37 2.4. Self-mode-locking SDLs
Chapter 2. Passively Modelocked Semiconductor disk lasers 38 six-mirror SDL-cavity configuration [57]. However, they attributed the origin of pulsed operation to the intensity dependent Kerr lensing effect arising in the semiconductor gain medium. In that work, the mode-locked operation has been shown in two different config-urations. Firstly, stable mode-locking was observed when the cavity was operated near its stability limit. In such configuration, single pulses with durations of 1.5 ps at an average output power of 700 mW at 200 MHz repetition rate could be achieved. Secondly, mode-locked operation could also be achieved by operating the cavity in its stability region and by inserting a hard aperture near the output. Pulses with durations of 930 fs could be achieved at a 210 MHz repetition rate.
It did not take long time and other groups observed the SML phenomena. Albrecht et al. also predicted KLM operation for both soft and hard apertures placed at the optimal intra-cavity positions [58]. Their system delivered pulses with durations of below 500 fs at 1 GHz repetition rate. Nevertheless, in their measurements, they observed a residual background or pedestal which can be attributed to CW background; in addition the pulse train fluctuated over a time scale of some microseconds. Alternatively, in [60] Moloneyet al. claimed to enhance the Kerr lensing effect with an extra Kerr medium inside the cavity.
For this, they utilized an yttrium orthvanadate crystal which exhibits a nonlinear refractive index three times higher than that of titanium sapphire. However, a pulse duration of about 850 fs sits on a high background pedestal indicating a strong quasi-CW component in the emission. On the other hand, Lianget al. (in the Chen-group) [61] supposed that the occurrence of SML can be assisted by the existence of high-order transverse modes.
Lianget al.observed a threshold for SML which coincided with the threshold of high-order transverse modes.
39 2.4. Self-mode-locking SDLs
2.4.1 Kerr-lensing in an SDL gain chip
As discussed before in section 2.2.1, in the majority of solid state lasers, KLM originates from the optical Kerr effect in the gain-medium hosting crystal, while it is possible that the Kerr medium is separate from the gain structure itself. On the other hand, Albrechtet al.
analyzed the potential for KLM operation in a simple SDL cavity as a consequence of the ultrafast Kerr nonlinearity in the semiconductor gain chip itself [58]. They considered a typical linear SDL cavity of lengthd, consisting of a curved mirror with radiusR, and a flat end mirror with the gain (Kerr) medium.
Using standard text book ABCD matrix formalism, they calculated the modulation (relative change in beam radius) at any point (z) in the cavity as:
ω(z, Ppeak)−ω(z,0)
ω(z,0) ≈γ(zk)Ppeak Pc
L 2z0n0
1−z2/z02
1 +z2/z02. (2.11) whereLis the Kerr medium thickness,Ppeak is the intracavity peak power,z0 = (dR(1− d/R))1/2is the Rayleigh rang of the linear cavity,Pc≈aλ2/8πn0n2is the self-focusing crit-ical power, andn2is the nonlinear refractive index, whileγis a geometric cavity parameter given by:
γ(zk) =− R/z0
2(1 +zk2/z20)+ (d/z0)(1−zk/d)2
(1 +zk2/z02)2 . (2.12)
Next, Albrechtet al. explored the feasibility of KLM operation in SDLs for typical experi-mental parameters ofPpeak = 10kW,L = 4µm, andn2 =−1×10−12cm2/W. Figure 2.5 depicts essentially an intracavity z-scan, where the calculated change in the beam radius (from Eq. 2.11) at the locations of gain chip and the curved mirror are shown as a function
Chapter 2. Passively Modelocked Semiconductor disk lasers 40
Figure 2.5: Calculated beam-radius modulation (using Eq. 2.11) at the gain chip (blue) and the curved mirror (red) as a function of the distance of the gain medium from the flat mirror. Negative change (in y-axis) implies beam narrowing. Reproduced with permission [58]. Copyright 2013, Optical Society of America.
of position of the Kerr medium. The negative sign, implying beam narrowing, can there-fore be exploited for mode-locking. As shown in the figure, the beam narrowing due to the negative Kerr effect at the gain chip occurs for all positions of the gain chip.
2.4.2 Z-scan measurements of SDL gain medium nonlinear refractive index
As was mentioned before, the mechanism responsible for SML has not been identified yet, with some proponents suggesting that Kerr lensing in the gain medium is responsible and others suggesting that mode-locking results from saturable absorption in unpumped quan-tum wells. Motivated by this uncertainty and for the sake of a deeper analysis, Quarterman et al. described measurements of the nonlinear refractive index (n2) of an SDL gain medium and demonstrated that the magnitude of the resulting Kerr lens is sufficiently large to cause an appreciable perturbation in a typical SDL cavity [119].
The authors of that study measuredn2of an antiresonant 1050 nm SDL gain medium with
41 2.4. Self-mode-locking SDLs
Figure 2.6: Extracted values ofn2as a function of pump intensity shown on the left-hand y-axis, and the corresponding inverse focal lengths of nonlinear lenses shown on the right-hand y-axis.
Reproduced with permission [119]. Copyright 2015, AIP publishing LLC
11 InGaAs QWs using a reflection-type z-scan system, with a 1064 nm, 10-ps-pulse laser as a probe, and a fiber-coupled 808 nm diode pump laser for carrier injection. They found, thatn2 depends approximately linearly on the applied pump intensity, having a value of
−1.5(0.2)×10−12cm2/W at zero excitation but increasing to take on positive values at typ-ical SDL operating conditions. The focal lengths of corresponding Kerr lenses were cal-culated using typical SDL pulse intensities, which turned out to be sufficiently short to be comparable to the SDL's cavity mirror distances, implying that KLM may be responsible for the observation of SML in SDLs. The obtained values ofn2 are plotted in Fig. 2.6 as a function of incident pump intensity. In the chart, the nonlinear refractive index increases approximately linearly with increasing pump power. It should be noted, that theoretical predictions ofn2 in active semiconductor structures are difficult to obtain, owing to the large number of effects which can contribute ton2. Notice that, the presented values ofn2 are many orders of magnitude larger than in solid state gain-medium hosting crystals, such as sapphire. This large value ofn2is however compensated by the small thickness of the semiconductor gain medium, which is typically of the order of a fewµm.
Chapter 2. Passively Modelocked Semiconductor disk lasers 42