Optical: systems and elements – Optical amplifier – Optical fiber
Reexamination Certificate
2001-11-06
2004-11-30
Moskowitz, Nelson (Department: 3663)
Optical: systems and elements
Optical amplifier
Optical fiber
Reexamination Certificate
active
06825974
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to fiber optics, fiber lasers, and fiber amplifiers, and more specifically, it relates to a rare-earth-doped fiber that, when optically pumped, has significantly higher gain for one linear polarization state than for the orthogonal state.
2. Description of Related Art
Introduction
Single-mode, rare-earth-doped fiber lasers and amplifiers are increasingly used in applications requiring compact, rugged, electrically efficient optical sources with high beam quality. Stable, linear polarization is required for many of these applications, including fiber-optic gyroscopes, interferometric fiber sensors, pumping of optical parametric oscillators and amplifiers, nonlinear frequency conversion, construction of mode-locked fiber lasers and narrow-linewidth fiber sources, polarization multiplexing, and most designs of phase or amplitude modulators. Conventional fiber sources have a time-varying (in general, elliptical) output polarization because of birefringence in the optical fiber and its variation with thermal and mechanical fluctuations.
The prior art includes a variety of methods for addressing fiber birefringence in both passive fibers and active fibers (i.e., fibers with optical gain). A discussion of the prior art provides the context for the present invention. For simplicity, most of the discussion will assume a step-index refractive-index profile for the fiber; this assumption affects some of the quantitative details, but the main conclusions of the analysis and the relevant design considerations will apply to other fiber types.
The following symbols are used herein:
a: core radius of the fiber.
&lgr;: free-space wavelength; most calculations will use &lgr;=1100 nm (a typical value for Yb-doped fiber).
n
i
j
: index of refraction; used with a subscript, i, to define the polarization state and superscript, j, to define the medium (e.g., n
x
core
is the index of refraction of x-polarized light in the fiber core); explicit definitions will be given in the text.
NA: numerical aperture; related to the acceptance angle of the fiber by NA=sin &thgr;
max
, where &thgr;
max
is the maximum angle of incidence for a ray that will be guided by the fiber; for a step-index fiber, the NA is determined by the refractive indices of the core and cladding (n
core
and n
clad
, respectively) according to NA=((n
core
)
2
−(n
clad
)
2
)
1/2
.
V: fiber V-number (also called the “normalized frequency”); V=2&pgr;NA a/&lgr;. V is useful for characterizing the guiding properties of a fiber and is a critical parameter in specifying the fiber design for the present invention. A step-index fiber is single-mode for V<2.405.
LP
01
: the fundamental (lowest-order) mode of a fiber, and the only guided mode for a single-mode fiber, consists of two, nearly linearly polarized states (generally referred to as x-polarized and y-polarized).
&ohgr;
0
: the mode-field radius for the LP
01
mode, measured at the 1/e
2
power density.
&Dgr;n
i
: difference in the refractive index (e.g., &Dgr;n
xy
for the difference in index between x-polarized and y-polarized light); again, a superscript may be used to indicate the medium, and explicit definitions will be given below.
L
b
: beat length (the length of birefringent fiber over which the x- and y-polarized modes experience a phase shift of 2&pgr;); L
b
=&lgr;/&Dgr;n
xy
, i.e., the beat length is inversely proportional to the fiber birefringence. Beat lengths will be given at &lgr;=633 nm unless otherwise noted.
Other definitions will be introduced in the text as needed. Units of dB will generally be used to express the ratio of two optical powers, e.g., the extinction ratio in dB between the x- and y-polarized modes (with powers P
x
and P
y
, respectively) is given by −10 log(P
y
/P
x
).
Passive Fibers
A “perfect” optical fiber, with no internal or externally applied stresses, will not be birefringent and will maintain the polarization state of light injected into the core. Any real fiber has birefringence from stresses developed in the manufacturing and subsequent handling (including bending or coiling) of the fiber. Because of this birefringence, light injected into the fiber will not maintain its polarization state, and the output polarization state will vary on the time scale over which the mechanical and thermal environment changes (S. C. Rashleigh, J. Lightwave Technol. 1, 312 (1983)). A linear polarizer placed after the fiber will ensure linear polarization but will cause power fluctuations as the output polarization state varies. Similarly, polarization controllers can convert a given elliptical polarization state to linear polarization, but they require adjustment as the output polarization changes.
Extensive research during the 1980's led to the development of passive polarization-maintaining (PM) fiber, in which a relatively large, stress-induced, linear birefringence is frozen into the fiber during manufacture (J. Noda et al., J. Lightwave Technol. 4, 1071 (1986)). This birefringence is provided by the incorporation of stress elements or rods into the fiber cladding. The stress elements (often composed of borosilicate glass) have a different (usually larger) thermal expansion coefficient than does the surrounding cladding glass (generally silica, possibly doped with germanium, phosphorous, and other materials); as the fiber cools after being drawn, the different expansion coefficients cause stress to accumulate in the fiber, which induces linear birefringence. Linearly polarized light launched into the fiber with its polarization vector aligned either along or perpendicular to the stress rods (denoted x-polarized and y-polarized, respectively) will maintain its linear polarization state because the induced birefringence “overwhelms” the other sources of birefringence. (An alternative approach uses an elliptical core, but this design is less popular because the core is not well matched to standard, circular-core fibers and because the output beam is elliptical.)
FIGS. 1A-1D
show several designs of commercially available passive PM fiber. Beat lengths are typically in the range of 1 mm to 1 cm at &lgr;=633 nm (a standard wavelength at which to report L
b
); the corresponding values of &Dgr;n
xy
are 6.33×10
−4
to 6.33×10
−5
. (For comparison, typical fibers have an index difference between the core and the cladding (&Dgr;n
c
) that is a factor of ~10 smaller than &Dgr;n
xy
: &Dgr;n
c
=2.2×10
−3
to 1.4×10
−2
, corresponding to NA values of 0.08-0.20, respectively.) L
b
values as low at 0.55 mm (&Dgr;n
xy
=1.2×10
−3
) have been obtained using “bow-tie” stress elements (R. D. Birch et al., Electron. Lett. 18, 1036 (1982)). Recently, a highly birefringent “photonic crystal” or “holey” fiber has been reported, in which the cladding contained an array of air holes; a beat length of 0.42 mm at &lgr;=1540 nm (&Dgr;n
xy
=3.7×10
−3
) was obtained, corresponding to L
b
<0.2 mm at &lgr;=633 nm (A. Ortigosa-Blanch et al., Opt. Lett. 25, 1325 (2000)).
For many applications, fiber that supports only a single linear polarization state would be preferable. Such “polarizing” (PZ) fiber has been demonstrated, although it is not as readily available as PM fiber. Obtaining PZ operation of a passive fiber entails introducing substantial loss for one linear polarization state (e.g., y-polarized) and relatively little loss for the orthogonal state (x-polarized). As discussed below, most PZ fibers are highly birefringent.
FIG. 2A
shows the refractive-index profile for a non-birefringent fiber and
FIGS. 2B-2E
show the refractive-index profiles for several possible designs of birefringent fiber; the birefringent designs lead to a number of mechanisms for excess loss of one polarization state. The demonstrated or suggested approaches to fabricating PZ fiber are as follows:
1) In
FIGS. 2B and 2C
, the birefringence is lar
Kliner Dahv A. V.
Koplow Jeffery P.
Evans Timothy P.
Hughes Deandra M.
Moskowitz Nelson
Sandia National Laboratories
Wooldridge John P.
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