HG-LG Mode Conversion with Stressed 3-Mode Fibers under Polarization

doi:10.4236/ojapps.2012.24033

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Open Journal of Applied Sciences, 2012, 2, 224-227

doi:10.4236/ojapps.2012.24033 Published Online December 2012 (http://www.SciRP.org/journal/ojapps)

HG-LG Mode Conversion with Stressed 3-Mode Fibers

under Polarization

Henning Soller

Institut für Theoretische Physik, Rupprecht-Karls-Universität Heidelberg, Heidelberg, Germany

Email: [email protected]

Received September 11, 2012; revised October 14, 2012; accepted October 25, 2012

ABSTRACT

We have coupled an upright HG mode into a fiber-optic waveguide and used the application of stress to generate a

Laguerre-Gaussian laser mode. We have generalized previous results by McGloin et al. by using a polarized input beam,

a true 3-mode fiber and by applying the stress on a stripped piece of the optical waveguide. These generalizations are

necessary in order to perform quantum information experiments and obtain reliable information on the stress imposed

on the optical fiber.

Keywords: Mode Conversion; Stress; Optical Fiber; Laguerre-Gaussian Laser Mode

1. Introduction

Recently the production of Laguerre-Gaussian (LG) laser

modes has again attracted considerable interest [1]. It

arose mainly from the fact that these modes have a well

defined orbital angular momentum equal to

[2] which may be used to transfer information. The an-

gular momentum content of LG beams has been trans-

ferred successfully to microscopic particles [3] and a

comparison of the spin angular momentum has shown it

to be ([4,5]). Orbital angular momentum is

of special interest for quantum information processing

since different Fourier components of LG beams have

been shown to be independently addressable [6]. Also

their importance for producing heralded single photons in

arbitrary spatial modes has been addressed [7]. Four dif-

ferent possibilities for creating LG modes have been

discussed. First, LG beams can be produced from a laser

directly [8]. Furthermore, there are two classes of mode

converters for Hermite-Gaussian (HG) laser modes that

can be obtained more easily in open cavity lasers. The

first type of mode converter includes spiral phase plates

[9,10] and computer-generated holographic converters

[11,12]. In these devices, an azimuthal phase depen-

dence is introduced into an00 beam. The third class of

converters is based on cylindrical lenses [13,14]. Unlike

the methods using spiral phase plates or holographic

converters this method allows to produce pure LG modes.

Finally, the fourth type of converter uses a stressed fi-

ber-optic waveguide and an HG mode input laser [1].

Compression of the fiber optic waveguide causes the

non-cylindrically symmetricand modes to

experience differing phase velocities as they propagate

through the fiber. The nonzero relative phase shift is

controllable by the magnitude and direction of the ap-

plied stress. If these phase shifts are such that the two

HG modes undergo phase shifts that differ by 90˚ the

resultant field distribution is an LG mode with

photon/l

HG 10 HG



and 0



In this paper we want to show how the result of [1] can

be generalized in three ways: first, in the previous ex-

periment the stress has been put onto the fiber directly.

We wanted to see whether it is possible to strip the fiber

and consequently allow to apply stress in a more con-

trolled manner. Second we did not want to use an HG

mode that is coupled in at a specific angle but just to use

an upright HG mode and see whether leaking of one HG

mode into the other inside the optical fiber can produce

the required angle by itself. Finally quantum information

experiments (e.g. [7]) require to do the experiments also

for polarized input beams and fibers as close to a 3-mode

fiber as possible. We will illustrate the possibility to pro-

duce Laguerre-Gaussian laser modes with heralding pho-

tons in the second part of this report.

2. Experiment

In this research we used a fiber of 1-m length. Using dif-

ferent types of optical fibers we made sure to have a real

3-mode fiber. Figure 1 shows the experimental apparatus

used to convert the HG input beam. The input laser was

forced to oscillate in an HG10 mode by the inclusion of

an intracavity cross wire. The output beam is polarized

nd expanded to fill the back aperture of a microscope a

H. SOLLER 225

Figure 1. The figure shows the experimental arrangement. We couple in an upright HG mode, that leaks into the rotated

mode and can therefore be transformed into an LG mode. The incoming mode is polarized and coupled into an optical

waveguide via a microscope objective. The stress is applied via lead blocks on the stripped fiber.

objective mounted on an x, y, z stage to couple the beam

into a 3-mode optical fiber (780 nm). The fiber was

stressed over a 100 mm region by lead weights put di-

rectly on top of the stripped fiber. One lead block on a

stage was put below the fiber and two old fiber pieces of

the same kind were used on the sides to get homogene-

ous stress.

The input mode of the optical fiber before the com-

pression stage may be assumed to be a 45 degree rotated

HG mode

4501 10

HGHG HG

, (1)

where we leave out normalization factors. Depending on

the stress induced a relative phase shift between the

modes occurs that may lead to a relative phase factor of

so that

π/2

eii

4501100

HGHGHGLG ,i

  (2)

Further stress leads to relative phase shift of

so that [1]

3π/2

eii

450110 0

HGHGHGLG ,i

 (3)

Consequently both linear momentum components of

the first LG mode can be addressed using the compres-

sion method.

The overall efficiency of this mode converter has been

measured to be approximately 2% - 3%. We should

stress that the usage of a 3-mode fiber instead of the 1.06

μm fiber used in [1] considerably complicates the cou-

pling but only this way higher order LG modes can be

discarded. We used different methods for stripping the

optical waveguide, e.g. burning the cladding, chemical

etching and mechanical stripping. Both chemical etching

and burning have caused considerable damage to the

optical waveguide and only mechanical stripping has

proven to allow for controllable operation of the fiber

afterwards.

We needed about 1.5 kg of lead to observe the mode

change to , again also under polarization. After the

addition of 1.5 kg of further lead blocks the output went

back to an HG mode rotated approximately 90˚ with re-

spect to the input mode. No further mode changes have

been observed even under extreme stress of about 11 kg

of lead. However, it is remarkable that the fiber works

even under such extreme conditions.

3. Heralded Single Photons

This setup may now be used in combination with the

Sagnac interferometer described in [7] to produce her-

alded single photons, see Figure 2. In the setup a 45˚

rotated HG laser pump is used.

We had shown above that one could also use a dif-

ferent rotation and an optical fiber to achieve the required

rotated beam. Using the nonlinear crystal one achieves

that the resulting input state is predominantly a superpo-

sition of the vacuum and a two-photon state ph2

 that

we can use to achieve the heralding of the photons. Since

the vacuum state is not relevant for us we focus on the

H. SOLLER

226

Figure 2. Proposed scheme to produce heralded single photons in arbitrary first-order transverse spatial states: S represents

a Sagnac interferometer. The stripped and stressed 3-mode fiber is pumped with a rotated HG pump laser. The HG laser

pump additionally goes through a nonlinear cry stal.

biphoton wavefunction from now on. In the basis of HG

modes of the two photons it takes the form ([15,16])



2HV VH,

ph nm



  (4)

where H and V denote the horizontal and vertical

single-photon polarizations and nm



denotes the spa-

tial part of the biphoton wavefunction. This one we can

further expand in terms of spatial HG modes but since

we limit ourselves to the usage of 3-mode fibers we can

immediately truncate the series and obtain [7]



00 45

HG HGHV VH

nm AB ABAB



 . (5)

A and B label the different angular momentum comp-

nents of the wavefunction. Since the Sagnac interfere-

ometer sorts different angular momentum components [7]

these two labels also correspond to the different output

ports of the interferometer.

Now we can use the results gained above. Using the

compression stage in the setup depicted in Figure 2 we

can induce stress and obtain the mode conversion from

HG  to or as shown in Equations (1)

and (2).

LG 1

LG

Consequently the output photon in A heralds an output

photon in B with a stress dependent well-defined first-

order spatial mode



LGHVVH.

B

  (6)

Indeed these two different compressions possible al-

low to cover the entire Poincaré sphere of first-order

transverse spatial modes [17].

4. Conclusion

In this paper we have generalized the results of [1] as we

have worked with a polarized non-rotated beam and a

true 3-mode fiber that has been stripped in the stress re-

gion. We have investigated different methods of fiber

stripping and have shown that the method works even for

a 3-mode fiber as needed for experimental proposals, e.g.

in [7]. We investigated the heralding of single photons

using our approach.

5. Acknowledgements

The author would like to thank C. C. Leary, M. G. Ray-

mer and B. J. Smith for their hospitality at the University

of Oregon and I. M. Deppner for many interesting dis-

cussions.

REFERENCES

[1] D. McGloin, N. B. Simpson and M. J. Padgett, “Transfer

of Orbital Angular Momentum from a Stressed Fiber-

Optic Waveguide to a Light Beam,” Applied Optics, Vol.

37, No. 3, 1998, pp. 469-472.

doi:10.1364/AO.37.000469

[2] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw and J. P.

Woerdman, “Orbital Angular Momentum of Light and the

Transformation of Laguerre-Gaussian Laser Modes,”

Physical Review A, Vol. 45, No. 11, 1992, pp. 8185-8189.

doi:10.1103/PhysRevA.45.8185

[3] H. He, M. E. J. Friese, N. R. Heckenberg and H. Rubin-

sztein-Dunlop, “Direct Observation of Angular Momen-

tum to Absorptive Particles from a Laser Beam with a

Phase Singularity,” Physical Review Letters, Vol. 75, No.

5, 1995, pp. 826-829. doi:10.1103/PhysRevLett.75.826

[4] M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop and N. R.

Heckenberg, “Optical Angular Momentum Transfer to

Trapped Absorbing Particles,” Physical Review A, Vol.

54, No. 2, 1996, pp. 1593-1596.

doi:10.1103/PhysRevA.54.1593

[5] N. B. Simpson, K. Dholakia, L. Allen and M. J. Padgett,

“Mechanical Equivalence of Spin and Orbital Angular

Momentum of Light: An Optical Spanner,” Optics Letters,

Vol. 22, No. 1, 1997, pp. 52-54. doi:10.1109/9.402235

[6] R. Čelechovský and Z. Bouchal, “Optical Implementation

of the Vortex Information Channel,” New Journal of Phy-

sics, Vol. 9, No. 9, 2007, p. 328.

doi:10.1088/1367-2630/9/9/328

[7] C. C. Leary, L. A. Baumgardner and M. G. Raymer,

“Stable Mode Sorting by Two-Dimensional Parity of

H. SOLLER 227

Photonic Transverse Spatial States,” Optics Express, Vol.

17, No. 4, 2009, pp. 2435-2452.

doi:10.1364/OE.17.002435

[8] M. Harris, C. A. Hill and J. M. Vaughan, “Optical Helices

and Spiral Interference Fringes,” Optics Communications,

Vol. 106, No. 4-6, 1994, pp. 161-166.

doi:10.1016/0030-4018(94)90314-X

[9] M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen

and J. P. Woerdman, “Helical-Wavefront Laser Beams

Produced with a Spiral Phaseplate,” Optics Communica-

tions, Vol. 112, No. 5-6, 1994, pp. 321-327.

doi:10.1016/0030-4018(94)90638-6

[10] G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen

and M. J. Padgett, “The Generation of Free-Space La-

guerre-Gaussian Modes at Millimetre-Wave Frequen-

cies by Use of a Spiral Phaseplate,” Optics Communica-

tions, Vol. 127, No. 4-6, 1996, pp. 183-188.

doi:10.1016/0030-4018(96)00070-3

[11] N. R. Heckenberg, R. McDuff, C. P. Smith and A. G.

White, “Generation of Optical Phase Singularities by

Computer-Generated Holograms,” Optics Letters, Vol. 17,

No. 3, 1992, pp. 221-223. doi:10.1364/OL.17.000221

[12] N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsz-

tein-Dunlop and M. J. Wegener, “Laser Beams with

Phase Singularities,” Optical and Quantum Electronics,

Vol. 24, No. 9, 1992, pp. 951-962.

doi:10.1007/BF01588597

[13] E. Abramochkin and V. Volostnikov, “Beam Transfor-

mations and Nontransformed Beams,” Optics Communi-

cations, Vol. 83, No. 1-2, 1991, pp. 123-135.

doi:10.1016/0030-4018(91)90534-K

[14] M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen

and J. P. Woerdman, “Astigmatic Laser Mode Converters

and Transfer of Orbital Angular Momentum,” Optics Com-

munications, Vol. 96, No. 1-3, 1993, pp. 123-132.

doi:10.1016/0030-4018(93)90535-D

[15] P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V.

Sergienko and Y. Shih, “New High Intensity Source of

Polarisation-Entangled Photon Pairs,” Physical Review

Letters, Vol. 75, No. 24, 1995, pp. 4337-4341.

doi:10.1103/PhysRevLett.75.4337

[16] S. P. Walborn, S. Pádua and C. H. Monken, “Conser-

vation and Entanglement of Hermite-Gaussian Modes in

Parametric Down-Conversion,” Physical Review A, Vol.

71, No. 5, 2005, p. 053812.

doi:10.1103/PhysRevA.71.053812

[17] S. J. van Enk, “Geometric Phase, Transformations of

Gaussian Light Beam and Angular Momentum Transfer,”

Optics Communications, Vol. 102, No. 1-2, 1993, pp. 59-

64. doi:10.1016/0030-4018(93)90472-H