Abstract

A fast and accurate measurement technique employing a calibrated CCD array is described to measure the intensity and phase distributions of the asymmetric mode profiles associated with optical waveguides. A Shack–Hartmaan wavefront sensor incorporated in the system provides the phase information. The transform describing the near-field (NF) to far-field (FF) transitions of the asymmetric mode profiles is investigated both experimentally and theoretically. The simulated NF to FF transitions using the transform are compared with the measured profiles at different positions from the end face of the waveguide. Good agreement is obtained between the measured and the computed profiles proving the accuracy of the measurement technique and also the transform used for propagation of the asymmetric mode profiles.

© 2008 Optical Society of America

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References

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  1. K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120-1124 (1986).
    [CrossRef]
  2. L. McCaughan and E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241-244 (1983).
    [CrossRef]
  3. W. T. Anderson and D. L. Philen, “Spot size measurements for single-mode fibers--a comparison of four techniques,” J. Lightwave Technol. 1, 20-26 (1983).
    [CrossRef]
  4. M. Artiglia, G. Coppa, P. D. Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139-1152 (1989).
    [CrossRef]
  5. F. M. E. Sladen, D. N. Payne, and M. J. Adams, “Determination of optical fiber refractive index profiles by a near-field scanning technique,” Appl. Phys. Lett. 28, 255-258 (1976).
    [CrossRef]
  6. “Optical fibres--measurement methods and test procedures--mode field diameter,” IEC 60793-1-45, ed. 1.0, Method C, (IEC, 2001).
  7. I. Fatadin, D. Ives, and M. Wicks, “Accurate magnified near-field measurement of optical waveguides using a calibrated CCD camera,” J. Lightwave Technol. 24, 5067-5074 (2006).
    [CrossRef]
  8. A. J. Parker, “Near field measurement of fiber mode field diameters: effects of defocusing,” IEEE Trans. Instrum. Meas. 44, 458-460 (1995).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics (Pergamon, 1998).
  10. A. J. Parker and K. W. Raine, “An investigation into the performance of microscope objectives with near infrared light,” Meas. Sci. Technol. 2, 159-163 (1991).
    [CrossRef]
  11. J. E. Geary, Wavefront Sensors, (SPIE Press, 1995) Vol. TT18.
    [CrossRef]
  12. A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).
  13. M. Brucksch, M. Frohlich, W. Sohler, E. Strake, R. Volk, and H. Ziegler, “Two-dimensional measurement of intensity distributions of optical modes of Ti:LiNbO3 channel waveguides and comparison with numerically calculated results,” Proc. SPIE 651, 246-251 (1986).

2006

1995

A. J. Parker, “Near field measurement of fiber mode field diameters: effects of defocusing,” IEEE Trans. Instrum. Meas. 44, 458-460 (1995).
[CrossRef]

1991

A. J. Parker and K. W. Raine, “An investigation into the performance of microscope objectives with near infrared light,” Meas. Sci. Technol. 2, 159-163 (1991).
[CrossRef]

1989

M. Artiglia, G. Coppa, P. D. Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

1986

K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120-1124 (1986).
[CrossRef]

M. Brucksch, M. Frohlich, W. Sohler, E. Strake, R. Volk, and H. Ziegler, “Two-dimensional measurement of intensity distributions of optical modes of Ti:LiNbO3 channel waveguides and comparison with numerically calculated results,” Proc. SPIE 651, 246-251 (1986).

1983

L. McCaughan and E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241-244 (1983).
[CrossRef]

W. T. Anderson and D. L. Philen, “Spot size measurements for single-mode fibers--a comparison of four techniques,” J. Lightwave Technol. 1, 20-26 (1983).
[CrossRef]

1976

F. M. E. Sladen, D. N. Payne, and M. J. Adams, “Determination of optical fiber refractive index profiles by a near-field scanning technique,” Appl. Phys. Lett. 28, 255-258 (1976).
[CrossRef]

Appl. Phys. Lett.

F. M. E. Sladen, D. N. Payne, and M. J. Adams, “Determination of optical fiber refractive index profiles by a near-field scanning technique,” Appl. Phys. Lett. 28, 255-258 (1976).
[CrossRef]

IEEE Trans. Instrum. Meas.

A. J. Parker, “Near field measurement of fiber mode field diameters: effects of defocusing,” IEEE Trans. Instrum. Meas. 44, 458-460 (1995).
[CrossRef]

J. Lightwave Technol.

K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120-1124 (1986).
[CrossRef]

L. McCaughan and E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241-244 (1983).
[CrossRef]

W. T. Anderson and D. L. Philen, “Spot size measurements for single-mode fibers--a comparison of four techniques,” J. Lightwave Technol. 1, 20-26 (1983).
[CrossRef]

M. Artiglia, G. Coppa, P. D. Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

I. Fatadin, D. Ives, and M. Wicks, “Accurate magnified near-field measurement of optical waveguides using a calibrated CCD camera,” J. Lightwave Technol. 24, 5067-5074 (2006).
[CrossRef]

Meas. Sci. Technol.

A. J. Parker and K. W. Raine, “An investigation into the performance of microscope objectives with near infrared light,” Meas. Sci. Technol. 2, 159-163 (1991).
[CrossRef]

Proc. SPIE

M. Brucksch, M. Frohlich, W. Sohler, E. Strake, R. Volk, and H. Ziegler, “Two-dimensional measurement of intensity distributions of optical modes of Ti:LiNbO3 channel waveguides and comparison with numerically calculated results,” Proc. SPIE 651, 246-251 (1986).

Other

J. E. Geary, Wavefront Sensors, (SPIE Press, 1995) Vol. TT18.
[CrossRef]

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1998).

“Optical fibres--measurement methods and test procedures--mode field diameter,” IEC 60793-1-45, ed. 1.0, Method C, (IEC, 2001).

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Figures (7)

Fig. 1
Fig. 1

Confocal focusing mode setup.

Fig. 2
Fig. 2

Measurement setup for intensity and phase distributions in the NF to FF transitions.

Fig. 3
Fig. 3

Two-dimensional mode profile for a Ti : LiNbO 3 waveguide measured from the magnified NF system.

Fig. 4
Fig. 4

Intensity profiles parallel and perpendicular to the substrate surface showing a sidelobe at point S.

Fig. 5
Fig. 5

Measured and simulated intensity contour plots at different propagation distances, z, in the NF to FF transitions. Each panel is 75 × 75 μm .

Fig. 6
Fig. 6

(a) Intensity and (b) phase profiles parallel and perpendicular to the substrate surface in the FF limit obtained by taking the Fourier transform.

Fig. 7
Fig. 7

Simulated and measured phase profiles across the peak intensity perpendicular to the substrate surface compared at propagation distances (a)  z = 100 μm and (b)  z = 200 μm .

Equations (12)

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R = 0.61 · λ NA ,
ϕ ( x , y ) = θ x ( x , y ) i ^ + θ y ( x , y ) j ^ ,
ϕ x = θ x , ϕ y = θ y ,
G x , y , z = 0 = 2 π 1 w exp [ ( x 2 + y 2 ) w 2 ] ,
G x , y , z = 2 λ Im ( 1 z i π λ w 2 ) exp [ i π ( x 2 + y 2 ) λ ( z i π λ w 2 ) ] .
F { Ψ x , y , z } = F { Ψ x , y , z = 0 } × F { G x , y , z } F { G x , y , z = 0 } ,
A exp [ ( x 2 + y 2 ) σ 2 ] F A σ 2 π N 2 exp [ ( u 2 + v 2 ) σ 2 π 2 N 2 ] ,
F { G x , y , z = 0 } = 2 π w π M 2 N 2 exp [ ( u 2 + v 2 ) w 2 π 2 M 2 N 2 ] ,
F { G x , y , z } = 2 λ ( π w 2 λ z 2 + π 2 w 4 λ 2 ) ( i λ z + w 2 π M 2 N 2 ) exp [ ( u 2 + v 2 ) ( i λ z π + ( w π ) 2 ) M 2 N 2 ] ,
F { G x , y , z } F { G x , y , z = 0 } = i × exp [ ( u 2 + v 2 ) i λ z π M 2 N 2 ] .
I x , y , z = Ψ x , y , z × Ψ x , y , z * ,
Ψ ˜ FF ( u , v ) = Ψ NF ( x , y ) e i [ x u + y v ] d x d y ,

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