Temperature dependence of the spectral characteristics of distributed-feedback resonators

Abstract

We characterize the spectral response of a distributed-feedback resonator when subject to a thermal chirp. An AlO rib waveguide with a corrugated surface Bragg grating inscribed into its SiO top cladding is experimentally investigated. We induce a near-to-linear temperature gradient along the resonator, leading to a similar variation of the grating period, and characterize its spectral response in terms of wavelength and linewidth of the resonance peak. Simulations are carried out, showing good agreement with the experimental results and indicating that the wavelength of the resonance peak is a result only of the total accumulated phase shift. For any chirp profile we are able to calculate the reflectivities at the resonance wavelength, and this information largely explains how the linewidth of the resonance changes. This result shows that the increase in linewidth is governed by the increase of the resonator outcoupling losses.

Accumulation of Distributed Phase Shift in Distributed-Feedback Resonators

“…With increasing computing power, the characteristic-matrix approach [24] has become an attractive alternative, which we exploit for our numerical calculations. More details can be found in [18].…”

“…In semiconductor materials, the refractive-index change with temperature is particularly large. However, since the Bragg-grating reflection changes accordingly, the position of resonance within the reflection band and, hence, the grating reflectivity at the resonance wavelength, does not necessarily change [18]. Thirdly, a chirp of the Bragg grating causes a strong deviation of the resonance wavelength from the designed wavelength [18].…”

“…However, since the Bragg-grating reflection changes accordingly, the position of resonance within the reflection band and, hence, the grating reflectivity at the resonance wavelength, does not necessarily change [18]. Thirdly, a chirp of the Bragg grating causes a strong deviation of the resonance wavelength from the designed wavelength [18]. Such a chirp is introduced either unintentionally by optically pumping a DFB laser only from one waveguide end, thereby thermally inducing the chirp, as in high-power fiber-Bragg-grating lasers, where the temperature increase is often significant [19], or deliberately, based on the theory of Bragg gratings [20].…”

“…Lines: reflection bandwidth (full-width-at-half-maximum value). The simulations were carried out using the characteristic-matrix approach [18], [24]. light intensity extends over a length comparable to the distributed-phase-shift region.…”

“…Refractive-index profile δn p s (z) (red curve) of Eq. (4), normalized light intensity I (z)/I max (blue curve) calculated at λ res by use of the characteristic-matrix approach[18],[24], and overlap product δn p s (z)I (z)/I max (purple area) as the integrand of Eq. (8) versus position z along the resonator axis for two different grating coupling coefficients of κ = 450 m −1 and 1249 m −1 and two different designed phase shifts of δφ design = 0.17π and 0.79π.…”