Lasing wavelength in dielectric distributed-feedback lasers with a distributed phase shift

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.

[1]  A. Yariv.  Coupled-mode theory for guided-wave optics , 1973 .

[2]  Cristine Calil Kores,et al.  Accumulation of Distributed Phase Shift in Distributed-Feedback Resonators , 2019, IEEE Photonics Journal.

[3]  Purnawirman,et al.  C- and L-band erbium-doped waveguide lasers with wafer-scale silicon nitride cavities. , 2013, Optics letters.

[4]  E. H. Linfoot.  Principles of Optics , 1961 .

[5]  J. Kinoshita,et al.  Performance of 1.5 mu m DFB lasers with a narrow stripe region , 1991 .

[6]  M. Pollnau,et al.  Temperature dependence of the spectral characteristics of distributed-feedback resonators. , 2018, Optics express.

[7]  Cristine Calil Kores,et al.  Fabry-Pérot resonator: spectral line shapes, generic and related Airy distributions, linewidths, finesses, and performance at low or frequency-dependent reflectivity. , 2016, Optics express.

[8]  H. Soda,et al.  GaInAsP/InP phase-adjusted distributed feedback lasers with a step-like nonuniform stripe width structure , 1984 .

[9]  J.S. Roberts,et al.  Single-mode operation of a surface grating distributed feedback GaAs-AlGaAs laser with variable-width waveguide , 1995, IEEE Photonics Technology Letters.

[10]  M. Pollnau,et al.  Reliable Low-Cost Fabrication of Low-Loss $\hbox{Al}_{2}\hbox{O} _{3}{:}\hbox{Er}^{3+}$ Waveguides With 5.4-dB Optical Gain , 2009, IEEE Journal of Quantum Electronics.

[11]  M. Pollnau,et al.  Ultra-narrow-linewidth, single-frequency distributed feedback waveguide laser in Al2O3:Er3+ on silicon. , 2010, Optics letters.

[12]  J. Bradley,et al.  Optically pumped rare-earth-doped Al2O3 distributed-feedback lasers on silicon [Invited]. , 2018, Optics express.

[13]  Edward H. Bernhardi,et al.  Monolithic Distributed Bragg Reflector Cavities in Al2O3 with Quality Factors Exceeding 106 , 2011 .

[14]  R. Kashyap.  Fiber Bragg Gratings , 1999 .

[15]  H. Kogelnik,et al.  Coupled‐Wave Theory of Distributed Feedback Lasers , 1972 .

[16]  Edward H. Bernhardi,et al.  Intra‐laser‐cavity microparticle sensing with a dual‐wavelength distributed‐feedback laser , 2013 .

[17]  H. Kogelnik,et al.  STIMULATED EMISSION IN A PERIODIC STRUCTURE , 1971 .

[18]  Michael L Davenport,et al.  Arrayed narrow linewidth erbium-doped waveguide-distributed feedback lasers on an ultra-low-loss silicon-nitride platform. , 2013, Optics letters.

[19]  Y. Matsui,et al.  Narrow spectral linewidth semiconductor lasers , 1992 .

[20]  Markus Pollnau,et al.  Erbium‐doped integrated waveguide amplifiers and lasers , 2011 .

[21]  G. Ball,et al.  Standing-wave monomode erbium fiber laser , 1991, IEEE Photonics Technology Letters.

[22]  Yoshiaki Nakano,et al.  Proposal of a distributed feedback laser with nonuniform stripe width for complete single-mode oscillation , 1984 .

[23]  A. Yariv,et al.  High-coherence semiconductor lasers based on integral high-Q resonators in hybrid Si/III-V platforms , 2014, Proceedings of the National Academy of Sciences.

[24]  M. Pollnau,et al.  Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching , 2007 .

[25]  S. Akiba,et al.  Asymmetric λ/4-shifted InGaAsP/InP DFB lasers , 1987 .

[26]  A. Tehranchi,et al.  Realization and optimization of phase-shifted distributed feedback fiber Bragg grating Raman lasers , 2018 .

[27]  Hartmut Hillmer,et al.  Application of DFB lasers with individually chirped gratings , 1995, Photonics West.

[28]  S. Blaize,et al.  Multiwavelengths DFB waveguide laser arrays in Yb-Er codoped phosphate glass substrate , 2003, IEEE Photonics Technology Letters.

[29]  M. Kamp,et al.  DFB laser diodes in the wavelength range from 760 nm to 2.5 microm. , 2004, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.