According to the Ibn Ezra, Achashverosh was angry from the time he woke up from his drunken stupor after following Haman’s decree to rid himself of Vashti (Esther 2:1) until Haman was ultimately hanged.
The Me’am Loez explains the subsiding of the king’s fury as calm that returned to the universe.
This is because, as the Sfas Emes writes, when Amalek is in power, H-Shem is more noticeable through His characteristic of din, judgment. This is similar to what Rashi writes in his commentary on Torah (Shemos 17:16).
Haman’s end brought with it a sense of peace. The Talmud in several places (Rosh HaShanah 12a, Sanhedrin 108b, Zevachim 113b) points out that regarding the Flood, the verse (Bireishis 8:1) says “vayishku mayim” (“and the water subsided”) when the waters cooled down, whereas the phrase in this verse is “v’chamas hamelech shichacha” (“and the fury of the king subsided”). The contrast in phrasing implies that the flood waters were hot to match the burning passions of the licentious people of that time, mida kineged mida.
Parenthetically, perhaps another connection between the flood and Haman’s downfall is the Midrashic opinion (Yalkut Shimoni 6:1056) that Haman built the gallows from the beams of Noach’s ark.
Interestingly, shachacha (“subsided”) is a unique word in TaNaCh. R’ Samson Raphael Hirsch (Collected Writings, Volume IV, 319) comments that the word, shachach is phonetically related to shagag, (“not by choice”). In other words, the king’s anger was not something Achashverosh put effort into controlling. It came and subsided without any input from him.
The Talmud (Megillah 16a) considers that the unique spelling of shacha with an extra letter chuf to read shachacha is due to the fact that two angers were cooled; one belonged to the King of the Universe and the other belonged to Achashverosh. Also, Achashverosh calmed down about the situation of Esther, and the situation of Vashti.
As Rashi explains, Achashverosh was doubly angry because Haman was seemingly responsible for the death of Vashti, and was now a threat to Esther.
The Maharsha emphasizes that Achashverosh was still angry from that point (Esther 2:1), chronologically almost a decade earlier.
R’ Dovid Feinstein explains that Achashverosh had held himself responsible for Vashti’s fate all of this time, but now realizes that he was deceived and manipulated.
The Vilna Gaon says that the king whose fury subsided was H-Shem, King of the World. This may refer to the Zohar (III 133a), which translates the verse (Tehillim 144:15) that describes the Jewish people as “ha’am shekacha Lo,” or as “the nation that calms Him,” implying that the Jewish people have a tremendous power, if only we were to utilize it.
The Zer Zahav writes that Esther’s not forgiving Haman finally caused Shaul to be forgiven for taking unwarranted pity on Agag, Haman’s ancestor.
The Ginzei HaMelech writes that the Shir Ma’on quotes the Sha’aris Yisroel that quotes the great scholars who lived through the Chmielnicki Massacres of 5408-5409 (1648-1649 CE), which was one of the worst attempts at the genocide of the Jewish people in our history. They note that the large letter ches (Esther 1:6) and the large letter suf (Esther 9:29). Together, the letters spell out tach, a Hebrew way to reference the year 5408. This means that the massacre was a manifestation of Haman’s evil decree.
The Ginzei HaMelech heard from others the contention that the Chmielnicki Massacre was not the end of the effects of Haman’s decree. Rather, the Holocaust of tasha, 5705 (1945 CE), was the final manifestation of Haman’s decree. He proves this from the unique spelling of shachacha; since H-Shem was “calmed” about the Jewish people twice – once in tach, and once in tasha. There is proof of this in the mispar katan of the word shachacha (300+20+20+5=345= 12= 3) being the same as the mispar katan of tasha (400+300+5=705 = 12= 3). H-Shem is no longer anger.
The Ginzei HaMelech also quotes from Rav Michel Weissmandel that there is a hint to this in the traditional sizes of the letters in the list of Haman’s sons (Esther 9:7-9) as found in the Megillas Esther. The letters suf (400), shin (300), and zayin (7) there are smaller than the surrounding text, which refer to the year tashaz (1946 CE), the year in which ten Nazi officers were hanged at the Nuremberg Trials. There is also a large letter vuv (6), alluding to the sixth officer, Julius Streicher, who shouted “Purim Fest 1946” as he was being led to the gallows, despite the hanging taking place on Hoshana Rabba, the holiday on which the Zohar (III 31b-32a) says H-Shem judges the gentile nations. There was another Nazi who was supposed to be executed that day, Herman Goring, who committed suicide in his cell. He is likened to Haman’s daughter, who also killed herself. The comparison is extenuated by the fact that Goring famously enjoyed wearing women’s clothing.
Furthermore, the gematria of shachacha is the same as Moshe (40+300+5=345) because even good leaders are taken when H-Shem chooses to punish a generation. As the Talmud (Brachos 62b) teaches, a plague takes away the greatest of the generation together with the masses. Indeed, a storm sweeps away the good grain together with the chaff.
According to the Nachal Eshkol, another reason this gematria corresponds to Moshe is because the Midrash (Esther Rabba 6:2) says that yet another reason the Jews were saved from genocide was in the merit of Moshe. His merit should continue to be with us, and rescue us finally from this exile, bimheira biyameinu.