### 5.2.1. Laser threshold and efficiency when pump is focused and defocused on cuvette

Here we will show in detail what happens to laser threshold and efficiency when we focus and defocus pump (10 µs) on the gain medium. Though Figure 5.9 provides information about laser efficiency when the pump was defocused by moving lens in one direction, here we will show laser efficiency and threshold by translating the lens in both +z and -z direction.

we designed a long cavity 19.8 cm using 200 mm output coupler as shown in Figure 5.11. Such long cavity was designed not to change cavity mode (on cuvette) significantly during cuvette translation

<figure><img src="image_101.png" /><figcaption>Figure 5.11: Plano-concave laser cavity to investigate laser efficiency and threshold when cuvette or lens moves away from focus.</figcaption></figure>

while laser efficiency largely depends on mode matching between pump and cavity mode as already discussed. Another modification made in current experiment was that we used a 60 mm lens instead of 35 mm to focus the pump (Figure 5.5) to have an efficient mode matching between pump (86 ± 2 µm in radius as shown in Figure 3.3) and cavity (88 µm in radius) mode which is very necessary to compare laser efficiency and threshold between a mode matched and mismatched case. Laser efficiency and threshold as a function of lens position is shown Figure 5.12. It is seen here that laser threshold is the minimum when the lens focused pump at the middle of the cuvette. Similar threshold behavior was found when we moved the cuvette (not shown here) few mm before and after focus. This lowest threshold is just another meaning of the shortest laser build-up time observed in Figure 5.6 when pump was focused at the middle of cuvette. As soon as the lens was moved from 0 position, laser threshold started to increase because of low pump power resulting from increased pump area. However, to
<figure><img src="image_102.png" /><figcaption>Figure 5.12: Laser threshold (left y axis) and efficiency (right y axis) as a function of lens position.</figcaption></figure>

<figure><img src="image_103.png" /><figcaption>Figure 5.13: Laser temporal profile when the lens was placed at focus and moved 1 mm forward or backward from lens focal plane.</figcaption></figure>

understand laser efficiency observed in Figure 5.12 let's concentrate on Figure 5.14. It shows that two things happen in a mode matched laser cavity when pump is defocused on cuvette – a) spatial overlap
between pump and cavity mode gradually becomes less efficient and b) pulse duration or laser energy per pulse also increases as already shown before and here in Figure 5.13. Since laser efficiency depends

<figure><img src="image_104.png" /></figure>

Figure 5.14: A schematic to show that in a mode matched laser cavity, mode overlap becomes less efficient when pump size is increased through defocusing the pump on cuvette. On the contrary, experiments showed that laser pulse duration increases when pump is defocused on cuvette. Since optical efficiency of laser depends on both mode overlap and pulse energy, laser efficiency as a function of pump focusing or defocusing may look like the resultant.

on both mode overlap and pulse energy, the resultant of those two effects may result such efficiency pattern in Figure 5.12. To clarify, when cuvette is at focus, the shortest laser pulse duration results the lowest efficiency even if the mode matching is perfect. As soon as the pump is defocused by moving the focusing lens up to around 0.5 - 1 mm, laser pulse duration becomes as long as the pump and hence laser efficiency becomes maximum. Probably, such amount of defocusing does not disturb mode-matching significantly. But, when the pump is defocused more, laser pulse duration does not have the room to increase more, and mode-matching becomes the key factor to decrease laser efficiency which is observed in Figure 5.12.

However, the efficiency plot also indicates that it might not be optimum to tightly focus at the middle of cuvette. Because laser pulse duration became as long as the pump (10 µs) when the pump was slightly defocused. 10 µs lasing is rare in organic laser without using any triplet quencher or solution flow
system. Therefore, it triggered the interest to understand why long pulse lasing became favorable when pump was just defocused on cuvette.

### 5.2.2. Investigation of dye laser pulse duration under different pumping strategy (focused and defocused)

As already stated before, we did not completely understand why dye laser pulse duration is longer when pump is defocused. But in this section, we will present our efforts and possible directions to understand that issue.

Indeed, few things happen when pump is defocused on gain medium-

a) thermal load is reduced on gain medium along with the reduction of unwanted excited state phenomena e.g., singlet excited state absorption which is detrimental for having long pulses in organic laser.

b) mode-matching between pump and cavity mode is disturbed which favors the multimode operation of a laser as already discussed at the beginning of this chapter.

To check if reducing thermal load on gain medium can increase laser pulse duration, we just reduced

<figure><img src="image_105.png" /><figcaption>Figure 5.15: Laser temporal profile for different pump (10 µs) power densities (kW/cm²).</figcaption></figure>
pump power from 89.3 $kW/cm^2$ to 21 $kW/cm^2$ by fixing the lens at a specific position (0 mm: as shown in Figure 5.6). This resulted an increase in laser pulse duration from 1.3 µs to 2.7 µs respectively with a sacrifice of significant drop of laser peak power as shown in Figure 5.15.

In clear contrast, using similar pump power densities obtained through defocusing pump in Figure 5.6, we achieved around 10 µs lasing without significant drop in laser peak power. The difference in laser pulse duration when reducing pump power densities in two different ways mentioned above is shown in Figure 5.16. Here, it is seen that the tendency of increasing laser pulse duration is more significant when pump power densities are decreased by increasing pump size compared to just decreasing pump power by lowering diode current. For instance, at around 20 $kW/cm^2$ power density obtained through

pump defocusing up to 0.5 mm (Figure 5.6) lens position resulting a pump radius around 125 µm (calculated from similar simulation shown in Figure 5.8), the laser pulse duration was just above 6 µs. As a clear contrast, laser pulse duration was only 2.7 µs at same pump power density obtained by reducing diode currents when the diode beam was focused to a 60 µm (in radius) spot on cuvette. To have a better insight of this issue, we used different pump sizes on cuvette but maintained similar pump power densities in other word same thermal load and excited state phenomena on gain medium. In this case, laser pulse duration was the longest and as well as the peak power was the highest for the largest pump size used. This is shown in Figure 5.17 but difference in the pulse duration (FWHM) is shown separately in Figure 5.18. This figure shows that despite using similar pump power density, laser pulse duration increased from 5.9 µs to 8.9 µs when pump radius was increased from 125 µm to 167 µm respectively. The results of Figure 5.15 - Figure 5.18 proved that only reduction of thermal load or ESA on gain medium cannot explain 10 µs operation of liquid dye laser but pump and cavity beam sizes should also be considered to explain it. Indeed, in above experiments the longest laser pulse was obtained when pump mode was significantly larger than cavity mode reaching a condition for multimode lasing.

<figure><img src="image_106.png" /><figcaption>Figure 5.16: Impact on laser pulse duration when pump power is reduced by increasing pump size and when pump power is reduced without changing pump size.</figcaption></figure>
<figure><img src="image_107.png" /><figcaption>Figure 5.17: Laser temporal profile for different pump (10 µs) radii but similar power density.</figcaption></figure>

<figure><img src="image_108.png" /><figcaption>Figure 5.18: Laser pulse duration (FWHM) as a function of pump beam radius at similar pump power density ~ 12 kW/cm².</figcaption></figure>

Therefore, there remains a high probability that 10 µs or longer pulse lasing is only favorable in a Plano-concave cavity liquid organic laser when minimum thermal load or ESA on gain medium and multimode laser operation can be achieved simultaneously. This possibility is investigated in the following where we kept the cuvette in the path of defocused pump as shown in Figure 5.19. In this way the thermal load
<figure><img src="image_109.png" /></figure>

Figure 5.19: Schematic of experimental set up consisting of a Plano-concave laser cavity having L_cavity=15 mm. The cuvette is placed close to the plane mirror after the focus of 35 mm lens to make large pump area which is fixed (pump radius = 166 µm) in this experiment. Different radii of curvature output couplers (with same reflectivity) are used to vary cavity beam sizes to match or mismatch with the pump area.

<figure><img src="image_110.png" /></figure>

Figure 5.20: Cavity beam radii on cuvette (left y axis) and mode matching ratio between pump and cavity mode (right y axis) as a function of radius of curvature of output coupler (concave mirror).

load was kept low on the cuvette. This defocused pump diameter (332 µm) was chosen based on previous experiment of Figure 5.6 where the pump beam diameter was simulated to be 334 µm (Figure 5.8) when
the focusing lens was moved up to 0.7 mm. However, to fulfill the second condition of achieving multimode lasing, we choose 25 mm output coupler which created 125 µm (in diameter) (in a fixed length cavity) cavity mode radius on the cuvette resulting a mode matching ratio around 37% as shown in Figure 5.20. Using pump power (approximately 12 kW/cm²) and this cavity configuration we obtained lasing as long as the pump (10 µs) as shown in Figure 5.21. M² of this laser was measured to be 1.95 verifying it to be a multimode laser. Then to compare the pulse duration of this multimode laser with pulse duration of single transverse laser using same pump power density (thermal load) and cavity configuration, we used several output couplers i.e. 50 mm, 100 mm and 200 mm (Figure 5.19). In this way, we increased fundamental (TEM₀₀) cavity mode sizes on cuvette (Figure 5.20) hence achieved better mode matching as shown in Figure 5.20 compared to the case when we used 25 mm output coupler. The result of changing output coupler ROC was straightforward as can be seen in Figure 5.21 – “10 µs operation from a multimode laser using 25 mm mirror was sacrificed in the process of obtaining a diffraction limited single transverse mode laser using 200 mm mirror.” For a diffraction limited (M² = 1.08) laser using 200 mm output coupler, peak power was found to be the highest compared to others. However, as the pulse energy was also the lowest it does not render the maximum efficiency even if

<figure><img src="image_111.png" /><figcaption>Figure 5.21: Laser temporal profile using different ROC output couplers in a 15 mm Plano-concave laser cavity. M² values of those lasers have been given to show the difference between pulse duration of a multimode and diffraction limited laser.</figcaption></figure>

the beam originated from mode matched laser cavity. This phenomenon has already been discussed in Figure 5.12.
The plot of beam radius vs camera position after lens to extract the value of M² of those lasers using different ROC output couplers are shown in Figure 5.22 (a - d). Here the highest value of M² ~ 1.95 (for

<figure><img src="image_112.png" /><figcaption>Figure 5.22 : M² of laser beam generated in a Plano-concave laser cavity (Figure 5.19) using different radius of curvature output coupler mirrors: a) 200 mm, b) 100 mm, c) 50 mm, d) 25 mm.</figcaption></figure>

a mode mismatched cavity) approached to 1 when we increased cavity mode size by using different radius of curvature mirrors to match the size of pump beam. Interestingly, a related experiment with multimode laser having M²>3 showed that when we blocked few transverse modes to further oscillate in the laser cavity, the laser M² decreased with a decrease in laser pulse duration. A Hemispherical laser cavity designed for this experiment is shown in Figure 5.23 where we see that a razor blade can be translated across the cavity axis. Such laser cavity can produce very small cavity mode when the gain medium is kept close to the plane mirror which is already discussed in chapter 4. Therefore, a multimode laser is expected since pump was defocused on cuvette to ensure a larger pump mode compared to the cavity mode.
<figure><img src="image_113.png" /><figcaption>Figure 5.23: Experiment to block transverse laser modes by translation of razor blade across a near hemispherical laser cavity.</figcaption></figure>

<figure><img src="image_114.png" /><figcaption>Figure 5.24: a) M² of a multimode laser, b) M² of laser when razor blade was in an arbitrary position to get temporal profile (a) of Figure 5.25 and c) M² of laser beam when razor blade was in another arbitrary position to get (c) of Figure 5.25.</figcaption></figure>
$M^2 > 3$ of this laser is shown in Figure 5.24 (a) confirming it to be highly multimode. But when we start to translate the razor blade across the laser beam, laser $M^2$ was approaching towards unity (Figure 5.24 (b) – (c)) confirming that a portion of transverse modes were blocked. Interestingly, the laser pulse duration also started to decrease when the transverse modes were blocked. Laser temporal dynamics

<figure><img src="image_115.png" /><figcaption>Figure 5.25: Pulse duration of a highly multimode laser ($M^2>3$) follows pump (9 µs) pulse. When transverse laser modes are blocked gradually by translating a razor blade across the laser beam, laser intensity and pulse duration also decreased with an improvement of $M^2$ value. The values of $M^2$ have been used from Figure 5.24.</figcaption></figure>

is shown in Figure 5.25. Several things can be interpreted from this experiment. Introducing the razor blade across the cavity beam causes high losses for higher order laser modes but also creates moderate but still higher losses for low order modes. This explains why $M^2$ is decreases and at the same time build up time increases. At same extent, if we admit that pushing razor blade more starts to add losses for TEM$_{00}$, this can explain the pulse shortening according to the experiment shown in chapter 3. Still, no reason was found explain the long pulse operation of a multimode laser.

However, Figure 5.21 or Figure 5.25 does not indicate a lasing limit which interested us to investigate the longest pulse duration achievable in above discussed method. Unfortunately, our laser diode driver (PCO-7141, ENERGY INC.) was limited to produce longer than 10 µs pulse from laser diodes as already stated before. Therefore, we employed a new laser diode driver (Figure 5.26) to pump our cuvette with longer than 10 µs pulse. For this experiment, we used the same near hemispherical laser cavity with 25 mm output coupler (shown in Figure 5.23). In this case, we achieved up to 80 µs lasing as shown in Figure 5.27. In this experiment, pump pulse duration was increased from 20 µs – 80 µs keeping pump
power fixed still, we observed decrease in laser intensity, but laser pulse duration was as long as pump duration in all the cases. As stated before, we could not go to the details of the experiment performed

<figure><img src="image_116.png" /><figcaption>Figure 5.26 : Laser diode driver (PCO 6131, DIRECTED ENERGY INC.) which can drive diode lasers from 100 ns to CW.</figcaption></figure>

<figure><img src="image_117.png" /><figcaption>Figure 5.27 : Laser temporal behavior when pumped with long pulses (20 µs – 80 µs).</figcaption></figure>

with this new driver due to time constraint. But it can be investigated in future when we will employ
this driver for mode-locking experiments. However, a similarity visible in the laser temporal profiles of
Figure 5.27, Figure 5.25 and also in Figure 5.21 is wave like patterns especially when the laser was multimode. We are going to investigate this issue in the following.

### 5.2.3. An unusual observation in laser temporal profile

We observed wave like patterns in laser temporal profiles of Figure 5.27, Figure 5.13 and also in Figure 5.21. Although stochastic pulse instabilities of liquid dye laser have been reported in literatures,¹⁰⁷⁻¹¹⁰ those wavy patterns in our case were not just instantaneous fluctuations which could occur due to e.g. thermal perturbation in the laser medium. In fact, they were persistent in laser profile since those profiles were recorded through averaging over 512 pulses at 10 Hz repetition rates. Therefore, we wanted to understand that phenomenon. However, current cavity configuration having the cuvette parallel to the cavity mirrors would complicate the situation due to Vernier Effects as already discussed before. Therefore, we redesigned our cavity placing the cuvette at Brewster angle. In this situation, the longitudinal mode distribution is more simple and does not contain sub cavity filtering effects as already discussed in chapter 3 (Figure 3.15 - Figure 3.18). Following that, we focused pump (5 µs) on the cuvette using 60 mm lens to create 88 µm (in radius) pump spot. We choose 25 mm output coupler mirror to create a cavity mode around 45 µm (in radius) on cuvette in a 24 mm long Plano-concave cavity. In this case we obtained lasing as long as the pump duration (Figure 5.29 (a)) with a multimode behavior of the laser beam (we measured its $M^2 = 4.2$ as given in Figure 5.28). Similar result was also obtained in the experiment of Figure 5.23 using similar cavity geometry. The difference is, here we observe several dips in the laser temporal profile as can be seen in Figure 5.29 (a) which were probably smoothened in Figure 5.23 due to Vernier Effect.

We thought those dips in laser temporal profile might be related to transverse modes in a multimode laser. To investigate that we blocked few transverse modes by translating a razor blade across cavity beam as explained in Figure 5.23. By doing so, we let just one deep to exist in the laser temporal profile (Figure 5.29 (b)) which would simplify the situation for the following experiment we are going to discuss. However, this is already one indication that those dips in temporal profile are related to higher order transverse modes. It is also interesting to observe

<figure><img src="image_118.png" /><figcaption>Figure 5.28: $M^2$ of laser beam generated in a near hemispherical cavity containing cuvette at Brewster angle and enclosed by 25 mm radius of curvature output coupler mirror.</figcaption></figure>
the narrowing of laser spectrum (at FWHM) when we blocked few transverse modes (Figure 5.29 (b)) compared to the spectrum of a multimode laser (Figure 5.29 (a)).

<figure><img src="image_119.png" /><figcaption>Figure 5.29 : (a) Temporal behavior along with spectrum of a multimode laser, (b) when a razor blade is used to block few transverse modes. (c) – (g): Laser temporal profiles when cavity length is decreased by translating the 25 mm concave mirror towards plane mirror without moving the razor blade. Pump duration used for this experiment was 5 µs.</figcaption></figure>
Another interesting observation was that, when we decreased cavity length by translating the output
coupler mirror up to 0.5 mm with 0.1 mm step, a shift of the deep was visible (after each step of
translation) in Figure 5.29 (c - g). After a reduction of 0.5 mm in cavity length, the deep in the temporal
profile was found at 2.6 µs which was originally at 3.7 µs before decreasing cavity length. Such decrease
in cavity length (Figure 5.29 (c - g)) resulted a shortening of its pulse duration which agrees with our
previous findings (Figure 5.6). However, the shift of dip was also observed when we increased the cavity
length by same amount. As expected, this time the deep shifted in opposite direction (Figure 5.30)
compared to previous case in Figure 5.29 (c - g). In Figure 5.30, a clear increase in laser build-up time
onca again validates the effect of increasing cavity length. This time the laser pulse duration remained
as long as the pump for each increased cavity length along with slightly low intensity due to a reduction
in mode matching efficiency.

<figure><img src="image_120.png" /><figcaption>Figure 5.30: Temporal behavior of a multimode laser when increasing the cavity length by translating output coupler mirror.</figcaption></figure>

One question still remains regarding the origin or formation process of those dips. In this regard we can
say that those deeps may result from the beating of transverse and longitudinal modes in a multimode
laser.¹¹¹ The frequency spacing of longitudinal modes (FSR = $\frac{c}{2L}$) of our 24 mm laser cavity is in the
range of GHz whereas from Figure 5.29 (a), it can be estimated that the spacing between the dips is in
MHz regime which eliminate the possibility of beating between only longitudinal modes to explain this
scenario. However, according to ¹¹¹, the resonant frequency of a two-mirror laser cavity can be written as,

$$v_{qmn} = \frac{c}{2L} [q + (m + n + 1) f(L)] \qquad (5.1)$$

Where, q = longitudinal mode number, m and n are transverse mode numbers which can take the values of 0, 1, 2,.. as briefly discussed at the beginning of this chapter and f (L) is the Gouy phase shift for a stable laser cavity which can be written here as,

$$f(L) = \frac{1}{\pi} \cos^{-1} \sqrt{\left(1 - \frac{L}{R_1}\right)\left(1 - \frac{L}{R_2}\right)} \qquad (5.2)$$

For a Plano-concave ideal hemispherical cavity where $R_1 = \infty$ and $R_2 = L$ that leads to $f(L) = \frac{1}{2}$. This value of f(L) creates equal possibility for a hemispherical cavity to show mode degeneracy like the case of a confocal laser cavity ($R_1 = R_2 = L$). To give more insight, let us calculate the transverse mode frequency for TEM$_{00}$ and TEM$_{01}$ mode in our near Hemispherical laser cavity (considering $f(L) = \frac{1}{2}$) according to (5.1) and (5.2).

$$\text{For TEM}_{q00}, \quad v_{q00} = \frac{c}{2L} [q + (m + n + 1)f(L)] = \frac{c}{2L} [q + f(L)] \qquad (5.3)$$

$$\text{For TEM}_{q01}, \quad v_{q01} = \frac{c}{2L} [q + (m + n + 1)f(L)] = \frac{c}{2L} [q + 2f(L)] \qquad (5.4)$$

Therefore, the separation between TEM$_{00}$ and TEM$_{01}$ becomes,

$$\Delta v = v_{01} - v_{00} = \frac{c}{4L} \qquad (5.5)$$

Similarly, the separation between TEM$_{00}$ and TEM$_{10}$ modes is also $\frac{c}{4L}$, hence TEM$_{10}$ and TEM$_{01}$ modes are degenerate as shown in the schematic of Figure 5.31. In this figure, longitudinal modes are represented by q, q+1, q+2 and their separation are $\frac{c}{2L}$. The odd symmetry transverse modes (10, 01) (of qth longitudinal mode) are degenerate at $\frac{c}{4L}$ between q and q+1 longitudinal modes ⁹⁰. Interestingly, if we perform the same calculation to obtain equation (5.5) for q02 and q20 modes, we
<figure><img src="image_121.png" /><figcaption>Figure 5.31: Degeneracy of modes in a hemispherical Plano-concave laser cavity.</figcaption></figure>

will find that they are exactly degenerate at $q+2,00$ mode as also shown in the schematic of Figure 5.31

⁹⁰

However, these calculations are based on the fact that cavity length is equal to the radius of curvature of output coupler in a Plano-concave laser cavity. In our experiment, as one can see in Figure 5.29, this condition is not exactly fulfilled. Therefore, longitudinal and transverse modes are not exactly degenerate but might maintain a close difference in frequency resulting beating with each other. Such explanation can be verified from experiment too. Firstly, We observed shift of deep position (Figure 5.29 and Figure 5.30) corresponding to the change in cavity length which is obvious from equation (5.1). Secondly, in Figure 5.30, when we increased the cavity length hence the cavity configuration was close to fulfill the condition ($L_c$ = Radius of curvature of output coupler) of mode degeneracy, there could be a pure chance that deep was almost vanished from temporal profile. This means that there remains a high possibility that most of the deeps in temporal profile would be vanished when the cavity becomes pure hemispherical and hence the modes are all perfectly degenerate. However, in that case laser build up time is also higher with pulse duration as long as the pump which can be seen in Figure 5.30. This once again indicates that the multimode laser with inefficient mode matching can be a choice to design a long pulse dye laser with no circulation.

Now, to show that what happens to the deeps of laser temporal profile when mode matching becomes efficient, we just changed the radius of curvature of output coupler mirrors to 50 mm and 100 mm. The result can be found in Figure 5.32. Here, for 100 mm output coupler the mode matching was efficient
<figure><img src="image_122.png" /><figcaption>Figure 5.32: Laser temporal behavior when the cuvette is placed at Brewster angle inside a Plano-concave laser cavity. Three different ROC output coupler has been used to vary the spatial mode overlap between pump and cavity beam. The mode overlap is inefficient when using 25 mm coupler which becomes partially good and efficient for 50 and 100 mm output coupler respectively.</figcaption></figure>

<figure><img src="image_123.png" /><figcaption>Figure 5.33: Laser beam M² using (a) 50 mm and (b) 100 mm output coupler mirror in a 24 mm laser cavity where cuvette was placed at Brewster angle between the two-mirror cavity.</figcaption></figure>

(pump mode 88 µm in radius, cavity mode 95 µm in radius), and the deeps were almost vanished and also the laser pulse was the shortest. Due to efficient mode matching, the laser beam was also diffraction limited TEM₀₀ as given in Figure 5.33 (b). In contrary, for 50 mm coupler the mode matching (pump
mode 88 µm in radius, cavity mode 70 µm in radius) was partially good which resulted lasing for slightly
longer duration compared to the lasing duration using 100 mm coupler. For this output coupler, the laser
beam was also slightly multimode as can be seen said from its $M^2 = 1.69$ (Figure 5.33 (a)). Finally, as
expected the longest laser pulse was obtained using 25 mm output coupler for which the mode matching
was the most inefficient in a way that favors multimode operation of the laser.

**5.3. Conclusion**

In conclusion of this chapter, we can say that the longest pulse lasing up to 80 µs is achieved in
circulation free liquid dye (DCM) laser. In the process to achieve such long pulse lasing, an interesting
physics has been found that circulation free liquid dye laser can produce long pulse when they are highly
multimode provided the effects of triplets and thermal are neglected at low pump repetition rate (10 Hz
in this case). In this study, we obtained multimode lasing by increasing the pump size on gain medium
compared to the cavity beam size by defocusing pump on cuvette. However, during long pulse operation
their multimode behavior was confirmed by measuring beam $M^2$ which was found to be higher than 1.
Interestingly, under same pump and cavity configuration when we changed output coupler ROC to
match the large pump size in order to improve mode matching or blocked few transverse modes, laser
pulse duration started to decrease. In both cases, improved value of $M^2$ confirmed that the laser was
turning towards a single mode operation sacrificing its longer pulse duration. A perfect blocking of
higher order laser modes would be possible if we could use a circular aperture able to block all higher
order modes except TEM$_{00}$. That can be a perspective for cleaner demonstration but is not expected to
change our findings. Interesting structures were found in the temporal profile of multimode long pulse
laser when we placed the cuvette at Brewster angle. From experimental investigation, we related those
structures to the beating of different transverse modes in a highly multimode laser. However, this might
not be enough and hence further study is required to investigate this issue in detail. For instance, in a
confocal laser cavity longitudinal and transverse modes become degenerate hence by designing a
confocal resonator for similar experiments may rule out or significantly reduce those patterns in
temporal profile. Indeed, our work also lacks (due to time constraint) answer to the question "why an
organic laser provides long pulse operation only when they are multimode." In this regard, in addition
to theoretical understanding experimental demonstration is also required by studying the temporal
dynamics of their transverse modes. Such understanding might be useful for the future perspective of
this work towards demonstrating a mode-locked circulation free liquid dye laser.
# CHAPTER 6

## Conclusion and future perspective
# 6. Conclusion of thesis

While organic laser community keeps on developing novel lasing materials or improving their ongoing research to fight against photostability issue as well as to unveil long pulse (CW/q-CW) operation of state-of-art organic laser, we have walked slightly off the track to reach the same goal. We investigated a liquid dye (DCM) laser without any circulation tubing under low-cost diode pumping. This kind of laser set-up is comparable to a low cost, compact and user-friendly solid-state dye laser but even simpler to implement skipping all types of fabrication step. Interestingly, such simple laser showed very high photostability up to almost billion (10⁹) of pulses at 1 kHz repetition rates. Such stability is almost comparable to older generation liquid dye lasers. Whereas in the same experimental environment (same laser cavity, pump power etc.) a solid-state dye laser using same gain medium showed photostability up to only ~10⁴ no. of pulses which is 5 order or magnitude lower than the stability of the circulation-free liquid dye laser. Their high photostability reflects the fact that diffusion or slow convection of dye molecules due to localized heating in the dye solution helps to efficiently replenish them between consecutive pump pulses. This statement can be experimentally verified by measuring their photo-stability at different repetition rates to increase/decrease localized heating inside dye solution which can be a future extension of this work. However, such high photostability of the laser system triggered our interest to also investigate their maximum rate operation since solid-state dye lasers are rarely found to operate at high repetition rate e.g., several kHz mainly due to avoid fast photo degradation. In that regard, we found that, despite showing high photostability, their lasing repetition rate was limited to only 2.4 kHz which could not be explained from their triplet state lifetime. Therefore, we related that limitation to the creation of a thermal lens in the laser medium which tended to destabilize the laser cavity at certain repetition rates. Though thermal lens is aberrative in nature, quadratic part of thermal lens can be corrected by knowing its focal length. To materialize that, we designed a pump probe experiment and measured thermal lens focal lengths for different pump repetition rates. Knowing the static value of thermal lens focal length for 15 kHz pump, we employed a suitable focal length (opposite to the focal length of thermal lens) correction lens inside our Plano-concave laser cavity and obtained up to 14 kHz lasing. To verify if this finding is not unique to DCM laser only, we tested Coumarin-540 laser in the same experimental setup and obtained similar results. In addition, we realized that designing a thermal lens insensitive laser resonator could also result similar performance (in repetition rate) from circulation free liquid dye lasers. In this work, though we proved this principle by designing a near hemispherical laser cavity, a concentric cavity would be the most suitable candidate for that purpose which can also be a future perspective of this work. It would be really interesting to hit the lifetime of triplet state by obtaining higher repetition rate lasing adopting either of above methods to investigate organic laser behavior in that regime. Anyway, these results suggest that thermal lensing of laser medium is the primary barrier for circulation free liquid dye lasers to be operated at high repetition rates. The final part
of this thesis turned to be more interesting when we started to investigate long pulse operation in
circulation free liquid dye laser but could not understood the observations completely. We found that
the liquid dye laser can produce long pulses up to several tens of µs when it is highly multimode (mixing
of TEM₀₀, TEM₀₁, TEM₁₀ and so on in laser mode). Usually, our longitudinal pumping scheme results
diffraction limited TEM₀₀ beam quality, but we switched from this single mode to multimode lasing by
making the pump size larger through defocusing pump on the cuvette which lets the possibility open for
higher order modes along with fundamental cavity mode to oscillate in the cavity. At first, we thought
that such behavior might be resulting from thermal effect and also excited state phenomena (e.g. T-T
absorption) when long pump pulse is focused on cvette. Therefore, we reduced thermal load significantly
by reducing pump size on gain medium and found that long pulse lasing (10 µs) could only be observed
when there was a huge mismatch between pump and cavity mode, a condition achieved using 25 mm
ROC output coupler. As soon as the mode matching was improved by using 50 mm, 100 mm and 200
mm output couplers without changing cavity length, the laser pulse duration clearly shortened for same
thermal load, hence same excited state phenomena (e.g. T-T absorption). Similar behavior was obtained
when we blocked few higher order modes (in not a very quantitative way) by razor blade and observed
that the laser pulse duration decreased with an improvement of M² the laser beam. In both cases, the
pump size was unchanged hence thermal load and excited state phenomena were similar which verifies
that the long and short pulse operation was related to the multimode and single transverse mode behavior
of the laser, respectively. When the laser was multimode, we observed wavy patterns in a laser temporal
profile which turned into fine dips when the cuvette was placed at Brewster angle. It suggested that those
patterns did not come out as a result of Vernier effect when cuvette was placed parallel to the cavity
mirrors, but they were resulting from the two-mirror cavity. We explained those dips in temporal profile
as an outcome of mode beating between transverse and longitudinal modes as the cavity was near
hemispherical. In that case, longitudinal and transverse modes should be degenerate but can be slightly
shifted in frequency if the cavity is not perfectly hemispherical like the one we had. This was
experimentally verified by observing shifts (in position) of those dips in temporal profile during any
change in cavity length, hence beat frequency. Although, mode beating could explain the dips in laser
temporal profile, we could not understand why a multimode laser can produce lasing in long pulse
regime which was up to 80 µs in our case. It will be interesting to investigate the temporal behavior of
the transverse modes to understand if their joint contribution can favor long pulse operation in organic
lasers.

However, their long pulse operation certainly opens the possibility to investigate their mode-locking
regime to demonstrate diode pumped compact, low-cost, user-friendly mode-locked dye lasers.
Pathways toward that goal will be given in the following.
# 6.1. Future perspectives

## 6.1.1. Introduction

Diode pumped organic lasers have never been mode-locked at the time when this PhD started. Probably, the main reason behind that is the unavailability of long pulse organic lasers at that time while mode-locking is the technique to generate ultrashort pulses (< 1 ns) from an ideally CW or q-CW laser. Since in this thesis we obtained several tens of microsecond operation from them, we want to push our research forward to build a mode-locked ultra-fast organic laser as already mentioned before. Meanwhile we want to clarify that mode-locking has not been obtained during this thesis. But this chapter will give some general guidelines to lighten the path for future mode-locking studies.

Ultra-short pulse (USP) lasers have wide applications in different fields of science and technology. They can produce very high peak power in the order of MW/GW without generating excessive heat on the target. At the beginning, liquid dye lasers were the popular choice to generate USP due to their wide emission spectrum and highly multimode (longitudinal) characteristics. However, gradually they lost popularity owing to their complex design with solution flow system and also for their expensive pump sources. Therefore, soon after the invention of Ti:Sa crystal which has wider emission spectrum compared to liquid dye laser became state-of-art for generating ultra-short pulses. Recently, more solid-state materials are found to routinely generate ultra-short pulses<sup>112-116</sup> with comparable performance to Ti:Sa lasers. Being solid-state, these materials eliminate the solution handling issues related to the liquid dye laser. With the advent of high-power diode lasers, diode pumped USP lasers have successfully reduced the cost of mode-locked laser system.<sup>117-122</sup> A step further in compactness of laser system has been achieved through the demonstration of mode-locked VECSELS.<sup>123</sup>

Despite above achievements in solid-state mode locked lasers, they cannot completely replace liquid dye lasers. Because all solid-state mode locked lasers are found to lase in the near infrared and hence unable to cover the spectral range between 400 nm – 700 nm.<sup>124</sup> Though their second or third harmonic can reach few specific wavelengths in visible, still cannot cover the full visible wavelengths. However, above spectral range is demanding in the field of spectroscopy, medicine, isotope separation and so on. Historically dye lasers have been the key player to fulfill those demands. Moreover, they also show wide tunability over visible spectrum. Another problem associated with solid-state mode locked laser especially with Ti:Sa crystal is its high cost as well as the complex mode locking technique based on Kerr lens which is very sensitive to mechanical perturbations.<sup>124</sup> For above reasons, a diode pumped circulation free liquid dye laser can be very attractive to build future low cost, compact, simple, user friendly and tunable mode-locked sources.
### 6.1.2. Mode-locking

We have already briefed about longitudinal modes of a laser cavity. Indeed, a laser may have millions of those modes dancing in the cavity at different frequencies with no specific phase relation among them. If by some external means one can establish a fixed phase relationship between the longitudinal modes, a train of ultrashort pulses separated by cavity round trip time ($\frac{2L}{c}$) will come out of the laser cavity as shown in Figure 6.1.¹²⁵

<figure><img src="image_124.png" /><figcaption>Figure 6.1: Mode-locking technique to produce ultrashort pulses by establishing a fixed phase relationship among the modes in the cavity. All waves of different frequencies interfere at time an interval equal to the cavity round trip time and produce a short burst of intense light.¹⁵⁰</figcaption></figure>

There exist active and passive techniques to establish a fixed phase relationship between longitudinal modes. In active mode locking technique, acousto optics or electro optics modulators are used to periodically modulate the cavity losses at a repetition rate (c/2L) equal to the cavity round trip time. In that case, one needs to insert an acousto optic or electro optic modulator inside laser cavity which cannot be considered as a suitable technique for mode locking in our case. Because we are obliged to keep our cavity short (several mm - cm) since the cavity length imposes adverse effects on laser efficiency in a pulsed laser as already discussed in the first chapter. In fact, this mode locking technique is used in true CW solid-state laser (e.g., Nd:Yag). Therefore, we want to adopt passive mode locking technique where a saturable absorber is used inside laser cavity which acts as a high loss for lower intensity light but becomes transparent for high intensity pulses that able to saturate the absorber. In the following, we will discuss the limited progress made during this thesis to build a future mode locked organic laser.

### 6.1.3. Advancement towards future mode-locking

Demonstration of few tens of microsecond long pulses from organic laser in previous chapter can be considered a step forward towards the goal to obtain mode-locking. Because the buildup of mode-locking requires time to complete several round trips in a laser cavity. For a passively mode locked Ti:Sa
laser with 1.75 m long laser cavity, mode locking build-up time was calculated to be 60 µs. ¹²⁶ Therefore, it can be expected to be much shorter when a cm sized cavity would be involved. For example, in a 15 cm VECSEL, the mode-locking (ps pulses) was observed after 1000 round trips indicating the mode locking build up time was around 1 µs (since 1 ns is required to complete 1 round trip ($\frac{2L}{c}$) in a 15 cm cavity). It clearly verifies the fact that why organic laser with several hundreds of ns pulse duration had never been investigated for mode-locking and at the same time suggests that it cannot not be a wild dream anymore to hope for a mode locked organic laser provided that their lasing duration is found to be longer than 1 µs and we can easily make more than 15 cm cavity (Figure 5.11). Although, several issues need to be understood regarding their long pulse operation which will be dealt prior to future mode-locking experiment. However, here we want to mention our preference regarding the SA we want to use for passive mode-locking.

### 6.1.3.1. Selection of appropriate saturable absorber and further characterization

**Issues considered prior to choose saturable absorber**

Early era of femtosecond pulse generation in a liquid dye laser routinely used a dye saturable absorber called DODCI.¹²⁷ The performance of that saturable absorber despite having a slow recovery time in the order of ns was quite good to mode-lock CW liquid dye lasers having quite long cavity length (meters). However, to mode-lock a pulsed dye laser like the one we have with cavity length in the range between mm to cm, those saturable absorbers are not suitable anymore. Because in short cavities the round-trip time is shorter than the recovery time of those saturable absorbers. Therefore, a saturable absorber having recovery time in the range of ps would be suitable for our work.

Semiconductor Saturable Absorber Mirror (SESAM) with fast recovery time developed during the 90's by U. Keller ¹²⁸,¹²⁹ would be a perfect candidate for this. Apart from fast recovery time, other optical characteristics of SESAM for instance a low saturation fluence and weak non-saturable losses, high modulation depth, have made them state-of-art to mode-lock laser sources ¹²³,¹³⁰⁻¹³² for example vertical external cavity lasers (VECSELs). However, their operation bandwidth or absorption band in other word is found to cover the infrared part of the spectrum due lattice-matching issues (except few examples of deep red-operating SESAM using GaInP/AlGaInP, ¹³³⁻¹³⁵ but currently the rest of the visible spectrum cannot be covered).

**Proposed SA to be used for building our mode-locking laser**

Not a long time back from now, high quality monolayer (single atomic layer) graphene ¹³⁶ has flourished the market hence opened the door for many research applications,¹³⁷ Well established companies e.g., Graphenea (in spain) have mastered the technology to produce monolayer high quality graphene films
which can be transferred on any desired surface without the need of any special skill. Interestingly 1cm×1cm monolayer film of graphene can be found in ~100$. Apart from their low cost, this material possesses interesting optical properties such as ultrafast recovery time (ps or less) which makes them suitable for mode-locking ¹³⁸⁻¹⁴¹ or q-switching ¹⁴² laser sources, easy integration with solution-process techniques (graphene flakes can be inserted into polymer layers for example). More importantly, graphene shows absorption properties from visible to infrared band of the spectrum,¹³⁷ All those properties of graphene fulfill the requirement of the SA we are looking for.

## ➤ Graphene characterization

We bought monolayer (easily transferrable) graphene from Graphenea (https://www.graphenea.com/) and transferred it on a cavity mirror (HT at 445 nm and HR at 590 nm – 632 nm) to use it directly in mode-locking laser cavity. The procedure is presented in Figure 6.2 taken from Graphenea website. The graphene was supplied to us on top of a polymer and the film was covered by a sacrificial layer as shown

### Graphene Transfer Procedure in 3 simple steps

<figure><img src="image_125.png" /><figcaption>Figure 6.2: Graphene transfer procedure from polymer to a desired substrate (https://www.graphenea.com/).</figcaption></figure>

in the most left of Figure 6.2. To transfer it on a desired surface (cavity mirror in our case), we followed the first step by putting the graphene in de-ionized. Within seconds, the graphene with sacrificial layer was detached from the polymer and we placed our mirror inside water to fish the floating graphene film from below. After that the mirror containing graphene (and sacrificial layer) was kept in open air for 30 minutes which was followed by 1h of annealing in an oven under 150°C temperature. Before removing the sacrificial layer, which was still present, the graphene coated mirror was kept 24h in a vacuum chamber for better attachment to the surface. Finally, the sacrificial layer was removed by an acetone bath for 1 hour followed by another bath in isopropanol for another 1h. This procedure removes the sacrificial layer. It is recommended to use a blow of N₂ gas to make it dry before using. Following graphene transfer on mirror it was necessary to verify if the graphene was monolayer since saturation intensity would be higher if the number of layer increases. We verified that using Raman Spectroscopy
facility of another lab named ‘Laboratoire des Sciences des Procédés des Matériaux’ (LSPM) of our university - thanks to LSPM for its kind co-operation. Indeed, Raman spectroscopy provides information on the vibrational modes of molecules and is frequently used to obtain the structural fingerprints of molecules, but it has also been used to determine graphene layer numbers in flakes.¹⁴³

<figure><img src="image_126.png" /><figcaption>Figure 6.3 : (a) Trace of Raman signal of our monolayer graphene, (b) an example of Raman signal found when graphene layer increases. (SLG: Single layer graphene, BLG: Bi-layer graphene and so on).¹⁴³</figcaption></figure>

The result of Raman spectrum of our graphene (on top of mirror) is shown in 6.3 (a) along with a similar plots (Figure 6.3 (b)) adopted from literatures ¹⁴³ for comparison. The most prominent spectral feature of carbon-based materials is the appearance of G-band and a 2D band ¹⁴⁴ which are clearly seen in our sample (Figure 6.3 (a)). G band (1587 cm⁻¹) corresponds to an in-plane vibrational mode of SP² carbon atoms which exist both in monolayer and multi-layer graphene (Figure 6.3 (b)). The 2D band corresponds to a vibrational mode that is very strong having quite sharp peak in monolayer graphene compared to the graphene having more layers. ¹⁴³,¹⁴⁵ Therefore, $\frac{I_{2D}}{I_G}$ is a good indicator of graphene’s quality (monolayer or multilayer). However, from here we confirmed that our graphene on the mirror was a monolayer one.

➤ Saturation intensity of monolayer graphene SA
It is better to have an idea regarding the laser intensity required to saturate graphene which might give
a good direction towards cavity design for mode-locking. Perhaps we need to design a cavity to have
different cavity beam spot sizes on gain medium and graphene in order to saturate graphene SA which
will be discussed later. Currently we do not have any credible experimental value of the laser intensity
to saturate our monolayer graphene. However, there are huge discrepancies in literature regarding the
value of saturation intensity of monolayer/ multi-layer graphene. In fact, it depends on the quality of
graphene (fabrication process), laser used for the experiment (fs, ps or ns), laser spot size used on
graphene during experiment and wavelength of the laser. Interestingly, depending on the laser pulse
duration used (fs/ps), the saturation intensity of monolayer graphene can go up to 100 MW/cm² or more
whereas their saturation intensity has been reported to be as low as in the range of few tens of MW/cm²
or even lower when a ns laser was used.¹⁴⁶ For instance, using 100fs laser N. H. Park et al. ¹⁴⁷ measured
saturation intensity of monolayer graphene as ~75 MW/cm². However, a detail of above discussion can
be found in literature. ¹⁴⁶

6.1.3.2. A proposition of laser cavity for mode-locking

We propose following cavity configuration (Figure 6.4) for future mode-locking experiment. In such cavity configuration, we can play with cavity mode sizes on gain medium and graphene as well.

<figure><img src="image_127.png" /><figcaption>Figure 6.4: A proposition for mode-locked cavity.</figcaption></figure>
At the same time we should also think about the design aspects of saturable absorber deposited on commercially bought DBR mirror. It has been demonstrated that using a spacer layer between SA and mirror helps to control saturable and non-saturable losses of SA.<sup>148</sup> In thesis, we are not going to the details of that issue but both parameters are crucial needs to be investigated before mode-locking experiment. Very encouraging results have been shown that mode locking with graphene SA is possible by just using a monolayer graphene on the top of a commercially bought broadband DBR mirror.<sup>149</sup> Still, significant research is required to understand the physics prior to make an efficient device compatible with applications.
# Appendix

## Appendix 1: Investigation of novel dyes for lasing application

We already stated that investigation of novel organic lasing materials can be a potential application of our laser setup due to its simplicity, compactness, low-cost and user friendliness. To prove this, first we invested lasing properties of two lasing materials developed by Haixia Lee (former PhD student) in Sorbonne Marie-Curie University, Paris. The experimental setup to investigate lasing is described in Figure 3.8. Here, the laser cavity consisting of a plane and concave mirror was around 13 mm long where the concave mirror (1% loss between 450 – 530 nm) had 25 mm radius of curvature. It is useful to mention here that we used 80 µm pump spot (in radius) on the gain medium while the pump pulse duration was 500 ns. The results are given as follows along with the chemical structure of those dyes:

### DYE-1:

<figure><img src="image_128.png" /><figcaption>A1. 1: Chemical structure of Dye-1.</figcaption></figure>

Figure A1. 1 shows the chemical structure of Dye-1. This dye has sufficiently high absorption around 445 nm which made it suitable to test in our setup. The dye was dissolved in Toluene in a way to obtain more than 80% absorption of pump wavelength (445 nm) inside 1 mm cuvette. Toluene was selected considering higher quantum yield (>80%) of the dye solution when dissolved in Toluene rather than other solvents (ethanol, propanol etc.). However, the absorption spectrum of the dye solution is given in the inset of Figure A1. 2 together with its lasing spectrum. Peak of the laser spectrum was around 523 nm. There was no overlap between absorption and laser emission. Here, the plot of laser energy vs absorbed pump energy clearly shows lasing laser threshold at around 8.3 µJ of absorbed pump energy
which corresponds to a pump power density of 83 kW/cm². This lasing threshold can be further reduced by improving matching between pump (80 µm in radius) and cavity (~ 45 µm in radius) mode.

<figure><img src="image_129.png" /><figcaption>A1.2: Laser energy (nJ) vs absorbed pumped energy (µJ) using dye-1 in solution (Toluene). Inset: Absorbance of dye-1 in Toluene and its lasing wavelength.</figcaption></figure>

However, we were also interested to explore if this dye can be used to make solid-state laser or not.
Therefore, we spin coated 18 µm film of dye-1 doped (1% in weight) PMMA on the plane mirror.

<figure><img src="image_130.png" /><figcaption>A1.3: Solid-state laser using Dye-1 doped 18 µm PMMA film. Inset: Laser spectrum with clear Fabry-Perot peaks originated from the thin film inside cavity.</figcaption></figure>
Lasing from solid-state film was obtained by designing a short ~ 2/3 mm plano-concave cavity with same mirrors described above. Here, 30 ns pump was used since the solid-state gain medium was degrading very fast under 500 ns pump used to investigate lasing in their liquid counterpart. Such behavior is also found in our work hence demonstrates why a circulation-free liquid dye laser is advantageous over its solid-state counterpart. However, the lasing threshold ~ 150 kW/cm² was found to be higher compared to the threshold found in liquid dye laser. It might be surprising because laser threshold in this case should be lower than the liquid dye laser described above with slightly longer (13 mm) cavity length. But, larger gain inside a mm size cuvette compared to few microns film, longer pump (500 ns) (which can reduce laser build time hence threshold) used to investigate liquid dye laser might play a role to lower laser threshold. Experiments with comparable gain medium thickness, cavity (length) as well as pump (pulse width) parameters are required to make a fair comparison of laser performance between a solid-state and circulation free liquid dye laser. Unfortunately, we did not investigate further into this since it does not comply with the interest of this thesis. However, the laser spectrum containing Fabry-Perot peaks (with higher intensities) at 523.3 nm and 528.6 nm can be seen at the inset of Figure A1. 3. Using the values of those peaks the thickness of the 18 µm film can be calculated from the formula given in (3.6)⁹⁰.

### DYE-2:

<figure><img src="image_131.png" /><figcaption>A1. 4: Chemical structure of Dye-2.</figcaption></figure>

Figure A1. 4 shows the chemical structure of Dye-2 which is slightly different compared to Dye-1. However, the peak absorption of this dye was similar to Dye-1, hence it was also suitable to be pumped by 445 nm laser diodes in our setup. In the following, Figure A1. 5 and A1. 6 represent its lasing in circulation-free solution and solid-state film respectively. Similar discussion on its lasing properties (threshold, spectrum etc.), cavity used can be found above. Therefore, we only present the Figures and skip further discussions on them.
<figure><img src="image_132.png" /><figcaption>A1.5: Laser energy (nJ) vs absorbed pumped energy (µJ) using dye-2 in solution (Toluene). Inset: Absorbance of dye-2 in Toluene and its lasing wavelength.</figcaption></figure>

<figure><img src="image_133.png" /><figcaption>A1.6: Solid-state laser using Dye-2 doped 18 µm PMMA film. Inset: Laser spectrum with clear Fabry-Perot peaks originated from the thin film inside cavity.</figcaption></figure>

**DYE-3:** Dr. Mykhaylo Potopnyk from Polish Academy of Sciences visited our Lab to investigate lasing properties of few dyes synthesized in his Lab. Most of his dyes showed highest absorption around 355 nm except one which had the highest absorption around 445 nm. Therefore, we choose this dye to investigate its lasing property in our setup. Unfortunately, we are not authorized to show the chemical
structure of this dye but its absorption in solution (Toluene) and lasing characteristics are presented in the following:

<figure><img src="image_134.png" /><figcaption>A1. 7: Left: Absorbance of the dye-3 solution (in Toluene) inside a 1 mm cuvette. Right: Emission spectra from the dye solution under different pump power.</figcaption></figure>

Left portion of Figure A1. 7 shows the absorption spectrum (spanning between 350 nm – 550 nm) of dye-3 solution (in Toluene) inside 1 mm cuvette. It shows very high absorption (~ 98%) at our laser diode wavelength (445 nm) while more than 80% absorption of pump wavelength can be enough to obtain lasing.

However, the same experimental setup as Figure 3.8 has been used here to investigate lasing of dye-3 solution in 1 mm cuvette. Cavity length was 13 mm and mirror reflectivity was adapted according to the emission band (fluorescence) of the dye. Pump (1-µs pulse duration) spot size on the cuvette was 70 µm (in radius) on cuvette and pump power was varied to record the emission spectra of the dye solution. Right portion of Figure A1. 7 shows a series of emission spectra at different pump power. One of the defining properties of any laser is narrow spectrum with a clear threshold of spectral narrowing what is exactly seen in the right portion of Figure A1. 7. It is evident from there that below 60 kW/cm² pump power, the emission spectrum is a broad fluorescence spectrum. Spectral narrowing starts at 60 kW/cm² indicating the start of lasing. This is highlighted as lasing threshold in Figure A1. 7 (right portion). As pump power is increased beyond this threshold, the emission spectra always remains narrow indicating a steady-state lasing operation.
Finally, we want to mention here that rest of Dr. Mykhaylo's dyes having peak absorption around 355 nm were also investigated in another experimental setup. As a pump laser we used frequency tripled solid-state laser (400 ps) able to emit at 355 nm. The experimental setup was kept similar to Figure 3.8 except we did not use any fiber since the beam quality of the laser was already good. Using this experimental bench, we obtained lasing from 4 more dyes of Dr. Mykhaylo. We do not show them here since those results are not obtained under diode pumping although lasing was obtained from circulation-free solution inside cuvette.

Anyway, above results clearly justifies one of the applications of our work in investigating novel laser dyes. From our experience, we are certain that it is much easier to investigate lasing from their solution skipping any complexity of fabrication.

## Appendix 2: Concept of Brewster angle

<figure><img src="image_135.png" /><figcaption>A2: Concept of Brewster angle.</figcaption></figure>

The concept of Brewster angle can be explained from Figure A2. It shows that, an unpolarized light is incident at an angle of $θ_B$ (with surface normal) on the boundary between two transparent media. Medium 2 is denser than medium 1 hence, $n_2 > n_1$. The electric field of the incident light wave can be resolved into two components – let's assume that the component with double arrows is parallel to plane of the paper while the dots are in the plane perpendicular to the paper. Generally, the reflected and refracted rays are partially polarized i.e. the two components do not have equal magnitude. However, for a certain incident angle, known as Brewster angle ($θ_B$), the reflected light is completely polarized in the plane perpendicular to the paper while the refracted/transmitted light is slightly polarized. In other words, Brewster angle is defined as the angle of incidence at which a certain polarization of light is
perfectly transmitted without any reflection through a transparent surface. At Brewster angle, the angle between reflected and transmitted light becomes 90° as indicated in Figure A2. Brewster angle can be easily calculated from Snell's law. For the case of Figure A2, Snell's law can be written as,

$$n_1 \sin\theta_B = n_2 \sin\theta_2 \quad (i)$$

Equation (i) can be reduced to,

$$n_1 \sin\theta_B = n_2 \sin(90^\circ - \theta_B) = n_2 \cos\theta_B \quad [\text{Since, } \theta_1 + \theta_2 = 90^\circ, \text{ and } \theta_1 = \theta_B]$$

$$\text{Or, } \theta_B = \tan^{-1}\left(\frac{n_2}{n_1}\right)$$

Brewster angle can be calculated from here once the values of $n_1$ and $n_2$ are known.
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