Stefan Evans, John Noé, Harold Metcalf.

Laser Teaching Center,
Stony Brook University, Stony Brook, NY 11794.

Phase removal: Friday, June 14, 2013

         John Elgin gave some useful advice on how to better analyze the behavior of LG beams. The aim in simulating obstructions in the path of these beams is to have a better understanding of how clusters of atoms will interact with the beam in different locations. So far, the MATLAB simulations described in the Report section of this webpage show us that a dark region inside the LG beam will refill to some extent without producing Airy rings as is the case for Gaussian beams. The question is whether orbital angular momentum will transfer to atom clusters placed in different regions of the beam, which will likely not be interacting with the entire beam profile. In order to build on the simulations experimentally, he mentioned that one can place an iris to select different regions of the beam profile, allowing only part of it through. This way, we are treating the region as the only part that's interating with the atoms, which Elgin mentioned is far smaller than the typical waist size of these beams. This may yield more useful information than simply obstrucitng the beam with a dot of ink and moving it around, as was the original idea, mimicing the simulation. Therefore this coming week the goal is to let only part of an LG beam of charge ℓ and send it back through to impose -ℓ, to have a better idea as to whether it still posesses some OAM that can be transferred to the atom.


Phase removal: Friday, April 5, 2013


Corrected setup to make an ℓ = +4 and bringing it back to zero, resulting in what we believe is an Airy pattern. The beam is normal to the VPP in both directions.

We have sucessfully removed helical phase from the LG beam by sending it back through the VPP though the opposite direction. Refer to the Report section for images and simulations. The output was what appears to be an Airy pattern with a bright spot in the center, which shows that there is no longer any OAM.


LG beam spatial filtering: Friday, March 29, 2013

         We achieve a high quality collimated LG beam of charge 4 using spatial filtering. We use a 150 micrometer pinhole in order to make an Airy pattern, which is closer to a Gaussian shape than what comes out of the laser cavity, and then collimate it using a lens and cur out the outer rings with another iris, leaving only the bright spot. Now this passes throught the spiral phase plate to form a nice helical phase, but requires two more collimeting lenses with a 200 micrometer pinhole to clean up the diffraction from the steps in the plate. In the far field our beam was stable. Refer to the Report section for an image.


Phase plate and other generation methods: Monday, March 11, 2013

        The next step is to see whether we can create a Gaussian beam out of a LG beam. This may be possible with the phase plate (VPP-633) after it also creates the mode, since it appears to accept small angles from the normal without significant warping. Below is a setup where an LG beam is formed (slightly warped) offset at a small angle. With an even number of reflections, the topological charge is reversd twice and the same charge is sent back, but this time into the phase plate from the opposite side, so that it imposes a flipped charge.

Figure 1: Setup to make an ℓ = +1 and bringing it back to zero. The angle offset from the normal into the phase plate is equal to half the angle between incident and reflected beams, so that it is equal in both directions. We must determine whether warping is doubled or cancelled out.

We compare the capabilities of different generation methods, with personal experience and reference to past projects on the Laser Teaching Center site.

Device Reversable? Quality
VPP-633 To be determined Good: it is easy to achieve nearly perfectly
symmetric profiles. Diffraction effects are to
be cleaned with a lens and pinhole setup.
SLM (forked) Yes, with a spiral
phase on screen
Good: near perfect profiles can be made
adjusting the grating's period, beam waist and
compensating for warped screens.
Open Cavity &
Cylindrical Lenses
With another pair of
lenses, it can be made
back into an HG mode
Good: some modes were warped but with
careful alignment there were images of
symmetric profiles (Meltzer, LTC).
Forked Grating No Poor: "the forked grating is relatively
inefficient" (Nair, LTC).


Phase plate: Friday, March 8, 2013

        We can tell which charge we make by noting faint lines on different sections of the phase plate when deciding where to put our Gaussian beam. These lines correspond to the number of 0 to 2π steps in the Helical wave front, where there is a necessary sudden change in the plate's thickness. It is easy to arrange the plate so that the LG beam's intensity profile is symmetrical. There are a few diffraction effects that Dr. Noe mentioned, including the circular rings and faint fringes in the radial direction corresponding to the steps in the plate, extending outwards from faint darker spots lining the core (for higher orders). We need to confirm that these can be cleaned up with a lens and pinhole.

        In comparison with the Spatial Light Modulator projecting a forked diffraction grating, both create high quality symmetric LG beam profiles. The SLM's screen is warped at times, but this can be adjusted with an extra phase mapped on to the screen. For the phase plate, we avoid large incident angles from the normal (not significant at small angles, as Dr. Noe mentioned). In both cases we prevent any warping of the LG beams.


Wednesday, Feb 27, 2012

        In "Enhanced Quadrupole Effects for Atoms in Optical Vortice" [4], an optical vortex is detuned to emphasize quadrupole forces on a cluster of atoms, where the topological charge is proportional to the "potential distributions" of the atoms, their likely positions and velocities about the beam axis. Steady state force is defined as dissipative force + qualdrupole force, where "The dissapative force can now be understood as a quadrupole absorption followed by spontaneous emission of light by the atom, while the quadrupole force, which is proportional to the gradient of the Rabi frequency, is responsible for confining the atom to the maximal intensity regions of the field" (p.3). This brings up a new concept not mentioned in “On Exchange of Orbital Angular Momentum...”, where rather than having a torque symmetry affecting the atoms in the center, a new symmetry about the rmax intensities at different ℓ charges prevent radial motion at a certain radii, but it is unclear whether the same type of scattering occurs where ℓ is reversed, since it is a new type of symmetry. Detuning is mentioned, in order to "maximize quadrupolar effects", where the laser's frequency is tailored to resonate with the quadrupole force mentioned. Recent experiments are mentioned on trapping atoms into "annular ringlike regions of space created by counter-propagating beams" (4), and that in certain cases the beam can be tailored so that both dipole and quadrupole forces are significant.
Aim & Questions:
Investigate the dipole optical potential distribution and compare with quadrupole forces and their potential distibutions (computed in this paper), and whether the dipole force confines the atoms to the region of maximum intensity or the center.
Is transfer of orbital angular momentum, as computed for atoms in the center of the beam (Basil et. all), compatable with dipole or quadrupole forces acting on the cluster of atoms?


Wednesday, Feb 20, 2012

        Two of the devices for generating an LG beam at the Laser teaching center are an open laser cavity and a RPC Photonice Vortex Phase Plate (VPP) - m633. The open laser cavity forms a first order Hermite-Gaussian (HG) mode, where its two lobes are π phase apart. We manipulate this mode in the same manner that a linear polarization oriented at 45 degrees is divided into its x and y components, where one of the two is given a π/2 phase shift. We place a pair of cylindrical lenses, oriented at +/- 45 degrees from the HG beam axis (this can be the axis of 0 intensity), where it divides ino two orthogonal modes of equal intensity. One of the two modes is given a geometric phase shift of π/2, and they recombine to form an LG mode. The VPP gives a Gaussian beam a helical wavefront, where the thickness of the plate varies to give a difference in phase about the beam axis.

Figure 2: The plates range in charge from ℓ = 1 - 8, where each square is a centimeter wide.

Below is a potetnial setup, creating an LG beam and restoring it to its Gaussian mode, where the VPP is fl ipped to impose an ℓ = -1 charge to an ℓ = 1 beam.

Figure 3: Setup to make an ℓ = +/- 1 and imposing an ℓ = -/+ 1, bringing it back to a zero. We must determine whether this is considered a superposition of opposite charges, resulting in an HG mode, or simply a helical phase being unwound and turned into a plane wave (Gaussian).


Wednesday, Feb 13, 2012

        In recent paper "On Exchange of Orbital Angular Momentum Between Twisted Photons and Atomic Electrons" [1], there is a theoretical transfer of 2ℓ of photon's LG beam charge to the atomic azimuthal quantum number M=2L+1 (p.1,2). Specifically, the atom is located in the center of the beam, where electron orbit radius a<<λ,w. There is a transfer of orbital angular momentum in forward scattering, while transfer of spin angular momentum in the case of forward scattering is forbidden, where ℓf=-ℓi, Li=Lf=abs(ℓ), described as a perpendicular to the beam direction, so that the process is “force-free but not torque-free.” (p.10,11). The paper brings up the question of different types of transfer occuring wen the atom is not located in the center of the beam, where the torque acting on the electron is not symmetric.
What is meant by atomic scattering in this case? Is it reflection or absorption and emission?
In the case of interaction with atoms where w>>a, what is the role of optical trapping? Can forward scattering still be expected when the local k vectors that impose torque on the atom are not symmetrical?
The transfer is described for beams with intensities ranging from single photons to many. In the case of a small obstruction (not a single atom, but still smaller than w), is there a difference between interaction with a single photon and many in terms of direction of scattering?


Wednesday, Jan 23, 2012

        The mistake has been resolved at the IUSL. Fourier transform is analogous to focusing a beam, where the larger the waist, the smaller the focal point. Reducing the beam waist w (for ℓ=0) to n/64 pixels on the grid (n=768), it is nearly equivalent to that of the Fourier Transformed beam. If we decrease w further, wFT blows up, but we have insufficient pizels to put in obstructions. However there is now a limit to how small the pixels are relative to the beam waist. The Fourier Transform function has to be analyzed in greater depth so that we can accomodate for the factor by which pixels are reduced, in order to achieve higher definition and more flexibility in simulating obstructions.


Wednesday, Dec 26, 2012

        The goal is to generate a Gaussian distribution of points where we can vary the position on the LG beam, FWHM, and number of points. These points, where Intensity is set to zero, simulate particles sent in front of the LG beam. We want to determine what size of the distribution and amount of particles it takes to break the symmetry of the LG beams in the far field, using the same far field diffraction functions. We generate the LG beam and make the zero distribution, which is visible in the near field. The LG beam is not following the Fourier tranform and making a far field pattern, so more changes to the code need to be made.


Wednesday, Dec 19, 2012

        The goal is to set a part of the LG intensity profile to 0, ie:(I=zeros(X>n/2)) so that we can observe the near field before any diffraction of the remaining uncut LG beam and the far field using the fft2 and fftshift Matlab functions for a Fourier Transform of the beam equivalent to observing the beam in the far field of at the focal length of an added lens. The error in the code so far is the number of elements not agreeing with each other. Perhaps some of the variables need to be changed from scalar to vector.


Papers to investigate:

[1]Basil S. Davis, L. Kaplan, and J.H. McGuire, “On Exchange of Orbital Angular Momentum Between Twisted Photons and Atomic Electrons,” J. Opt. 15 (2013) 035403
[2]Leach, J., Keen, S., Padgett, M.J., Saunter, C., and Love, G.D., “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Optics Express, 14. pp. 11919-11924. ISSN 1094-4087 (2006).
[3]M. J. Padgett and L. Allen, “The Poynting Vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36-40 (1995).
[4]V. E. Lembessis and M. Babiker, “Enhanced Quadrupole Effects for Atoms in Optical Vortices,” PRL 110, 083002 (2013)


Summer 2011: Geometric Phase Summary

        This summer we investigated geometric phase transformations in Laguerre-Gaussian (LG) beam mode space. We describe opposite orbital and spin angular momentum states as opposite poles of Poincare spheres. Poincare spheres demonstrate that when a beam state is taken from one pole to another, topological charges reverse. When the reverse transformation is made to restore the mode states, an offset angle between two pi converters creates geometric phase. As the LG modes are composed of two orthogonal Hermite-Gaussian (HG) beam modes with a pi/2 retardance, cylindrical lenses separate the two for an additional pi lag, determining where the HG mode separation occurs. The orientation of HG modes is a function of phase, or in this case, a result of the lenses' orientation. This demonstrates a connection between polarization and mode space, where the position of circularly polarized electric field vectors are phase dependent. In the case of a linear polarization, a set of many polarizers of an infinitesimal change in theta rotate the polarization without loss of intensity, so long as the original axis is parallel to the polarization. In a similar manner, the offset axes of cylindrical lens pairs rotate the decomposed HG modes. This can be described as a force acting upon the beam to rotate the mode space, which we experimentally observe as lobe structure, very mysterious!


Friday November 12, 2010

        The investigation of diffraction begins with beam obstructions. An open laser-cavity helium neon Gaussian laser beam was partially obstructed by a sheet of paper and a razor. The result was interesting; while a wavefront curves around the obstruction, resulting in a partial restoration of intensity in the region which was obstructed, a streak of light spanned the opposite direction as well. However, a wavefront could not bend away from the obstruction; in the direction of the undisturbed portion of the beam. There is the possibility that the streaks, which appeared in both directions, are simply a result of contact with the edge of the obstruction, which may have a scattering effect. While a sheet of paper and a razor produced the same effect, a thinner object may be required to investigate such obstructions further.

The Huygens-Fresnel principle states that a well defined obstruction acts as a secondary source, producing an additional wavefront. This was used to explain the knife-edge effect, where diffraction creates interference between the two wavefronts. Could this account for the two streaks? Shouldn't diffraction be observable? If so, the locations would be significant, since they would indicate whether the original wavefront is bending away from the obstruction.


Tuesday, November 2, 2010 -- Prof. Metcalf's Lecture

        Dr. Metcalf describes the history of laser beam cooling and advances made via atom manipulation in today's colloquium. The first complication was the varying Doppler shift found in the atoms that must be excited to create the beam. The frequency intake varied with each different Doppler shift, according to the atoms' velocities. While it was difficult to use a varying frequency, the atomic frequency was adjustable when a magnetic field was applied to tailor the atoms' location and velocity to specific Doppler shifts. This allowed for the development of "optical molasses", where the input and reflected beams interact with the cluster of atoms, creating a net force of zero, where any velocity is opposed. Here the temperature falls to the range of microkelvin, far more manageable.


Wednesday, October 20th, 2010 -- AMO Seminar

        A lecture on quantum computing and NOON states highlights entangled pairs of photons' quantum effects on diffraction fringes. When photons of a specific wavelength are superimposed, the resulting diffraction pattern fits that produced by a shorter wavelength.


Week of October 13th, 2010 -- SPIE Conference Proceedings

        There were several interesting papers on the generation of optical vortex beams and investigations of effects on the beam's frequency profile. What was most striking was the classification of different types of optical vortices according to the composition of the singularity. In the case of fully coherent polarization and phase vortices, it is defined simply as a null region of destructive interference. However, in the case of partially coherent geometric vortices, the singularity is described as having an infinite amplitude.

Source: Soskin, Polyanski. New Polarization Singularities of Partially Coherent Light Beams.

Is it possible to distinguish between the two types of singularities according to any differences in their diffraction patterns?

        A journal on the red and blue shifts found around a beam's singularity highlights important properties of vortices which ought to be explored. A mono-chromatic fully coherent vortex beam with a converging spherical wave front was found to exhibit a symmetric wavelength profile at the area of focus. Wavelength was measured at theta with 45 degree increments. At each interval there is a transition between a zone of red shift and one of blue shift.

Source: Gbur, Visser and Wolf. Singular Optics with Polychromatic Light

Are the wavelength shifts created geometrically by the convergence, or by the nature of a singularity? The article mentioned that the effect is not limited to the focal point. Why is it necessary for the beam to be converging?

        Multiple wave front interference creates "vortex streets" of null intensity where there is phase addition. One finds what appears to be a forked diffraction grating. When considering the wave nature of light, there is a correlation between singular optics and fluid dynamics, as vortices found elsewhere in nature share properties with those in optics.

Source: Terriza, Petrov and Torner. Optical Vortex Streets

Many types of vortices, including those in fluids, exhibit centripetal forces about the singularity. Meanwhile their resulting centrifugal forces have a correlation with the intensity distribution of beams with topological charge used for astronomy. Could this fluid property of light have a measurable effect in diffraction when a vortex beam is partially obstructed by an edge? If it was only a null region, an axis along the wave front would not bend as a wave would, but this should not be the case for a singularity.


Week of October 6th, 2010

        This week in the Laser Teaching Center, we went over Linux programming basics. Among the most important functions are running several programs simultaneously in the background, including text documents, function plotting, and figure editing. This system will be used for journal entries.

Instruction examples:

-(name of program) & -to run in the background
-ps aux -history
-gnuplot->variables -function plotting
-cd_public_html->ls_-1->pico_bio.txt -open document
-cntrl. j -restore lines
-tab -complete program name while typing