The present work is aimed at generating and characterizing arrays using different interferometric configurations. Expressions for the intensity distribution were developed for all the configurations presented in the thesis and compared with experimental observations.
Introduction
Review of array illuminators
- Diffraction techniques
- Interference Techniques
- Waveguide Techniques
By adjusting the angles of inclination of the mirrors, the arrays with desired spatial frequencies can be generated. The schematic of the experimental setup they use for the production of arrays in hexagonal geometry is shown in Figure 1.8.
Summary of work
The resulting intensity distributions in the output plane for the polarized as well as randomly polarized setup described in chapter 2 are derived. The expression for electron density is derived in terms of edge shift for the measurement of space-resolved electron density profile in the spark plasma.
Experimental Setup
- Generation of Collimated Beam
- Randomly Polarized Interferometric Setup
- Four Beams Interferometric Setup
- Eight beams interferometric setup
- Polarized setup
- Two beam interferometric setup
- Polarized four beam interferometric setup
- Measurement of light coupling efficiency
- Applications of the interferometric setup
- Laser ablation setup
- Plasma diagnostic setup
The output of the four-beam interferometric setup (output from BS3) illuminated the second Michelson interferometer (third stage) consisting of beam splitter BS4 and mirrors M5 and M6. The first stage of the interferometer is the same as the two-beam interferometric setup in Fig.2.5, so the output from PBS1 resulted in two orthogonal plane polarized light.
Theoretical deduction
- Theoretical Background
- Interference
- Superposition of two waves
- Michelson and Mach Zehnder interferometer
- Spatial frequency
- Electric field for the four beams in randomly polarized setup
- Electric field for the Eight beam Setup
- Interference of two polarized beams
- Phase shift due to the rotation of Analyzer (θ )
- Rotation of quarter wave plate Q 2 of one of the arm (ρ)
- Rotation of quarter wave plate Q 3 at the output (ρ 2 )
- Polarized four beam setup
- Array generation
- QWP rotation of Q 5 (ρ 1 ) of the 2 nd stage interferometer
- QWP Q 6 (ρ 2 ) rotation at the output plane
- Fringe Visibility
- Plasma Diagnostics
- Relation between plasma density and fringe shift
The electric field for the four beams at the output plane of the fig.2.3 is given below. Consequently, the complex field distribution of the entire set of eight beams at the output plane of the fig.2.4 is given by. The experimental setup for the interference of the orthogonally polarized beam is shown in fig.2.5.
To check the relative ellipticity of the two beams on the interference pattern, Q2 and P2 were aligned at 450 and Q3 was rotated, the field distribution at the output plane of the two interfering beams from Eq. If the output polarizer P2 is kept at 45°, the complex field distribution of the entire set of four rays at the output plane is given by. For the generation of the arrays with maximum contrast, θ =ρ1 =ρ2 = 45°, then the expressions for the electric field for the four beams at the output plane from Eq.
If Q5 and P2 were aligned at 450 and Q6 was rotated, the field distribution is on the output plane of the two interfering beams.
- Square and rectangular arrays of tiny light spots
- Hexagonal arrays of light spots
- Light coupling efficiency
- Conclusion
Square and rectangular arrays of near-field patterns recorded on a CCD using the setup in Figure 2.3 are shown in Figure 4.1 and Figure 4.2, respectively. The intensity distribution curves along the x-axis are plotted in Fig. 4.5 and fig. 4.6 for square and rectangular arrays from fig. 4.1 or fig. 4.2. A recorded far-field pattern at a distance of 2.5 m is shown in Figure 4.9 and Figure 4.10 for square and rectangular array geometries.
The compressed recorded pattern is shown in fig.4.16 which contains more than 900 dots/mm2 with more than 2500 small light dots. Three interferometers in tandem, as shown in fig.2.4, were used to generate eight interfering beams. The hexagonal near-field model of regular geometry recorded on photographic film is shown in fig. 4.17.
The corresponding calculated pattern from Eq.(14), including the Gaussian distribution as expressed in Eq.(6)-(13) is shown in fig.4.22.
Results of interference of multiple polarized beams
Two beam interferometers
- Phase shift due to change of azimuth of analyzer
- Fringe visibility due to the change of orientation of Q 2
- Fringe visibility due to the relative change
The interference pattern of two interfering polarized beams in the exit plane is completely dependent on the orientation of the polarizing components. The intensity distribution of the pattern changes due to the changing orientations of the polarizers and QWPs. The orientation of P2 introduces the relative phase shift in the two orthogonally polarized beams after Q3.
QWPs Q2 and Q3 were aligned at 450 with respect to the polarization plane of the incident beam at the corresponding QWP and the analyzer (P2) was rotated (θ). It is clear from Figure 5.1 that the 1800 rotation of the analyzer causes one fringe shift, which confirms the additional phase difference of 2π developed between the two interfering rectangular beams. The intensity distribution of the samples was scanned and the visibility of the fringes was measured as a function of ρ1.
The small variation in the theoretical and experimental visibility curves at the edges can be attributed to the deviation of the incident beams on the polarized components from the normal angle of incidence.
Four polarized beam interferometer
- Array generation from the polarized beams
- Fringe visibility of arrays due to the change of
- Fringe visibility due to the change of orientation of Q 6
Because the beams propagated with a small angular distance, the interference pattern can be observed over large longitudinal distances. For a beam of radius 2w, the pattern can be observed up to a longitudinal distance of 2w/tanθi. Then gradually the overlap area between the beams will decrease and thus the size of the pattern, and eventually all the beams will separate without any overlap.
The arrays were scanned up to a distance of 2.5 meters without observing any significant distortion and contrast loss. The orientation of Q5 from 45° leads to the unequal intensities of two pairs of the beam and the edge contrast will be modified. The orientations of Q6 (ρ2) introduce the relative changes in the ellipticity of the two pairs of beams.
The small differences in the magnitude of the theoretical and experimentally measured values of fringe visibility may be due to little deviation from the normal appearance on the QWPs and polarizer.
Light coupling efficiency of arrays from polarized setup
Conclusions
The interference pattern was observed without significant loss of quality up to large longitudinal distances, confirming the formation of delocalized polarized arrays. The experimentally measured fringe visibility as a function of QWP orientation in the interferometer output shows good agreement with theoretically calculated values. After successfully developing and analyzing different interferometric configurations for the matrix illuminator, the setup was tested for their use in a) lithography for patterning periodic structures by selective laser ablation and b) diagnostics for a pulsed plasma system.
Lithography Techniques
Atom lithography using the dipole force24, 25 is another future scheme to generate the periodic structure of the order of tens of nanometers. In this scheme, the atoms are subjected to a dipole force which originates from the interaction of the induced dipole moment with a near-resonant, non-uniform light field. With the right choice of parameters, the trajectories of atoms under this force can be modified to focus the atomic beam on the nanometer scale.
In this technique, thin films of metals, semiconductors, polymers, or any other complex compound can be selectively removed by illuminating it with the interference pattern formed by the high-power laser. The periodicity of the grating formed in this way will depend on the spatial frequency of the interference pattern. The width of the lines depends on the laser intensity and the damage threshold of the thin film material.
The intensity distribution of this interference pattern is shown in fig.6.2 with the line marked for the damage threshold.
Results of selective laser ablation
- Two beam interferometer for 1-D grating
- Four beam interferometers for two dimensional arrays
Using this technique, one can write the periodic structures as lattices or two-dimensional arrays of tiny spots in a single step with the advantage of having online control over the configuration of micro-nano structures just by changing the interference pattern. Thin films of indium were deposited on the glass substrate using thermal evaporation coating unit. The area of the thin film that received the bright spots was removed, leaving the area of dark fringes unaffected.
The experimental setup used to write lines on thin layers of indium is shown in Figure 2.7. The experimental setup was used for two-dimensional arrays on an indium thin film, which is shown in Figure 2.8. The micrograph of these holes, shown in Figure 6.4, confirms the formation of a matrix of holes in a square geometry with a periodicity of ~ 20 µm and a hole diameter of ~ 10 µm.
Therefore, since the Nd:YAG laser did not provide perfect TEM00 mode, some non-uniformity in the formation of gratings as well as in holes has been observed.
Measurement of electron density
Interferogram recorded in the presence of plasma for vertical edges (edges perpendicular to the axis of the electrodes) and horizontal edges (edges parallel to the axis of the electrodes) are shown in Figures 6.6a and 6.6b, respectively. Distortion in the edges of the plasma region is very clearly visible in both interferograms. The line-integrated electron density profile is estimated by measuring the deviation from the edges (Eq. 47-49).
The integrated electron density profiles perpendicular to (Y-axis) as well as parallel to (X-axis) the electrode axis are presented respectively in fig.6.7 and fig.6.8, corresponding to the interferogram of fig.6.6a and 6.6b . respectively. The axis and the origin of the graph of fig. 6.7 and fig. 6.8 are clearly labeled in the corresponding interferograms (the axis is shown in fig. 2.11.). The electron density measured in the spark gap of the present structure is in the range of about 1017 cm-3.
It clearly reflects the formation of two high-density lobes well separated around the location of the electrodes and in the center of the electrodes the density is minimal.
Several possible applications
Due to the interaction of this induced dipole moment with the non-uniform distribution of light, the dipole force is created109. This dipole force can modify the trajectories of atoms and with careful choice of parameters can lead to concentrated atom points of order tens of nanometers111 having periodicity up to λ/8.112 interference fringes113 have been used for alignment and manipulation. with low-index sphere optical tweezers. The interference of polarized beams can also be used to generate periodic microstructures.
Thus, AIL can be used to write down in a single shot the three-dimensional photonic crystal114. By controlling the relative polarization of four interfering beams and their angular separations, the periodicity and linewidth can be controlled. By changing the geometry and spatial frequencies of the AIL, periodic multiple structures can also be generated, providing the additional fine-tuning to the bandgap.
These photonic band gap materials have promising applications in the fabrication of optical waveguides, high-capacity data storage devices, and other related fields.
Conclusions
Conclusions
The only limitation of the above configuration with randomly polarized light is its low light efficiency. The ellipticity of the interfering beams from the polarized interferometric setup can be controlled by the orientation of the quarter-wave plate in the output plane as well as in one of the arms of the interferometer. Interference patterns were recorded by changing the azimuth of the fourth wave plate in the output plane as well as in one of the interferometer arms for both two, two beam and four beam polarized interferometric setups on the CCD.
Edge visibilities were measured for all models as a function of the azimuth angle of the fourth wave plates from the recorded interferograms. For this, the sample can be placed in one of the arms of each interferometric stage. The periodicity of the grating thus formed was controlled by a focusing lens placed at the exit of the interferometer in front of the thin film.
Yang and L.Z.Cai, “Wave design of the interference of three non-coplanar beams for microfiber manufacturing,” Optics Communications.
