Query: “Phase noise and spectral line shape in semiconductor lasers

Candidate papers:

abstract: Experimental results concerning the study of phase noise in single mode semiconductor lasers are reported, which show a strict connection between phase and intensity noise. In particular, phase noise spectrum is found to present a sharp peak at the same peak frequency of intensity noise spectrum, a fact which is proven to be responsible for the appearance of satellite peaks in the emission line shape. Direct measurements of the line shape, performed by means of a Fabry Perot interferometer, are in agreement with the line shape evaluated by using phase noise spectrum measurements.
author_names: Benedetto Daino

Paolo Spano

Mario Tamburrini

Sabino Piazzolla
title: Phase noise and spectral line shape in semiconductor lasers
year: 1983

abstract: In this paper, we present a full analysis of noise in semiconductor lasers. Time covariance and cross covariance functions of all variables governing single mode semiconductor laser behavior are given including all Langevin noise sources and considering all terms of the laser rate equations, RIN, carrier noise spectrum, frequency noise spectrum, coherence between the FM and AM noise, variance of the phase change and coupling between amplitude and phase are investigated analytically in their more general form. Spectral line shape has been derived showing dissymmetrical satellite lines centered at multiple integers of relaxation frequency around a central line. It is shown that neglecting the shot noise and considering only the carrier contribution in phase dynamics (common procedure) are too general approximations.
author_names: Lotfi Hassine

Zeno Toffano

Francoise Lamnabhi-Lagarrigue

Alain Destrez

Irene Joindot
title: Volterra functional series expansions for noise in semiconductor lasers
year: 1994

abstract: This paper considers the effect of phase conjugate feedback (PCF) on the noise characteristics of semiconductor lasers. By using the single mode, rate equation formalism, it is shown that semiconductor lasers can achieve a steady state as long as the amount of PCF is below a critical value. For an ideal phase conjugate mirror, the average value of the steady state phase of the semiconductor laser is found to be locked to a fixed value, determined by the linewidth enhancement factor of the laser. The noise characteristics in the presence of PCF are studied by adding the Langevin noise terms representing the effect of spontaneous emission to the rate equations and solving them approximately. Both the intensity noise and the frequency noise are reduced at low frequencies (below 100 MHz) In particular, the frequency noise nearly vanishes at zero frequency because of the phase locked nature of the steady state solution. The spectral line shape does not remain Lorentzian in the presence of PCF. The satellite peaks occurring at the relaxation oscillation frequency are considerably enhanced because of a reduction in the damping rate of such oscillations.
title: Effect of phase conjugate feedback on the noise characteristics of semiconductor lasers.
venue: Physical review. A, Atomic, molecular, and optical physics
year: 1992

abstract: Continuous phase frequency shift keying (CPFSK) is a promising technique for optical communication systems using either coherent or direct detection since it utilizes direct modulation of the semiconductor lasers [1 4] More importantly, the CPFSK signal features a compact spectrum which is necessary for the implementation of an optical frequency division multiplexing (FDM) network [1 2] Knowledge of the spectral density for optical CPFSK signals corrupted by laser phase noise is essential for the design and analysis of CPFSKbased systems, for example, the crosstalk analysis for optical FDM systems using coherent detection [1] or direct detection [2] the analysis of nonlinear effects [3] and the receiver filter design [4] The spectrum was previously obtained by means of numerical convolution of the CPFSK spectrum without phase noise and the laser spectrum with Lorentzian line shape [1 3] In this paper, closed analytical expressions are derived for the power spectral density of optical CPFSK signals with an arbitrary laser linewidth. They are useful for the design and analysis of optical communication systems using CPFSK modulation. where RF(t) is the autocorrelation function of the CPFSK signal without phase noise. Dn is the laser full width half maximum (FWHM) linewidth (without CPFSK modulation) A Lorentzian laser line shape is assumed.
author_names: Q Jiang

Mohsen Kavehrad
title: Spectral Density Function of Optical CPFSK Signals in the Presence of Laser Phase Noise
year: 1994

abstract: We consider the performance of quadratically detected heterodyned lightwave signals in the presence of a laser's relaxation oscillations. Here the limiting form of the channel presents both additive white Gaussian noise (AWGN) of spectral density N/sub 0/ and the laser's phase noise. The widely accepted model for the laser's phase noise is a Brownian motion giving rise to a Lorentzian line spectrum. However, the actual line shape of semiconductor lasers deviates from this simplified and idealized statistical characterization. The analytical techniques provided here show that this deviation may have a significant impact on the communication system performance.
author_names: Yeheskel E Dallal

Gunnar Jacobsen

Shlomo Shamai
title: On the impact of laser's relaxation oscillation on quadratically detected heterodyned lightwave signals
venue: Proceedings of 1995 IEEE International Symposium on Information Theory
year: 1995

abstract: This article reports on extensive investigations of the influence of external optical feedback (OFB) on the spectral line shape and the associated spectra of relative intensity noise (RIN) and frequency noise (FN) in semiconductor lasers. The study is based on a generalized simulation model that treats the OFB as a multiple roundtrip time delay of the lasing field in the external cavity. We present criteria to apply the famous Lang Kobayashi model to predict the operation characteristics of lasers under OFB. The accuracy of approximated models of calculating the spectral linewidth from the low frequency components of the frequency noise is examined. We characterize the spectral line shape and the spectra of the RIN and FN in five distinct operating regions, namely, continuous wave (cw) weak OFB induced pulsation, period doubling route to chaos, chaos or coherence collapse, and strong OFB induced pulsation. InGaAsP lasers emitting in a wavelength of 1.5 mm are included in the calculations. The results sho.
author_names: Moustafa Ahmed

Minoru Yamada
title: Field fluctuations and spectral line shape in semiconductor lasers subjected to optical feedback
year: 2004

abstract: Beating between the lasing main mode and the non lasing side modes is one of the intensity noise sources of single longitudinal mode lasers. Its characteristics were investigated experimentally recent years. This paper presents a theoretical study of mode beating noises in semiconductor lasers, and intends to explain the experimentally observed phenomena. The effects of coherent population oscillation (CPO) induced by mode beating on gain coefficient and on reflective index are analyzed based on Maxwell Bloch equation and rate equations. The power ratio of the side mode over its conjugation mode generated by four wave mixing (FWM) is discussed; formulas of amplitude and frequency of mode beating intensity noise are given with relations to pump levels and mode orders. The obtained results are suitable for the edge emitting diode lasers and the external cavity lasers. The line shape of mode beating intensity noises is discussed based on CPO induced phase noise, giving explanations of the experimentally observed phenomenon of multiple sub peak spectra. The roles of intensity noise reduction by nonlinear optical absorber (NLA) inserted in the laser cavity are described. More factors related to the mode beating noise are discussed qualitatively, such as spectral hole burning of gain (SHB) the effect of external cavity, and higher order FWM.
author_names: Zujie Fang

Fang Wei

Kang Ying

Qing Ye

Haiwen Cai
title: Intensity Noise of Semiconductor Lasers Induced by Inter Mode Beating
venue: IEEE Journal of Quantum Electronics
year: 2021

abstract: The effect of optical feedback on the intensity noise spectrum and the longitudinal mode line shape of a 1.55 mm InGaAsP laser is investigated for reflections arising from the far end of a 7.5 km long fiber. The intensity noise near the relaxation oscillation frequency is significantly enhanced by the reflection feedback. Owing to the intercavity coupling, the enhancement is, however, frequency dependent and the noise spectrum exhibits high contrast modulations with a period corresponding to the fiber cavity longitudinal mode separation. A simple rate equation model is used to explain the observed behavior.
author_names: Govind P Agrawal

Nils Anders Olsson

Niloy K Dutta
title: Effect of fiber far end reflections on intensity and phase noise in InGaAsP semiconductor lasers
year: 1984

abstract: An exact result for the spectral density of intensity variations that occur after propagation of ergodic light in a medium having lowest order only group velocity dispersion is obtained and applied to the problem of semiconductor laser phase noise to intensity noise conversion in a single mode optical fiber. It is shown that the intensity spectrum after propagation formally approaches, for a large laser linewidth or a long (or high dispersion) fiber, the intensity spectrum of a thermal source having the same line shape as the laser.
author_names: William K Marshall

Bruno Crosignani

Amnon Yariv
title: Laser phase noise to intensity noise conversion by lowest order group velocity dispersion in optical fiber: exact theory.
venue: Optics letters
year: 2000

abstract: 1 Introduction. 2 Basic Laser Characteristics. 2.1 Double heterostructure characteristics. 2.2 Direct and indirect semiconductors. 2.2.1 Energy and momentum conservation. 2.2.2 Semiconductor materials for direct and indirect semiconductors. 2.3 Emission and absorption. 2.3.1 Density of photon oscillation states. 2.3.2 Principal mechanisms of radiative transitions. 2.3.3 Carrier lifetime and lifetime of spontaneous emission. 2.3.4 Gain and stimulated emission. 2.4 Lasing characteristics of Fabry Perot type lasers. 2.4.1 Lasing conditions. 2.4.2 Dynamic characteristics of laser operation. 2.4.3 Light current characteristics, threshold current and quantum efficiency. 2.4.4 Basic laser structures. 2.4.5 Modifications for the spontaneous emission term. 2.5 Dynamic single mode laser structures. 2.5.1 DFB laser characteristics. References. 3 Longitudinal Mode Spectrum of Lasing Emission. 3.1 Multimode rate equations. 3.2 Spectral envelope for Fabry 1 Introduction. 2 Basic Laser Characteristics. 2.1 Double heterostructure characteristics. 2.2 Direct and indirect semiconductors. 2.2.1 Energy and momentum conservation. 2.2.2 Semiconductor materials for direct and indirect semiconductors. 2.3 Emission and absorption. 2.3.1 Density of photon oscillation states. 2.3.2 Principal mechanisms of radiative transitions. 2.3.3 Carrier lifetime and lifetime of spontaneous emission. 2.3.4 Gain and stimulated emission. 2.4 Lasing characteristics of Fabry Perot type lasers. 2.4.1 Lasing conditions. 2.4.2 Dynamic characteristics of laser operation. 2.4.3 Light current characteristics, threshold current and quantum efficiency. 2.4.4 Basic laser structures. 2.4.5 Modifications for the spontaneous emission term. 2.5 Dynamic single mode laser structures. 2.5.1 DFB laser characteristics. References. 3 Longitudinal Mode Spectrum of Lasing Emission. 3.1 Multimode rate equations. 3.2 Spectral envelope for Fabry Perot type lasers (linear gain) 3.3 Influence of nonlinear gain on the spectral characteristics. 3.3.1 Symmetric nonlinear gain. 3.3.2 Asymmetric nonlinear gain. 3.3.3 Nonlinear gain, conclusions. References. 4 Intensity Modulation Characteristics of Laser Diodes. 4.1 Modulation characteristics by studying single mode rate equations. 4.1.1 Turn on delay. 4.1.2 Rate equations, small signal analysis. 4.1.3 Relaxation oscillation damping. 4.1.4 Upper limits for the modulation bandwidth of laser diodes. 4.2 Influence of lateral carrier diffusion on relaxation oscillation damping. 4.3 Modulation bandwidth limits due to parasitic elements. 4.4 Examples for high speed modulation of laser diodes. 4.5 Modulation and longitudinal mode spectrum. 4.5.1 Transient spectra of laser diodes. 4.5.2 Lasing spectra under high speed modulation. 4.5.3 Dynamic single mode condition. 4.6 Modulation with binary signals. 4.7 Harmonic and intermodulation distortions (without fibre interaction) 4.7.1 Harmonic and intermodulation distortions for low modulation frequencies. 4.7.2 Harmonic and intermodulation distortions for high modulation frequencies. References. 5 Frequency Modulation Characteristics of Laser Diodes. 5.1 Relation between intensity modulation and frequency modulation. 5.2 Current/frequency modulation characteristics. 5.3 Chirp effects in directly modulated laser diodes. 5.3.1 Spectral line broadening due to laser chirping. 5.3.2 Chirp reduction by proper pulse shaping. 5.3.3 Time bandwidth product of chirped pulses. 5.3.4 Transmission of chirped pulses over single mode fibres. 5.4 Possibilities of modifying the chirp parameter 5.4.1 Dispersion of the chirp parameter 5.4.2 Chirp of laser diodes, coupled to optical cavities. References. 6 Instabilities and Bistability in Laser Diodes. 6.1 Repetitive self pulsations due to lateral instabilities. 6.2 Instability and bistability in laser diodes with segmented contacts. References. 7 Noise Characteristics of Solitary Laser Diodes. 7.1 Relative intensity noise (RIN) 7.1.1 Basic properties of noise signals. 7.1.2 Definition and measurement of RIN. 7.1.3 Requirement of RIN for intensity modulated systems. 7.2 Introduction of the spontaneous emission noise. 7.3 Intensity noise of laser diodes. 7.3.1 Intensity noise of laser diodes by studying single mode rate equations. 7.3.2 Mode partition noise. 7.3.3 Mode partition noise analysis for nearly single mode lasers. 7.3.4 Mode hopping noise. 7.3.5 1/f intensity noise. 7.4 Statistics of intensity noise. 7.4.1 Statistics of amplified spontaneous emission. 7.4.2 Probability density distribution for the total laser light output. 7.4.3 Statistics of mode partition noise. 7.4.4 Turn on jitter in laser diodes. 7.5 Mode partition noise for the transmission of pulse code modulated (PCM) signals. 7.5.1 Multimode lasers. 7.5.2 The mode partition coefficient k. 7.5.3 Nearly single mode lasers. 7.6 Phase and frequency noise. 7.6.1 Phase and frequency noise characterization in general. 7.6.2 Spectral line shape for white frequency noise. 7.6.3 Spectral line shape for 1/f frequency noise. 7.6.4 Frequency noise and spectral linewidth for single mode laser diodes. 7.6.5 Power independent contribution to the linewidth of laser diodes. 7.6.6 Correlation between FM noise and AM noise. References. 8 Noise in Interferometers Including Modal Noise and Distortions. 8.1 Noise in interferometers. 8.1.1 Complex degree of coherence. 8.1.2 Interferometric noise analysis for single mode lasers. 8.1.3 Interferometric set ups for measuring the linewidth and the degree of coherence. 8.1.4 Interferometric noise analysis for multimode lasers. 8.2 Modal noise. 8.2.1 Modal noise for monochromatic light sources. 8.2.2 Modal noise for single mode lasers with finite spectral linewidth. 8.2.3 Modal noise for multimode laser diodes. 8.2.4 Modal distortions. 8.3 Modal noise and distortions in single mode fibres. References. 9 Semiconductor Lasers with Optical Feedback. 9.1 Amplitude and phase conditions for laser diodes with external cavities. 9.1.1 Short external reflectors for longitudinal mode stabilization. 9.1.2 Emission frequency shifts due to optical feedback. 9.1.3 Single external cavity mode condition. 9.1.4 Spectral linewidth for laser diodes with external optical feedback. 9.2 Dynamics of laser diodes with external reflections. 9.2.1 Derivation of the time dependent electric field. 9.2.2 Modulation characteristics of external cavity lasers. 9.3 Laser diodes with distant reflections. 9.3.1 Classification of feedback regimes. 9.3.2 Phase and frequency noise of laser diodes with distant reflectors. 9.3.3 Intensity noise in laser diodes with distant reflectors. 9.3.4 Coherence collapse. 9.3.5 Tolerable feedback levels. References. 10 Laser Diodes with Negative Electronic Feedback. 10.1 Modulation characteristics of laser diodes with negative electronic feedback. 10.2 Linewidth narrowing and phase noise reduction with negative electronic feedback. References. 11 Circuitry for Driving the Laser Diode. 11.1 Schemes for stabilizing the bias current. 11.2 Laser drivers with optoelectronic integration. References.
author_names: Klaus Petermann
title: Laser Diode Modulation and Noise
year: 1988