Optical fiber channels present flat channel response per wavelength in general, owing to the ultra-wide available bandwidth of optical fiber and optical amplifiers. However, the recent transport capacity upgrade per wavelength from 10 to >100 Gbaud has given rise to severe power fading at the high frequency range. Especially, the modern optical networks may rely on a massive number of reconfigurable optical add and drop multiplexers (ROADM) to enhance the network flexibility with low latency. These cascaded ROADMs bring about a well-known filter-narrowing effect that has become a severe issue in the deployed networks. This strongly limits the channel bandwidth, and leads to an optical channel with colored signal-to-noise ratio (SNR). To address this issue, we utilize the water-filling, an optimum power allocation that determines the capacity of colored-SNR Gaussian channels, and proposes multicarrier entropy loading to offer a theoretically optimum strategy to approach the Shannon capacity. Within each subcarrier, probabilistic constellation shaping is exploited to design Gaussian sources. Compared with the conventional uniform-entropy modulation, entropy loading possesses fundamental advantages on channel coding: it maximizes the channel mutual information under fixed channel coding rate when the system operates below the channel capacity, and approaches the capacity with less coding overhead. Entropy loading can be generalized to any applications under colored-SNR Gaussian channels beyond the optical communication.