# Online Measurement of Internal Parameters in a Quasi-CW Diode-Pumped Nd:YAG Laser
## 1 Introduction  
All-solid-state neodymium doped yttrium aluminum garnet Nd:YAG lasers pumped by laser diodes (LDs) have been studied extensively for various applications, including material processing [1], nonlinear optics [2; 3], lidars [4], the military domain [5; 6], and medical surgery [7] due to their inherent advantages of a high output power, good beam quality, and high stability. The internal parameters of a laser, especially the small-signal gain, internal optical losses, and saturation parameter, and the optimization of a laser's output coupler are essential to the production, maintenance, and design of Nd:YAG laser systems.  
A variety of methods for measuring the small-signal gain and internal round-trip loss have been presented [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. The first one was single-pass measurement, in which a probe laser beam is injected into the laser being measured [8; 9; 10]. In single-pass measurement, a probe laser line should be strictly aligned with the laser line being measured. However, it is not easy in fact to satisfy the condition because of the difficulty in constructing identical laser systems [11]. The most popular one was proposed by [PERSON] and [PERSON] [12]. By using a few sets of output couplers with different transmittances, the corresponding threshold pump powers are recorded, the intra-cavity round-trip loss is obtainedby a numeric calculation, and then the small-signal gain as a function of the input power is plotted. In [PERSON] and [PERSON]'s approach, the work of measurement is heavy because the output couplers need to be frequently replaced, leading to the inevitable realignment of the resonator [13; 14]. Some variable intra-cavity loss methods [14; 15; 16; 17; 18] were further developed by observing the dependence of the input or output powers on some adjustable loss parameters, such as introducing internal reflective loss by a rotatable plate [15; 16], introducing internal modulation loss by nonlinear loss [14], and using an adjustable interferometer output coupler [17; 18]. In these intra-cavity loss methods, the output coupler of a laser is often replaced by an adjustable loss device, e.g., the rotatable plate with a total reflector as an output coupler in [16] and the adjustable interferometer as an output coupler, which are suitable for a laser optimization design process. The adjustable loss output device would be replaced by an optimized cavity mirror, except as part of a laser product. Furthermore, the intra-cavity round-trip loss is usually determined by the [PERSON] and Clay approach of recording the threshold pump powers [18]. However, the power supply of a pump source is often integrated into a laser product, such as a laser range finder, lidar, and industrial lasers. Thus, the pump power is fixed after the optimization of a laser's design because the laser parameters are dependent on the input pump powers. Therefore, the above methods are difficult to apply to online measurement of internal parameters, especially the measurement of Nd:YAG laser products. Although the relaxation oscillation spikes frequency measurements (ROF) method is available for in situ small-signal gain determination of continuous-wave (CW) solid-state lasers [11], it is not easy to use in high pump power and pulsed lasers, where the serious thermal effects would change the ROF frequency [14]. Consequently, it is necessary to find a simple and practical online measurement method.  
In this paper, we present a simple online method for measuring the internal parameters of a quasi-CW diode-pumped Nd:YAG laser. A measurement cell that produces variable polarization reflective loss is introduced. A theoretical model is derived and the internal parameters are measured online. Experiments to investigate validity and the optimization of an output coupler are conducted, and the results are discussed and analyzed. The experimental investigations verify the good measurement accuracy and the applicability of the online measurement method.