Alice C. Linsley
In Genesis 18: 13 we read that Sara laughed when she heard that she would bring forth a son in her old age. Her laughter seems to be out of shock and disbelief, a natural response for a woman past child bearing years.
Then we are told that Sarah denied laughing, another natural response given that Sara would not have wanted to insult her esteemed guests. Sara apparently did not know that this was a divine announcement, certainly not in the way that the Virgin Mary knew at the Annunciation that she was hearing a word directly from God. Unlike Mary, Sara was not the direct recipient of the message. The Lord made a promise to Abraham, which caused Abraham to laugh as well .
When Isaac was born, Sara laughed again (Gen. 21:6). The basic sense of the verb that appears in the Hebrew is “to laugh.” The initial צְחֹק (in a rare participial form) refers to Sara's joyful laughter upon giving birth to a son. This suggests that the name Sara is derived from the African word saran, meaning joy. The word saran is also found in Hindi and is usually translated refuge. The word was probably introduced into India by the ancient Sudra (Nilotes and Proto-Saharans) who established the Harappa civilization. Har-appa means "Horus is father" in Dravidian.
There is a third implication of joy or laughter in the story. The child is named Isaac which means laughter. The name is Yitzak in Hebrew. The implication doesn't end here, however.
Genesis 26:8 says that Yitzak was caressing his wife Rebecca. The word "caressing" is the Piel/intensive form of the word "laugh" so the verse would more accurately read "He laughs was laughing intensively with his wife." Hebrew scholars suggest that this is a euphemism for having sex. That is a possible interpretation, yet the structure of laughter upon laughter upon laughter suggests a connection to the divine council or the heavenly ones who enjoy perfection and peace.
Exploring African and Dravidian Connections
The association of laughter with the name Sara is suggested by several Afro-Asiatic languages. The verb to laugh in Hausa, a Chadic language, is dara. Dara and Sara may be regarded as cognates since the letters d and s are interchangeable in Dravidian and many African languages. 
Sara might also be related to the Amharic sak', meaning to laugh, which is a cognate to the Kambaata word osalut, meaning ‘laughter’.
It is also possible that Sarah is related to the old Coptic sá nah meaning to make live. This would stress Sarah's birthing of her son. It likely also references the idea of refuge.
It is interesting to note also that the largest population group in Chad is called the Sara. Sara society is organized by patrilineal descent from a common male ancestor. There is a 3-clan confederation such as characterizes Abraham's people. The qir ka are the eastern Sara, the qin ka are those living in central Chad, and the qel ka are the western groups. The Sara are descendants from an earlier 3-tribe confederation of warriors and kingdom builders. According to legend, there were giants among them. Were these the elohiym (deified rulers) who comprised the divine council spoken of in Genesis?
1. Genesis 17:17: Then Abraham fell upon his face, and laughed, and said in his heart, Shall a child be born to man who is one hundred years old? And shall Sarah, that is ninety years old, bear a child?
2. Dravidian languages are spoken in southern India and Sri Lanka. These languages are related to African languages of Chad, Sudan, Egypt and Somalia. Read more here.
3. The Sara make up to 30% of Chad's population. About a sixth of them are Christians and live in southern Chad. The Sara people include the Ngambaye, Mbaye, and Goulaye.
Related reading: False Correlations; The Afro-Asiatic Dominion; Recovering the African Background of Genesis