Abstract

We have proposed and demonstrated a novel measurement technique for characterizing nonlinear frequency sweep in high-speed tunable laser sources by using a simple self- homodyne setup and Hilbert transformation. Measurement results, such as the variation in frequency scanning rate during a frequency sweeping process, are presented for a temperature-tuned distributed feedback laser diode and external cavity tunable laser. The time-varying optical phase of the incident light of a laser is calculated from the integration of the instantaneous optical frequency, and the tuning rate is obtained from its derivative.

© 2007 Optical Society of America

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References

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  1. R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
    [CrossRef]
  2. M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
    [CrossRef]
  3. N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
    [CrossRef]
  4. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, "High-speed optical frequency-domain imaging," Opt. Express 11, 2953-2963 (2003).
    [CrossRef] [PubMed]
  5. T.-J. Ahn and D. Kim, "High-resolution differential mode delay measurement for a multimode optical fiber using a modified optical frequency domain reflectometer," Opt. Express 13, 8256-8262 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-8256.
    [CrossRef] [PubMed]
  6. T.-J. Ahn, S. Moon, Y. Youk, Y. Jung, K. Oh, and D. Kim, "New optical frequency domain differential mode delay measurement method for a multimode optical fiber," Opt. Express 13, 4005-4011 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-4005.
    [CrossRef] [PubMed]
  7. B. Boggs, C. Greiner, T. Wang, H. Lin, and T. W. Mossberg, "Simple high-coherence rapidly tunable external-cavity diode laser," Opt. Lett. 23, 1906-1908 (1998).
    [CrossRef]
  8. K. S. Repasky and J. L. Carlsten, "Simple method for measuring frequency chirps with a Fabry-Perot interferometer," Appl. Opt. 39, 5500-5504 (2000).
    [CrossRef]
  9. T.-J. Ahn, J. Y. Lee, and D. Y. Kim, "Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation," Appl. Opt. 44, 7630-7634 (2005).
    [CrossRef] [PubMed]
  10. U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," J. Lightwave Technol. 11, 1377-1384 (1993).
    [CrossRef]
  11. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).
  12. "Hilbert transform," Wikipedia, (2005), Answers.com (28 July 2006), http://www.answers.com/topic/hilbert-transform.
  13. "Continuous Fourier transform," Wikipedia, (2005), Answers.com (28 July 2006), http://www.answers.com/topic/continuous-fourier-transform.

2005 (3)

2003 (1)

2002 (1)

N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
[CrossRef]

2001 (1)

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

2000 (1)

1998 (1)

1994 (1)

R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
[CrossRef]

1993 (1)

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

Ahn, T.-J.

Boggs, B.

Bouma, B. E.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

Brinkmeyer, E.

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

Carlsten, J. L.

de Boer, J. F.

Gilgen, H. H.

R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
[CrossRef]

Gisin, N.

R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
[CrossRef]

Glombitza, U.

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

Greiner, C.

Iftimia, N.

Ito, H.

N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
[CrossRef]

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

Jung, Y.

Kim, D.

Kim, D. Y.

Lee, J. Y.

Lin, H.

Moon, S.

Mossberg, T. W.

Nakamura, K.

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

Namibhira, Y.

N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
[CrossRef]

Oh, K.

Passy, R.

R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
[CrossRef]

Repasky, K. S.

Tearney, G. J.

von der Weid, J. P.

R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
[CrossRef]

Wang, T.

Yoshida, M.

N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
[CrossRef]

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

Youk, Y.

Yun, S. H.

Zou, N.

N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

N. Zou, M. Yoshida, Y. Namibhira, and H. Ito, "PMD measurement based on delayed self- heterodyne OFDR and experimental comparison with ITU-T round-robin measurements," Electron. Lett. 38, 115-116 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

J. Lightwave Technol. (2)

R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, "Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources," J. Lightwave Technol. 12, 1622-1630 (1994).
[CrossRef]

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Other (3)

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

"Hilbert transform," Wikipedia, (2005), Answers.com (28 July 2006), http://www.answers.com/topic/hilbert-transform.

"Continuous Fourier transform," Wikipedia, (2005), Answers.com (28 July 2006), http://www.answers.com/topic/continuous-fourier-transform.

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Figures (7)

Fig. 1
Fig. 1

Schematic of a Michelson-type fiber interferometer for optical frequency chirp measurement of the temperature-tuned DFB-LD (3 dB, 50% fiber coupler; LO, local oscillator; Ref., reference arm; PC, polarization controller; D, detector; DAQ, data acquisition board; Trig., trigger signal).

Fig. 2
Fig. 2

Optical frequency variation with respect to time of the DFB-LD on the temperature tuning by TEC controller and its frequency tuning rate obtained by the derivative of the frequency variation.

Fig. 3
Fig. 3

(a) Actual spectrum of the beating signal in the interferometer, as shown in Fig. 1, based on the DFB-LD with temperature tuning (round-trip time delay, 5 ns) and (b) calculated beating spectrum by use of the recovered optical phase through the integral of the optical frequency variation as presented in Fig. 2. All spectra are normalized by the maximum intensity.

Fig. 4
Fig. 4

Measured phases of beating signals and corresponding instantaneous frequencies of a temperature-tuned DFB-LD for various tuning conditions. (Input amplitudes of the sawtooth waveform from the function generator: 400–2000 mV with the span of 200 mV ).

Fig. 5
Fig. 5

(a) Optical frequency variation of the DFB-LD during the frequency-tuning process for various repetition rates of the sawtooth waveform (200, 250, 340, and 500 mHz ). (b) Time-varying frequency-tuning rates of a temperature-tuned DFB-LD with respect to the repetition rates of the waveform.

Fig. 6
Fig. 6

(a) Beating spectrum with respect to beating frequency of the external cavity TLS (Agilent 81640A) with the set tuning rate of 5 nm / s ( 626.37 GHz / s ) . Difference in frequency between main and side peaks is approximately 200   Hz , whereas the difference between small peaks is approximately 50   Hz . Inset represents the original beating signal, which is chirped. (b) Optical frequency variation with respect to time of the external cavity TLS obtained by Hilbert transform of the beating signal, as shown in the inset of (a).

Fig. 7
Fig. 7

Time-varying frequency tuning rate of the TLS during wavelength sweeping. The mean value of the data is approximately 613.0   GHz / s for a set tuning rate of 626.37   GHz / s   ( 5   nm / s ) .

Equations (12)

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y ( t ) = y 0 sin ( φ ( t ) φ ( t τ ) + ξ 0 ) ,
S ^ ( t ) = HT { s ( t ) } = p ( t ) s ( t ) = 1 π s ( τ ) t τ d τ ,
P ˜ ( f ) = FT { h ( t ) } = + j , f o r f < 0
= j , f o r f > 0.
FT { S ^ ( t ) } = P ˜ ( f ) S ˜ ( f ) ,
sin ( 2 π f 0 t ) FT δ ( f f 0 ) δ ( f + f 0 ) 2 j , cos ( 2 π f 0 t ) FT δ ( f f 0 ) + δ ( f + f 0 ) 2 ,
FT { S ^ ( t ) } = j δ ( f f 0 ) j δ ( f + f 0 ) 2 j = δ ( f f 0 ) + δ ( f + f 0 ) 2 ,
HT { y ( t ) } = y 0 cos ( 2 π τ ν ( t ) + ξ 0 ) ,
Φ ( t ) = 2 π τ ν ( t ) + ξ 0 = tan 1 [ y ( t ) / HT { y ( t ) } ] .
ν ( t ) = 1 2 π n c Δ L [ tan 1 ( y ( t ) / HT { y ( t ) } ) ξ 0 ] ,
φ ( t ) = 2 π ν ( t ) d t .
ν ( t ) = A + B 1 t + B 2 t 2 + B 3 t 3 ,

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