Intensity Modulation Response Research Articles

Dynamics and feedback sensitivity of vertical-cavity surface-emitting lasers with arbitrary optical feedback intensity

Vertical cavity surface emitting lasers (VCSELs) are the key laser sources in the high-performance computers (HPCs) and data centers (DCs). The explosive growth of data traffic in the HPCs and DCs requires increased bandwidths of VCSELs. In this paper, we deduce the Time-Delay (T-D) model considering the multiple round trips of light in VCSELs with an optical feedback cavity to enhance the modulation bandwidth. The T-D model is suitable for the VCSEL with an arbitrary optical feedback intensity. The influences of the round trip time m of light in the optical feedback cavity on the intensity-modulation responses with strong and weak optical feedback are studied. The feedback coefficients considering the multiple round trips of light in the optical feedback cavity and the dispersions of the distributed Bragg reflector are deduced, and are suitable for the arbitrary optical feedback intensity. The feedback coefficients are influenced by the value of m and the optical feedback intensity, and decrease as the value of m under arbitrary optical feedback intensity increases. The feedback coefficients under strong optical feedback are larger than that under weak optical feedback with the same value of m. The theories are useful for the high-speed VCSELs with optical feedback.

Parameter Extraction For Quantum Well DFB Lasers Based on 1D Traveling Wave Model

Extracting the parameters of a laser from the measured results is critical for laser design, modeling and optimization. This work presents a parameter extraction method for quantum well distributed feedback (DFB) lasers based on the one-dimensional traveling wave model (1D TWM). Facet reflectivities, grating coupling coefficient and the other parameters can be extracted by fitting the lasing spectrum, light-current (L-I) curve, intensity modulation (IM) response and large-signal chirp. During the extraction progress, the 1D TWM is simplified to improve the extraction efficiency. The feasibility of this extraction method is verified by extracting parameters from preset simulation results and experimental results, respectively. The 1D TWM can reflect the physical properties of the laser profoundly and the parameter extraction method based on 1D TWM will be a valuable tool for laser design, optimization or processing improvement.

Low-Frequency-Drop of Electroabsorption Modulated Lasers and the Improvement With Partially Corrugated Grating Based DFB Lasers

Electroabsorption modulated lasers (EMLs) is sensitive to the residual facet reflection (RFR), which can cause a low-frequency drop (LFD) in the modulation response. The LFD may result in output waveform distortion, especially for high-data rate and multi-level modulation. We verify by simulation and experiments that the effect of LFD on the EML performance and propose to use LFD as one of the key performance indices for qualifying EMLs in high-speed optical transceivers. LFD can be suppressed by incorporating partial-corrugated-grating (PCG) in the laser section. With PCG-DFB structure, the EMLs can maintain high single-mode yield (SMY) and an excellent quality factor even with a strong modulator reflection from EAM section. This provides the robustness in applying the PCG-DFB to achieve a flat intensity modulation response or to enhance the output waveform under large signal modulation. By designing the PCG-EML to have about 60% of grating region, it can reach >80% of SMY and improve the average Q-value from the reduced LFD in the modulation response. The PCG-EML with reduced LFD can enhance the eye-opening through reduced waveform undershoot and overshoot for transmitting 56-Gbaud/s or beyond PAM-4 signals.

VCSEL with multi-transverse cavities with bandwidth beyond 100 GHz

Abstract To fulfill the demands of high-speed photonic applications, researchers, and engineers have been working to improve the modulation bandwidth (MBW) of semiconductor lasers. We extend our prior work on modeling a vertical-cavity surface-emitting laser (VCSEL) with multiple transverse-coupled-cavities (MTCCs) to evaluate the feasibility of boosting MBW beyond 100 GHz in this study. Because of the strong coupling of slow-light feedback from nearby lateral transverse coupled cavities (TCCs) into the VCSEL cavity, the laser has a high modulation performance. The intensity modulation response of the VCSEL design using one, two, four, and six TCCs is compared. Due to the optical-feedback (OFB) from short TCCs, which achieves 3 dB MBW reaching 170 GHz, photon–photon-resonance (PPR) is projected to occur at ultra-high frequencies beyond 145 GHz. In terms of the Fourier spectrum of the relative intensity noise (RIN), we characterize the noise features of the MTCC-VCSEL in the ultra-high bandwidth domain.

Improvement on Direct Modulation Responses and Stability by Partially Corrugated Gratings Based DFB Lasers With Passive Feedback

DFB lasers with ultrashort cavities or integrated DFB lasers with passive waveguide reflectors are frequently proposed to realize directly modulated lasers (DMLs) for carrying ultrahigh data rate signals. The former suffers from poor heatsink and laser cleavage yield, while the single-mode stability of the latter scheme is seldom addressed. The mode selection and device performance of a DFB laser is well known to be very sensitive to the facet reflection and external optical feedback. The DFB lasers with partial corrugated gratings and passive feedback (PCG-PFL) are proposed here to overcome the challenging issues for the aforementioned two schemes. With PCG structure, the DFB lasers can maintain high single-mode yield (SMY) even with a high-reflection-coating on the rear facet and strong reflection from the integrated passive section. This provides the robustness in applying the integrated passive reflector to reshape the modulation response or to enhance the 3-dB bandwidth by using the photon-photon resonance (PPR) effect. By designing the PCG-PFL to have 150-μm long laser section, 50-μm long passive section, and 30% front-facet reflectivity, it can have about 86% of SMY, reduced resonant peak in the intensity modulation response, and reduced waveform overshoot and undershoot for transmitting 56-Gbaud/s PAM-4 signals. By using a longer passive reflector, enhanced bandwidth can be achieved by the PPR effect.

Modulation Response and Relative Intensity Noise Spectra in Quantum Cascade Lasers

Static properties, relatively intensity noise and intensity modulation response in quantum cascade lasers (QCLs) studied theoretically in this paper. The present rate equations model consists of three equations for the electrons density in the conduction band and one equation for photons density in cavity length. Two equations were derived to calculate the noise and modulation response. Calculations in this paper focused on the effect of optical phonon emission rateτij, a number of stages and the gain coefficient on the noise spectrum and modulation response in this types of semiconductor lasers. The results indicate the strong effect of optical phonon emission rate, the gain coefficient and a number of stages on the dynamics properties of QCLs. The static properties such as the population inversion, the threshold injection current and the steady state photons density deviate from the ideal values with increasing in τ21 .The effect of optical phonon emission rateτ21 has similar effect to the effect of photon lifetime on the noise spectrum in comparison with other times.

Modulation performance of semiconductor laser coupled with an ultra-short external cavity

We present modeling on the evaluation of the modulation performance of semiconductor laser coupled with an ultra-short external cavity in terms of the intensity modulation (IM) response, relative intensity noise (RIN), carrier to noise ratio (CNR), and frequency chirp. The modulation is characterized along the period-doubling (PD) route to chaos induced by optical feedback (OFB). We focus on the possibility of increasing the modulation bandwidth by improving the carrier–photon resonance (CPR) frequency or inducing resonant modulation due to photon–photon resonance (PPR). We show that along the route to chaos, OFB could increase the CPR frequency and improve the 3dB-modulation bandwidth from 19GHz to 28GHz. When strong OFB keeps the continuous wave (CW) operation or induces periodic oscillation (PO), PPR becomes significant and reveals resonance modulation over mm-frequency passband exceeding 50GHz. Both CNR and frequency chirp are also enhanced around the CPR and PPR frequencies. The highest CNR peak is obtained when modulating the CW or PO laser, whereas the maximum peak of chirp corresponds to non-modulated chaotic laser.

Stabilizing optical feedback-induced chaos by sinusoidal modulation beyond the relaxation frequency in semiconductor lasers

We report on stabilizing the chaotic dynamics of semiconductor lasers under optical feedback (OFB) by means of sinusoidal modulation at frequencies far beyond the relaxation frequency of the laser. The laser is assumed to be coupled to a short external cavity, which is characterized by a resonance frequency spacing higher than the relaxation frequency. The study is based on a time delay rate equation model of OFB, which is suitable for treating the regime of strong OFB and considering multiple reflections in the external cavity. We show that the intensity modulation response of the chaotic laser under strong OFB is enhanced over a narrow frequency band near the doubled relaxation frequency due to a photon-photon resonance. Within this high-frequency band, the sinusoidal modulation may convert the chaotic attractor to a limit cycle, and the small-signal modulation suppresses the relative intensity noise (RIN) to a level only 2 dB higher than the RIN level of the solitary laser.

Multimode analysis of relative intensity noise associated with intensity modulation of semiconductor lasers

This paper analyzes the relative intensity noise (RIN) associated with intensity modulation (IM) of multilongitudinal mode semiconductor lasers. We considered two states of operation; namely, stable single-mode and multimode hopping that correspond to weak and strong asymmetric gain suppression. The former is typically considered by AlGaAs lasers, whereas the latter is considered by InGaAsP lasers. We introduce comparison of the influence of the modulation parameters on both the total and modal RIN between both lasers. We show that the IM response and 2HD display a peak at the relaxation frequency. The multimode hopping in the InGaAsP laser induces levels of signal distortion much higher than those in the AlGaAs laser in the regime of low modulation frequencies. Under weak modulation, the total and modal RINs of both the lasers vary little from those of the non-modulated lasers. The deep modulation releases the multimode hopping phenomenon in the InGaAsP laser and suppresses the mode-hopping peak in the RIN spectrum.

Transmission improvement due to pre-emphasis of multi-band OFDM-UWB signals in LR-PONs using directly modulated lasers

The transmission improvement obtained through the usage of pre-emphasis (PE) of single-band and multi-band orthogonal frequency division multiplexing (OFDM) ultra-wideband (UWB) signals using directly modulated lasers (DML) along long-reach passive optical networks is experimentally evaluated. Additionally, OFDM-UWB sub-bands with central frequencies above the cut-off frequency of the DML are experimentally considered in order to evaluate extending the transmission capacity through the usage of PE. In case of single-band transmission, PE improves the bit error ratio (BER) of several OFDM-UWB sub-bands by more than two orders of magnitude in back-to-back conditions as well as after transmission along 100 km of standard single-mode fiber transmission (SSMF). Such improvement is limited by the reduced intensity modulation response variation of the DML within the passband of each OFDM-UWB sub-band, as fixed modulation index is considered in all tested cases. Considering multi-band transmission along 100 km of SSMF, PE allows doubling the number of transmitted sub-bands before a BER exceeding is achieved for any of the sub-bands and an optical signal-to-noise ratio of 25 dB0.1 nm. Such improvement is obtained as PE changes the effective modulation depth of each transmitted OFDM-UWB sub-band, so that equalized signal power after detection and almost identical BER in all OFDM-UWB sub-bands occur.

Modeling of millimeter-wave modulation characteristics of semiconductor lasers under strong optical feedback.

This paper presents modeling and simulation on the characteristics of semiconductor laser modulated within a strong optical feedback (OFB-)induced photon-photon resonance over a passband of millimeter (mm) frequencies. Continuous wave (CW) operation of the laser under strong OFB is required to achieve the photon-photon resonance in the mm-wave band. The simulated time-domain characteristics of modulation include the waveforms of the intensity and frequency chirp as well as the associated distortions of the modulated mm-wave signal. The frequency domain characteristics include the intensity modulation (IM) and frequency modulation (FM) responses in addition to the associated relative intensity noise (RIN). The signal characteristics under modulations with both single and two mm-frequencies are considered. The harmonic distortion and the third order intermodulation distortion (IMD3) are examined and the spurious free dynamic range (SFDR) is calculated.

Comments on “Large-Signal Theory of the Effect of Dispersive Propagation on the Intensity Modulation Response of Semiconductor Lasers”

In a previously published paper <citerefgrp xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><citeref refid="ref1"/> </citerefgrp> , a large-signal theory of propagation in a dispersive fiber of an optical wave with sinusoidal amplitude and frequency modulation has been proposed. Following the assumptions made in <citerefgrp xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><citeref refid="ref1"/></citerefgrp> , we have verified that some of the presented equations are incomplete; paradoxically, however, the missing terms in such equations could not always improve the model accuracy. In this comment, we present both the correct equations and an explanation for the referred paradox. In addition, we have corrected inconsistencies in the equation for the Fourier coefficients used in the exact large-signal theory in the Appendix A of <citerefgrp xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><citeref refid="ref1"/></citerefgrp> .

Rate equation analysis of injection-locked quantum cascade lasers

The modulation properties of optical injection-locked quantum cascade lasers (QCLs) are investigated theoretically via a simple low dimensional rate equation model. It is found that both strong injection level and positive optical frequency detuning increase the modulation bandwidth, while a large linewidth enhancement factor (LEF) contributes to the enhancement of the peak magnitude in the intensity modulation (IM) response. As opposed to conventional injection-locked interband lasers, it is demonstrated that no dip occurs in the QCL's IM response, which is beneficial for a series of broadband microwave photonic applications. Computations also show that the value of the LEF can critically modify both the locking and stability regions on the optical frequency detuning injection level map.

Improved two level model of mid-infrared quantum cascade lasers for analysis of direct intensity modulation response

The direct intensity modulation response of quantum cascade lasers can be accurately calculated from a three-level model. However, the calculations are algebraically complex. An alternative two-level model gives simpler expressions and more readily provides insight into the role of parameters influencing the modulation response. The object of this paper is to improve the two-level model and analyze the direct intensity modulation response. The modified model will simplify theoretical investigation of modulation related phenomena.

Spontaneous induction of the uniform lying helix alignment in bimesogenic liquid crystals for the flexoelectro-optic effect

Using in-plane electric fields, the electrical induction of the uniform lying helix (ULH) alignment in chiral nematic liquid crystals is reported. This process permits spontaneous induction of the ULH alignment to give an in-plane optic axis, without the need for complex processing. Flexoelectro-optic switching is subsequently obtained by holding the in-plane electrodes at a common voltage and addressing via a third, plane-parallel electrode on a second, or upper, substrate to give a field across the device in the viewing direction. For this device, in optimized bimesogenic materials, we demonstrate full intensity modulation and sub-millisecond response times at typical device temperatures.

Modeling and simulation of InAs/GaAs quantum dot lasers

Based on the analysis of carrier dynamics in quantum dots (QDs), the numerical model of InAs/GaAs QD laser is developed by means of complete rate equations. The model includes four energy levels and among them three energy levels join in lasing. A simulation is conducted by MATLAB according to the rate equation model we obtain. The simulation results of PI characteristic, gain characteristic and intensity modulation response are reasonable. Also, the relations between the left facet reflectivity of laser cavity and threshold current as well as modulation bandwidth are studied. It is indicated that the left facet reflectivity increasing can result in reduced threshold current and improved modulation bandwidth, which is in accordance with experimental results. The internal mechanism of QD lasers is fully described with the rate equation model, which is helpful for QD lasers research.

Mueller matrix-based optimization of reflective type twisted nematic liquid crystal SLM at oblique incidences

Mueller matrix measurements were used to characterize the polarization properties of liquid crystal-based reflective type twisted nematic (TN) special light modulator (SLM) at oblique incidence of the laser beam. The experimentally obtained Mueller matrices were used to obtain the combination of polarization optics required to optimize it for phase only modulation. The results indicate that minimum intensity modulation is obtained with the use of a polarizer followed by a quarter wave plate (QWP) in polarization state generator (PSG) arm and a QWP followed by an analyzer in polarization state analyzer arm (PSA). Polarization parameters such as retardance, rotation and depolarization were calculated from the experimentally obtained Mueller matrices using polar decomposition method at different angle of incidences of the laser beam and the results has been discussed. The similarity between retardance and depolarization curve as a function of address voltage of TNSLM indicated that depolarization is mainly associated with errors in retardance values. Further, spectral Mueller matrix measurements were used to obtain intensity modulation response in the range of wavelengths 450–700 nm for broadband applications.

Laser Optimization Guidelines for Dispersion Supported Transmission Systems Operating at Arbitrary Bit Rates

Laser guidelines for the performance optimization of dispersion supported transmission (DST) systems operating at arbitrary bit rates, not exceeding 40 Gbit-s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> , are presented. These laser guidelines are derived by numerical simulation for 40 Gbit-s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> and analytically validated for other bit rates. The laser guidelines are settled in order to accomplish two DST system goals: maximizing the back-to-back sensitivity and the total dispersion tolerance, with fixed laser bias and modulation currents, thus avoiding the usual DST laser current tailoring to the fiber length. The laser optimization guidelines are expressed in terms of the intrinsic laser response parameters as in the following. The -3 dB intensity modulation (IM) bandwidth normalized by bit rate must be about 0.7; the zero of frequency modulation response normalized by bit rate must be about 0.75; the damping ratio of IM response must be about 0.7; the steady-state frequency deviation normalized by bit rate must be about 0.55; and the extinction ratio must be about 5.5. Numerical results show that these rules hold for lasers with parasitics with a cutoff frequency as low as 30% of bit rate, as well as for different current pulse shapes, laser gain, and compression models, and receiver electrical filters.

Equivalent circuit models of quantum cascade lasers for SPICE simulation of steady state and dynamic responses

The electrical equivalent circuits of quantum cascade lasers (QCLs) under steady state and under an ac small-signal are developed by employing simplified rate equations for electronic transitions between two levels and the rate equation for photon numbers. Two interactive circuits represent the steady state behaviour and another two coupled circuits model the ac small-signal performance of a QCL. The equivalent circuits are then used for SPICE simulation. The steady state equivalent circuit reproduces the light current curve of QCLs. The ac equivalent circuit yields the intensity modulation response, which matches almost exactly with the curve obtained from reported numerical calculations based on a third-order system model. In addition, the ac model is employed for SPICE simulation to give values of the modulation bandwidth for different values of photon lifetime. The SPICE model gives a slightly different curve for the bandwidth against photon lifetime from the curve plotted using the approximate analytical expression.

Mode Locking and Electrical Tuning of a Hybrid Laser Source Using a Connectorized Ultra-Short Fiber Bragg Grating

Electrical tuning and mode locking of an external-cavity semiconductor laser with an ultrashort (0.4 mm) fiber-Bragg-grating (FBG) reflector are studied theoretically and experimentally. Evolution of electrical tuning of longitudinal modes in a laser with broad-bandwidth FBG is analyzed theoretically. Tuning over an 11.4-nm range was experimentally possible by mechanically changing the connectorized FBG reflector in the external cavity of a diode laser package. With a 40%-reflection FBG, the external cavity laser was mode locked and generated at < 50-ps optical pulses at (6.3 plusmn 0.3) GHz within a broad frequency range of 600 MHz. The authors have simulated the intensity-modulation response of this laser and have shown that the broad frequency range mode locking of these lasers is determined by a chirp-related resonance rather than an external cavity resonance. The theoretical analysis agrees with the experimental results