<img src="http://www.trcind.com/temp/100_...t;/img>
Not that I understand or care... :-)

But back to the topic.

Is that "rope" moving longitudinally or perpendicularly?
What do you exactly need to detect? Absence (tear)? How fast should they react?

You might perhaps try to experiment with a stock silicon phototransistor and a bunch of LEDs; only the mechanical arrangement is cumbersome. Silicon has a maximum of sensitivity in the near infrared around 950nm, but decays relatively slowly into the visible thanks to it indirect bandgap, so it has still some 1/3 of its peak sensitivity around green (unless packaged in that "black" plastic which is an IR filter).

There are also many industrial solutions available, but the cost is relatively high. We use various Omron brand optical sensors, and the fibre sensors come into my mind - E3X-NA series head and E32-Dxx fibre or other - they use red light. It is often very convenient to place the relatively bulky head farther from the sensed object, and position only the end of fibres to the vicinity of the object.

Just an idea.

JW