Probability density function for the phase and frequency noise in a semiconductor laser

A physical definition for the phase and frequency noise of a semiconductor laser is given, which can be applied in determining the performance of coherent optical communication systems. The definition allows a filtered Poisson model to be developed for the probability density function (pdf) of the laser output phase or frequency noise, based on evaluating the cumulants of the noise processes. A condition is derived to quantify under what laser and system conditions a Gaussian pdf is a good approximation. It is shown that the phase and frequency noise can increase significantly for bit rates approaching the relaxation oscillation frequency of the laser diode.     

An integrated equivalent circuit model for relative intensity noise and frequency noise spectrum of a multimode semiconductor laser

Relative intensity noise (RIN) and the frequency/phase noise spectrum (FNS) equivalent circuit of a multimode semiconductor laser diode are derived from multimode rate equations with the inclusion of noise Langevin sources. FNS is an important parameter in optical communication systems, and its circuit model is presented, for the first time, in this paper. Both circuit models for RIN and FNS are integrated in one circuit. RIN and FNS are calculated as functions of frequency, output power, and mode number. It is shown that the RIN of the main mode is increased in the multimode lasers with higher mode numbers. Furthermore, we show that RIN and FNS are enhanced for higher output power. The dependency of a multimode laser diode linewidth on output power is also analyzed using the model.     

Noise properties of injection lasers due to reflected waves

This paper describes the theoretical investigation of the origin, qualitative, and quantitative properties of the low frequency noise appearing in the light output of the laser diode, which is strongly coupled to optical fibers. This kind of noise has caused serious problems for reliable optical communications, especially for analog-modulation systems. It is shown that there are two different phenomena which generate such noise. One of them is the double cavity state, and the other is the external light injection state. The cause of our noise considered in the double cavity state is the phase variation due to the variation of the equivalent length between the laser and the reflection point generated by mechanical vibrations. On the other hand, the cause in the external light injection state is the random generations of locking and unlocking states due to the frequency variation (or mode jumping) caused by the variation of the internal temperature of the laser diode. We conclude from our theory that an effective method to reduce such noise is to operate the laser diode at well above the threshold current. The complete elimination will be attained by use of the optical isolator inserted between the laser diode and the transmission lines.     

A reduction of interferometric phase-to-intensity conversion noisein fiber links by large index phase modulation of the optical beam

A noise reduction scheme for long haul fiber amplitude modulation (AM) systems is proposed and analyzed. Such systems suffer from intensity noise which results from interference between the (twice) Rayleigh scattered light and the directly transmitted beam. This interference converts the fundamental phase noise of the laser to intensity noise. It is shown that a strong phase modulation of the output of the laser beam causes a large reduction of the detected signal noise in the vicinity of the detected signal components     

Phase synchronization in a satellite-mobile channel

This paper studies several aspects relevant to the design of phase synchronization circuits for land mobile satellite systems (LMSS). First, the results of a propagation experiment are presented, with special focus on the effects of vehicle mobility on the signal phase. It is found that the changes of speed and direction cause frequency variations that can be modelled as linear. Bounds for the frequency derivative are given for different percentages of time. The use of third-order PLLs is considered, as they are optimum for tracking a frequency ramp embedded in white Gaussian noise. The model of third-order PLL employed is presented, as it is an original model, developed by the authors. Then the performances of second- and third-order PLLs are compared. Theoretical, as well as simulation, results are given. It is shown that third-order loops give better performance in the presence of frequency variations of the kind observed in this link, but they suffer from a higher sensitivity to oscillators' phase noise. Several conclusions regarding the use of third-order loops in future systems are presented.     

Phase noise reduction by self-phase locking in semiconductor lasersusing phase conjugate feedback

A theoretical analysis of the behavior of the frequency/phase noise of semiconductor lasers with external phase conjugate feedback is presented. It is shown that the frequency noise is drastically reduced even for lasers with butt-coupled phase conjugate mirrors. In this laser system, the phase noise takes a finite-low value corresponding to a state of first-order self-phase locking of the laser. As a result, the spectral shape of the laser signal does not remain Lorentzian but collapses around the carrier to a delta function with a close to carrier noise level of less than -137 dBc/Hz. The total phase variance of this laser signal, in a 20 GHz noise bandwidth, is less than 0.002 rad²      

High-quality photonic sampling streams from a semiconductor diodering laser

We report on the development of an ultralow-noise, external-cavity, actively mode-locked semiconductor diode laser for application in next-generation photonic sampling systems. A summary of harmonically mode-locked noise characteristics in a 65-MHz ring cavity is presented through the range of pulse repetition frequencies between 130 MHz and 8.3 GHz (2nd-128th harmonic). Important implications regarding the use of gain-versus-loss modulation as the active modelocking mechanisms are discussed. We also report what are, to our knowledge, the lowest noise characteristics achieved to date for a semiconductor diode laser operating at 10 GHz. Individually optimized results of 0.12% rms amplitude noise (10 Hz-10 MHz), and 43 fs rms residual phase jitter (10 Hz-10 MHz) provide a theoretical resolution of 8.6 bits in a 10-GSPS optical analog-to-digital converter. We have also achieved dispersion-compensated pulsewidths; as short as 1.2 ps, and shown successful operation of a novel phase-locked-loop capable of reducing the rms; residual phase noise by as much as 91% within its response bandwidth. Finally, the first measurements of residual phase noise out to the Nyquist frequency (5 GHz) are presented, providing an upper bound on the rms residual phase jitter of 121 fs (10 Hz-5 GHz)     

采用射频频率调制光谱实现半导体激光器稳频

利用半导体激光器可直接对注入电流进行高速调制的特点，将20MHz射频(RF)信号直接加在半导体激光器的高频调制端口，射频信号的一部分经过相移器后，与雪崩光电探测器(APD)所探测的饱和吸收光谱信号进行混频，经低通滤波器后产生了类色散曲线；将半导体激光器的输出频率稳定在铯原子D2线的^6S1/2(F=4)→^6P2/2(F'=5)的超精细跃迁线上，实验所测的10s内典型的频率起伏小于1MHz；这种稳频技术不需锁相放大器，具有可避免低频段较高的强度噪声和较大的频率捕获范围的优点。     

Multichannel image-rejection coherent detection system

An analysis is made of and data is presented from a prototype of an image channel rejection systems for the coherent detection of densely packed wavelength division multiplexed (WDM) channels. The system can simultaneously process a number of channels with a single-local laser diode and can extract the feedback control signals required to adjust critical system parameters. Although the system operates most simply for frequency shift keying (FSK) and phase-shift keying (PSK), it also operates for all the usual modulation schemes with minor adjustments. The control system aspects of the system are not affected by laser-diode phase noise     

Chaos control and noise suppression in external-cavitysemiconductor lasers

Feedback-induced chaos and intensity noise enhancement in a laser diode with external optical feedback are studied by computer simulations. The enhancement of relative intensity noise (RIN) that is often observed in experiments is considered as a result of the feedback-induced deterministic chaos and the intensity noise suppression is treated from the viewpoint of chaos control. Especially, the conventional noise suppressing technique known as a high-frequency injection modulation is turned into a problem of stabilizing chaos through parameter modulations. We developed an analytical method which allows to optimize the modulation frequency from the linear stability analysis of the dynamical model that describes the laser diode with external feedback. The robustness of the modulation with respect to the modulation frequency and depth is verified and the results suggest the feasibility of applying our method to actual noise suppression. The RIN in the low-frequency region (up to 100 MHz) is shown to be reduced to the solitary laser level when the feedback-induced chaos is effectively controlled with the optimized modulation frequency     

Demodulation scheme fibre interferometric sensors employing laser frequency switching

A demodulation technique suitable for use with fibre interferometric sensors is described. The scheme employs a frequency switched diode laser and an unbalanced Mach-Zehnder interferometer. Minimum phase sensitivity ? 2× 10-5 rad is obtainable, and can be shown to be limited by the laser phase noise.     

Frequency division multiplexed microwave and baseband digitaloptical fiber link for phased array antennas

A frequency-division multiplexed optical fiber link is described in which microwave (1-8 GHz) and baseband digital (1-10 Mb/s) signals are combined electrically and transmitted through a direct-modulation microwave optical link. The microwave signal does not affect bit error rate (BER) performance of the Manchester-coded baseband digital data link. The baseband digital signal affects microwave signal quality by generating second-order intermodulation noise. The intermodulation noise power density is found to be proportional to both the microwave input power and the digital input power, enabling the system to be modeled as a mixer (AM modulator). The conversion loss for the digital signal is approximately 68 dB for a 1-GHz microwave signal and is highly dependent on the microwave frequency, reaching a minimum value of 41 dB at 4.5 GHz corresponding to the laser diode relaxation oscillation frequency. It is shown that Manchester coding on the digital link places the intermodulation noise peak away from microwave signal, preventing degradation of close-carrier phase noise (<1 kHz offset). A direct trade-off between intermodulation noise and digital link margin is developed to project system performance     

Intensity noise of semiconductor laser diodes in fiber optic analog video transmission

This paper presents an investigation of the effects of laser diode noise on analog video transmission in the HF and VHF bands, which resulted in the development of several designs of graded-index multimode fiber systems that can ignore reflection induced laser noise. The contents of the investigation include: 1) The evaluation of intrinsic laser noise of various laser structures and the evaluation of modulation effects on laser diode noise characteristics. It was found that the relative intensity noise (RIN) is less than -145 ∼ -150 [dB/Hz] when the modulation factor is less than 0.7 for index-guide mode stabilized lasers; 2) The quantitative evaluation of reflected laser beam effects on laser noise characteristics. The maximum laser-coupled reflected optical power that does not increase laser noise was determined as-65 ∼ -73 dB or less depending on the kind of laser structure; and 3) The evaluation of optical power reflected back into the laser in graded-index multimode fiber systems.     

Stabilization of millimeter-wave frequencies from passivelymode-locked semiconductor lasers using an optoelectronic phase-lockedloop

The use of an optoelectronic phase-locked loop to stabilize the pulsation frequency of a three-section, passively mode-locked quantum well laser diode at 41 GHz is discussed. It is shown that the free-running mode-locked signal, with a radio frequency (RF) linewidth of 770 kHz, can be stabilized to the linewidth of a reference RF oscillator (<1 kHz). The stabilized mode-locked signal has a phase noise of -70 dBc/Hz at 370 kHz offset. Tracking of the mode-locked signal to the external reference RF oscillator is maintained over 11 MHz. This is, in effect, an actively mode-locked laser source at 41 GHz     

Phase noise cancellation in a carrier recovered optical heterodynereceiver

The performance and application of an optical heterodyne receiver which uses a carrier recovery demodulator are described. Phase sensitive demodulators used in coherent optical transmission are compared, and the suppression of both phase noise and frequency instability of light sources by a carrier recovery (CR-) demodulator is described. A carrier recovered PSK (CR-PSK) demodulator and a phase noise canceling circuit (PNC) for a coherent SCM receiver are introduced as examples of CR-demodulators. The relationship between laser diode spectral linewidths and the delay time difference between the two paths in the CR-PSK demodulator necessary to keep the system performance within a certain power penalty is then derived. In a preliminary experiment using 560-Mb/s CR-PSK transmission, a receiver sensitivity of -51.6 dBm was obtained, and a laser phase noise suppression of about ¹/₂ that of DPSK was confirmed. The results suggest the possibility of constructing a heterodyne receiver which has no AFC-loop. Applications of a CR-demodulator to an optical frequency division multiplexing (OFDM) system and to a multivalue modulation scheme are discussed     

Laser diodes in photon number squeezed state

A laser diode with an intrinsic layer as the space charge limited current region is expected to emit a low noise (less than the shot noise level) light. However, when one applies the intrinsic layer to the laser diode, severe difficulty is faced. Because the intrinsic layer has a very high resistivity, the applied voltage to operate the laser diode is too large and causes catastrophic damage to the laser diode. Here we propose novel laser diodes which emit a low noise light. The first is an AlGaAs laser diode having an undoped layer between the active layer and the cladding layer which acts as the space charge limited current region. Fano factor, F_m, of this laser diode is 28% smaller than the shot noise level (standard quantum limit, F_m=1) at 21 mA (output power, P₀=20 mW). The second one is an InGaAsP laser diode having two tunnel barrier layers whose bandgap energy is larger than that of the cladding layer. The region between the barriers acts as the space charge limited current region, Fano factor, F_m of this laser diode is 47% smaller than the shot noise level at 21 mA (P₀=10 mW). On the other hand, an AlGaAs laser diode with the two tunnel barrier layers has Fano factor, F_m which is 43% smaller than the shot noise level at 21 mA (P₀=20 mW). The calculated amplitude noise spectral densities of the latter two laser diodes are in good agreement with the calculated values from Langevin method. However, the calculated amplitude noise spectral density of the former laser diode does not agree with the calculated value from Langevin method. This disagreement is also discussed     

Study of unipolar pulsed ramp and combined ramped/constant voltage stress on mos gate oxides

MOS gate oxide capacitors over a wide range of oxide thicknesses (10.9–28 nm) were stressed using a unipolar pulsed voltage ramp and combined ramped/constant voltage stress measurements. The reliability measurements were performed with several different bias conditions in order to assess the effects of the measurement conditions on times to breakdown and breakdown fields. In the first part it was verified that the unipolar pulsed ramp yields breakdown distributions which are identical to those of a widely used staircase ramp. In the second part the unipolar pulsed ramp was used for pre-stress prior to a constant stress and measurement results were compared to those of a ramped/constant stress with a staircase ramp. In several cases a ramp prior to a constant stress increases time to breakdown. The observations made in this study imply that the time to breakdown of a constant stress in the Fowler-Nordheim tunneling regime is strongly dependent on charge trapping and, therefore, on the stressing history of the oxide. Finally, it is shown that the combined ramped/constant voltage stress is a valuable tool for monitoring extrinsic and intrinsic breakdown properties when applying stress parameters in the correct way.     

Semiconductor Diode Lasers for Terahertz Technology

We discuss different concepts for generating terahertz (THz) radiation with semiconductor diode lasers. Photomixing enables the generation of continuous wave THz radiation by difference frequency generation of two lasers or of two-colour lasers. Pulsed THz radiation for time domain THz spectroscopy is generated with modelocked diode laser systems including amplification and chirp compression. Finally, we analyse the concept of quasi time domain spectroscopy based on broadband diode laser systems.     

Superimposition of a strong microwave signal on the laser injectioncurrent: spectral characteristics and impact on modal noise

In multimode fiber systems the strongest high-frequency modal noise generated by laser mode partitioning appears at the shorter distances where the modal dispersion is smaller than the laser coherence time. It is shown that the addition of an auxiliary microwave signal (AMS) reduces the laser mode partitioning and thus provides a reduction in the modal noise level. The optimum AMS frequency is 80-90% of the relaxation frequency, and the optimum AMS modulation index is 1.5-2.0. At these values the mode partition k-factor is reduced by a factor 3 in a 1 Gb/s system which gives rise to an estimated reduction in the detected modal noise level of 9.5 dB. The improvement in mode partitioning and modal noise reduction increases as the ratio between the relaxation frequency and the bit rate increases     

Noise-Modulated Optomechatronic Distance-Measuring System

A novel measuring system for optical distance sensing of solid targets is described. The system simply applies a noise-frequency-modulated laser diode for illuminating the target and an interferometer/photodetector device for coherent beam detection. This configuration is treated here as an optomechatronic correlator. The delay in travel time of the target beam in the interferometer yields a stochastically modulated electrical beat frequency in the photodetector output. Its mean frequency value is a measure for the target distance. Additionally to the required stochastic modulation of the injection current, the natural phase noise modulation of the laser diode also has to be taken into account. Theory delivers nonlinear measurement characteristics with strongly increased slope at the short-distance range. The experimental verification in a distance range up to 4 m shows a relative distance measurement error from$hbox10^-3$to$hbox10^-2(1sigma)$for an averaging time range from 10 to 1 s. The system is potentially qualified for approach sensing in mechatronic devices like tool machinery and robotics.