [CrossRef]  

21. V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993). [CrossRef]  

22. M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

23. N. Destouches, J. C. Pommier, O. Parriaux, T. Clausnitzer, N. M. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006). [CrossRef]   [PubMed]  

24. M. Abdou Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and Th. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32, 1824–1826 (2007). [CrossRef]   [PubMed]  

25. F. Brückner, D. Friedrich, T. Clausnitzer, O. Burmeister, M. Britzger, E. B. Kley, K. Danzmann, A. Tünnermann, and R. Schnabel, “Demonstration of a cavity coupler based on a resonant waveguide grating,” Opt. Express 17(1), 163–169 (2009). [CrossRef]   [PubMed]  

26. M. A. Ahmed, M. Haefner, M. M. Vogel, C. Pruss, A. Voss, W. Osten, and T. Graf, “High-power radially polarized Yb:YAG thin-disk laser with high efficiency,” Opt. Express 19(6), 5093–5104 (2011). [CrossRef]   [PubMed]  

References

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  1. V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, “Waveguide coupling gratings for high-sensitivity biochemical sensors,” Sens. Actuators B Chem. 39(1-3), 360–364 (1997).
    [CrossRef]
  2. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
    [CrossRef] [PubMed]
  3. S. S. Wang and R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19(12), 919–921 (1994).
    [CrossRef] [PubMed]
  4. S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617–1626 (1997).
    [CrossRef]
  5. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
    [CrossRef]
  6. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
    [CrossRef]
  7. V. A. Sychugov and A. V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Quantum Electron. 10, 326–331 (1980).
  8. A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
    [CrossRef]
  9. P. Vincent and M. Nevière, “Corrugated Dielectric Waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
    [CrossRef]
  10. E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
    [CrossRef]
  11. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).
  12. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11(11), 2816–2828 (1994).
    [CrossRef]
  13. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14(11), 2985–2993 (1997).
    [CrossRef]
  14. A. V. Tishchenko, “A generalised source method: new possibilities for waveguide and grating problems,” Opt. Quantum Electron. 32, 971–980 (2000).
    [CrossRef]
  15. L. B. Mashev and E. G. Loewen, “Anomalies of all-dielectric multilayer coated reflection gratings as a function of groove profile: an experimental study,” Appl. Opt. 27(1), 31–32 (1988).
    [CrossRef] [PubMed]
  16. O. Boyko, F. Lemarchand, A. Talneau, A.-L. Fehrembach, and A. Sentenac, “Experimental demonstration of ultrasharp unpolarized filtering by resonant gratings at oblique incidence,” J. Opt. Soc. Am. A 26(3), 676–679 (2009).
    [CrossRef]
  17. F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23(15), 1149–1151 (1998).
    [CrossRef] [PubMed]
  18. O. Parriaux and G. J. Veldhuis, “Normalized analysis for the sensitivity optimization of integrated optical evanescent-wave sensors,” J. Lightwave Technol. 16(4), 573–582 (1998).
    [CrossRef]
  19. S. Soria, T. Katchalski, E. Teitelbaum, A. A. Friesem, and G. Marowsky, “Enhanced two-photon fluorescence excitation by resonant grating waveguide structures,” Opt. Lett. 29(17), 1989–1991 (2004).
    [CrossRef] [PubMed]
  20. V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
    [CrossRef]
  21. V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993).
    [CrossRef]
  22. M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).
  23. N. Destouches, J. C. Pommier, O. Parriaux, T. Clausnitzer, N. M. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006).
    [CrossRef] [PubMed]
  24. M. Abdou Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and Th. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32, 1824–1826 (2007).
    [CrossRef] [PubMed]
  25. F. Brückner, D. Friedrich, T. Clausnitzer, O. Burmeister, M. Britzger, E. B. Kley, K. Danzmann, A. Tünnermann, and R. Schnabel, “Demonstration of a cavity coupler based on a resonant waveguide grating,” Opt. Express 17(1), 163–169 (2009).
    [CrossRef] [PubMed]
  26. M. A. Ahmed, M. Haefner, M. M. Vogel, C. Pruss, A. Voss, W. Osten, and T. Graf, “High-power radially polarized Yb:YAG thin-disk laser with high efficiency,” Opt. Express 19(6), 5093–5104 (2011).
    [CrossRef] [PubMed]

2011 (1)

2009 (2)

2007 (1)

2006 (2)

N. Destouches, J. C. Pommier, O. Parriaux, T. Clausnitzer, N. M. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006).
[CrossRef] [PubMed]

M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

2004 (2)

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

S. Soria, T. Katchalski, E. Teitelbaum, A. A. Friesem, and G. Marowsky, “Enhanced two-photon fluorescence excitation by resonant grating waveguide structures,” Opt. Lett. 29(17), 1989–1991 (2004).
[CrossRef] [PubMed]

2000 (1)

A. V. Tishchenko, “A generalised source method: new possibilities for waveguide and grating problems,” Opt. Quantum Electron. 32, 971–980 (2000).
[CrossRef]

1998 (2)

1997 (3)

1994 (2)

1993 (2)

V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993).
[CrossRef]

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
[CrossRef] [PubMed]

1989 (1)

A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

1988 (1)

1986 (2)

A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
[CrossRef]

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[CrossRef]

1985 (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
[CrossRef]

1980 (2)

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).

V. A. Sychugov and A. V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Quantum Electron. 10, 326–331 (1980).

1979 (1)

P. Vincent and M. Nevière, “Corrugated Dielectric Waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Abdou Ahmed, M.

Ahmed, M. A.

M. A. Ahmed, M. Haefner, M. M. Vogel, C. Pruss, A. Voss, W. Osten, and T. Graf, “High-power radially polarized Yb:YAG thin-disk laser with high efficiency,” Opt. Express 19(6), 5093–5104 (2011).
[CrossRef] [PubMed]

M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

Avrutskii, A.

A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
[CrossRef]

Avrutsky, A.

A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

Bel'tyugov, V. N.

V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993).
[CrossRef]

Blanc, D.

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

Boyko, O.

Brioude, V.

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

Britzger, M.

Brückner, F.

Burmeister, O.

Chandezon, J.

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).

Clausnitzer, T.

Danzmann, K.

Destouches, N.

Fehrembach, A.-L.

Friedrich, D.

Friesem, A. A.

Giovannini, H.

Golubenko, G. A.

A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
[CrossRef]

Graf, T.

Graf, Th.

M. Abdou Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and Th. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32, 1824–1826 (2007).
[CrossRef] [PubMed]

M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

Haefner, M.

Katchalski, T.

Kley, E. B.

Lemarchand, F.

Li, L.

Loewen, E. G.

Lyndin, N. M.

N. Destouches, J. C. Pommier, O. Parriaux, T. Clausnitzer, N. M. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006).
[CrossRef] [PubMed]

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, “Waveguide coupling gratings for high-sensitivity biochemical sensors,” Sens. Actuators B Chem. 39(1-3), 360–364 (1997).
[CrossRef]

Magnusson, R.

Marowsky, G.

Mashev, L.

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[CrossRef]

Mashev, L. B.

Maystre, D.

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[CrossRef]

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).

Molloy, J.

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

Moser, T.

M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

Nevière, M.

P. Vincent and M. Nevière, “Corrugated Dielectric Waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Osten, W.

Parriaux, O.

Pigeon, F.

M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

Pommier, J. C.

Popov, E.

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[CrossRef]

Protsenko, S. G.

V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993).
[CrossRef]

Pruss, C.

Raoult, G.

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).

Reynaud, S.

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

Rosenblatt, D.

Saoudi, R.

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

Schnabel, R.

Schulz, J.

Sentenac, A.

Sharon, A.

Soria, S.

Svakhin, A. S.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
[CrossRef]

Sychugov, V. A.

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, “Waveguide coupling gratings for high-sensitivity biochemical sensors,” Sens. Actuators B Chem. 39(1-3), 360–364 (1997).
[CrossRef]

A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
[CrossRef]

V. A. Sychugov and A. V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Quantum Electron. 10, 326–331 (1980).

Talneau, A.

Teitelbaum, E.

Tibuleac, S.

Tishchenko, A. V.

A. V. Tishchenko, “A generalised source method: new possibilities for waveguide and grating problems,” Opt. Quantum Electron. 32, 971–980 (2000).
[CrossRef]

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, “Waveguide coupling gratings for high-sensitivity biochemical sensors,” Sens. Actuators B Chem. 39(1-3), 360–364 (1997).
[CrossRef]

A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
[CrossRef]

V. A. Sychugov and A. V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Quantum Electron. 10, 326–331 (1980).

Tonchev, S.

N. Destouches, J. C. Pommier, O. Parriaux, T. Clausnitzer, N. M. Lyndin, and S. Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence,” Opt. Express 14(26), 12613–12622 (2006).
[CrossRef] [PubMed]

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

Troitski, Y. V.

V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993).
[CrossRef]

Tünnermann, A.

Veldhuis, G. J.

Vincent, P.

P. Vincent and M. Nevière, “Corrugated Dielectric Waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

Vogel, M. M.

Voss, A.

Wang, S. S.

Appl. Opt. (2)

Appl. Phys. (Berl.) (1)

P. Vincent and M. Nevière, “Corrugated Dielectric Waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

J. Opt. (Paris) (1)

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).

J. Opt. Soc. Am. A (4)

Laser Phys. Lett. (1)

M. A. Ahmed, T. Moser, F. Pigeon, O. Parriaux, and Th. Graf, “Intra-cavity polarizing element for Nd:YAG laser,” Laser Phys. Lett. 3, 129–131 (2006).

Opt. Acta (Lond.) (1)

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

A. V. Tishchenko, “A generalised source method: new possibilities for waveguide and grating problems,” Opt. Quantum Electron. 32, 971–980 (2000).
[CrossRef]

Proc. SPIE (2)

V. Brioude, R. Saoudi, D. Blanc, S. Reynaud, S. Tonchev, N. M. Lyndin, and J. Molloy, “Resonant grating biosensor platform design and fabrication,” Proc. SPIE 5252, 209–216 (2004).
[CrossRef]

V. N. Bel'tyugov, S. G. Protsenko, and Y. V. Troitski, “Polarizing laser mirrors for normal light incidence,” Proc. SPIE 1782, 206–211 (1993).
[CrossRef]

Quantum Electron. (1)

V. A. Sychugov and A. V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Quantum Electron. 10, 326–331 (1980).

Sens. Actuators B Chem. (1)

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, “Waveguide coupling gratings for high-sensitivity biochemical sensors,” Sens. Actuators B Chem. 39(1-3), 360–364 (1997).
[CrossRef]

Sov. J. Quantum Electron. (2)

A. Avrutskiǐ, G. A. Golubenko, V. A. Sychugov, and A. V. Tishchenko, “Spectral and laser characteristics of a mirror with corrugated waveguide on its surface,” Sov. J. Quantum Electron. 16(8), 1063–1065 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectrique waveguide,” Sov. J. Quantum Electron. 15(7), 886–887 (1985).
[CrossRef]

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