Modified differential overlap factor and modal gain equalization criteria based comparative analysis of 4M-EDFA 980;1480 nm towards identification of unique Erbium doping profile for 4M-EDFA1480 nm system

Abstract Space division multiplexing (SDM) based four mode erbium doped fiber amplifier (4M-EDFA) system is explored with 𝐿𝑃01;980 𝑛𝑚 and 𝐿𝑃01;1480 𝑛𝑚 pump power respectively. Main objective of this work is reduction in inherent differential modal gain (DMG) and differential spectral gain (DSG) between amplified signal modes 𝐿𝑃𝑙𝑚 (𝐿𝑃01; 𝐿𝑃11; 𝐿𝑃21 and 𝐿𝑃02) while maintaining high modal gain. Differential modal noise figure (DMNF) and differential spectral noise figure (DSNF) parameters are introduced to quantify amplified spontaneous emission (ASE) impact in 4M-EDFA980 𝑛𝑚; 1480 𝑛𝑚 system. A modified erbium ion inclusive overlap factor (𝜂𝑠𝑝) and more decisive DMG related differential modal overlap factor (DMOF) and DSG related differential spectral overlap factor (DSOF) parameters are extracted using coupled mode equations. Calculations reveal 𝜂𝑠𝑝 favourably high in 4M-EDFA980 𝑛𝑚 than in 4M-EDFA1480 𝑛𝑚 system. However, calculated DMOF and DSOF values are also unfavorably high in the former than in latter. Thereby, 4M-EDFA1480 𝑛𝑚 is further explored for the simultaneous reduction in DMOF and DSOF values. Modified erbium doped profile (MEDP) 4M-EDFA980 𝑛𝑚;1480 𝑛𝑚 system is simulated with erbium ion profile variants: uniform, 𝑁𝑖𝑛𝑣(𝑟) and 𝑁𝑜𝑝𝑡 (𝑟) in the order of their improved performances. 𝑁𝑖𝑛𝑣(𝑟) is extracted from inverse sum of normalised signal intensities related function and subsequently unique 𝑁𝑜𝑝𝑡 (𝑟) profile is proposed that satisfies reasonably differential modal gain equalization criteria. In 4M-EDFA1480 𝑛𝑚 system at 1550 nm wavelength respective values with 𝑁𝑖𝑛𝑣(𝑟) and 𝑁𝑜𝑝𝑡 (𝑟) for average modal gain is 24.05 dB, 24.17 dB; DMG is 2.4388 dB, 0.3624 dB and DMNF is 2.6862 dB, 0.3278 dB.