SUNY at Stony Brook

Optics Rotation Project 1, Fall 2001

Advisors: Prof. Hal Metcalf / Dr. John Noé

(1)

both the Hermite Gaussian

(2) |

(3) |

Therefore it is possible to transform HG modes into LG modes and vice versa:

Experimentally this was realized by astigmatic mode conversion. The mode converter consists of two cylindrical lenses canonically disposed with respect to one another. This system of lenses introduces a Guoy phase shift and converts the incoming HG10 mode into the LG01 mode

The field distribution in the HG mode HG_{1,0}
rotated 45^{o} or 135^{º }relative to the x-axis
( without the propagation factor ) is equivalent to the sum ( or difference ) of two HG_{
0,1 }and HG_{1,0 }modes,

(4)

Approximated field distribution : two out-of-phase fundamental Gaussian beams

(5)

The intensity distributions corresponding to the fields (4) and (5) are similar (see Fig.)

Intensity distribution for a Hermite-Gaussian beam HG

to the x-axis (a) and for two out-of-phase fundamental Gaussian beams (b).

Beam splitter BS1 splits a beam from a He-Ne laser oscillating in the fundamental mode into two beams. The mirrors
and the beam splitter BS2 are adjusted so that the beam from the two arms are slightly misaligned.
Changing the relative phase between the beams by moving a prism we can get the required field distribution at the
input of the mode convertor.

I deeply appreciate Dr. John Noe for his instruction and
generous help, both for the physics and the webpage. I would like to thank
Prof. Harold Metcalf's group members for help and supply.

1. Dmitri V.Petrov, Fernando Canal, Lluis Torner, Opt. Comm. 143 (1997) 265-267

"A simple method to generate optical beams with a screw phase dislocation"

2. M.W.Beijerbergen, I.Allen, H.E.I.O. van der Veen, and J.P.Woeman, Opt.Comm.96 (1994) 123-132

"Astigmatic laser mode converters and transfer of orbital angular momentum"

3. M. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64 (1), 1996

"An experiment to observe the intensuty and phase structure of Laguerre-Gaussian laser modes"

4. J.Courtial, M.J.Padgett, Opt.Comm. 159 (1999) 13-18

" Performance of cylindrical lens mode converter for producing Laguerre-Gaussian modes"

5. L.Allen,M.W.Beijersbergen,R.J.C.Spreeuw,and J.P.Woerdman, Physics Review A, 45 (1992)8185-8189

"Orbital angular momentum of light and transformation of Laguerre-Gaussian laser modes"

6. Chr.Tamm, Physics Review A, 38 (1988)5960-5963

"Frequency locking of two transverse optical modes of a laser"

7. Alipasha Vaziri, Alois Mair, Gregor Weihs, Anton Zeilinger

Institut für Experimentalphysik Universität Wien, Austria

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