Conclusions …

We have demonstrated a novel compact, low cost, non-planar, and multi-reentrant two-mirror ring cavity by using one gain medium and two spherical couplers which the amplitude noise can be maintained at 0.3%. The laser cavity is compact which the volume can be as small as 1.46 cm³ and suitable for applications in cases where unidirectional propagation is required. Numerical simulation in polarization is also performed. In the numerical simulation, the factors which affect the polarization state within the cavity were considered, the thermally induced optical axis rotation in the gain medium is also derived, and the equivalent temperature-dependent dielectric tensor of the gain medium at various pump powers was determined, which enable Jones matrix analysis on the polarization in the non-planar ring laser cavity.

We not only prove that the multi-reentrant laser system is feasible experimentally, but also use fundamental laser theory to find the relation among cavity length, number of points, number of circulation, and the distance between center of gain medium and optical axis. The exact solution we obtained is experimentally verified with good agreement. A comparison between exact solution and paraxial approximation is also performed. The beam paths observing from the top, side, and end view are analyzed for various multi-reentrant laser cavities. The stability of the cavity is numerically analyzed and experimentally verified with good agreement, too. The differences in cavity configuration between TEM01 mode and the figure-8 mode are also compared.

This ring cavity configuration can produce single frequency IR and green laser effectively. It is also applicable to trace gas sensing, mode locked laser, as well as lasergyro. In the aspect of the Q-switched high power pulse laser, the timing jitter

problem can be improved significantly. The timing jitter is reduced around more than thirtieth (1/30) compare to the typical linear cavity. In the future, one of our studies is utilizing our optical coating technique and this multi-reentrant cavity to demonstrate a compact mode-locked laser with dispersion compensated output couplers.

Appendix A

Considering the cavity configuration shown in Fig. A1, the laser beam bounces back and forth between the two cavity mirrors, M1 and M2, and obeys the reflection law. With the assumption that all the laser spots at the mirrors have the same distance from the optical axis, we can assign the coordinates for three consecutive reflection points as,

It is also clear from Fig. A1(b) that, using Pythagorean theorem, the following equation holds:

Plugging (A1) into (A2), we obtain

( )

In one bounce and return between M1 and M2, the laser beam rotates in the x-y plane by a 2ϕ angle. Assuming the beam completes a round trip with N bounce and ₁ back, the constrain below on ϕ should be followed, ₁

( )

2 ₁ 2 M

( )

N ϕ = π

where M is an integer. Substituting (A4) into (A3), we obtain

( )

A5 2 cos

cos 2

2 ² π θ

N M R

L = −

Figure A1. Beam path in (a) 3D view, (b) side view, and (c) end view.

y z x

1 2

(a)

L x

z 1 2

L L x

M1 M2

m2 m1

(b)

1 2

3 2ϕ1

(c)

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[151] A. Agnesi, S. Dell’Acqua, and G. C. Reali, “1.5 Watt passively Q-switched diode-pumped cw Nd:YAG laser,” Opt. commun. 133 (1997) 211.

[152] A. Agnesi, S. Dell’Acqua, and G. C. Reali, “High performance Cr4+:YAG Q-switched CW diode pumped Nd:YAG laser,” Optical and Quant. Elec. 29 (1997) 429.

[153] S. L. Huang, T. Y. Tsui, C. H. Wang, and F. J. Kao, “Timing jitter reduction of a passively Q-switched laser,” Jpn. J. Appl. Phys. 38 (1999) 239.

[154] 崔宗元，“被動式 Q 開關 Nd:YAG/Cr⁴⁺:YAG 雷射研究” ，國立中山大學光

電工程研究所碩士論文，1998。

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[156] W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1999).

Biography

姓名：黃碧鈴 (Huang, Pi-Ling) 性別：女

出生年月日：民國六十四年一月二十二日籍貫：台灣省台南市

學經歷：台灣省立台南女子高級中學 (1990.6-1993.6) 私立文化大學物理系畢業(1993.9-1997.6) 國立中山大學光電工程研究所(1997.8-2003.6) 博士論文題目：雙球面鏡之多次再入射環型共振腔雷射之研

究及應用

The study and application of multi-reentrant

two-spherical-mirror ring lasers

Publication List

I. SCI listed paper：

[1] P. L. Huang, C. J. Weng, H. T. Tuan, S. C. Pei, Y. H. Chang, and S. L. Huang

“Polarization analysis of a non-planar and reentrant ring laser cavity”, Jpn. J.

Appl. Phys. Vol.42 (2003).

[2] C. Y. Lo, P. L. Huang, T. S. Chou, L. M. Lee, T. Y. Chang, S.-L. Huang, L. C.

Lin, H. Y. Lin, and F. C. Ho, “Efficient Nd:Y3Al5O12 crystal fiber laser,” Jpn. J.

Appl. Phys. vol. 41 (2002) pp. L1228.

[3] S. L. Huang, Y. H. Chen, P. L. Huang, J. Y. Yi, and H. Z. Cheng,

“Multi-Reentrant Nonplanar Ring Laser Cavity,” IEEE J. Quantum Electron.

vol. 38 (2002) pp. 1301.

[4] C. W. Wang, Y. L. Weng, P. L. Huang, H. Z. Cheng, and S. L. Huang,

“Passively Q-switched quasi-three-level laser and its intracavity frequency doubling,” Appl. Opt., vol. 41 (2002) pp.1075.

[5] P. L. Huang, C. R. Weng, H. Z. Chang, and S. L. Huang, “A passively Q-switched laser constructed by a two-mirror reentrant ring cavity,” Jpn. J.

Appl. Phys. vol. 40 (2001) pp. L508.

[6] H. Z. Chang, P. L. Huang, and S. L. Huang, “Reentrant two-mirror ring resonator for generation of a single-frequency green laser,” Opt. Lett., vol. 25 (2000) pp. 542.

[7] S. L. Huang, W. L. Wu, and P. L. Huang, “Measurement of temperature gradient in diode-laser-pumped high-power solid-state laser by low-coherence reflectometry,” Appl. Phys. Lett., vol. 73 (1998) pp. 3342.

II. Conference paper：

[1] P. L. Huang and S. L. Huang, “The analysis of polarization in a non-planar ring laser,” Conf. on Lasers and Electro-Optics, paper CFM, Baltimore, Maryland, U.S.A., 2003.

[2] J. Y. Yi, P. L. Huang, H. T. Tuan, and S. L. Huang, “Planar and non-planar multi-reentrant 2-mirror ring cavities,” Conf. on Lasers and Electro-Optics, paper CThO12, Long-beach, U.S.A., 2002.

[3] C. Y. Lo, T. S. Chou, P. L. Huang, L. M. Lee, and S. L. Huang, “High-efficient Nd:YAG crystal fiber laser,” Conf. on Lasers and Electro-Optics, paper CTuP6 Long-beach, U.S.A., 2002.

[4] P. L. Huang, C. J. Weng, H. T. Tuan, S. C. Pei, and S. L. Huang “Polarization

Taiwan, 2002.

[5] P. L. Huang, Y. L. Weng, C. W. Wang, H. Z. Cheng, and S. L. Huang,

“Passively Q-switched three-level laser and its intracavity frequency-doubling,”

The 4^th Pacific Rim Conference on Lasers and Electro-Optics, paper WI1-1, Chiba, Makuhari Messe, Japan, 2001.

[6] J. Y. Yi, P. L. Huang, H. T. Tuan, Y. H. Chen, S. L. Huang, “Multi-reentrant ring laser cavity,” Optics and Photonics Taiwan, paper FD2-2, Taiwan, 2001.

[7] C. Y. Lo, T. S Chou, P. L. Huang, L. M. Lee, and S. L. Huang, L. C. Lin, C. S.

Chang, H. Y. Lin, and F. C. Ho, “Diode laser pumped crystal fiber lasers with

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