The pastoral crucifix staff has become one of the most identified emblems of the papal office. There is some confusion as to what is and is not a "crosier". Usually, as crosier is a curved staff carried by a bishop. See picture below:
Etymologically, the term "crosier" refers to standard bearing a "cross", hence "crosier". So technically, a true crosier bears a cross.
While bishops have carried the curled shepherds crook depicted above, the Pope has traditionally carried a true crosier, that is a staff bearing a cross - a triple barred cross. See image below:
Pope Paul VI instituted the familiar silver crucifix crosier with the downward bending crossbeam. There have been some complaints over the years that this crucifix is modern and therefore not fitting of the papal office. However, I think that the silver crucifix has become so thoroughly accepted that it is now permanently "traditional". John Paul II Magnus carried that standard across the globe. Moreover, it is in fact a traditional image. It is based on a rough sketch composed by St John of Cross who lived in the 16th century. See image below:
As you can see, the papal crosier closely resembles this rather traditional design. For all you art fans, Salvador Dali used this sketch by St. John of the Cross for his familiar painting, appropriately named "Christ of St. John of the Cross". See below image:
It reminds me also of the famous altar piece painted by Matthias Grunewald. See image below: