Ridge waveguides in amorphous Al2O3:Yb3+ are produced by reactive co-sputtering and reactive-ion etching. Their spectroscopic properties, optical gain, and cooperative upconversion are studied and explained based on a model of distinct ion classes.

Ridge waveguides in amorphous Al2O3:Yb3+ are produced by reactive co-sputtering and reactive-ion etching. Their spectroscopic properties, optical gain, and cooperative upconversion are studied and explained based on a model of distinct ion classes. 

Distributed-feedback waveguide lasers based on Bragg-grating resonators generate ultranarrow-linewidth emission. Oscillation at the center of the reflection band ensures maximum reflectivity, hence minimum linewidth. The required pi/2 phase shift is often introduced by a distributed change in effective refractive index, e.g., by widening the waveguide. Despite careful design and fabrication, the experimentally observed resonance wavelength deviates from the designed wavelength. Even when thermally induced chirp or fabrication errors are negligible, this deviation is still present. Here, we show theoretically and experimentally that this deviation is of fundamental nature. The decay of light intensity during propagation from the phase-shift center into both sides of the Bragg grating due to reflection by the periodic grating and the refractive index change causes an incomplete accumulation of designed phase shift, thereby systematically shifting the resonance to a shorter wavelength. Considering the overlap integral between the distributed phase shift and light intensity in the design provides the desired performance.

Distributed-feedback waveguide lasers based on Bragg-grating resonators generate ultranarrow-linewidth emission. Oscillation at the center of the reflection band ensures maximum reflectivity, hence minimum laser linewidth. The required μ/2 phase shift is often introduced by a distributed change in effective refractive index, e.g. by adiabatically widening the waveguide. Despite careful design and fabrication, the experimentally observed resonance wavelength deviates, thereby placing the resonance and laser emission at a position with lower reflectivity inside the reflection band. This effect is usually incorrectly attributed to fabrication errors. Here we show theoretically and experimentally that the decay of light intensity during propagation from the phase-shift center into both sides of the Bragg grating due to (i) reflection by the periodic grating and (ii) the adiabatic refractive-index change causes an incomplete accumulation of designed phase shift, thereby systematically shifting the resonance to a shorter wavelength. Calculations are performed based on the characteristic-matrix approach. Experimental studies are carried out in a distributed-feedback channel-waveguide resonator in amorphous Al2O3 on silicon with a distributed phase shift introduced by adiabatic widening of the waveguide according to a sin2 function. Calculations and experiments show good agreement. Considering in the design the overlap integral between distributed phase shift and light intensity provides the desired performance.

We calculate intensity distributions in a Bragg grating. At the Bragg wavelength the distribution shows a perfectly exponential decay. At wavelengths far away from the Bragg wavelength it becomes sinusoidal, equivalent to damped harmonic oscillators. 

Bragg-grating-based distributed-feedback waveguide resonators, with a discrete phase shift introduced inside the Bragg grating, exhibit within their grating reflection band a Lorentzian-shaped resonance line with an ultranarrow linewidth. If the phase shift is π/2, the resonance is located at the center of the reflection band, i.e., at the Bragg wavelength, where the grating reflectivity is maximum, hence the resonance linewidth is minimum. Alternatively, the required π/2 phase shift is often introduced by a distributed change in effective refractive index, e.g. by adiabatically widening the waveguide. Despite careful design and fabrication, the experimentally observed resonance wavelength deviates from the designed one. Besides deviations owing to fabrication errors, a fundamental, systematic shift towards shorter wavelengths occurs. We show theoretically and experimentally that the decay of light intensity during propagation from the phase-shift center into both sides of the Bragg grating due to (i) reflection by the periodic grating and (ii) the adiabatic refractive-index change causes an incomplete accumulation of designed phase shift by the oscillating light, thereby systematically shifting the resonance to a shorter wavelength. Calculations are performed based on the characteristic-matrix approach. Experimental studies are carried out in distributed-feedback channel-waveguide resonators in an amorphous aluminum oxide thin film on silicon with a distributed phase shift introduced by adiabatic widening of the waveguide according to a sin2 function. Calculations and experiments show good agreement. Considering in the design the overlap integral between distributed phase shift and light intensity provides a performance that is much closer to the desired value.

Distributed-feedback (DFB) resonators [1, 2] are of interest for inherently producing narrow-linewidth laser emission, without the need of external cavities or filters. The single-frequency emission is obtained by designing an additional phase shift δϕdesign of π/2, thereby producing a resonance that is spectrally located at the centre of the reflection band. Conventionally, δϕdesign is introduced abruptly in the Bragg grating, but this method has the important disadvantage of causing spatial-hole burning in the laser resonator due to a high photon density where the phase shift is located. An attractive solution is to distribute the phase shift, e.g. by widening the waveguide region, thus increasing the effective refractive index [3].