Dag Roar Hjelme

Theory of timing jitter in actively mode-locked lasers

An analysis of the pulse-to-pulse timing jitter in an actively mode-locked laser is presented. The model includes spontaneous emission noise, mode-locker driver phase noise, and cavity length detuning. Analytical expressions for the laser pulse train phase noise spectrum, the intensity power spectrum, and the RMS timing jitter are given. The timing fluctuations are characterized by a time constant proportional to the cavity round-trip time times the number of locked modes squared divided by the modulation depth. The contribution from the mode-locker driver phase noise will dominate unless high-stability RF sources are used. The residual timing jitter due to spontaneous emission noise is very sensitive to cavity detuning. >

Semiconductor Laser Stabilization By External Optical Feedback

We have developed a theory describing the effect of external optical feedback on the steady-state noise characteristics of a single-mode semiconductor laser. This theory is valid for arbitrarily strong feedback and arbitrary external cavity. The general formalism includes relaxation oscillations, and allow us to analyze the effect of feedback on both the laser linewidth,frequency noise, relative intensity noise and the relaxation oscillation sidebands in the field spectrum.

Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers

Semiconductor-field interaction is analyzed by using a semiclassical density-matrix approach. Using an exact elimination procedure for the dipole moments, corrections to the standard rate equation are obtained and shown to result in gain nonlinearities. The gain nonlinearities are due to carrier-density-dependent dispersion at the lasing frequency. Using available measured data of the frequency dependence of the carrier-induced refractive index change, gain compression coefficients in agreement with experimental values are obtained. >

An optically driven phased array antenna utilizing heterodyne techniques

An optically driven phased array antenna system that utilizes heterodyne techniques to generate the microwave carrier frequency and phases is proposed. The heterodyning at each antenna element requires three injection-locked lasers. The microwave carrier frequency is determined by the order of the modulated sideband used in the injection-locking scheme. A design is also presented for an integrated optical fast Fourier transform (FFT). This device can perform the necessary phase processing for both beam steering and detection-of-arrival angle. Recent results on the noise properties of injection-locked semiconductor lasers are applied to the proposed antenna system. The effect of noise on the gain, signal-to-noise ratio, and the bandwidth of the antenna system is examined. It is shown that the performance degradation of the system, due to the noise in the lasers, is minimal, and therefore the bandwidth promise of optical drive could well be achieved with the use of heterodyne laser locking techniques. >

Two-dimensional mapping of the microwave potential on MMICs using electrooptic sampling

An accurate technique for mapping the two-dimensional microwave potential in microwave circuits has been developed and tested. Using the direct electooptic sampling technique and a de-embedding algorithm to remove substrate-variation-induced measurement errors, accurate two-dimensional potential maps with a dynamic range of 50 dB and spatial resolution of 10 mu m are obtained. De-embedding of the microwave potential from the measured, electrooptically modulated signal is achieved by deducing the substrate parameters from the measured average reflected optical power. Once the substrate is characterized, the microwave potential can be calculated from the electrooptic signal. The de-embedding procedure technique was successfully tested on a through-line and an open-end line of a through-reflect-line (TRL) microstrip calibration standard. >

Voltage calibration of the direct electrooptic sampling technique

A detailed study of various voltage calibration factors or the direct electrooptic sampling technique is presented. In reflection mode optical probing, the circuit substrate forms an etalon for the optical probe beam. Analytical expressions for the calibration factors due to etalon effects and decaying surface potentials are derived. on the length of the sampling pulse relative to the substrate transit time, the etalon will affect either the voltage calibration factor or the system bandwidth: For pulses that are long compared to the transient time, interference at the surface results in a probe wavelength dependent storage time effect. The resulting electrooptic signal shows a resonant behavior as a function of wavelength or substrate thickness. For pulses that are short compared to the substrate transit time, multiple reflections reduce the effective system bandwidth to a bandwidth less than that given by the single transit time or the sampling pulse width. Experimental verification of the theoretical results is presented. Various deembedding procedures for implementing the voltage calibration are discussed. >

Effects of noise on transients of injection locked semiconductor lasers

Semiconductor laser injection locking transients are analyzed. By adiabatically eliminating the carrier dynamics, a single nonlinear stochastic differential equation is obtained for the relative phase between the master and slave lasors. The corresponding Fokker-Planck equation is used to study the steady-state locked conditions as well as phase transients of the locking process. Noise causes the steady-state relative phase between the master and the slave lasers to be a random variable with a standard deviation of approximately a few degrees for typical injection levels. The standard deviation can be reduced by using a phase detector with a limited bandwidth. The mean locking time in the presence of noise is slightly less than the deterministic prediction. Noise also causes the locked lasers to have a finite probability to momentarily unlock. >

Microbending and modal noise.

The effect of microbending loss on SNRs received from multimode graded-index fibers excited by single-mode laser sources is considered. Analytical expressions are derived which describe the combined effects of microbending loss and detector misalignment loss on the integrated intensity statistics in the fiber. The theoretical predictions for the SNR are experimentally checked and found to be in good agreement with the experimental data.

Transfer function analysis of measured transfer matrices

Measurements of mode transfer matrices of various multimode fiber optic connectors are presented. To analyze the accuracy and repeatability of such measurements, a theoretical framework which employs mode transmission functions is derived. It is shown that the transfer function can be used to find transfer matrices for any set of launches. A procedure for determination of the mode transfer function is given.

Analysis and measurements of coplanar waveguide discontinuities

A technique for characterizing the field distribution and modeling discontinuities in coplanar waveguides is presented. Several passive devices with discontinuities and parasitics have been fabricated on GaAs substrates and analyzed, and the models have been verified using network analysis and an optical sampling technique.<<ETX>>