Abstract:
The general principles of Maxwell’s electromagnetic theory and quantum mechanics were well established much before the invention of lasers. However, after the first report of laser in 1960 and subsequent advancement in the field of laser technology, these theories have been revisited to understand the effects of higher order interactions between intense laser light beams and matter in terms of nonlinear susceptibilities. As such, the study of behavior of light in nonlinear media, in which the dielectric polarization responds nonlinearly to the electric field of the light, has given birth to a new branch of optics called nonlinear optics.
Typically nonlinear optical effects are studied using laser beams with Gaussian intensity distribution. However, in recent times, structured coherent optical beams including optical vortices, hollow Gaussian beam, and Airy beam have found wide range of applications in variety of fields in science and technology. All existing techniques used to date to generate such beams suffer from different limitations including lower output power and restricted wavelength range. On the other hand, interactions of such beams with nonlinear media are
mostly unexplored.
During my PhD we have studied the nonlinear interaction of optical beams with different spatial structures. We have used second order nonlinear interactions such as second harmonic generation (SHG), where two photons from same laser get annihilated to produce a new photon of double energy, and sum frequency generation (SFG), where two photons of two different lasers get annihilated to produce a new photon of energy equal to the sum of the energies of the annihilated photons. The study also includes the nonlinear generation of structured beams such as Laguerre Gauss beams (optical vortices), a new class of vortex beam known as “perfect” vortex beams, hollow Gaussian beam, and Airy beam in different spectral and temporal domains.
Most of the lasers (but not all) produce electromagnetic radiation in Gaussian intensity profile. However, due to unavailability of suitable laser gain medium, the nonlinear optical effects play pivotal role in generating coherent optical radiation with wavelength inaccessible to lasers. Using an ultrafast femtosecond laser at 1064 nm we have studied the second order nonlinear interactions such as SHG and SFG in different nonlinear crystals to produce ultrafast coherent radiation at 532 nm and 355 nm in Gaussian intensity profiles. Such
beams have variety of applications, including spectroscopy, material processing, pumping of optical parametric oscillators and generation of structured optical beams. The efficiency of nonlinear optical processes varies proportional to the square of the length of the nonlinear crystal and the intensity of the laser beam. However, use of longer crystal length and increase of laser intensity through tight focusing do not necessarily increase the overall efficiency of the nonlinear process. There is always an optimum focusing condition for efficient nonlinear interactions, [1] have predicted such optimum condition for SHG of
continuous wave (cw) or long-pulse lasers. However, the optimum focusing condition in the presence of temporal walk-off arising from the use of ultrafast lasers can be different from that of the cw and long-pulse lasers [2, 3]. We have also investigated the optimum focusing condition for single-pass SHG and SFG of ultra-short femtosecond pulses for generating the optical beams at 532 and 355 nm in Gaussian intensity distribution respectively.
We have also done a comparative SHG performance study of the crystals having different temporal and spatial walk-off parameters. We have further investigated the effect of the ratio of confocal parameters (beam focusing condition) and power ratio of the interacting pump beams in SFG process.
Knowing the effect of Gaussian beam in nonlinear frequency conversion processes, we have studied the interaction of orbital angular momentum (OAM) of the laser beams with nonlinear medium. Unlike Gaussian beams, optical vortex beams, spatially structured beams with helical wave-front [4], carry photons with OAM. These beams have doughnut shaped intensity profile with zero intensity at the point of phase singularity. Optical vortices
are characterized by its topological charge (order), or winding number, l and are found to carry OAM of l} per photon. Using second order nonlinear crystals we have studied the frequency doubling characteristics of high-power, ultrafast, optical vortex beams by generating optical vortices of order up to 12 at 532 nm and 266 nm wavelengths. We have experimentally verified the OAM conservation law, the OAM of the generated photon is equal to the sum of the OAMs of the annihilated photons, in SHG process. We have also demonstrated a new scheme to generate optical vortices of orders l = 1 to 6 by using only two spiral phase plates (linear optical elements to generate optical vortices of a fixed order) of phase winding 1 and 2. We further observed that the efficiency of vortex SHG process decreases with the order of the vortex. We attributed such effect to the increase of the area of vortex beam with its order. However, it was not possible to overrule the contribution (if any) of OAM in the SHG process as the area and order of the vortex are not mutually independent parameters.
The decrease of SHG efficiency of optical vortices with order restricts the study of nonlinear interaction of vortices to a certain order. Additionally, the dependence of beam area with its order does not provide clear information about the contribution of vortex order (OAM) in nonlinear frequency conversion process. However, a recent advancement in the field of structured beam has produced a new class of vortex beam, known as “perfect” vortex. These beams have area independent of the vortex order. Using such vortices we have experimentally verified that the vortex SHG efficiency does not depend upon the order (OAM) of the optical vortices. We have also studied the nonlinear frequency conversion of such beams to produce "perfect" vortex beam of order up to 12 with power as high as 1 W for all orders. We verified OAM conservation of "perfect" vortices in SHG process. Due to the OAM conservation in SHG process, the OAM of the frequency doubled vortex beam is twice that the pump beam. But what will happen to the output beam if the interacting photons in the nonlinear process have opposite OAMs? To study such effect we have studied the SFG (SHG is the special case of SFG process) process of two pump beams having equal vortex orders but opposite in sign (direction of the helical phase variation). As expected, due to OAM conservation law the output beam was found to have no OAM (l = 0). However, the output beams have no light (dark) region at the center of the beam similar to the vortex beam. This is a new class of structured beam known as hollow Gaussian beam (HGB) [5] and our method gives a new way of generating HGB through nonlinear processes. The increase of annular ring radius of these beams with the order of the input vortex beams signifies that HGBs also have certain orders. However, there is no experimental or theoretical means to determine the order of such beams. We have devised
a new way to determine the order of hollow Gaussian beams.
To broaden our study and to address other structured beams we have generated Airy beam and characterized its properties. Unlike other structured beams, Airy beam has peculiar properties such as beam shape invariance with propagation (non-divergence), propagation along curved trajectory in free space (self-acceleration), and self-restoration (selfhealing) of beam shape even after obstruction by small objects. Using intracavity cubic phase modulation of an ultrafast singly resonant optical parametric oscillator (SRO), we have generated ultrafast beam in 2- D Airy intensity distribution with wavelength tunability across the near-IR wavelength range. In addition to the Airy beam, the SRO produces Gaussian output beam in the near- to mid-IR wavelength range across 1.4 - 1.7 mm with power as much as 1.54 W.