This article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities. We describe in detail the underlying principles of the discontinuous Galerkin technique and its application to the simulation of complex nanophotonic structures. In addition, formulations for both time- and frequency-domain solvers are provided and specific advantages and limitations of the technique are discussed. The potential of the discontinuous Galerkin approach is illustrated by modelling and simulating several experimentally relevant systems.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/lpor.201000045

Discontinuous Galerkin methods in nanophotonics

A tunable multiwavelength Brillouin-erbium comb fiber laser with ultra-narrow wavelength spacing and a large wavelength number, employing a 135-m highly nonlinear fiber, has been experimentally demonstrated. The simultaneous presence of Brillouin pump and Stokes lines within the ring cavity initiate higher-order Stokes and anti-Stokes lines via multiple four-wave mixing processes. The experiment demonstrates that this is an effective solution of increasing the number of lasing lines. Up to 150 lasing lines in single-longitudinal-mode operation with a rigid wavelength spacing of 0.075 nm have been achieved at 1480 nm pump powers of 165 mW and Brillouin pump power of 12.0 dBm. The multiwavelength source exhibits a good stability on both the operating wavelengths and the output powers, and a 6-nm tuning range from 1562 nm to 1568 nm is obtained.

Tunable multiwavelength generation based on Brillouin-erbium comb fiber laser assisted by multiple four-wave mixing processes

We have demonstrated a novel multiwavelength Brillouin-erbium fiber laser (BEFL), in which the Brillouin pump is self-excited within the linear cavity, instead of the injection from the external cavity or direct generation in the intracavity. By using this simple scheme, the generation of more than 160 Brillouin Stokes lines has been experimentally demonstrated, which is the largest one achieved in BEFLs to the best of our knowledge. Also, the single longitudinal mode operation and the low noise performance of output wavelength line have been confirmed. Meanwhile, the experiment demonstrates that the BEFL performs good stability on both the operating wavelengths and the output power of each wavelength.

160-line multiwavelength generation of linear-cavity self-seeded Brillouin-Erbium fiber laser.

A multi-wavelength Erbium-doped fiber (EDF) laser based on four-wave-mixing is proposed and experimentally demonstrated. The 5 km single mode fiber in the cavity enhances the four-wave-mixing to suppress the homogenous broadening of the erbium-doped fiber and get the stable multi-wavelength comb. The lasing stability is investigated. When the pump power is 300 mW, the fiber laser has 5-lasing lines and the maximum fluctuation of the output power is about 3.18 dB. At the same time, a laser with 110 m high nonlinear fiber (HNFL) is demonstrated. When the pump power is 300 mW, it has 7-lasing lines (above -30 dBm) and the maximum fluctuation is 0.18dB.

Multi-wavelength Erbium-doped fiber laser based on four-wave-mixing effect in single mode fiber and high nonlinear fiber

A multiwavelength erbium-doped fiber (EDF) laser based on a nonlinear amplifying loop mirror (NALM) is proposed and experimentally demonstrated. The NALM provides intensity-dependent transmissivity to equalize different-wavelength powers and the transmission can be uniquely optimized by controlling the cavity loss associated with a section of un-pumped EDF, which also enhances the output signal-to-noise ratio (SNR). Through adjusting the polarization controllers (PCs), under only 70 mW pump power, up to 62-wavelength output with channel spacing of 0.45 nm has been achieved. Also, the lasing tunability and stability are verified.

http://www.physics.sjtu.edu.cn/laserlab/sites/www.physics.sjtu.edu.cn.laserlab/files/2012-Multiwavelength%20erbium-doped%20fiber%20laser%20based%20on%20a%20nonlinear%20amplifying%20loop%20mirror%20assisted%20by%20un-pumped%20EDF.pdf

Multiwavelength erbium-doped fiber laser based on a nonlinear amplifying loop mirror assisted by un-pumped EDF

We propose and demonstrate a self-seeded multiwavelength Brillouin-erbium fiber laser with an internally self-excited Brillouin pump, which is achieved by incorporation of a length of single-mode fiber together with a Sagnac loop mirror into a fiber ring cavity. In this simple scheme the Brillouin pump is self-excited in the fiber ring cavity and then used to seed the Brillouin multiwavelength comb in the single-mode fiber. Stable generation of more than 120 Brillouin Stokes wavelengths with relatively uniform amplitudes is demonstrated with this scheme. It is also shown that such a self-seeded Brillouin laser has good stability and repeatability.

https://otip.sjtu.edu.cn/publication/Journal/2005-OL-Y.%20J.%20Song-Self-seeded%20multiwavelength%20Brillouin–erbium%20fiber%20laser.pdf

Self-seeded multiwavelength Brillouin-erbium fiber laser.

An obvious improvement on both the gain and noise figure (NF) is demonstrated in the new double-pass L-band erbium-doped fiber amplifier (EDFA) with incorporating a fiber Bragg grating (FBG). Compared with the conventional L-band EDFAs, the gain is improved by about 6 dB in the new configuration for a 1580-nm signal with an input power of -30 dBm at 60 mW of 980-nm pump power. It is important that the NF is greatly reduced in the new configuration, as the FBG greatly compresses the backward amplified spontaneous emission. For the economical utility of pump power and erbium-doped fiber length, such a configuration may be a very competitive candidate in the practical applications of L-band EDFAs.

Improvement of gain and noise figure in double-pass L-band EDFA by incorporating a fiber Bragg grating

Multiwavelength self-seeded Brillouin-erbium fiber laser with 45-nm tunable range

A new design of all-optical gain-clamped L-band double-pass (DP) erbium-doped fiber amplifier (EDFA) has been proposed and demonstrated, in which the input port and the odd-channel output port of an interleaver are connected with the DP configuration EDF through a circulator to form lasing ring cavity for clamping gain, and the even port is utilized to export the amplified signals. The low noise figure can be achieved because the lasing power copropagates with the signals, and it is exported separately from the amplified signal thanks to interleaver. Meanwhile, the fiber Bragg grating incorporated in DP configuration suppresses the backward amplified spontaneous emission generation, and therefore improves efficiently the gain and lowers the noise figure. In such a way, the clamped gain of 16.3 dB with a variation below 0.2 dB and noise figure below 5 dB are achieved in the new L-band all-optical gain-clamped EDFA.

J.H. Ji

Papers

160-line multiwavelength generation of linear-cavity self-seeded Brillouin-Erbium fiber laser.

Self-seeded multiwavelength Brillouin-erbium fiber laser.

Improvement of gain and noise figure in double-pass L-band EDFA by incorporating a fiber Bragg grating

Multiwavelength self-seeded Brillouin-erbium fiber laser with 45-nm tunable range

Low noise-figure gain-clamped L-band double-pass erbium-doped fiber ring lasing amplifier with an interleaver