*Towards Enhancing the Efficiency of Nonlinear Optical Generation DOI: http://dx.doi.org/10.5772/intechopen.80816*

*Nonlinear Optics - Novel Results in Theory and Applications*

**3.2 Results and discussion**

be estimated from this figure as ~8.0%.

was AR coated over broad range covering 5–10 micron on both input and exit faces for normal angle of incidence (AOI), the small Fresnel reflection from the entrance face of the crystal, that was inevitable at oblique AOI, was utilised to monitor both energy and temporal profile of the pump pulse. The energy and temporal profile of the SH beam were monitored after blocking the residual pump beam, that also emerged with it through the exit face of the crystal, by a sapphire plate. By virtue of its multi-atmosphere operation, the CO2 laser possessed intrinsically very high gain

Towards finding the efficiency of the SHG process as a function of the pump energy for the conventional case of uniform illumination (**Figure 2a**), we gradually increased the input and monitored the corresponding SH energy and the dependence is as shown in **Figure 8**. The maximum SH energy conversion efficiency can

In the next set of experiments we subjected the crystal to alternate regions of high and low intensities along its length. This was readily possible by constructing a Fabry-Perot cavity comprising of the output coupler of the pump laser 'M1' (R ~80%@10.72 μm, T ~20%@5.36 μm) and a plane dichroic mirror 'M2' (R > 90%@10.72 μm, T > 90%@5.36 μm) located at the exit end of the crystal (refer to **Figure 2b**). The pump energy incident on the crystal, as measured by Detector D1, showed a dramatic increase as 'M2' was fine tuned to establish its parallelism with 'M1', resulting, in turn, in a corresponding improvement in the measured SH output. In effect, there are now two inputs to the crystal; (a) Forward Input: the actual input on the entrance face in the forward direction that comes directly from the pump laser and (b) Reverse Input: the pump, that stays unconverted after its passage through the crystal, gets reflected off 'M2' and shines on the exit face of the crystal from the opposite direction. When the cavity is perfectly aligned, the interference of these two components creates alternating nodal and anti-nodal intensity regions inside the cavity and partly contributes towards the observed dramatic enhancement of SH conversion by the crystal. At every instant, the reverse

*Second harmonic output as a function of the input pump energy in the conventional operation wherein the* 

*crystal is uniformly illuminated by the pump beam along its conversion length.*

and thus delivered a pulse of relatively short duration (FWHM ~110 nsec).

**98**

**Figure 8.**

component, after traversing through the crystal, is reflected off M1 and falls in step with the pump photons emerging through it resulting in an effective increase in the energy incident on the entrance face of the crystal as measured by the detector D1. At this point, towards gaining a deeper insight into this process, we gradually varied the pump (forward) input and measured both, the corresponding reverse input and the generated SH. The difference in the energy measured by D1 with M1 aligned and misaligned gives the measure of the reverse input. **Figure 9** depicts the dependence of the reverse input on the forward input to the crystal while **Figure 10** shows the SH output as a function of the total effective input to the crystal which is now the sum total of the forward and the corresponding reverse components. It is apparent from **Figure 9** that the reverse input does not exactly bear a linear relationship with the forward input and this behaviour owes its origin to the square dependence of the SH output on the intensity of the input at the fundamental wavelength as is evident from **Figure 8**. The square dependence basically means that as the pump intensity rises, increasingly higher fraction of it gets converted into SH and thus less of it is left to constitute the reverse input to the crystal. This explains the observed departure from the linear dependence of the reverse input on the forward input to the crystal.

The increase in the effective input to the crystal in case of an aligned cavity due to addition of forward and reverse components leads to the generation of higher SH output as revealed in **Figure 10**. For instance, the maximum pump input of 6.5 mJ in case of uniform illumination (**Figure 8**) gets enhanced to 10.34 mJ (**Figure 10**) in the aligned cavity condition giving rise to almost 2.54 fold increase in the SH conversion efficiency. However a closer examination of **Figure 10**, in conjunction with **Figure 8**, reveals a wealth of information, hitherto unexplored, that constitutes the central theme of this study and is captured in the traces of **Figure 11**. It is clearly evident from this figure that SH output in case of non-uniform illumination of the crystal is significantly higher compared to the case of its uniform illumination even when the total input to the crystal is maintained the same. Let us consider a typical input of 4.1 mJ that in case of uniform illumination generates 0.22 mJ (refer to **Figure 8**) of SH at a conversion efficiency of ~5.36%. It can be readily estimated from **Figure 9** that this input of 4.1 mJ in case of non-uniform illumination comprises of a forward component of 2.5 mJ and a reverse component of 1.6 mJ. Thus,

**Figure 9.** *Dependence of the reverse input to the crystal as a function of the forward component.*

## **Figure 10.**

*Dependence of second harmonic output on the effective input pump energy in case of non-uniform illumination.*

when the same total input of 4.1 mJ is made to shine on the crystal as two separate beams of 2.5 and 1.6 mJ from opposite directions by taking advantage of a cavity, a SH output of 0.325 mJ (refer to **Figure 10**) is generated at an efficiency of 7.93%; a clear advantage of ~48% in the SH conversion efficiency by going for non-uniform illumination. As discussed before this is attributed to the alternate high and low intensity regions seen by the crystal as a result of the interference of the forward and reverse beams travelling through the crystal in the latter case.

In order to estimate the expected advantage of the situation when the crystal is non-uniformly illuminated over the case of uniform illumination, we used the

## **Figure 11.**

*Experimental SH conversion efficiency as a function of the total input to the crystal is shown for both uniform and non-uniform illumination cases. The % gain of SH conversion in case of non-uniform illumination over the uniform illumination case, defined as [(SHNUI-EFF−SHUI-EFF)/SHUI-EFF] × 100, is also shown here as a function of the overall input to the crystal.*

**101**

**Uniform illumination**

**Input (EUI) (mJ)**

**Estimated SH SHUI-EST**

**Forward** 

**Reverse** 

**Total input** 

**Standing Wave Intensities**

**(ENUI = EF**

**input** 

**input** 

**(EF) (mJ)**

**(ER) (mJ)**

**+ ER) (mJ)**

**Anti-node** 

**(EAN = EF + ER + 2**

**√(EF × ER)**

**(EN = EF + ER**

 **− 2**

> 0.07

0.09 0.11 0.12 0.14 0.17

**Node** 

**α EUI2**

3.33 4.14 4.61 4.94

5.9 6.53 **Table 1.**

*recorded in* **Figures 2***,* **3** *and* **4***.*

42.64

4.0 *\*Estimated overall gain (%) = [(SH NUI-EST−SHUI-EST)/SH UI-EST] × 100.*

2.53

6.53 *To be noted that the total input to the crystal in the two cases viz., uniform and non-uniform illumination has been always maintained same.*

*Estimation of the % gain obtainable in case of non-uniform illumination over the uniform illumination through reconstruction of the standing wave parameters from the experimental data* 

12.89

34.81

3.6

2.3

5.9

11.65

24.40

3.0

1.94

4.94

9.76

21.25

2.8

1.81

4.61

9.11

17.11

2.5

1.64

4.14

8.18

11.09

2.0

1.33

3.33

6.59

**Non-uniform illumination**

*Towards Enhancing the Efficiency of Nonlinear Optical Generation*

*DOI: http://dx.doi.org/10.5772/intechopen.80816*

**Overall Estimated Gain (%)\***

**Estimated SH** 

**SHNUI-EST α**

**[EAN 2 + EN**

**2]/2**

21.72 33.46 41.50 47.64 67.87 83.09

94.86

94.97

95.23

95.29

95.6

95.85

**√(EF × ER)**

