## Limitation and improvement in the performance of recirculating delayed self-heterodyne method for high-resolution laser lineshape measurement |

Optics Express, Vol. 20, Issue 11, pp. 11679-11687 (2012)

http://dx.doi.org/10.1364/OE.20.011679

Acrobat PDF (2097 KB)

### Abstract

This paper presents a detailed analysis of the performance of a recirculating delayed self-heterodyne (R-DSH) method for high-resolution laser lineshape measurement. For increasing the delay time the R-DSH method utilizes circulation of light in a heterodyne ring interferometer (HRI) containing a frequency shifter, delay fiber, and fiber amplifier. It is shown both theoretically and experimentally that unwanted higher order frequency-shifted components induce distortion in the beat signal spectra, which significantly limits the maximum number of circulations. An effective technique is proposed and demonstrated for reducing the distortion by using optical filtering at the HRI output. Furthermore, a practical limit on the number of circulations is investigated by comparing the shape of observed beat signal spectra with theory. It is shown that the maximum delay is limited to about 180 km even with the use of the optical filtering technique.

© 2012 OSA

## 1. Introduction

2. M. Alalusi, P. Brasil, S. Lee, P. Mols, L. Stolpner, A. Mehnert, and S. Li, “Low noise planar external cavity laser for interferometric fiber optic sensors,” Proc. SPIE **7316**, 73160X (2009). [CrossRef]

3. K. Numata, J. Camp, M. A. Krainak, and L. Stolpner, “Performance of planar-waveguide external cavity laser for precision measurements,” Opt. Express **18**(22), 22781–22788 (2010). [CrossRef] [PubMed]

4. J. Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photon. Technol. Lett. **17**(9), 1827–1829 (2005). [CrossRef]

5. A. Suzuki, Y. Takahashi, M. Yoshida, and M. Nakazawa, “An ultralow noise and narrow linewidth λ/4-shifted DFB Er-doped fiber laser with a ring cavity configuration,” IEEE Photon. Technol. Lett. **19**(19), 1463–1465 (2007). [CrossRef]

*et al.*in 1980 [6

6. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. **16**(16), 630–631 (1980). [CrossRef]

7. O. Ishida, “Novel method of estimation flicker frequency noise in lasers,” IEEE Photon. Technol. Lett. **2**(11), 784–786 (1990). [CrossRef]

8. H. Tsuchida, “Laser frequency modulation noise measurement by recirculating delayed self-heterodyne method,” Opt. Lett. **36**(5), 681–683 (2011). [CrossRef] [PubMed]

9. H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photon. Technol. Lett. **23**(11), 727–729 (2011). [CrossRef]

10. H. Tsuchida, “Simple technique for improving the resolution of the delayed self-heterodyne method,” Opt. Lett. **15**(11), 640–642 (1990). [CrossRef] [PubMed]

*et al.*[11

11. J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. **4**(9), 1063–1066 (1992). [CrossRef]

11. J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. **4**(9), 1063–1066 (1992). [CrossRef]

*etc.*, leading to a decrease in measurement accuracy. To address this issue, beat signal spectra measured for various delays are compared with the theoretical spectra that are calculated from the FM noise PSD [9

9. H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photon. Technol. Lett. **23**(11), 727–729 (2011). [CrossRef]

## 2. Influence of higher-order frequency-shifted components - Theory

*f*

_{s}and a delay

*τ*

_{d}and is amplified to compensate for the propagation, coupling, and insertion losses. The EDFA gain is adjusted to prevent the self-oscillation of the HRI. Therefore, the laser light after

*n*-times (

*n*is an integer) circulation in the HRI has the relative frequency shift and delay of

*nf*

_{s}and

*nτ*

_{d}, respectively, with respect to the input light. At the PD output multiple heterodyne beat signals with the frequency of

*nf*

_{s}are generated simultaneously, which can be separately detected and analyzed with an RF spectrum analyzer. As compared with the conventional DSH method,

*n*-times enhancement in the delay time is realized by detecting the beat signal at

*nf*

_{s}.

*nf*

_{s}is generated mainly from the LO light and the frequency-shifted component after

*n*-times circulation, there are additional contributions from the pairs of the frequency-shifted components with the frequency difference of

*nf*

_{s}. In the following, a theoretical analysis is presented for evaluating the distortion of the beat signal spectra arising from these unwanted frequency-shifted components.

*E*(

_{k}*k*= 0, 1, 2, …) represents the amplitude of each light. As shown in Fig. 1(b), the heterodyne beat signal at frequency

*nf*

_{s}is generated not only from the mixing of the LO and frequency-shifted components at

*ν*

_{0}and

*ν*

_{0}+

*nf*

_{s}, respectively, but also from the mixing of the higher-order frequency-shifted components such as those with frequencies of

*ν*

_{0}+

*f*

_{s}and

*ν*

_{0}+ (

*n*+ 1)

*f*

_{s}.

*I*

_{DSH}(

*t*) at the PD output is given bywhere

*ξ*represents the PD responsivity. To simplify the calculation I proceed with a phasor representation of Eq. (3) expressed asThe ACF

*R*

_{DSH}(

*τ*) of Eq. (4) is given byIt is convenient to express the ACF

*R*

_{DSH}(

*f*) in terms of the FM noise PSD

*S*(

_{ν}*f*) given by Eq. (1) [8

8. H. Tsuchida, “Laser frequency modulation noise measurement by recirculating delayed self-heterodyne method,” Opt. Lett. **36**(5), 681–683 (2011). [CrossRef] [PubMed]

9. H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photon. Technol. Lett. **23**(11), 727–729 (2011). [CrossRef]

12. K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor-laser linewidth residual in high-power limit,” IEEE J. Quantum Electron. **25**(4), 684–688 (1989). [CrossRef]

*S*

_{DSH}(

*f*) can be calculated by Fourier transforming

*R*

_{DSH}(

*τ*) asEquations (6) and (7) state that beat signal spectra

*S*

_{DSH}(

*f*) can be derived from FM noise PSD

*S*(

_{ν}*f*), which will be used to calculate the theoretical spectra in the next sections.

*S*

_{R-DSH}(

*f*) observed with the R-DSH method taking account of the contribution from the higher-order frequency-shifted components, and relate it to the

*S*

_{DSH}(

*f*) observed with the DSH method. For simplicity, I consider only the lowest order contribution resulting from the mixing of the frequency-shifted components with frequencies

*ν*

_{0}+

*f*

_{s}and

*ν*

_{0}+ (

*n*+ 1)

*f*

_{s}. The phasor of the beat signal is given by

*R*

_{R-DSH}(

*τ*) of Eq. (8) can be expressed in terms of the ACF

*R*

_{DSH}(

*τ*) of Eq. (6) by

*S*

_{R-DSH}(

*f*) corresponding to Eq. (9) is given byThe second and third terms in the parenthesis represent the contributions from the higher-order frequency-shifted components. The second term is a constant and does not change the spectral shape, whereas the third term represents the distortion that modulates the spectrum with a period of the reciprocal of the single-path delay time

*τ*

_{d}. The modulation amplitude depends on the electric field amplitudes of the lights that contribute to beat signal generation. For reducing the spectrum distortion, it is necessary to remove higher-order frequency-shifted components (

*E*

_{1}and

*E*

_{n + 1}in Eq. (10)), which will be described in Section 4.

## 3. Influence of higher-order frequency-shifted components - Experiment

2. M. Alalusi, P. Brasil, S. Lee, P. Mols, L. Stolpner, A. Mehnert, and S. Li, “Low noise planar external cavity laser for interferometric fiber optic sensors,” Proc. SPIE **7316**, 73160X (2009). [CrossRef]

3. K. Numata, J. Camp, M. A. Krainak, and L. Stolpner, “Performance of planar-waveguide external cavity laser for precision measurements,” Opt. Express **18**(22), 22781–22788 (2010). [CrossRef] [PubMed]

^{7}. These values were evaluated from the measured FM noise PSD using the R-DSH method [9

**23**(11), 727–729 (2011). [CrossRef]

*n*= 1 in Eq. (10), where curves with red and blue lines correspond to the theoretical (Eq. (12) shown below) and experimental results, respectively. The total delay of the HRI is adjusted so that the product

*f*

_{s}

*τ*

_{d}is nearly equal to a positive integer. In this case Eq. (10) reduces toEquation (12) indicates that the magnitude of spectrum distortion depends on the ratio

*E*

_{2}/

*E*

_{0}. The curves A - E in Fig. 2(a) represent the results for different values of

*E*

_{2}/

*E*

_{0}, which is adjusted by changing the gain of the EDFA. The values

*E*

_{0}and

*E*

_{2}are estimated by observing the HRI output with a scanning Fabry-Perot interferometer. It can be seen that the undulation of the beat signal spectra increases with increasing the EDFA gain and that the experiment results agree well with the theoretical calculation. From these results it can be concluded that there is a restriction in the EDFA gain in order to avoid spectrum distortion, which limits the maximum number of circulation in the lineshape measurement using the R-DSH method, which will be discussed in Section 5.

## 4. Reduction of spectrum distortion by optical filtering

*nf*

_{s}can be used for selectively transmitting the lights with the frequencies of

*ν*

_{0}and

*ν*

_{0}+

*nf*

_{s}while rejecting other frequency-shifted components. For stable operation the resonant frequency of the interferometer should be locked to that of the incident light. This scheme is not suitable when the number

*n*of circulations is small, because higher order frequency-shifted components at

*ν*

_{0}+

*knf*

_{s}(

*k*= 2, 3, …) are transmitted at the same time. Moreover, this configuration is not flexible due to the difficulty in tuning the free spectral range over wide frequency range.

## 5. Estimation of the maximum delay

8. H. Tsuchida, “Laser frequency modulation noise measurement by recirculating delayed self-heterodyne method,” Opt. Lett. **36**(5), 681–683 (2011). [CrossRef] [PubMed]

**23**(11), 727–729 (2011). [CrossRef]

12. K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor-laser linewidth residual in high-power limit,” IEEE J. Quantum Electron. **25**(4), 684–688 (1989). [CrossRef]

13. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. **15**(23), 1351–1353 (1990). [CrossRef] [PubMed]

14. M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. **4**(11), 1269–1272 (1992). [CrossRef]

**23**(11), 727–729 (2011). [CrossRef]

## 6. Summary

## References and links

1. | M. Seimetz, |

2. | M. Alalusi, P. Brasil, S. Lee, P. Mols, L. Stolpner, A. Mehnert, and S. Li, “Low noise planar external cavity laser for interferometric fiber optic sensors,” Proc. SPIE |

3. | K. Numata, J. Camp, M. A. Krainak, and L. Stolpner, “Performance of planar-waveguide external cavity laser for precision measurements,” Opt. Express |

4. | J. Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photon. Technol. Lett. |

5. | A. Suzuki, Y. Takahashi, M. Yoshida, and M. Nakazawa, “An ultralow noise and narrow linewidth λ/4-shifted DFB Er-doped fiber laser with a ring cavity configuration,” IEEE Photon. Technol. Lett. |

6. | T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. |

7. | O. Ishida, “Novel method of estimation flicker frequency noise in lasers,” IEEE Photon. Technol. Lett. |

8. | H. Tsuchida, “Laser frequency modulation noise measurement by recirculating delayed self-heterodyne method,” Opt. Lett. |

9. | H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photon. Technol. Lett. |

10. | H. Tsuchida, “Simple technique for improving the resolution of the delayed self-heterodyne method,” Opt. Lett. |

11. | J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. |

12. | K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor-laser linewidth residual in high-power limit,” IEEE J. Quantum Electron. |

13. | J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. |

14. | M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(140.2020) Lasers and laser optics : Diode lasers

(120.3688) Instrumentation, measurement, and metrology : Lightwave analyzers

(060.2840) Fiber optics and optical communications : Heterodyne

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: April 17, 2012

Revised Manuscript: May 2, 2012

Manuscript Accepted: May 2, 2012

Published: May 7, 2012

**Citation**

Hidemi Tsuchida, "Limitation and improvement in the performance of recirculating delayed self-heterodyne method for high-resolution laser lineshape measurement," Opt. Express **20**, 11679-11687 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-11679

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### References

- M. Seimetz, High-Order Modulation for Optical Fiber Transmission (Springer, 2009), Chap. 7.
- M. Alalusi, P. Brasil, S. Lee, P. Mols, L. Stolpner, A. Mehnert, and S. Li, “Low noise planar external cavity laser for interferometric fiber optic sensors,” Proc. SPIE7316, 73160X (2009). [CrossRef]
- K. Numata, J. Camp, M. A. Krainak, and L. Stolpner, “Performance of planar-waveguide external cavity laser for precision measurements,” Opt. Express18(22), 22781–22788 (2010). [CrossRef] [PubMed]
- J. Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photon. Technol. Lett.17(9), 1827–1829 (2005). [CrossRef]
- A. Suzuki, Y. Takahashi, M. Yoshida, and M. Nakazawa, “An ultralow noise and narrow linewidth λ/4-shifted DFB Er-doped fiber laser with a ring cavity configuration,” IEEE Photon. Technol. Lett.19(19), 1463–1465 (2007). [CrossRef]
- T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett.16(16), 630–631 (1980). [CrossRef]
- O. Ishida, “Novel method of estimation flicker frequency noise in lasers,” IEEE Photon. Technol. Lett.2(11), 784–786 (1990). [CrossRef]
- H. Tsuchida, “Laser frequency modulation noise measurement by recirculating delayed self-heterodyne method,” Opt. Lett.36(5), 681–683 (2011). [CrossRef] [PubMed]
- H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photon. Technol. Lett.23(11), 727–729 (2011). [CrossRef]
- H. Tsuchida, “Simple technique for improving the resolution of the delayed self-heterodyne method,” Opt. Lett.15(11), 640–642 (1990). [CrossRef] [PubMed]
- J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett.4(9), 1063–1066 (1992). [CrossRef]
- K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor-laser linewidth residual in high-power limit,” IEEE J. Quantum Electron.25(4), 684–688 (1989). [CrossRef]
- J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett.15(23), 1351–1353 (1990). [CrossRef] [PubMed]
- M. Murakami and S. Saito, “Evolution of field spectrum due to fiber-nonlinearity-induced phase noise in in-line optical amplifier systems,” IEEE Photon. Technol. Lett.4(11), 1269–1272 (1992). [CrossRef]

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