M. Munroe

Sampling of photon statistics and density matrix using homodyne detection

The photon statistics and, moreover, the density matrix (quantum state) of a single light mode can be sampled using homodyne detection. That is, the density matrix is computed by averaging a set of sampling functions with respect to the measured quadrature values. We develop a practical procedure for evaluating these functions. The algorithm is simple, stable, has small computer-memory requirements, and is fast enough for real-time data processing. (Interestingly, our method involves unnormalizable solutions of the stationary Schrodinger equation. We develop the annihilation-and-creation formalism for these solutions and derive their semiclassical approximations.) We quantify the bin width required to determine the density matrix up to a maximal quantum number. Finally, we show how the statistical errors of the reconstructed density matrix can be determined from the measured data.

Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier

We present calculations of the intensity smoothing of stochastic light by a semiconductor optical amplifier (SOA). We predict spectral changes of the light that are due to amplitude-to-phase coupling in the gain medium. The intensity smoothing of noisy optical signals with an SOA carries a penalty of spectral broadening (increased phase noise) that increases with increasing alpha parameter (linewidth enhancement factor). The spectral broadening also increases with increasing strength of the intensity fluctuations being smoothed.

Total intensity modulation and mode hopping in a coupled-cavity laser as a result of external-cavity length variation.

Subwavelength variation in the length of an external cavity strongly coupled to a very short (100 μm) dye laser results in large changes in the total intensity and frequency hopping of the lasing modes. These measurements are in agreement with a multimode theory of coupled-cavity laser dynamics. The modulation in the total intensity is due to the frequency-dependent gain associated with the coupled-cavity mode structure, while the mode hopping characteristics can be attributed to frequency-dependent losses caused by very weak (~10−3) reflections or diffuse scattering from the glass surfaces in the system.

Turn-on transient statistics and dynamics in a multimode, short-cavity laser

The statistics of turn-on delay times for a longitudinal mode and the total intensity from a multimode, standing-wave, short-cavity dye laser are measured and compared with numerical simulations of a multimode theory of laser dynamics. Differences between the measurements and the theory for the average and standard deviation of the turn-on time are due to transitory modes that decay as a result of frequency-dependent losses and gains. Associated with this phenomenon is a kink in the time evolution of the mode intensity that represents a transition in the dynamics from domination by independent growth of all modes to domination by competition between modes with differing net gains. This unequal competition increases the average and standard deviation of the mode turn-on time.

Ultrafast balanced-homodyne chronocyclic spectrometer

We describe an optical detection system for simultaneous time- and frequency-resolved measurements: the Balanced-Homodyne Chronocyclic Spectrometer (chrono equals time; cyclic equals frequency). This system uses balanced, optical homodyne detection, with a wavelength- tunable, pulsed local-oscillator (LO) field to time resolve the spectrum of weak light pulses. The LO field defines the time and frequency window in which the signal field is sampled. The method time resolves the photon statistics as well as the mean intensity. Measurement examples are given for: (1) Temporal oscillations of laser pulses transmitted through a semiconductor quantum well in an optical microcavity and (2) The time-frequency profile of a linearly chirped ultrashort laser pulse.

Turn-on transient dynamics in a multimode, compound-cavity laser

The turn-on-time statistics for an individual longitudinal mode and the total intensity of a multimode laser are shown to be very different. In both experiment and theory we find that the differences are due mainly to transitory modes that decay as a result of frequency-dependent losses and gains. Associated with this phenomenon is a kink in the time evolution of the mode intensity, but not in the total intensity, that represents a transition in the dynamics from domination by independent growth of all modes to domination by competition between modes with different net gains. This unequal competition increases the average and the standard deviation of the individual mode turn-on time. The experimental dye-laser system has a thin gain medium (100 µm) that is strongly coupled to a short cavity (2.5 cm) and is adjacent to one of the cavity mirrors. The opposite cavity mirror serves as a relatively weak output coupler. The presence of the thin gain medium in the cavity causes the effective pump and loss rates to be frequency dependent. The result is a transient spectrum in which the cavity modes that have the highest net gain dominate the system more as the turn-on transient progresses. The gain spectrum is found to be strongly affected by the frequency dependence of the compound-cavity modes. Using realistic laser parameters, numerical simulations of a multimode laser model {developed in companion paper [J. Opt. Soc. Am. B14, 191 (1997)]} yield turn-on dynamics and statistics that agree well with those measured experimentally.

Compound-cavity laser modes for arbitrary interface reflectivity

Calculations of the longitudinal mode functions for the electric field of a compound-cavity laser show that the loss and gain coefficients are given by the Airy formula, as a function of the mode frequencies. Further, when the external cavity is longer than the gain-medium cavity, the frequency dependence of the gain is stronger than that of the loss, even when the intracavity surfaces are antireflection coated. These results provide a generalization of the oft used dielectric-bump model, in which the intracavity reflectivity has a lower bound fixed by the index mismatch at the interface between the gain medium and the external cavity.

High-Efficiency, Ultrafast Photon-Number Statistics from Phase-Averaged Homodyne Detection

The measurement of photon-number statistics is an essential element of quantum optics. Nevertheless, conventional techniques are limited in their ability to measure the photon-count distribution p(n) with high quantum efficiency (QE), high number resolution, and high spatial-temporal resolution. The present work reviews a recently developed technique --phase-averaged homodyne detection -- which can provide a nearly ideal method for measuring photon statistics.[1] Its QE can approach 100%, while maintaining high number resolution (can distinguish between p(n) and p(n +1)), as well as sub-picosecond temporal resolution and single-mode spatial discrimination. In addition, it provides simultaneous temporal and spectral resolution. [2]