H. A. Haus

Microring resonator channel dropping filters

Microring resonators side coupled to signal waveguides provide compact, narrow band, and large free spectral range optical channel dropping filters. Higher order filters with improved passband characteristics and larger out-of-band signal rejection are realized through the coupling of multiple rings. The analysis of these devices is approached by the novel method of coupling of modes in time. The response of filters comprised of an arbitrarily large dumber of resonators may be written down by inspection, as a continued fraction. This approach simplifies both the analysis and filter synthesis aspects of these devices.

Random walk of coherently amplified solitons in optical fiber transmission.

In an optical-communications system using soliton pulse transmission, periodic amplification is needed to maintain the energy of the solitons. We show that amplifier noise causes a solitons group velocity to undergo a random-walk process. The resultant timing errors at the receiver limit the systems product of length times bit rate, in one example, to about 24 000 GHz-km.

Mode-locking of lasers

The evolution of the theory of mode-locking over the last three and a half decades is reviewed and some of the salient experiments are discussed in the context of the theory. The paper ends with two-cycle pulses of a mode-locked Ti:sapphire laser.

77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser.

By incorporating a section of large positive-dispersion fiber in an all-fiber erbium ring laser, we obtain high-energy pulses with spectral widths of 56 nm. The chirp on these pulses is highly linear and can be compensated for with dispersion in the output coupling fiber lead. The result is a fully self-starting source of 77-fs pulse with 90 pJ of energy and greater than 1 kW of peak power at a 45-MHz repetition rate.

Ultra-compact Si-SiO 2 microring resonator optical channel dropping filters

Compact optical channel dropping filters incorporating side-coupled ring resonators as small as 3 /spl mu/m in radius are realized in silicon technology. Quality factors up to 250, and a free-spectral range (FSR) as large as 24 nm are measured. Such structures can be used as fundamental building blocks in more sophisticated optical signal processing devices.

GaAs FET device and circuit simulation in SPICE

We have developed a GaAs FET model suitable for SPICE Circuit simulations. The dc equations are accurate to about 1 percent of the maximum drain current. A simple but accurate interpolation formula for drain current as a function of gate-to-source voltage connects the square-law behavior just above pinchoff and the square-root law for larger values of the drain current. The ac equations, with charge-storage elements, describe the variation of the gate-to-source and gate-to-drain capacitances as the drain-to-source voltage approaches zero and when this voltage becomes negative. Under normal operating conditions the gate-to-source capacitance is much larger than the gate-to-drain capacitance. At zero drain-to-source voltage both capacitances are about equal. For negative drain-to-source voltages the original source acts like a drain and vice versa. Consequently the normally large gate-to-source capacitance becomes small and acts like a gate-to-drain capacitance. In order to model these effect it is necessary to realize that, contrary to conventional SPICE usage, there are no separate gate-to-source and gate-to-drain charges, but that there is only one gate Charge which is a function of gate-to-source and gate-to-drain voltages. The present treatment Of these capacitances permits simulations-in which the drain-to-source voltage reverses polarity, as occurs in pass-gate circuits.

Coupling of modes analysis of resonant channel add-drop filters

The operation principle of resonant channel add-drop filters based on degenerate symmetric and antisymmetric standing-wave modes has been described elsewhere using group theoretical arguments. In this paper, the analysis is carried out using coupling of modes in time. A possible implementation of such a filter is a four-port system utilizing a pair of identical single-mode standing wave resonators. The analysis allows a simple derivation of the constraints imposed on the design parameters in order to establish degeneracy. Numerical simulations of wave propagation through such a filter are also shown, as idealized by a two-dimensional geometry.

Channel drop filters in photonic crystals.

We present a general analysis of channel drop filter structures composed of two waveguides and an optical resonator system. We show that 100% transfer between the two waveguides can occur by creating resonant states of different symmetry, and by forcing an accidental degeneracy between them. The degeneracy must exist in both the real and imaginary parts of the frequency. Based on the analysis we present novel photonic crystal channel drop filters. Numerical simulations demonstrate that these filters exhibit ideal transfer characteristics.

Theory of mode locking with a fast saturable absorber

This paper presents a closed‐form analysis of saturable absorber mode locking of a homogeneously broadened laser. A solution is obtained for the case of a short relaxation time of the saturable absorber. This pulse is a hyperbolic secant as a function of time. For each choice of parameters two pulse widths are found. A stability analysis shows that the solution of greater width is stable. The requirements for achieving mode locking with a fast saturable absorber are stated. The effect of a time‐varying laser medium gain is investigated analytically.

Coupled-mode theory

The authors give a brief historic perspective of the coupled mode theory. The development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years are described. They then consider lossless coupling of two modes in time. Two coupled resonance circuits, or two coupled microwave or optical resonators, are the physical examples. The start-up of a parametric oscillator is another example. Then they look at the formal derivation of coupled mode theory and consider the more general case when the modes are not energy-orthogonal and the energies are not necessarily positive. A more detailed account of the nonorthogonal coupled mode theory developed in the last five years for optical waveguides is given. >