The pump power and thulium-doped fiber (TDF) length for both single-pass and double-pass Thulium-Doped Fiber Amplifiers (TDFA) are theoretically optimized by solving differential equations. The 1050 nm pump is used to provide both ground-state and excitedstate absorptions for amplification in the S-band region. The TDFA is saturated at a shorter length with a higher gain value as the operating pump power increases. The double-pass TDFA allows double propagation of the test signal in the gain medium, which increases the effective TDF length and thus improves the gain of the TDFA compared to the single-pass configuration. Therefore, a small signal gain improvement of approximately 15 dB is obtained in the 1465 nm region. However, a noise figure penalty of approximately 1 dB is also obtained in this wavelength region. The theoretical result is in agreement with the experimental result.
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