E XPERIMENT SETUP AND RESULTS

In order to confirm our numerical calculation, the experiment is performed in a Nd:YVO4 laser with a plano-concave cavity. The detail

setup similar to the previous Chapters is show in Fig. 5-2. A photodetector (rise time < 0.3 ns) together with a RF spectrum analyzer (HP8560E, bandwidth 2.9 GHz) was used for measuring the mode beating and the relaxation oscillation. The optical spectrum was measured by using a Fabry-Perot interferometer (FPI, Burleigh) having finesse > 150 corresponding to a spectral resolution of 100 MHz for a 15 GHz free spectral range (FSR). In addition, the pump size determined by the standard knife-edge method is 20 μm, which is less than one-fifth of the waist radius (108 μm) of the cold cavity mode. The cavity length corresponding to the degenerate resonator configuration is determined by minimum pump threshold [6]. In this experiment, we operated the laser around the 1/3-degeneracy (L = 6 cm), which corresponds to the longitudinal mode spacing of about 2.4 GHz.

Figure 5-3 shows a typical single-frequency optical spectrum measured by FPI when the laser is operated at γ < 1.8 (~ 1.78) in the conventional

cavity configuration (L = 6.06 cm). The second longitudinal mode appears when γc = 1.8 > 1.78 (threshold is 33 mW). The experiment observation agrees well with the theoretical estimation according to the Ref. 7. Figure 5-4 (a) and (b) respectively show the FPI and the RF spectra for γc

= 2.7 (pumping power Pp = 90 mW). We can clearly see the second longitudinal mode and the beating from these two longitudinal modes. As the pump power increases to over 133 mW (γc = 4), we found that an extra lasing mode appears at 1.1 GHz away from the main features of the FPI spectrum but no corresponding mode beating can be detected by the RF spectrum analyzer. Therefore, we suspected that the spectral spacing of these two lasing modes is larger than the bandwidth of the RF spectrum analyzer (2.9 GHz). Indeed, when the FPI with larger FSR (150 GHz or even 300 GHz) is used, the measured mode spacing becomes 40 GHz.

0 5 10 15 20 25

0.00 0.25 0.50 0.75

1.00 FSR = 15 GHz

Δν (GHz)

Intensity (a.u)

Fig. 5-3 Single frequency optical spectrum of the Fabry-Perot interferometer with FSR = 15 GHz when the pumping is set below 1.8 times threshold.

0 5 10 15 20 25

Fig. 5-4 Typical multiple optical frequency and corresponding RF spectrum for the common laser at L=6.06cm. (a) The Fabry-Perot interferometer shows two longitudinal lasing modes with spacing of about 2.42 GHz and (b) the beat frequency of two longitudinal modes measured by the RF analyzer.

On the other hand, as the cavity is adjusted to the degenerate resonator configuration (L = 6 cm), the single frequency operation is observed, as shown in Fig. 5-3, for the pump power as high as 30 mW. By raising the pump power to above 30 mW (γd = 2), we found that the second mode appear in the FPI spectrum which is located 58.6 GHz away from the first mode rather than ~2.4 GHz. The next nearest neighboring longitudinal mode is not observed even the pumping power increases as high as we can. The FPI and the corresponding RF spectrum at Pp = 310 mW or γd ~20 are shown in the Fig. 5-5(a) and (b) respectively. The inset of Fig. 5-5(b) shows that

bandwidth of the RF spectrum analyzer, the arrow in this figure shows only one relaxation oscillation peak (2.4 MHz) existing in the RF spectrum. One may doubt whether the mode spacing of 58.6 GHz comes from the intracavity etalon effect. We estimated the mode spacing resulting from etalon effect of 1mm-gain medium is 72 GHz; in addition, there is an antireflection coating at 1064 nm on the Nd:YVO4 facet to avoid the effect of intracavity etalons.

As the simulated results discussed in the previous section, the laser with the degenerate resonator configuration is able to deplete most of the population inversion in a homogeneous broadened gain medium. We therefore expect that the second mode 58.6 GHz away from the first mode may have different origin of emission or arise from different manifold of transition (sub-peak of inhomogeneous gain profile). Similarly, the sub-peak of the gain profile will also result in occurrence of the second mode in the conventional cavity at higher pump power, which is 40 GHz away from the first mode. In the Nd:YVO4 crystal, the crystal field interaction gives rise to the Stark splitting at the satellite of ⁴F3/2, ⁴I9/2, and ⁴I11/2 [9].

Under high-resolution absorption and luminescence studies, it was found that the satellite energy of ⁴F3/2 Æ ⁴I9/2 transition depended on the Nd³⁺

concentration [10]. The lasing transition around 1064 nm is attributed to

4F3/2 Æ ⁴I11/2. It contains two closely transitions R1 Æ Y1 and R2 Æ Y2 with frequency difference of 90 GHz under 2% Nd³⁺ doping and 21 GHz under 0.56% Nd³⁺ doping [11, 12]. The doping concentration used in our experiment is 1%, it is quite reasonable to obtain the frequency difference of

~42 GHz by simple interpolation. The frequency difference which is

estimated by interpolation is in good agreement with our observation in the conventional laser cavity. Note that because the second mode has a frequency more than 40 GHz away from the first mode, it would be easily filtered out, for example, by a grating with 1800 grooves/mm. In principle, it is possible to design a cavity that delivers the same tight beam size in a fundamental TEM00 mode and achieve the same effect. However, such a cavity is usually operating close to the edge of stability and needs to accurately adjust the cavity length according to the spot size of the pump beam. Our scheme, in contrast, is operated within the stability region away from the edge of stability. Without knowing the pump beam size in advance, the laser with a degenerate resonator configuration can self-adjust the mode distribution to match the small pump beam and as a result the spatial hole-burning effect is suppressed.

0 100 200 300

Fig. 5-5 Multiple optical frequency and corresponding RF spectrum under 310mW pumping at g1g2=1/4. (a) The FPI spectrum shows mode spacing of about 58.6GHz but without longitudinal beating of 2.42 GHz or transverse mode beating in the RF spectrum in (b). An arrow points out the peak due to relaxation oscillation.

5.3 Conclusion

We have theoretically shown and experimentally demonstrated that the spatial hole-burning effect can be suppressed by using a plano-concave cavity with degenerate resonator configuration under a tightly focusing pump beam. It not only has the merits of the lowest threshold and stable output but also is independent of the gain medium. The same resonator configuration has been employed to generate the multiple beam waists and

the optical bottle beam [13, 14], it has potential applications for trapping atoms in the dark field if the proper gain medium is chosen to generate blue-detuned single frequency laser beam.

References

[1]. V. Evtuhov and A. E. Siegman, Appl. Opt. 4, 142 (1965).

[2]. K. Otsuka and K. Kubodera, IEEE J. Quantum Electron. QE-16, 538 (1980).

[3]. K. Otsuka, P. Mandel and E. A. Viktorov, Phy. Rev. A, 56, 3226 (1997).

[4]. L. Meilhac, G. Pauliat and G. Roosen, Opt. Commun. 203, 341 (2002).

[5]. C. H. Chen, P. T. Tai, M. D. Wei, and W. F. Hsieh, J. Opt. Soc. Am. B 20, 1220 (2003).

[6]. H. H. Wu and W. F. Hsieh, J. Opt. Soc. Am. B 18, 7 (2001).

[7]. G. J. Kintz and T. Baer, IEEE J. Quantum Electron. 26, 1457 (1990).

[8]. Y. F. Chen, C. C. Liao and S. C. Wang, Appl. Phys. B 70, 487 (2000).

[9]. J. R. O’Connor, Appl. Phys. Lett. 9, 407 (1966).

[10]. Guillot-Noel, V. Mehta, B. Viana, D. Gourier, M. Boukhris, and S. Jandl, Phys. Rev. B, 61, 15338 (2000).

[11]. D. K. Sardar and R. M. Yow, Opt. Matter. 14, 5 (2000).

[12]. F. J. Manjon, S. Jandl, G. Riou, B. Ferrand, and K. Syassen, Phys. Rev.

B, 69, 165121 (2004).

[13]. P. T. Tai, C. H. Chen, and W. F. Hsieh, Opt. Express 12, 5827 (2004).

[14]. C. H. Chen, P. T. Tai, and W. F. Hsieh, Appl. Opt. 43, 6001-6006 (2004).