# Identifying the Contribution of Carrier Shot Noise and Random Carrier Recombination to Excess Frequency Noise in Tunable Lasers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

_{r}is the relaxation oscillation frequency, and Γ is the damping rate of the relaxation oscillation. Typically, semiconductor lasers are under-damped, hence the peak in the FM-noise SD plot. α

_{H}is Henry’s linewidth enhancement factor. The second term on the RHS of (1) describes the excess FM-noise or filtered FM-noise, and has a low-pass type response with cut-off frequency corresponding to the modulation dynamics of the passive tuning section [18,25,26]. It is this type of FM-noise that we are studying in this paper. The third term represents the typical 1/f noise, which is prevalent at low frequencies and is caused by 1/f noise on the drive currents and environmental factors [21,22]. This type of noise depends on the environmental and operating conditions, therefore the value of κ is merely for illustrative purposes. A plot of the full expression in (1) is given by the red curve, showing the excess FM-noise as well as the typical FM-noise of semiconductor lasers. The presence of the excess FM-noise term is typical of DBR-style lasers because the carrier density needed to tune the lasers remains unclamped, and hence carrier density noise transfers directly to the instantaneous frequency noise of the lasers [3,18]. Now that we have given a brief overview of the tuning mechanism and FM-noise characterization, we will numerate the contribution of shot noise to excess FM-noise of DBR-style lasers.

_{T}denoting the refractive index of the tuning section. We have already described Δn due to the shot noise. To estimate for dυ

_{T}/dn

_{T}, we can approximate the lasing frequency if we know the longitudinal mode spacing and longitudinal mode number. Ignoring dispersion in the frequency dependence of the refractive index, the lasing frequency is an integer multiple of the free spectral range (FSR), υ

_{L}= mΔυ

_{FSR}. Δυ

_{FSR}is related to the length and refractive index of the laser, and invoking an approximation in [5], we write:

## 3. Results

## 4. Implications

_{FSR}. However, since the FM-noise SD depends on I

_{0}and the dependency on the refractive index is (dn/dN)

^{2}, it is advantageous to allow an increase in the bias current while enjoying a decrease in the overall FM-noise, though larger input currents will heat up the device more and consideration needs to be given to the contribution of thermal tuning, which counteracts against carrier tuning [25,27]. The only physical parameter that can decrease the $dn/dN$ in (15) is the effective mass of electrons ${m}_{e}^{*}$. This is far from trivial to accomplish, but may be realised through judicious bandgap engineering.

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kikuchi, K. Fundamentals of Coherent Optical Fiber Communications. J. Lightw. Technol.
**2016**, 34, 157–179. [Google Scholar] [CrossRef] - ITU-T G.989.1 Next Generation PON 2 Specification; ITU-T: Geneva, Switzerland, 2013.
- Buus, J.; Amann, M.-C.; Blumenthal, D.J. Tunable Laser Diodes and Related Optical Sources, 2nd ed.; Wiley/SPIE Press/IEEE Press: Hoboken, NJ, USA, 2005; ISBN 0-471-20816-7. [Google Scholar]
- Coldren, L. Monolithic tunable diode lasers. IEEE J. Sel. Top. Quantum Electron.
**2000**, 6, 988–999. [Google Scholar] [CrossRef] - Coldren, L.A.; Corzine, S.W.; Masanovic, M.L. Diode Lasers Photonic Integrated Circuits; Wiley: Hoboken, NJ, USA, 2012; ISBN 978-0-470-48412-8. [Google Scholar]
- Morthier, G.; Vankwikelberge, P. Handbook of Distributed Feedback Laser Diodes, 2nd ed.; Artech House: Norwood, MA, USA, 2013; ISBN 978-1-608807-701-4. [Google Scholar]
- Daiber, A. Narrow-linewidth tunable external cavity laser for coherent communication. In Proceedings of the 2014 IEEE Photonics Conference, San Diego, CA, USA, 12–16 October 2014. [Google Scholar]
- Zhao, H.; Hu, S.; Zhao, J.; Zhu, Y.; Yu, Y.; Barry, L.P. Chirp-Compensated DBR Lasers for TWDM-PON Applications. IEEE Photonics J.
**2015**, 7, 7900809. [Google Scholar] [CrossRef] - Ward, A.; Robbins, D.; Busico, G.; Barton, E.; Ponnampalam, L.; Duck, J.; Whitbread, N.; Williams, P.; Reid, D.; Carter, A.; et al. Widely tunable DS-DBR laser with monolithically integrated SOA: design and performance. IEEE J Sel. Top. Quantum Electron.
**2005**, 11, 149–156. [Google Scholar] [CrossRef] - Wesström, J.-O.; Sarlet, G.; Hammerfeldt, S.; Lundqvist, L.; Szabo, P.; Rigole, P.-J. State-of-the-art performance of widely tunable modulated grating Y-branch lasers. In Proceedings of the Optical Fiber Communication Conference, Los Angeles, CA, USA, 22 February 2004. [Google Scholar]
- O’Dowd, R.; O’Duill, S.; Mulvihill, G.; O’Gorman, N.; Yu, Y. Frequency plan and wavelength switching limits for widely tunable semiconductor transmitters. IEEE J. Sel. Top. Quantum Electron.
**2001**, 7, 259–269. [Google Scholar] [CrossRef] - Yu, Y.; O’Dowd, R. Influence of mode competition on the fast wavelength switching of an SG-DBR laser. J. Lightw. Technol.
**2002**, 20, 700–704. [Google Scholar] - Connolly, E.; Smyth, F.; Mishra, A.K.; Kaszubowska-Anandarajah, A.; Barry, L.P. Cross-Channel Interference Due to Wavelength Drift of Tunable Lasers in DWDM Networks. IEEE Photonics Technol. Lett.
**2007**, 19, 616–618. [Google Scholar] [CrossRef] [Green Version] - Browning, C.; Shi, K.; Ellis, A.D.; Barry, L.P. Optical Burst-Switched SSB-OFDM Using a Fast Switching SG-DBR Laser. J. Opt. Commun. Netw.
**2013**, 5, 994–1000. [Google Scholar] [CrossRef] - Huynh, T.N.; Nguyen, A.T.; Ng, W.-C.; Nguyen, L.; Rusch, L.A.; Barry, L.P. BER Performance of Coherent Optical Communications Systems Employing Monolithic Tunable Lasers with Excess Phase Noise. J. Lightw. Technol.
**2014**, 32, 1973–1980. [Google Scholar] [CrossRef] - Maher, R.; Savory, S.J.; Thomsen, B.C. Fast Wavelength Switching Transceiver for a Virtualized Coherent Optical Network. J. Lightw. Technol.
**2015**, 33, 1007–1013. [Google Scholar] [CrossRef] - Walsh, A.J.; Mountjoy, J.; Shams, H.; Fagan, A.; Ellis, A.D.; Barry, L.P. Highly Robust Dual-Polarization Doubly Differential PSK Coherent Optical Packet Receiver for Energy Efficient Reconfigurable Networks. J. Lightw. Technol.
**2015**, 33, 5218–5226. [Google Scholar] [CrossRef] - Huynh, T.N.; Dúill, S.P.Ó.; Nguyen, L.; Rusch, L.A.; Barry, L.P. Simple analytical model for low-frequency frequency-modulation noise of monolithic tunable lasers. Appl. Opt.
**2014**, 53, 830–835. [Google Scholar] [CrossRef] [PubMed] - Huynh, T.N.; Nguyen, L.; Barry, L.P. Phase Noise Characterization of SGDBR Lasers Using Phase Modulation Detection Method with Delayed Self-Heterodyne Measurements. J. Lightw. Technol.
**2013**, 31, 1300–1308. [Google Scholar] [CrossRef] - Liu, F.; Lin, Y.; Liu, Y.; Anthur, A.P.; Yu, Y.; Barry, L.P. Investigation into the Phase Noise of Modulated Grating Y-Branch Lasers. IEEE J. Sel. Top. Quantum Electron.
**2017**, 23, 1–9. [Google Scholar] [CrossRef] - Amann, M.-C.; Hakimi, R.; Borchert, B.; Illek, S. Linewidth broadening by 1/f noise in wavelength-tunable laser diodes. Appl. Phys. Lett.
**1997**, 70, 1512–1514. [Google Scholar] [CrossRef] - Duan, G.; Gallion, P. Drive current noise induced linewidth in tunable multielectrode lasers. IEEE Photonics Technol. Lett.
**1991**, 3, 302–304. [Google Scholar] [CrossRef] - Henry, C. Theory of the phase noise and power spectrum of a single mode injection laser. IEEE J. Quantum Electron.
**1983**, 19, 1391–1397. [Google Scholar] [CrossRef] - Kikuchi, K. Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers. Opt. Express
**2012**, 20, 5291–5302. [Google Scholar] [CrossRef] - Yu, Y.; Mulvihill, G.; O’Duill, S.; O’Dowd, R. Performance implications of wide-band lasers for FSK modulation labeling scheme. IEEE Photonics Technol. Lett.
**2004**, 16, 39–41. [Google Scholar] - O’Dowd, R.; Yu, Y.; Mulvihill, G.; O’Duill, S.; Morthier, G.; Moeyersoon, B. Transmitters for two-tier optical data-packet labellingin advanced IP networks. IEE Proc. Optoelectron.
**2005**, 152, 163–169. [Google Scholar] [CrossRef] - Mulvihill, G.; O’Dowd, R. Thermal transient measurement, modeling, and compensation of a widely tunable laser for an optically switched network. J. Lightw. Technol.
**2005**, 23, 4101–4109. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Simplified schematic of a tunable distributed Bragg reflector (DBR) laser. (

**b**) Schematic of the tuning mechanism of DBR lasers.

**Figure 2.**Typical FM-noise spectral density (SD) profile of tunable lasers. The blue curve represents a theoretical FM-noise SD curve of semiconductor lasers without any 1/f noise nor excess FM-noise. The red curve shows the FM-noise of monolithic tunable lasers. The excess FM-noise portion is indicated, and this is the portion of the FM-noise curve that we concentrate on in this paper. At lower frequencies below 100 kHz, the 1/f FM-noise dominates the FM-noise spectrum. The green line denotes the sole contribution to 1/f FM-noise. Note that the 1/f FM-Noise is added for illustrative purposes and that log scales were used for both axes.

**Figure 3.**(

**a**) Calculated static carrier density with respect to injected current. (

**b**) Calculated carrier lifetime with respect to injected current. The values of the laser parameters are listed in Table 1.

**Figure 4.**Calculated SD of the carrier fluctuations. The bias current increases from 1 to 10 mA. The horizontal lines indicate analytical calculations of the carrier fluctuations SD. Note: log scales used.

**Figure 5.**Excess FM-noise SD calculations corresponding to the carrier fluctuations in Figure 4. The bias current is increased from 1 to 10 mA. Note: log scales used.

**Figure 6.**Temporal trace of the instantaneous laser frequency fluctuations, with the tuning current set to 10 mA and using the parameters in Table 1. The instantaneous frequency can vary by in excess of 50 MHz.

Symbol | Quantity | Value and Units |
---|---|---|

A | Shockley–Read–Hall recombination coefficient | 8 × 10^{8} s^{−1} |

B | Bimolecular recombination coefficient | 1 × 10^{−17} m^{3}/s |

C | Auger recombination coefficient | 1 × 10^{−41} m^{6}/s |

e | Quantum of electronic charge | 1.6 × 10^{−19} C |

V | Volume of tuning section | 10 × 10^{−18} m^{3} |

n_{eq} | Equivalent refractive index of laser other than the tuning section | 3.5 |

L_{eq} | Equivalent length of laser excluding the tuning section | 1 mm |

n_{T} | Refractive index of tuning section | 3.5 |

$\kappa $ | Strength of 1/f FM noise | 1 × 10^{10} s |

L_{T} | Length of tuning section | 100 µm |

${\upsilon}_{{L}_{0}}$ | Lasing wavelength with n_{T} = 3.5 | 193.00 THz |

${m}_{e}^{*}$ | Equivalent effective mass of electrons in InGaAsP | 0.02 × 9.1 × 10^{−31} kg |

${\epsilon}_{0}$ | Permittivity of free space | 8.85 × 10^{−12} F/m |

K | Excess refractive index factor | 4 |

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**MDPI and ACS Style**

O’Duill, S.; Lin, Y.; Barry, L.
Identifying the Contribution of Carrier Shot Noise and Random Carrier Recombination to Excess Frequency Noise in Tunable Lasers. *Photonics* **2019**, *6*, 4.
https://doi.org/10.3390/photonics6010004

**AMA Style**

O’Duill S, Lin Y, Barry L.
Identifying the Contribution of Carrier Shot Noise and Random Carrier Recombination to Excess Frequency Noise in Tunable Lasers. *Photonics*. 2019; 6(1):4.
https://doi.org/10.3390/photonics6010004

**Chicago/Turabian Style**

O’Duill, Sean, Yi Lin, and Liam Barry.
2019. "Identifying the Contribution of Carrier Shot Noise and Random Carrier Recombination to Excess Frequency Noise in Tunable Lasers" *Photonics* 6, no. 1: 4.
https://doi.org/10.3390/photonics6010004