ASE and parasitic lasing in thin disk laser with anti-ASE cap

Hiroaki Furuse; Haik Chosrowjan; Junji Kawanaka; Noriaki Miyanaga; Masayuki Fujita; Yasukazu Izawa

doi:10.1364/OE.21.013118

1. Introduction

The thin disk laser geometry is one of the most promising concepts for high power laser systems due to its efficient cooling technique and consequently reduced thermal issues [1]. Nowadays, thin disk lasers with output power of several kilowatts are commercially available for industrial applications [2,3]. Furthermore, the power scaling law of thin disk lasers up to 100 kW in CW mode has been already considered [4]. For developing such ultra-high power laser systems, besides the thermal problems, other significant issues like the laser gain reduction due to Amplified Spontaneous Emission (ASE) and Parasitic Lasing (PL) have to be addressed. ASE problem in any inverted medium is the subject of intense research since the invention of the laser [5,6], and to avoid the severe impact of ASE and PL, many technical approaches have been proposed such as an anti-ASE cap [7–9], ASE absorber [10,11], and edge-face tilting [12]. Particularly, the anti-ASE cap, made from a transparent material, prevents the trapping of Spontaneous Emission (SE) inside the laser gain layer and suppresses the ASE effect increasing the maximum output power [13].

Up to now, some numerical studies of ASE/PL effects in disk lasers were reported with experimentally obtained amplified gain data at steady state [10,14]. These analyses were in reasonable agreement with the experimental data, however, ASE and significant heating presented inside the laser material were not separated. Additionally, the ASE length in the sample was determined using numerical models with assumptions. In general, the ASE gain parameter g₀l_ASE is nebulously set to values less than 4 to prevent the PL onset and to keep ASE at a low level. For permitting more precise analysis and to confirm the threshold value of ASE gain, more detailed experimental investigations of ASE/PL effects are necessary by specifying the ASE gain length and excluding the losses inside the laser material due to thermal heating.

In this paper, we have studied time-resolved ASE/PL effects and Small Signal Gain (SSG) in thin-disk laser with anti-ASE cap to extend the knowledge for design of high power laser systems. We used a cryogenically-cooled Yb³⁺:YAG total-reflection active-mirror (TRAM) [15] as a laser material. It is a composite ceramics of un-doped YAG and 9.8 at.% 0.6 mm-thick Yb³⁺:YAG layer, as shown in Fig. 1. One of the purposes of the un-doped YAG part is to separate the input and output surfaces to avoid a damage threshold reduction due to the optical interference [16]. Another purpose is to function as an anti-ASE cap. The slopes of un-doped YAG with angles of 60 deg. were polished and anti-reflection (AR) coated at the laser wavelength of 1030 nm. The bottom face of Yb³⁺:YAG layer was polished and has no high-reflection (HR) coating, effectively eliminating any additional thermal resistance. The most important difference between our approach and the conventional thin disk concept is the use of the “total reflection geometry” for both pump and extraction. The beams are thus incident on the Yb³⁺ doped layer under angles larger than the critical angle for Total Internal Reflection (TIR). If the pump beam has a circular profile, then the pump area becomes elliptical on the active layer. Therefore, we can assume that the dominant ASE/PL direction is along the longer axis of this elliptical pump spot profile, as shown in Fig. 1. The time-resolved signals of ASE with gain length of l_ASE and SSG for one bounce were measured using photo diodes (PD) to reduce the heating effect contribution. The TRAM sample was attached to a specially designed Cu-made mount allowing us to capture the ASE/PL signal without being blocked by the side of the mount. From the ASE signal at time “zero” just after the switch-on of the LD pump, we clearly observed the crossover between SE, ASE and PL. We also found that SSG showed two-stage suppression due to ASE and PL effects.

Fig. 1 Schematic diagram of the measured TRAM sample.

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2. Experiments and discussions

Figure 2 shows the experimental setup for ASE/PL and SSG measurements. The composite ceramics sample was put into a liquid-nitrogen (LN₂) cryostat which has AR-coated windows for optical access and ASE/PL measurements. A CW 500 W, flat-top circular pump beam from a fiber-coupled laser diode (LD) was focused onto the Yb³⁺:YAG layer. As mentioned above, the pump beam becomes elliptic at the layer, and the fluorescence radiated in the direction of the longer axis of the ellipse was directly measured by using a photo diode (PD1). A linearly polarized, single-transverse-mode CW fiber laser (λ = 1029.4 nm, Δλ = 0.2 nm) was used as a seed beam for SSG experiments. The seed beam was expanded and collimated using lenses to about 50 mm diameter, and passed through an aperture set to the same size as the pump spot diameter. The seed beam profile after the aperture was almost flat top, with the fluence of 1 W/cm². The seed beam at the aperture was image relayed onto the Yb³⁺:YAG layer and then to PD2. We checked the amplification image using CCD camera to adjust the beam overlap between pump and laser beams. The amplified beam power was measured using the PD2. The SSG was evaluated by the ratio of the seed beam power captured by the PD2 with- and without the pump. For these experiments, the LD signal was used as a trigger.

Fig. 2 Experimental setup for time-resolved ASE and small signal gain measurements.

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Figure 3 shows the time-dependent profiles of ASE signal intensity and SSG after the switch-on of the LD, measured for the pump power of 340 W and the pump beam diameter of 4 mm. The sharp peak in ASE temporal profile seen at time “zero” represents the PL effect. The inset in Fig. 3 shows the same results within 0-10 msec time range. One can see that the ASE fast reaches the peak value at t ~2 msec. The sample temperature at the peak value can be considered equal to the boiling temperature of LN₂ (77 K) because of the short ASE rise-time. The SSG peak value was also reached at t ~2 msec and drops in time caused by the temperature rise. In our previous work, we evaluated the Yb:YAG temperature at steady state under the same pump conditions, and estimated that the temperature would increase to about 130 K [17].

Fig. 3 Experimentally obtained time-dependent profiles of ASE signal intensity and small signal gain. The inset shows the results within 0 - 10 msec time interval.

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Figure 4 shows the pump power dependence of (a) ASE and (b) SSG peak values in logarithmic scale at t ~2 msec. The pump beam diameter was 4 mm. The black circles show the experimental results. As can be seen in Fig. 4(a), the peak value of the ASE signal intensity increases in three phases shown in blue (1st phase), black (2nd phase) and red (3rd phase) colors, respectively. The dotted lines represent corresponding fitting curves for the 1st (linear: I_ASE = 5.44 x 10⁻³ P), 2nd (exponential: I_ASE = exp(1.04 x 10⁻² P – 1.50)) and 3rd (linear: I_ASE = 0.88 P – 266) phases, respectively. Here, I_ASE is the peak value of ASE and P is the pump power. For evaluation of the physical origin of phased ASE signal intensity increase, we start from the equation describing observed luminescence density change dI within a small solid angle given by

d I = \frac{E_{st}}{τ_{f}} \frac{Δ Ω}{4 π} d x .

Here E_st is the extractable energy density, τ_f is the excited state lifetime, ΔΩ is the solid angle and dx is the emission length change along the x axis. The small signal gain coefficient g₀ is expressed by

g_{0} = \frac{E_{st}}{I_{sat}},

where I_sat is the saturation fluence. By including the ASE gain along the x direction, the ASE intensity within a solid angle ΔΩ can be written as

\begin{array}{l} I_{ASE} = \frac{E_{st}}{τ_{f}} \frac{Δ Ω}{4 π} \int_{0}^{l_{ASE}} \exp [g_{0} (l_{ASE} - x)] d x \\ = \frac{I_{sat}}{τ_{f}} \frac{Δ Ω}{4 π} [\exp (g_{0} l_{ASE}) - 1] . \end{array}

For the case of low gain (SE), Eq. (3) becomes

I_{ASE} \sim \frac{E_{st}}{τ_{f}} \frac{Δ Ω}{4 π} l_{ASE},

and for the high gain (ASE) case it is expressed by

I_{ASE} \sim \frac{I_{sat}}{τ_{f}} \frac{Δ Ω}{4 π} \exp (g_{0} l_{ASE}) .

Note that E_st and g₀ are proportional to the pump power P, hence the ASE intensity as a function of P increases linearly in SE and exponentially in ASE regions, respectively. The ASE intensity in PL region, on the other hand, should increase linearly according to the laser output power formulas [18]. Therefore, the observed phased behavior shown in Fig. 4(a) can be obviously explained by the dominance of the SE in the 1st, ASE in the 2nd, and PL in the 3rd phases, respectively.

Fig. 4 (a) Peak ASE signal intensity in logarithmic scale as a function of the pump power. The dotted lines represent linear and exponential fitting curves. (b) Peak value of small signal gain in logarithmic scale as a function of the pump power and ASE gain parameter g₀l_ASE (upper scale). The dot-dashed line shows the numerical results, dashed and dotted lines show the exponential fitting curves.

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In Fig. 4(b), the blue dot-dashed line shows the numerical calculations of SSG given by G = exp(g₀l). The small signal gain coefficient can also be expressed by

g_{0} (P) = \frac{σ_{emi} τ_{f} η_{t} η_{Q} η_{S} η_{a} η_{B}}{h ν} \frac{P}{V} (1 - \exp (- \frac{t}{τ_{f}})),

where σ_emi is the stimulated emission cross section, η_t is the pump radiation transfer efficiency, η_Q is the quantum efficiency, η_S is the Stokes efficiency, η_a is the absorption efficiency of the pump power for one bounce, η_B is the beam overlap efficiency, hν is the photon energy of the laser, V is the pumped volume, and t is the pump duration. The optical length of the gain layer for one bounce l can be expressed by the Yb³⁺:YAG thickness d and the incident angle θ as l = 2d/cosθ. We used the following parameters in the calculations: σ_emi = 1.0 x 10⁻¹⁹ cm², τ_f = 1 msec, η_t = 0.96, η_Q = 1.0, η_S = 0.91, η_a = 0.95, η_B = 0.96, hν = 1.93 x 10⁻¹⁹ J, V = 0.015 cm³, d = 0.6 mm, and t = 2 msec, respectively. The beam overlap η_B was fitted to the experimental data in SE region. As can be seen in Fig. 4(b), the numerical results are in good agreement with experimental data for up to 165 W pump power. For P > 165 W, however, there is a discrepancy between experimental data and calculations. We attribute this to the gain reduction caused by the ASE and PL effects, oscillating between un-polished side surfaces of the Yb³⁺:YAG layer. Particularly, the threshold (~300 W) of the PL (Fig. 4(b)) is almost identical to the 3rd phase (dominating PL) threshold shown in Fig. 4(a). For the ASE (165 W

\leq

P

<

300 W) and PL (P

\geq

300 W) regions, we modified the equation of SSG by using the suppression factors η_ASE and η_PL as

\begin{array}{l} G_{ASE} (P) = \exp [g_{0} (165 W) l + η_{ASE} g_{0} (P - 165 W) l] \\ = \exp [g_{ASE} (P) l], \end{array}

and

\begin{array}{l} G_{PL} (P) = \exp [g_{ASE} (300 W) l + η_{PL} g_{0} (P - 300 W) l] \\ = \exp [g_{PL} (P) l] . \end{array}

The dashed and dotted lines in Fig. 4(b) show the calculations for ASE and PL regions, respectively. In the calculations, to fit the experimental data, we used the suppression factors η_ASE = 0.62 and η_PL = 0.06, respectively. In the PL region, the slope of the SSG becomes quiet low caused by the laser effect. The l_ASE = 8 mm is the length of the longer axis of the elliptical spot on the Yb³⁺:YAG layer for 4 mm pump beam diameter. From the data in Fig. 4(b), we can estimate that the SSG was reduced by ASE effect starting from g₀l_ASE ~3.1 and by PL effect from g₀l_ASE ~6.0, respectively. By considering the suppression factor due to ASE contribution (0.62g₀), the actual ASE gain at the PL threshold is estimated to be g_ASEl_ASE = 4.9.

We also performed experiments for the pump beam diameters of 2.4 mm and 6 mm (data not shown), and observed similar suppression behavior. The ASE thresholds for 2.4 and 6 mm pump beam diameters were g₀l_ASE = 2.9 and 3.0, respectively. The suppression factors in the ASE phase η_ASE were 0.66 and 0.68, respectively. Therefore, we conclude that the ASE suppression would start from g₀l_ASE ~3.0, and the SSG coefficient will be reduced down to about 65% for this sample. On the other hand, the actual ASE gain parameter at the PL threshold for 2.4 and 6 mm pump diameter conditions were 4.0, and 4.6, respectively. By assuming that the reflectivity of both sides of the Yb³⁺:YAG layer is the same, the reflectivity can be estimated from the oscillation condition to be around 0.7-1.8%. This reflectivity can be drastically reduced by using ASE absorber (e.g. a Cr⁴⁺:YAG cladding), edge face tilting or AR coating, further increasing the PL threshold.

3. Conclusions

In conclusion, we have experimentally studied the ASE/PL effects in thin-disk laser with anti-ASE cap and compared them with SSG to extend the knowledge of ASE/PL behavior in laser gain medium. Time-resolved ASE signal intensities in the direction of longer axis of the elliptical pump spot profile were directly measured, and peak ASE signal intensity (t ~2ms) clearly showed the phased transitions from SE to ASE and from ASE to PL. Both ASE and PL showed close correlations with SSG. Uniqueness of the TRAM sample such as the composite ceramics, large rectangular trapezoidal shape of the un-doped-YAG, slope surface with AR-coating and elliptical pump spot profile enabled us to study the ASE and PL effects quantitatively. From SSG results obtained for several pump conditions, it was estimated that the SSG suppression by ASE effect starts from the ASE gain at g₀l_ASE ~3. Starting from the ASE threshold and up to the PL suppression threshold, the gain coefficient was reduced to about 0.65g₀. To the best of our knowledge, this is the first detailed experimental study of the SE, ASE and PL phase changes in the thin disk laser with an anti-ASE cap. We believe that the presented results will be useful for designing high power laser systems based on the disk laser geometry with an anti-ASE cap. For the highest optical-to-optical efficiency, the ASE gain should be kept below 3.0 to avoid the gain suppression. At CW operation, the gain saturation due to high fluence of the laser should be also considered for optimally designed laser systems. We think that the ASE suppression factor would have a strong correlation with the effective Yb:YAG lifetime, τ_ASE [4,19]. To explain the suppression factor in more detail, ray-tracing method based calculations of the gain distribution in the gain layer will be performed. In addition, for the case of high pump intensity, the effect of pump intensity saturation will be considered in the gain calculations. We will also measure the ASE/PL thresholds for samples with different Yb³⁺:YAG thicknesses and Yb³⁺ doping concentrations to compare with the calculation results.

Acknowledgment

We thank Dr. Ryo Yasuhara and Dr. Daniel Albach for reading our manuscript and valuable comments.

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ASE and parasitic lasing in thin disk laser with anti-ASE cap

Abstract

1. Introduction

2. Experiments and discussions

3. Conclusions

Acknowledgment

References and links

Cited By

Figures (4)

Equations (8)

Optics Express