**1. Introduction**

There has been a constant endeavour to increase the number of available coherent sources allowing wider coverage of the electromagnetic spectrum. To this end, nonlinear optical conversion of the emission of a laser inside an appropriate nonlinear crystal by ensuring that the fundamental and generated waves are phase matched has emerged as one of the most attractive methods across UV [1], visible [2], infrared [3], and mid-infrared [4] regions of the electromagnetic spectrum. As the non-linearity of the crystal is responsible for effecting this conversion, an increase in the intensity of the pump radiation to which the crystal is subjected to increases the conversion efficiency too albeit in a non-linear fashion. Single crystals, specifically grown to provide a reasonable interaction length, invariably suffer from low optical damage threshold. This thus puts an upper limit on the pump intensity to which the crystal can be exposed to causing a corresponding reduction in the conversion efficiency. A significant under-utilisation of the pump beam is thus the end result. The crystals employed for the conversion in the mid infrared region have

inherently high refractive index and the problem thus gets further compounded as the entrance and the exit faces of the crystals need to be essentially anti-reflection coated to arrest losses due to Fresnel reflection. The pump intensity therefore, needs to be further reduced as the optical damage threshold of dielectric coatings is usually lower than the crystal bulk. This drawback can be surmounted by increasing the interaction length of the pump beam with the nonlinear medium giving due consideration to the thermal de-phasing effect that occurs along the length of the crystal [5]. Increasing the length of the crystal brings about a steep rise in its cost and therefore is not an economically viable option. Attempts have been made to use a number of crystals instead, either in tandem [6] or in parallel [7] to circumvent this problem. These schemes however, suffer from an inherent disadvantage as they present too many crystal surfaces off which the pump photons escape through Fresnel reflections. To be noted here that the same crystal has also been used in the past to enhance the interaction length by allowing the pump beam to make two [8] or multiple passes [9] through it. These methods have not gained much popularity as the cavity configuration employed in the former case limited the operation to a non-collinear phase matched mode while in the latter case it resulted in enhancing the second harmonic (SH) conversion of the SH wave itself. In case of frequency doubling of near infrared cw pump to the visible, the schemes that have gained importance use the crystal in the intra-cavity mode [10] or external cavity resonant enhancement mode [11]. Ring cavity configuration that has an inherent advantage of blocking any feedback into the pump cavity has generally been employed here. The applicability of these schemes for pulsed second harmonic conversion (SHG) is challenging due to the high intra-cavity flux that prevails in a pulsed laser. Literature on similar schemes for SHG in the mid infrared region is scanty primarily due to the possibility of thermal lensing effect that may lead to crystal damage. This has restricted the operation to quasi-cw regime with adequate precautions to forbid Q-switched lasing [12] while in the case of pulsed operation, the intra-cavity flux has been brought down by using appropriate attenuators [13].

Another approach has been to increase the intensity of the pump beam itself. That the generated SH output increases in a non-linear fashion with the intensity of the pump radiation to which the crystal is exposed is a fact known since the time SHG was reported more than half a century ago [14]. A direct consequence of this fact is that if the crystal can in some way be subjected to alternate high and low regions of pump intensity along its conversion length that results in an average intensity Iav, there would be a net gain with respect to SHG as compared to the conventional situation where the same crystal is subjected to a uniform pump intensity of Iav. These two cases are illustrated in **Figure 1**. In the first case (**Figure 1a**) the crystal of length '*l*' is illuminated by a pump beam of uniform intensity 'I' along its length. In the second case the incident pump intensity 'I' is redistributed as alternate periodic intensity packets of '2I' and '0' longitudinally along the crystal thus maintaining the same average intensity 'I' as before (**Figure 1b**). The square dependence of second harmonic conversion on the incident pump intensity can be represented mathematically for the two cases as follows:

For the case of **Figure 1a**: SH(output)<sup>∝</sup> *l* × I2 .

For the case of **Figure 1b**: SH(output)∝ [[(*l*/*2*) × 0] + [(*l/2)* × (*2*I)2 ]] <sup>∝</sup> **2** *l* × I2 .

This clearly suggests that the generated SH, in the second case, is enhanced by a neat 100% as against the first case when the crystal is illuminated uniformly. A nonlinear crystal placed inside a Fabry-Perot or a bidirectional ring cavity experiences flux from both ends and therefore is one of the most obvious ways of creating such a situation of non-uniform illumination. The interference of the forward and reverse beams creates alternate high (anti-nodal) and low (nodal) regions of intensity in the crystal and therefore should result in an enhancement of the SHG.

**91**

**Figure 2.**

**Figure 1.**

*Towards Enhancing the Efficiency of Nonlinear Optical Generation*

of non-uniform illumination of the non-linear medium.

**length between the pump and the non-linear medium**

This chapter dwells on the recent advances made by our group in these two areas viz., enhancing the conversion efficiency by way of (a) increasing the interaction length between the pump and the non-linear medium and, (b) exploiting the effect

*A non-linear crystal exposed to the pump radiation. (a) Uniform illumination of intensity 'I'. (b) Periodic illumination with intensity packets of '2I' and '0' thus maintaining the same average intensity 'I' as before.*

**2. Enhancing the SH conversion efficiency by increasing the interaction** 

By way of constructing a coupled plano-convex cavity external to the pump laser (**Figure 2**) that allowed to and fro passes of the unabsorbed pump through the crystal, we conceived a novel way to increase the effective interaction length between the non-linear medium and the pump beam [15]. An ideal situation demands that the coupling optics offers high transmission at the pump wavelength and high reflection too at the same wavelength to enable multiple passes through the crystal; a conflicting requirement indeed that is inherently taken care of in the above

*Schematic diagram of the experimental setup for second harmonic conversion of the emission of a CO2 laser in a AgGaSe2 crystal. G: Plane blazed grating, A1 and A2: Adjustable apertures, B1 and B2: ZnSe Brewster plates, M1: 70% R ZnSe concave mirror, D1 and D2: Energy/power detectors, M2: Dichroic mirror. (a) In case of single pass second harmonic generation, dichroic mirror M2 is absent. (b) In case of multi-pass second harmonic generation, dichroic mirror M2 in conjunction with pump laser output coupler M1 forms the unstable external cavity.*

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

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

## **Figure 1.**

*Nonlinear Optics - Novel Results in Theory and Applications*

inherently high refractive index and the problem thus gets further compounded as the entrance and the exit faces of the crystals need to be essentially anti-reflection coated to arrest losses due to Fresnel reflection. The pump intensity therefore, needs to be further reduced as the optical damage threshold of dielectric coatings is usually lower than the crystal bulk. This drawback can be surmounted by increasing the interaction length of the pump beam with the nonlinear medium giving due consideration to the thermal de-phasing effect that occurs along the length of the crystal [5]. Increasing the length of the crystal brings about a steep rise in its cost and therefore is not an economically viable option. Attempts have been made to use a number of crystals instead, either in tandem [6] or in parallel [7] to circumvent this problem. These schemes however, suffer from an inherent disadvantage as they present too many crystal surfaces off which the pump photons escape through Fresnel reflections. To be noted here that the same crystal has also been used in the past to enhance the interaction length by allowing the pump beam to make two [8] or multiple passes [9] through it. These methods have not gained much popularity as the cavity configuration employed in the former case limited the operation to a non-collinear phase matched mode while in the latter case it resulted in enhancing the second harmonic (SH) conversion of the SH wave itself. In case of frequency doubling of near infrared cw pump to the visible, the schemes that have gained importance use the crystal in the intra-cavity mode [10] or external cavity resonant enhancement mode [11]. Ring cavity configuration that has an inherent advantage of blocking any feedback into the pump cavity has generally been employed here. The applicability of these schemes for pulsed second harmonic conversion (SHG) is challenging due to the high intra-cavity flux that prevails in a pulsed laser.

Literature on similar schemes for SHG in the mid infrared region is scanty primarily due to the possibility of thermal lensing effect that may lead to crystal damage. This has restricted the operation to quasi-cw regime with adequate precautions to forbid Q-switched lasing [12] while in the case of pulsed operation, the intra-cavity flux

Another approach has been to increase the intensity of the pump beam itself. That the generated SH output increases in a non-linear fashion with the intensity of the pump radiation to which the crystal is exposed is a fact known since the time SHG was reported more than half a century ago [14]. A direct consequence of this fact is that if the crystal can in some way be subjected to alternate high and low regions of pump intensity along its conversion length that results in an average intensity Iav, there would be a net gain with respect to SHG as compared to the conventional situation where the same crystal is subjected to a uniform pump intensity of Iav. These two cases are illustrated in **Figure 1**. In the first case (**Figure 1a**) the crystal of length '*l*' is illuminated by a pump beam of uniform intensity 'I' along its length. In the second case the incident pump intensity 'I' is redistributed as alternate periodic intensity packets of '2I' and '0' longitudinally along the crystal thus maintaining the same average intensity 'I' as before (**Figure 1b**). The square dependence of second harmonic conversion on the incident pump intensity can be represented

.

This clearly suggests that the generated SH, in the second case, is enhanced by a neat 100% as against the first case when the crystal is illuminated uniformly. A nonlinear crystal placed inside a Fabry-Perot or a bidirectional ring cavity experiences flux from both ends and therefore is one of the most obvious ways of creating such a situation of non-uniform illumination. The interference of the forward and reverse beams creates alternate high (anti-nodal) and low (nodal) regions of intensity in

]] <sup>∝</sup> **2** *l* × I2

.

For the case of **Figure 1b**: SH(output)∝ [[(*l*/*2*) × 0] + [(*l/2)* × (*2*I)2

the crystal and therefore should result in an enhancement of the SHG.

has been brought down by using appropriate attenuators [13].

mathematically for the two cases as follows: For the case of **Figure 1a**: SH(output)<sup>∝</sup> *l* × I2

**90**

*A non-linear crystal exposed to the pump radiation. (a) Uniform illumination of intensity 'I'. (b) Periodic illumination with intensity packets of '2I' and '0' thus maintaining the same average intensity 'I' as before.*

This chapter dwells on the recent advances made by our group in these two areas viz., enhancing the conversion efficiency by way of (a) increasing the interaction length between the pump and the non-linear medium and, (b) exploiting the effect of non-uniform illumination of the non-linear medium.
