Evolution of a conically diffracted gaussian beam in free space

S. D. Grant, A. Abdolvand

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

Abstract

Summary form only given. A beam of light propagating along the optic axis of a biaxial crystal will be transformed to a cone of light and emerge from the crystal as a hollow cylinder as predicted by W. R. Hamilton in 1832 [1] and experimentally observed shortly thereafter by H. Lloyd [2]. Recent renewed interest in the phenomenon has led to the development of a more complete theory, many aspects of which have yet to be experimentally observed.In this contribution, we compare our observations on the free space evolution of a conically diffracted Gaussian beam with the recently advised paraxial theory [3]. The theory was successfully tested for four KGd(WO4)2 biaxial crystals of lengths: 7.40 mm, 16.94 mm, 19.40 mm, and 24.50 mm, in a single-crystal conical diffraction configuration. A collimated beam from a diode laser with λ=635nm was focused to a spot of Ȧ0=13.6 μm (1/e value). For each conical diffraction crystal (CDC) the longitudinal shift, ǻ, the ring radius, R, and the position of the spot with the highest axial intensity, Zf, were measured using a Spiricon SP620U beam profiler on a mechanical travel translation stage. The longitudinal shift was given by ǻ=L(1-1/n2) where n2 is one of the refractive indices of the CDC and had values of 3.78 mm, 8.66 mm, 9.92 mm and 12.52 mm. The measured values were found to be 3.4 mm, 8.6 mm, 9.7 mm and 12.75 mm respectively. The ring radii are proportional to the length of the crystal, L, and are found using R=AL, where A is the semiangle of the cone of conical diffraction. The theoretical values were found to be: 130.23 μm, 298.14 μm 341.33 μm and 431.16 μm for each crystal. The measured values were 130μm, 293μm, 335μm and 430μm respectively. Where λ is the wavelength of the incident beam and Ȧ0 is the radius of the incident beam at the beam waist. The theoretical Zf values were found to be 14.29 mm, 32.72 mm, 37.46 mm and 47.32 mm. The measured values were 16.35 mm, 33.80 mm, 33.45mm and 45.25mm respectively.In addition the evolution of the beam in free space was found by taking images at intervals of 0.5 mm over a range of -66 mm using CDC3 of length 19.4 mm and is shown in Figure 1. All of the reported values were found to be in good agreement with the paraxial theory derived by M. V. Berry [3] and the cross section was found to be in good agreement with the theoretically predicted image produced in [4].
LanguageEnglish
Title of host publicationThe European Conference on Lasers and Electro-Optics, CLEO_Europe 2013
PublisherIEEE
Number of pages1
ISBN (Print)9781479905942
DOIs
Publication statusPublished - 21 Apr 2014
Externally publishedYes
EventThe European Conference on Lasers and Electro-Optics, CLEO_Europe 2013 - Munich, Germany
Duration: 12 May 201316 May 2013

Conference

ConferenceThe European Conference on Lasers and Electro-Optics, CLEO_Europe 2013
CountryGermany
CityMunich
Period12/05/1316/05/13

Fingerprint

Gaussian beams
Crystals
Diffraction
crystals
Cones
diffraction
radii
cones
rings
shift
Semiconductor lasers
Optics
Refractive index
travel
hollow
Single crystals
semiconductor lasers
Wavelength
optics
refractivity

Keywords

  • laser beams
  • crystals
  • diffraction
  • optics

Cite this

Grant, S. D., & Abdolvand, A. (2014). Evolution of a conically diffracted gaussian beam in free space. In The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013 IEEE. https://doi.org/10.1109/CLEOE-IQEC.2013.6800987
Grant, S. D. ; Abdolvand, A. / Evolution of a conically diffracted gaussian beam in free space. The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013. IEEE, 2014.
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title = "Evolution of a conically diffracted gaussian beam in free space",
abstract = "Summary form only given. A beam of light propagating along the optic axis of a biaxial crystal will be transformed to a cone of light and emerge from the crystal as a hollow cylinder as predicted by W. R. Hamilton in 1832 [1] and experimentally observed shortly thereafter by H. Lloyd [2]. Recent renewed interest in the phenomenon has led to the development of a more complete theory, many aspects of which have yet to be experimentally observed.In this contribution, we compare our observations on the free space evolution of a conically diffracted Gaussian beam with the recently advised paraxial theory [3]. The theory was successfully tested for four KGd(WO4)2 biaxial crystals of lengths: 7.40 mm, 16.94 mm, 19.40 mm, and 24.50 mm, in a single-crystal conical diffraction configuration. A collimated beam from a diode laser with λ=635nm was focused to a spot of Ȧ0=13.6 μm (1/e value). For each conical diffraction crystal (CDC) the longitudinal shift, {\aa}́, the ring radius, R, and the position of the spot with the highest axial intensity, Zf, were measured using a Spiricon SP620U beam profiler on a mechanical travel translation stage. The longitudinal shift was given by {\aa}́=L(1-1/n2) where n2 is one of the refractive indices of the CDC and had values of 3.78 mm, 8.66 mm, 9.92 mm and 12.52 mm. The measured values were found to be 3.4 mm, 8.6 mm, 9.7 mm and 12.75 mm respectively. The ring radii are proportional to the length of the crystal, L, and are found using R=AL, where A is the semiangle of the cone of conical diffraction. The theoretical values were found to be: 130.23 μm, 298.14 μm 341.33 μm and 431.16 μm for each crystal. The measured values were 130μm, 293μm, 335μm and 430μm respectively. Where λ is the wavelength of the incident beam and Ȧ0 is the radius of the incident beam at the beam waist. The theoretical Zf values were found to be 14.29 mm, 32.72 mm, 37.46 mm and 47.32 mm. The measured values were 16.35 mm, 33.80 mm, 33.45mm and 45.25mm respectively.In addition the evolution of the beam in free space was found by taking images at intervals of 0.5 mm over a range of -66 mm using CDC3 of length 19.4 mm and is shown in Figure 1. All of the reported values were found to be in good agreement with the paraxial theory derived by M. V. Berry [3] and the cross section was found to be in good agreement with the theoretically predicted image produced in [4].",
keywords = "laser beams, crystals, diffraction , optics",
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Grant, SD & Abdolvand, A 2014, Evolution of a conically diffracted gaussian beam in free space. in The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013. IEEE, The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013, Munich, Germany, 12/05/13. https://doi.org/10.1109/CLEOE-IQEC.2013.6800987

Evolution of a conically diffracted gaussian beam in free space. / Grant, S. D.; Abdolvand, A.

The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013. IEEE, 2014.

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

TY - GEN

T1 - Evolution of a conically diffracted gaussian beam in free space

AU - Grant, S. D.

AU - Abdolvand, A.

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Y1 - 2014/4/21

N2 - Summary form only given. A beam of light propagating along the optic axis of a biaxial crystal will be transformed to a cone of light and emerge from the crystal as a hollow cylinder as predicted by W. R. Hamilton in 1832 [1] and experimentally observed shortly thereafter by H. Lloyd [2]. Recent renewed interest in the phenomenon has led to the development of a more complete theory, many aspects of which have yet to be experimentally observed.In this contribution, we compare our observations on the free space evolution of a conically diffracted Gaussian beam with the recently advised paraxial theory [3]. The theory was successfully tested for four KGd(WO4)2 biaxial crystals of lengths: 7.40 mm, 16.94 mm, 19.40 mm, and 24.50 mm, in a single-crystal conical diffraction configuration. A collimated beam from a diode laser with λ=635nm was focused to a spot of Ȧ0=13.6 μm (1/e value). For each conical diffraction crystal (CDC) the longitudinal shift, ǻ, the ring radius, R, and the position of the spot with the highest axial intensity, Zf, were measured using a Spiricon SP620U beam profiler on a mechanical travel translation stage. The longitudinal shift was given by ǻ=L(1-1/n2) where n2 is one of the refractive indices of the CDC and had values of 3.78 mm, 8.66 mm, 9.92 mm and 12.52 mm. The measured values were found to be 3.4 mm, 8.6 mm, 9.7 mm and 12.75 mm respectively. The ring radii are proportional to the length of the crystal, L, and are found using R=AL, where A is the semiangle of the cone of conical diffraction. The theoretical values were found to be: 130.23 μm, 298.14 μm 341.33 μm and 431.16 μm for each crystal. The measured values were 130μm, 293μm, 335μm and 430μm respectively. Where λ is the wavelength of the incident beam and Ȧ0 is the radius of the incident beam at the beam waist. The theoretical Zf values were found to be 14.29 mm, 32.72 mm, 37.46 mm and 47.32 mm. The measured values were 16.35 mm, 33.80 mm, 33.45mm and 45.25mm respectively.In addition the evolution of the beam in free space was found by taking images at intervals of 0.5 mm over a range of -66 mm using CDC3 of length 19.4 mm and is shown in Figure 1. All of the reported values were found to be in good agreement with the paraxial theory derived by M. V. Berry [3] and the cross section was found to be in good agreement with the theoretically predicted image produced in [4].

AB - Summary form only given. A beam of light propagating along the optic axis of a biaxial crystal will be transformed to a cone of light and emerge from the crystal as a hollow cylinder as predicted by W. R. Hamilton in 1832 [1] and experimentally observed shortly thereafter by H. Lloyd [2]. Recent renewed interest in the phenomenon has led to the development of a more complete theory, many aspects of which have yet to be experimentally observed.In this contribution, we compare our observations on the free space evolution of a conically diffracted Gaussian beam with the recently advised paraxial theory [3]. The theory was successfully tested for four KGd(WO4)2 biaxial crystals of lengths: 7.40 mm, 16.94 mm, 19.40 mm, and 24.50 mm, in a single-crystal conical diffraction configuration. A collimated beam from a diode laser with λ=635nm was focused to a spot of Ȧ0=13.6 μm (1/e value). For each conical diffraction crystal (CDC) the longitudinal shift, ǻ, the ring radius, R, and the position of the spot with the highest axial intensity, Zf, were measured using a Spiricon SP620U beam profiler on a mechanical travel translation stage. The longitudinal shift was given by ǻ=L(1-1/n2) where n2 is one of the refractive indices of the CDC and had values of 3.78 mm, 8.66 mm, 9.92 mm and 12.52 mm. The measured values were found to be 3.4 mm, 8.6 mm, 9.7 mm and 12.75 mm respectively. The ring radii are proportional to the length of the crystal, L, and are found using R=AL, where A is the semiangle of the cone of conical diffraction. The theoretical values were found to be: 130.23 μm, 298.14 μm 341.33 μm and 431.16 μm for each crystal. The measured values were 130μm, 293μm, 335μm and 430μm respectively. Where λ is the wavelength of the incident beam and Ȧ0 is the radius of the incident beam at the beam waist. The theoretical Zf values were found to be 14.29 mm, 32.72 mm, 37.46 mm and 47.32 mm. The measured values were 16.35 mm, 33.80 mm, 33.45mm and 45.25mm respectively.In addition the evolution of the beam in free space was found by taking images at intervals of 0.5 mm over a range of -66 mm using CDC3 of length 19.4 mm and is shown in Figure 1. All of the reported values were found to be in good agreement with the paraxial theory derived by M. V. Berry [3] and the cross section was found to be in good agreement with the theoretically predicted image produced in [4].

KW - laser beams

KW - crystals

KW - diffraction

KW - optics

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DO - 10.1109/CLEOE-IQEC.2013.6800987

M3 - Conference contribution book

SN - 9781479905942

BT - The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013

PB - IEEE

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Grant SD, Abdolvand A. Evolution of a conically diffracted gaussian beam in free space. In The European Conference on Lasers and Electro-Optics, CLEO_Europe 2013. IEEE. 2014 https://doi.org/10.1109/CLEOE-IQEC.2013.6800987