- How to deliver a wide range of optical power levels to a tissue area or section
during different categories of therapeutic healthcare sessions - How to access a diagnostic or treatment area within a living being with an
optical detection probe or a radiant energy source in the least invasive manner.
Depending on the application, all three of these factors may need to be addressed
at the same time. Because the unique physical and light-transmission properties of
opticalfibers can help resolve such implementation issues, various types of optical
fibers arefinding widespread use in biophotonics. Each opticalfiber structure has
certain advantages and limitations for specific uses in different spectral bands that
are of interest to biophotonics (as Fig.1.6illustrates). The descriptions in this
chapter of these characteristics give the essential information that biophotonics
researchers and implementers need to know when selecting afiber for a certain
application.
3.15 Problems.
3 :1 Consider the interface between the core of afiber and its cladding that have
refractive indices of n 1 and n 2 , respectively. (a) If n 2 is smaller than n 1 by 1
% and if n 1 = 1.450, show that n 2 = 1.435. (b) Show that the critical angle is
φc= 81.9°.
3 :2 Calculate the numerical aperture of a step-indexfiber having a core index
n 1 = 1.48 and a cladding index n 2 = 1.46. What is the acceptance angleθA
for thisfiber if the outer medium is air with n = 1.00?
3 :3 Consider a multimode step-index opticalfiber that has a core diameter of
62.5μm, a core index of 1.48, and an index differenceΔ= 0.015. Show that
at 1310 nm (a) the value of V is 38.4 and (b) the total number of modes is
737.
3 :4 A step-index multimodefiber with a numerical aperture of 0.20 supports
approximately 1000 modes at a wavelength of 850 nm.
(a) Show that the diameter of its core is 60.5μm.
(b) Show that thefiber supports 414 modes at 1320 nm.
(c) Show that thefiber supports 300 modes at 1550 nm.
3 :5 Consider a step-indexfiber having a 25-μm core radius, n 1 = 1.48, and
n 2 = 1.46.
(a) Show that the normalized frequency at 820 nm is 46.5.
(b) Verify that 1081 modes propagate in thisfiber at 820 nm.
(c) Verify that 417 modes propagate in thisfiber at 1320 nm.
(d) Verify that 303 modes propagate in thisfiber at 1550 nm.
(e) What percent of the optical powerflows in the cladding in each case?
(Answer: 4.1 % at 820 nm; 6.6 % at 1320 nm; 7.8 % at 1550 nm).3.14 Summary 85