In Islam, engagement in Islam is simply a commitment to marry at a future date. Its sole function and significance is to keep other suitors away. There are virtually no other legal consequences that accrue from the period of engagement. Thus, engagement does not make what was otherwise considered haram (prohibited) as halal (permitted).
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: Although you are allowed to look at the woman’s picture before deciding to marry her, you are not allowed to carry her picture around or continue to think or meditate about her until the marriage has been formally contracted.

Engagement in Islam is not considered as a lawful marriage contract; rather, it is simply a promise to be married at a future date, and as such, it does not in any way render anything that had been previously considered unlawful as lawful.
Therefore, as long as you are not married, you are not allowed to carry her picture around. You are, however, allowed to look at her picture carefully in order to make up your mind about marrying her. This is because the Prophet (peace and blessings be upon him) told the Companion who wished to marry a young woman, “Go and look at her first (before deciding), for it might (enable you to) foster your (marriage) relationship.”
The permission thus given is an exception granted in order to help a person to make a better choice than if he/she were simply marrying someone whom he/she never saw prior to marriage.
On the other hand, members of the opposite sex are forbidden from persistently looking at each other or their pictures, for it might lead to illicit thoughts and desires. According to Shari`ah principle, that which leads to haram (unlawful) is deemed as haram.