Gaussian-beam-induced vortices in vertical-cavity surface-emitting lasers

Francois Brown de Colstoun, Alexander V. Fedorov, Galina Khitrova, Tom R. Nelson, Curt W. Lowry, Hyatt M. Gibbs, Tom M. Brennan, B. Gene Hammons

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We have triggered transverse pattern modifications by injecting a CW monochromatic (10 MHz) beam in a vertical-cavity surface-emitting laser (VCSEL). The injected Gaussian beam has a frequency close to that of the natural TEM00 mode of the VCSEL (Fig. 1). The spot of the injection is not super-imposed with the original lasing spot (Fig. 2). However, it is close enough to lock the TEM00 mode, as seen in the interferogram of Fig. 3. As a result we observe a system of two Gaussian beams locked in frequency and in phase, propagating on parallel axes, and with waists of different size and location. The interferogram in Fig. 3 shows two vortices of opposite topological charges located on both sides of the system of two Gaussian beams. It has been shown theoretically that if such a system had the two beams propagating along the same axis, a series of vortices would appear, with their trajectories along concentric rims normal to the axis of propagation. These vortices do not display the phase singularity behavior in the plane normal to the axis of propagation and cannot be observed interferometrically. However, when the beams' axes are not collinear, vortices appear with their trajectories along lines oriented in the same direction as the axes, and thus can be observed as phase singularities in the plane normal to the axes of propagation. In our experiment, the image plane coincided with the focal plane of the injected beam. In this plane, in a bipolar coordinate system (r1, r2) with poles coinciding with axes of the beams, the locations of vortices are given by the following formulas: r12 = 2[1 + (m + 1/2 ) λ÷D] [D2 + π2 w14÷λ2], m = 0, ±1, ±2, . . . r22 = w22[r1÷w12 + λ2D22w12 - ln A1÷A2], where index 1 stands for the laser beam, and index 2 is for the injected beam. D is the distance between focal planes of the two beams; w, are half-waists of the beams; A, are beam amplitudes; and λ is the wavelength. The pair of vortices observed in the experiment corresponds to the order m = - 15. A neighboring pair of vortices should be located outwards at a distance of more than 5 μm from the observed vortices. In our experimental setup, it is currently out of observation. The distance between the beams' axes is not a parameter in the above formulas. Hence, bringing the beams closer increases the distance between the vortices, and vice versa. This dependence was clearly confirmed in the experiment. Likewise, r2 linearly depends on w2. When w2 increases, r2 increases also, separating the two vortices further. These changes in positions of the vortices were also clearly seen in the experiment.

Original languageEnglish (US)
Title of host publicationProceedings of the International Quantum Electronics Conference (IQEC'94)
PublisherPubl by IEEE
Pages70-71
Number of pages2
ISBN (Print)0780319737
StatePublished - 1994
EventProceedings of the 21st International Quantum Electronics Conference (IQEC'94) - Anaheim, CA, USA
Duration: May 8 1994May 13 1994

Other

OtherProceedings of the 21st International Quantum Electronics Conference (IQEC'94)
CityAnaheim, CA, USA
Period5/8/945/13/94

Fingerprint

Gaussian beams
Surface emitting lasers
Vortex flow
Experiments
Trajectories
Phase behavior
Laser modes
Laser beams
Poles

ASJC Scopus subject areas

  • Engineering(all)

Cite this

de Colstoun, F. B., Fedorov, A. V., Khitrova, G., Nelson, T. R., Lowry, C. W., Gibbs, H. M., ... Hammons, B. G. (1994). Gaussian-beam-induced vortices in vertical-cavity surface-emitting lasers. In Proceedings of the International Quantum Electronics Conference (IQEC'94) (pp. 70-71). Publ by IEEE.

Gaussian-beam-induced vortices in vertical-cavity surface-emitting lasers. / de Colstoun, Francois Brown; Fedorov, Alexander V.; Khitrova, Galina; Nelson, Tom R.; Lowry, Curt W.; Gibbs, Hyatt M.; Brennan, Tom M.; Hammons, B. Gene.

Proceedings of the International Quantum Electronics Conference (IQEC'94). Publ by IEEE, 1994. p. 70-71.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

de Colstoun, FB, Fedorov, AV, Khitrova, G, Nelson, TR, Lowry, CW, Gibbs, HM, Brennan, TM & Hammons, BG 1994, Gaussian-beam-induced vortices in vertical-cavity surface-emitting lasers. in Proceedings of the International Quantum Electronics Conference (IQEC'94). Publ by IEEE, pp. 70-71, Proceedings of the 21st International Quantum Electronics Conference (IQEC'94), Anaheim, CA, USA, 5/8/94.
de Colstoun FB, Fedorov AV, Khitrova G, Nelson TR, Lowry CW, Gibbs HM et al. Gaussian-beam-induced vortices in vertical-cavity surface-emitting lasers. In Proceedings of the International Quantum Electronics Conference (IQEC'94). Publ by IEEE. 1994. p. 70-71
de Colstoun, Francois Brown ; Fedorov, Alexander V. ; Khitrova, Galina ; Nelson, Tom R. ; Lowry, Curt W. ; Gibbs, Hyatt M. ; Brennan, Tom M. ; Hammons, B. Gene. / Gaussian-beam-induced vortices in vertical-cavity surface-emitting lasers. Proceedings of the International Quantum Electronics Conference (IQEC'94). Publ by IEEE, 1994. pp. 70-71
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author = "{de Colstoun}, {Francois Brown} and Fedorov, {Alexander V.} and Galina Khitrova and Nelson, {Tom R.} and Lowry, {Curt W.} and Gibbs, {Hyatt M.} and Brennan, {Tom M.} and Hammons, {B. Gene}",
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AU - Gibbs, Hyatt M.

AU - Brennan, Tom M.

AU - Hammons, B. Gene

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N2 - We have triggered transverse pattern modifications by injecting a CW monochromatic (10 MHz) beam in a vertical-cavity surface-emitting laser (VCSEL). The injected Gaussian beam has a frequency close to that of the natural TEM00 mode of the VCSEL (Fig. 1). The spot of the injection is not super-imposed with the original lasing spot (Fig. 2). However, it is close enough to lock the TEM00 mode, as seen in the interferogram of Fig. 3. As a result we observe a system of two Gaussian beams locked in frequency and in phase, propagating on parallel axes, and with waists of different size and location. The interferogram in Fig. 3 shows two vortices of opposite topological charges located on both sides of the system of two Gaussian beams. It has been shown theoretically that if such a system had the two beams propagating along the same axis, a series of vortices would appear, with their trajectories along concentric rims normal to the axis of propagation. These vortices do not display the phase singularity behavior in the plane normal to the axis of propagation and cannot be observed interferometrically. However, when the beams' axes are not collinear, vortices appear with their trajectories along lines oriented in the same direction as the axes, and thus can be observed as phase singularities in the plane normal to the axes of propagation. In our experiment, the image plane coincided with the focal plane of the injected beam. In this plane, in a bipolar coordinate system (r1, r2) with poles coinciding with axes of the beams, the locations of vortices are given by the following formulas: r12 = 2[1 + (m + 1/2 ) λ÷D] [D2 + π2 w14÷λ2], m = 0, ±1, ±2, . . . r22 = w22[r1÷w12 + λ2D2/π2w12 - ln A1÷A2], where index 1 stands for the laser beam, and index 2 is for the injected beam. D is the distance between focal planes of the two beams; w, are half-waists of the beams; A, are beam amplitudes; and λ is the wavelength. The pair of vortices observed in the experiment corresponds to the order m = - 15. A neighboring pair of vortices should be located outwards at a distance of more than 5 μm from the observed vortices. In our experimental setup, it is currently out of observation. The distance between the beams' axes is not a parameter in the above formulas. Hence, bringing the beams closer increases the distance between the vortices, and vice versa. This dependence was clearly confirmed in the experiment. Likewise, r2 linearly depends on w2. When w2 increases, r2 increases also, separating the two vortices further. These changes in positions of the vortices were also clearly seen in the experiment.

AB - We have triggered transverse pattern modifications by injecting a CW monochromatic (10 MHz) beam in a vertical-cavity surface-emitting laser (VCSEL). The injected Gaussian beam has a frequency close to that of the natural TEM00 mode of the VCSEL (Fig. 1). The spot of the injection is not super-imposed with the original lasing spot (Fig. 2). However, it is close enough to lock the TEM00 mode, as seen in the interferogram of Fig. 3. As a result we observe a system of two Gaussian beams locked in frequency and in phase, propagating on parallel axes, and with waists of different size and location. The interferogram in Fig. 3 shows two vortices of opposite topological charges located on both sides of the system of two Gaussian beams. It has been shown theoretically that if such a system had the two beams propagating along the same axis, a series of vortices would appear, with their trajectories along concentric rims normal to the axis of propagation. These vortices do not display the phase singularity behavior in the plane normal to the axis of propagation and cannot be observed interferometrically. However, when the beams' axes are not collinear, vortices appear with their trajectories along lines oriented in the same direction as the axes, and thus can be observed as phase singularities in the plane normal to the axes of propagation. In our experiment, the image plane coincided with the focal plane of the injected beam. In this plane, in a bipolar coordinate system (r1, r2) with poles coinciding with axes of the beams, the locations of vortices are given by the following formulas: r12 = 2[1 + (m + 1/2 ) λ÷D] [D2 + π2 w14÷λ2], m = 0, ±1, ±2, . . . r22 = w22[r1÷w12 + λ2D2/π2w12 - ln A1÷A2], where index 1 stands for the laser beam, and index 2 is for the injected beam. D is the distance between focal planes of the two beams; w, are half-waists of the beams; A, are beam amplitudes; and λ is the wavelength. The pair of vortices observed in the experiment corresponds to the order m = - 15. A neighboring pair of vortices should be located outwards at a distance of more than 5 μm from the observed vortices. In our experimental setup, it is currently out of observation. The distance between the beams' axes is not a parameter in the above formulas. Hence, bringing the beams closer increases the distance between the vortices, and vice versa. This dependence was clearly confirmed in the experiment. Likewise, r2 linearly depends on w2. When w2 increases, r2 increases also, separating the two vortices further. These changes in positions of the vortices were also clearly seen in the experiment.

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