Photonic Crystal Fiber Aziz Mahfoud Introduction

In the last decade, a great deal of work has been focused in photonic crystals due mainly

to their optical properties. An interesting characteristic display by such structure is the

selectivity of the electromagnetic field that can propagated along them, in other words the

propagation of certain frequency is prohibited. Recently applications have been devise in

the fields of optical communication, high resolution spectral filters, photonic crystals film

(counterfeit for credit cards), photonic crystal lasers. A new type of waveguide has assure

to perform in very way that traditional core-cladding fiber. Photonic crystal fibers

(hollow fiber, see figure 1) promise to become the next generation of ultra-low loss

transmission fiber, their also have applications in power deliveries , sensors and nonlinear

optics. In commercial available holey fibers more than 95 percent of the light travels in

the hollow core or in the holes of the cladding. Due to the air-holes Fresnel reflection at

the end of the endfaces estimated less than 10-4 . Since up to 85 % of the fiber cross

section is composed of fused silica, fusion splicing become easier than conventional

fibers, and also good temperature stability of optical properties, along with low bending

losses. More recently scientists from blaze photonics have reported transmission losses of

about .58 dB/km (0.18 background Rayleigh scattering, 0.13 dB/km hydroxyl absorption,

0.27 dB/km excess loss associated with the geometry of the fiber.) for a solid core fiber

at 1.55 um which approach 0.2 dB/km the standard single mode optical fiber. In the same

context Corning, have reduced the losses in air-core photonic crystal fiber (PCF) from

1000 dB/km to 13 dB/km.

Figure 1. Hollow core photonic bandgap fiber. Diameter of the holey region about 40 um, diameter of the silica cladding about 135 um, with coating (acrylate) diameter of 220 um.

Distance between cladding hole enters 2.3 um, with a core diameter of 9.3 um.

Fabrication

Photonic crystal fibers are made by stacking tubes and rods of silica glass into a large

structure (perform) of the pattern of holes required in the final fiber. The perform is then

bound with tantalum wire and then is taken to a furnace of fiber drawing tower . The

furnace is filled with argon and reach temperature about 2000 oC as consequence the

glass rods and tubes get soften. Later, the preform is fused together and reduced to 1mm

size with hole around 0.05 mm diameter (see figure 2). In other words by increasing the

furnace temperature the air hole size can be reduced. After reducing the preform to a size

that is 20 times smaller the structure thus formed (cane), the hole process is repeated and

spaces between the holes of 25 millionth of meter can be obtained. Defects are created by

replacing tubes for solid rods (as in the case of highly nonlinear PCF or by removing a

group of tubes from the preform (hollow core photonic PCF). Since the fabrication

process is quite robust complicated geometries can be achieved. For instance the

geometry of the center defect can be modified by the introduction of the thicker of

thinner tubes at different position around the defect.

Figure 2. Typical fabrication process in a photonic crystal fiber. The tub and rods are gather together and a furnace is used to heat the preform to 2000 oC,.The preform then fused together reducing its original size with a typical ratio of about 20.. The right hand side figure shows the first photonic crystal fiber

Guiding process

It is important to describe the mechanism or mechanisms through what the light is

guided in a photonic crystal fiber. Since a PCF is a structure that usually is formed by a

center core surrounding by a periodic structure (cladding), basically we can think in two

possible guiding mechanism. First, we can consider the case in which the center core has

a effective index of refraction than the cladding. In this case a total internal refraction

kind of process occurs. We know that a ray optics picture, is not a accurate description of

the electromagnetic propagation of a wave, and a wave formalism is necessary for a

better understanding. The reality is that the fundamental mode is confined to the core due

to the higher index of refraction, and it is enable to leak away since the corresponding

electromagnetic field are not a mode (solution of Maxwell’s equation for this geometry).

In the other hand, higher order modes can be leak away of the core (a higher field

distribution in the cladding compare with the fundamental mode). An important

characteristic of PCF if that for small enough holes (air) the fiber remains single mode at

all wavelength, this types of fiber are know “endlessly single mode fiber”.

The other guidance mechanism is a novel one and it is based in a concept

that has attracted the attention of many researchers worldwide. Photonic band gap (PGB)

theory has opened a numerous application including PCF. PBG exhibit the characteristic

that only certain wavelength can be transmitted. So, in a PCF the guidance process is

achieved by coherent backscattering of the light into the core. Light incident upon the

core-cladding interface is strongly scattered by the air-holes. For particular wavelengths

the scattering process results in constructive interference of the reflected rays in the core.

That guidance process enable to fabricate fiber with hollow cores (filled with air)

something that it is impossible with conventional fiber (in a conventional fiber if the core

is hollow, it is impossible to obtained a material with lower index of refraction than air as

cladding)

Optical properties of 2-D photonic crystals

Since PCF are based on the physics of PBG, I found very important to provide a

introduction of PBG and the ways of it can control the propagation of the radiation of

electromagnetic waves. In a photonic bandgap structure there are certain frequency that can not

propagate along the direction of the periodic structure, and is this property that is exploited for

controlling the electromagnetic radiation. In essence the band calculations show the functionality

between wave vector and frequency. The relationship between frequency and wave vector is

usually very complex and numerical techniques are necessary (the plane wave method is a well

employ technique to calculate band structure). More general, we can think that there are certain

frequencies that can not propagate in the plane of the periodic structure. That properties is what is

exploited in a photonic crystal fiber, and thus it constitute the principle behind the guidance

process in the fiber. Another important characteristic that distinguish photonic crystal fiber from

regular fiber is the fact that the fiber can make to support one mode for all wavelength. This is

quite remarkable since usually regular fiber become multimode a shorter wavelength. It is

interesting to see, that also photonic crystal fiber are not bound for the size limitation that must be

imposed in a regular fiber in order to obtained single mod operation, that allow PCFs suitable for

high power application Figure 3 shows a typical 2-D band structure calculation.

Fig.3 calculated photonic band structures of a hexagonal lattice of dielectric cylinders in air E-polarization (solid lines) and H-polarization (dashed lines). The cylinders have a refractive index of 3.6.

Applications

Large mode area fiber

We already have mentioned in our introduction, that certain geometries will

support only one mode, no matter the size of the core or the wavelength. These types of

fiber are called endlessly single mode crystal fiber, and are fabricated usually with a solid

core surrounding by air holes .This properties are very interesting and can have various

application, including high power single mode-fiber lasers and amplifiers.. Since PCFs

deliver more power compare with conventional fiber, they can lengthen the repeater

spacing in telecommunication links. Also since the fiber is made of only silica the fiber

has potential application in sensors and interferometers. Losses associated with this type

of fiber are usually less than 1 dB/km.

Figure 4. Solid core crystal fiber. This type of fiber remains single mode in a wide range of wavelength.

Properties

• Single-mode at all wavelengths • Attenuation as low as < 0.8 dB/km for λ = 1550 nm • Undoped fused silica core and cladding • Near-Gaussian mode profile • Delivery of broadband radiation in a single spatial mode • Short wavelength applications • Sensors and interferometers

Hollow Core Fiber Photonic Bandgap Fibers guide light in a hollow core, surrounded by a

microstructured cladding formed by a periodic arrangement of air holes in silica. Since only a

small fraction of the light propagates in glass, the effect of material nonlinearities is significantly

reduced and the fibers do not suffer from the same limitations on loss as conventional fibers made

from solid material alone. These fibers also have very low bending losses, and very low Fresnel

reflection. Since up to 85 % of the fiber cross section is made of silica, which facilitate the fiber

splicing.

Figure 5. Hollow fiber. This type of fiber has lower loss compare with solid core fiber and is more likely to become e the replacement for conventional long haul optical fiber

Dispersion compensation

A very interesting application of photonic crystal fiber is as dispersion tailoring devices.

For instance, more of the fiber installed were design to operate at 1.3 um, but know

transmission is preffered at 1.55 um and this fiber has considerable dispersion at this

wavelength. Photonic crystal fiber can be employed as dispersion compensation in orde

to eliminate or reduce the dispersion. As a general rule, the bigger the dispersion

compensation, the smaller the PCF length. What distinguish PCF as dispersion

compensation technique compare with other method, is the fact that the range at which

the compensation is made in a PCF (zero dispersion) is broad compare with the other

methods. This is especially important for WDM, where compensation must be done in a

broad range. The range at which compensation can be made is fundamental limited by the

index contrast of the fiber. So, to increase the dispersion the index contrast must be

increased, and this usually done by increasing the air-holes diameter. Figure 6 shows the

dispersion dependences on the air-hole size. This fiber was designed to have zero

dispersion at 1.55 um. The figure embedded illustrates the balances between waveguide

and material dispersion in a PCF. A typical number for the PCF dispersion, is around

2000 ps-nm-1-Km-1, that means that a photonic crystal fiber can compensate 100 times its

length (you only need 1cm of PCF for each meter of regular fiber).

Figure 6. the dispersion slope an be tuned while maintaining a fixed zero dispersion. Insert shows the balance between material and waveguide dispersion for a fiber with zero dispersion slope at 1.55 um.

Polarization maintaining PCF

Birefringence in a optical fiber arises as a consequence of stresses generated in the fiber

during the fabrication process . This anisotropy has a important effect in the transmission

characteristics of the fiber. Birefringence can also be induce by bending and thermal

effect. The net effect is the generation of different optical axes. Plane polarized light

propagating along the fiber will be resolved into components along in theses axes and as

they propagate at different speeds. As result phases differences are created resulting in

elliptically polarized light. Finally, this phases mechanism cause delays in the optical

signal, and this is know as polarization mode dispersion. PMD becomes important at high

transmission rate. Polarization maintaining PCF is emerging as a new competitor for

traditional polarization maintaining fiber. One advantage of PCF is that they remains

single mode and thus can transmit polarized light in a broad range of frequencies. Also

PCF has shorter beat length than common PMF which reduces bend-induced coupling

between polarization states and improve the extinction rate. PCF presents, more stable

temperature coefficient of birefringence. PCF’s find application in sensors gyroscopes

and interferometers. See figure 7.

Figure 7. Polarization maintaining PCF.

The incident field not restrain to the core

Figure 8. Shows the beam propagation method for a solid core, at 1.55 um. Notice that the radius of the incident beam is larger than the core of the fiber. Beam was propagated 100 um.

The incident field not restrain to the core

Figure 9. Shows the beam propagation method for a hollow core, at 1.55 um. Notice that the radius of the incident beam is larger than the core of the fiber. Beam was propagated 100 um

BPM profiles with wavelength dependence

Incident file (constraint to the core)

BPM results a 0.85 nm

Figure 10. Shows the beam propagation method for a hollow core, at 0.85 um. Notice that the radius of the incident beam is larger than the core of the fiber. Beam was propagated 100 um

BPM

Result a 1.3 nm

Result a 1.55 nm

Figure 11. Shows the beam propagation method for a hollow core, at 1.55 um and 1.3 um.

BPM profiles with at 1.55 um at two different number of ring

Incident file (constraint to the core)

Figure 12. Shows the beam propagation method for a hollow core, at 1.55 for two different number of rings

BPM Simulation and Summary In the BPM simulation I am presenting basic result of a propagation of a Gaussian

beam through a Photonic Crystal Fiber. The structure is formed with a cladding

compound of air cylinders with radius of 1.394 um and with a lattice pitch Λ=2.875. I

study two structure, one with hole fiber and the other with a solid core (with a radius of

3.106 um).The first part of the simulation will tend to study the propagation of the beam

in the structure, when the incident beam is not launched into the core but spread through

the structure. It is important to remember that light can not be couple into a slab

waveguide if the radiation is launched into the cladding. As figure 8 and 9 suggest the

light launched in either structure tend to be localized in the core of the fiber after

propagation, which can be advantageous for certain application in which is difficult to

assure that the beam is launched only in the core. The amount of power that remains in

the core for the solid core fiber is around 4.779873e-01 and the coupling efficiency is

0.783340. In the case of the hollow fiber the amount of power within the core is

8.067363e-01 and the coupling efficiency 9.250303e-01. Actually I was expecting to find

better coupling and better confinement for the solid core fiber (since has a higher

effective index in the core of the fiber), that illustrated the complexity of analyze PCF by

standard waveguide concepts.

Second, we want to study what happens when different wavelength are launched into

the structure. By launching light at 1.55, 1.3 and 0.85 um (see figure 11) with field

concentrated in the core of the fiber, we end up with a coupling efficiency of 6.216740e-

01, 6.05419e-01, 6.809596e-01. Notice that the coupling efficiency is higher, if the power

is launched in such a way that is not confined to the core. The reason for that behavior is

not clear but I simply think that by launching the power not confined to the core, the field

is seeing the periodic structure at the very beginning of the simulation, instead when is

confined in the core that have to propagate some distance before seeing any periodic

variation in index of refraction (the size of the core is bigger than the size of the field).

There is another unexpected result, the coupling efficiency is bigger for the

structure with fewer rings (see figure 12). The coupling coefficient for the larger structure

is 6.216740 e-01 and for the smaller is 6.434557e-01. That is hard to understand, since

the bigger the structure the better the response of the fiber. But the answer can be related

with the fact that in the bigger structure there are some defects, since there are some

cylinder missing in certain positions. Those defects can generate phases associated with

them and this can have a important effect on the coupling coefficient. But there is a

important observation we can do; it looks like that increasing the number of rings it does

not affect to much the coupling efficiency but defect can have bigger impact on the

overall coupling efficiency .

Bibliography

1 Http://optics.org/articles/news/9/10/23/1

2 http://www/optimun.tech.com/filesfornewslettersdownload/PCFpaper.htm

3 http://optics.org/articles/news/7/10/5/1

4 J. Broeng, E. Barkou, A. Bjarklev, C. Knight, T. Birks, optics communication

156(1998) 240-244.

5 K. Hansen, optics express, vol.11, No.13, 1503-1509,2003.

6 www.blazephotonics.com.

7 Y. Xu, A. Yariv, optics express, vol.28, No.20, 1885-1887, 2003.

8 http://unisci.com/stories/20001/0321014.htm.

9 N. Mortensen, M. Nielsen, optics letters, vol.28, No.6, 393-395,2003.

10 J. knight, T. Birks, J. Russel, J. de Sandro, optics materials ,11 143-151, 1999.

11 J. Limpert,T. Schreiber, s. Nolte,H. Zellmer,A. Tunnermann,J. Broeng, G. Vienne,

express, vol.11, No.7, 818-823,2003.

12 J. Broeng, D. Mogilevstev, A. Bjarklev, Optical Fiber technology, 5, 305-330, 1999.

13 http://homepages.udayton.edu/~sarangan/