Abstract

We demonstrate the coherent transfer of optical orbital angular momentum (OAM) to the center of mass momentum of excitons in semiconductor GaN using a four-wave mixing (FWM) process. When we apply the optical vortex (OV) as an excitation pulse, the diffracted FWM signal exhibits phase singularities that satisfy the OAM conservation law, which remain clear within the exciton dephasing time (~1ps). We also demonstrate the arbitrary control of the topological charge in the output signal by changing the OAM of the input pulse. The results provide a way of controlling the optical OAM through carriers in solids. Moreover, the time evolution of the FWM with OAM leads to the study of the closed-loop carrier coherence in materials.

© 2009 Optical Society of America

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2008

2007

R. Cêelechovský and Z. Bouchal, "Optical implementation of the vortex information channel," New. J. Phys. 9, 328 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007).
[CrossRef]

2006

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

2005

2004

2003

2002

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

2001

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

2000

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

1999

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999).
[CrossRef]

1997

T. Aoki, G. Mohs, T. Ogasawara, R. Shimano, and M. Kuwata-Gonokam, "Polarization dependent quantum beats of homogeneously broadened excitons," Opt. Express 12, 364-369 (1997).
[CrossRef]

1996

1993

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

1992

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," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Adachi, S.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999).
[CrossRef]

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," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406-1-4 (2006)
[CrossRef]

Aoki, T.

T. Aoki, G. Mohs, T. Ogasawara, R. Shimano, and M. Kuwata-Gonokam, "Polarization dependent quantum beats of homogeneously broadened excitons," Opt. Express 12, 364-369 (1997).
[CrossRef]

Arakawa, Y.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999).
[CrossRef]

Barnett, S. M.

Basistiy, I. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Beijersbergen, M. W.

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," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Carrasco, S.

Chen, Q.

W. Jiang, Q. Chen, Y. Zhang, and G.-C. Guo, "Computation of topological charges of optical vortices via nondegenerate four-wave mixing," Phys. Rev. A 74, 043811-1-4 (2006).
[CrossRef]

Courtial, J.

Dreischuh, A.

Franke-Arnold, S.

Gahagan, K. T.

Garcia, J. M

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Gibson, G.

Govorov, A. O.

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Guo, G.-C.

W. Jiang, Q. Chen, Y. Zhang, and G.-C. Guo, "Computation of topological charges of optical vortices via nondegenerate four-wave mixing," Phys. Rev. A 74, 043811-1-4 (2006).
[CrossRef]

Hatakenaka, N.

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Hoshino, K.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

Inagaki, K.

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Ishida, S.

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

Ishiguro, T.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

Jiang, W.

W. Jiang, Q. Chen, Y. Zhang, and G.-C. Guo, "Computation of topological charges of optical vortices via nondegenerate four-wave mixing," Phys. Rev. A 74, 043811-1-4 (2006).
[CrossRef]

Kivshar, Y. S.

Kolev, V. Z.

Kotthaus, J. P.

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Krolikowski, W.

Kuwata-Gonokam, M.

T. Aoki, G. Mohs, T. Ogasawara, R. Shimano, and M. Kuwata-Gonokam, "Polarization dependent quantum beats of homogeneously broadened excitons," Opt. Express 12, 364-369 (1997).
[CrossRef]

Lorke, A.

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Luyken, R. J.

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Mariyenko, I. G.

Metcalf, H. J.

Mohs, G.

T. Aoki, G. Mohs, T. Ogasawara, R. Shimano, and M. Kuwata-Gonokam, "Polarization dependent quantum beats of homogeneously broadened excitons," Opt. Express 12, 364-369 (1997).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007).
[CrossRef]

Moriwaki, O.

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

Mukai, T.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

Neshev, D. N.

Ogasawara, T.

T. Aoki, G. Mohs, T. Ogasawara, R. Shimano, and M. Kuwata-Gonokam, "Polarization dependent quantum beats of homogeneously broadened excitons," Opt. Express 12, 364-369 (1997).
[CrossRef]

Okajima, Y.

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Padgett, M. J.

Pasfko, V.

Petroff, P. M.

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406-1-4 (2006)
[CrossRef]

Saltiel, S.

Samoc, M.

Shimano, R.

T. Aoki, G. Mohs, T. Ogasawara, R. Shimano, and M. Kuwata-Gonokam, "Polarization dependent quantum beats of homogeneously broadened excitons," Opt. Express 12, 364-369 (1997).
[CrossRef]

Someya, T.

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Spreeuw, R. J. C.

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," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Strohaber, J.

Swartzlander, G. A.

Tachibana, K.

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

Tanda, S.

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Toda, Y.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007).
[CrossRef]

L. Torner, J. P. Torres, S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-81 (2005).
[CrossRef] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007).
[CrossRef]

L. Torner, J. P. Torres, S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-81 (2005).
[CrossRef] [PubMed]

Tsuneta, T.

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Uiterwaal, C. J. G. J.

van der Straten, P.

Vasnetsov, M.

Vasnetsov, M. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

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," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Yamaya, K.

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Zhang, Y.

W. Jiang, Q. Chen, Y. Zhang, and G.-C. Guo, "Computation of topological charges of optical vortices via nondegenerate four-wave mixing," Phys. Rev. A 74, 043811-1-4 (2006).
[CrossRef]

Appl. Phys. Lett.

O. Moriwaki, T. Someya, K. Tachibana, S. Ishida, Y. Arakawa, "Narrow photoluminescence peaks from localized states in InGaN quantum dot structures," Appl. Phys. Lett. 76, 2361-2363 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Nature

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, "Crystal topology: A Möbius strip of single crystals," Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

Nature Phys.

G. Molina-Terriza, J. P. Torres, L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007).
[CrossRef]

New. J. Phys.

R. Cêelechovský and Z. Bouchal, "Optical implementation of the vortex information channel," New. J. Phys. 9, 328 (2007).
[CrossRef]

Opt. Commun.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M Garcia, and P. M. Petroff, "Spectroscopy of Nanoscopic Semiconductor Rings," Phys. Rev. Lett. 84, 2223-2226 (2000).
[CrossRef] [PubMed]

Phys. Stat. Sol.

T. Ishiguro, Y. Toda, S. Adachi, T. Mukai, K. Hoshino, and Y. Arakawa, "Degenerate four-wave mixing spectroscopy of GaN films on various substrates," Phys. Stat. Sol.(b) 243, 1560-1563 (2006).
[CrossRef]

Prog. Opt.

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999).
[CrossRef]

Other

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic illustration of our experimental setup for degenerate FWM. Laser pulses whose center frequency satisfies the resonant condition of the free-exciton transitions of the sample are generated by the frequency doubling (SHG) of the mode-locked Ti:sapphire (ML:TiS). The output beam is split by the beam splitter (BS) into two beams labeled k 1 and k 2, both of which pass through a reflection-type spatial light modulator (SLM) which imposes the phase variation exp(iℓnφ) whose typical patterns together with the resulting beam profiles for =0 (left), 1 (middle), 2 (right) are shown in (b). The two beams with delay time τ are focused by a lens and the output FWM signals are obtained in the reflection geometry as shown in (c). The signals are observed by a monochromator or CCD camera. For the interferogram, one of the signals is superimposed on the third reference pulse with a delay denoted by t.

Fig. 2.
Fig. 2.

(a) A typical FWM spectrum obtained at delay time τ=0 ps. The spectrum consists of XA and XB exciton transitions. (b) FWM signals in the direction 2k 2-k 1(2 2- 1=2) and 2k 1-k 2(2 1- 2=-1) as a function of τ between k 1 and k 2. The solid lines show the fit using Eq.(2). A positive time delay is defined as pulse k 2 arriving first. The plots are obtained by spatial integration of the beam profile as shown in Fig 3.

Fig. 3.
Fig. 3.

(a) Output FWM profiles for (left) 2k 1-k 2, FWM=-1 and (right) 2k 2-k 1, FWM=2 at τ=±0.1, ±0.51, ±1.05, ±1.55 ps from top to bottom. The intensity scale is varied for each image to clearly show the dark hole(s). The split of the dark spot for FWM=2 indicates a weak contribution of the HG mode (HGbg). Simulation results for FWM=2 using (b) single LG2 and (c) LG2+HGbg for (upper) phase and (lower) intensity profiles.

Fig. 4.
Fig. 4.

(a)–(c) The output FWM beam profiles in the 2k 2-k 1 direction at τ≈0 ps, where 2 is fixed at 1 while 1 varies with 0, 1, 2, resulting in FWM(=2 2- 1)=2,1,0, respectively. Some fringe patterns appeared in the images arise from the artifact of the optics and not from the signal. (d)–(f) The corresponding interference patterns with a tilted reference pulse. The delay time t between the FWM and reference pulse is fixed at the position showing the highest contrast of the interference. (g)–(h) Theoretically calculated interference patterns.

Equations (3)

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P2k2k1(3) (t,τ0)ih̅3Θ(tτ)E22E1*eiω0tei(2k2k1).rei(221)φα,
α=μx4ex(tτ)eiΩx*τ,Ωx=ωxiγx
IFWM (τ) [1+cos(2πτTQB)]exp(2τT2),

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