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Considering Yosef’s relationship with his father, one would think that Yosef would make every effort to contact him after arriving in Egypt. Yet even after becoming Paroh’s right-hand man, Yosef still does not try to contact his father. Several possibilities are given:
The Ramban answers that Yosef did not communicate with Yaakov because he wanted the dreams he told to his brothers to come true. Yosef understood that the only way for Hashem’s plan to work would be if Yosef did not contact his family.
The Abarbanel explains that Yosef did not write so that his brothers could do proper Teshuva. This can explain Yosef’s behavior after his brothers arrived, but it does not fully explain why he did not write.
Rav Yoel Bin Nun (Megadim vol. 1) explains that Yosef did not know that his father thought he was dead. He expected his father to come rescue him when he learned about the sale. After many months passed, Yosef began to feel rejected and accepted his fate. This can be explained in two ways:
There is the “conspiracy theory,” in which Yosef was unaware that Yaakov was fooled into believing that Yosef was dead. Yosef concluded that no one came to rescue him because Yaakov received a prophecy saying that Yosef would not be part of the chosen nation, and thus sent Yosef to his brothers to do Yaakov’s dirty work.
The second theory is that after being sold, Yosef began to feel rejected. He decided to start a new life rather than return to his brothers. He was convinced that his family abandoned him. He decided that just as Esav established himself in Edom, Yosef would establish himself in Egypt. Even though Yosef would not be part of the chosen nation, he would try to bring his values to Egyptian society.