A technique to tune a magnetic quasi-phase matching in-fiber isolator through the application of stress induced by two mutually orthogonal capillary tubes filled with liquid ethanol is investigated numerically. The results show that it is possible to “tune” the birefringence in these fibers over a limited range depending on the temperature at which the ethanol is loaded into the capillaries. Over this tuning range, the thermal sensitivity of the birefringence is an order-of-magnitude lower than conventional fibers, making this technique well suited for magnetic quasi-phase matching.
Optical isolators play a critical role in the fabrication of high-power fiber amplifiers. Their purpose is to protect optical sources from light traveling in the backward direction which can cause damage to the optical source and instabilities in the output spectra. Optical isolators come in two flavors: polarization-dependent and polarization-independent. The polarization dependent isolator consists of an input polarizer, a Faraday rotator, and an output polarizer. Polarization independent isolators consist of an input birefringent wedge (with its ordinary polarization direction vertical and its extraordinary polarization direction horizontal), a Faraday rotator, and an output birefringent wedge oriented at 45° to the first. Ideally the birefringent crystals and Faraday rotator should have low absorption coefficients at the wavelengths of interests, low nonlinear refractive indices, and high damage thresholds. Also, the Faraday rotator should have a high Verdet constant to achieve the highest degree of rotation with minimal length to prevent self-focusing inside the material and other thermal effects, as well as nonreciprocal nonlinear polarization coupling at high power.
The major sources of backward traveling light in high-power fiber lasers and amplifiers are reflections from the fiber output facet, spontaneous Raleigh scattering (SRS), stimulated Brillouin scattering (SBS), and amplified spontaneous emission (ASE). While certain techniques may be employed to minimize backward-traveling light, it is often a safe practice to incorporate isolators capable of suppressing backward power of at least 1–5% of the output power of the laser or amplifier. Current (free space) isolators can handle average powers up to the order of 100 W with limited beam distortions. For fiber-coupled devices, the power levels are currently limited to about 50 W.
Recent demonstrations show continuous wave (CW) diffraction-limited power in fiber amplifiers scalable to the kW level [
By matching the beat length of birefringent single-mode fiber to the period of a spatially alternating magnetic field within the fiber, 45° Faraday rotation is achievable in undoped silica fiber in less than 1 m3. This configuration is shown in Figure
Example of quasi-phase matching technique. Two out of about 57 periods are shown.
The local magnetic field at any point along the fiber is given by [
Before entering the magnet array at
In the above equations,
The beat length
In order for the all-fiber isolator to be effective in a practical system, care must be taken to match the beat length of the fiber to the period of the magnetic array in order to keep
Using the parameters described in [
Practical parameters for Magnetic Quasi-Phase matching in a fiber.
24 (mm) | |
9.3 (mm) | |
12 (mm) | |
0.6 (mm) | |
0.748 T | |
1.129 radians/Tm | |
100 |
As shown in Figure
Backward (red) and Forward (blue) transmissions through in-fiber isolator using parameters of Table
Another consideration is isolation at multiple wavelengths. Traditional isolators have band passes on the order of 20 nm. Changes in the isolation over the band pass are typically very small. However, using the magnetic-quasiphase matching technique, the situation is quite different. Again using a typical birefringence of
One possible technique to control the birefringence in a fiber is to insert a set of perpendicular liquid-filled holes mutually orthogonal to the traditional borosilicate stress rods in PANDA fiber as shown in Figure
Example configuration of conventional fiber with a secondary set of mutually orthogonal capillary tubes filled with liquid ethanol.
In general, the birefringence in a fiber is given by
Example of standard (PANDA) fiber.
In the case of the plane-strain approximation,
With the addition of the pressure introduced in the walls of the liquid filled stress rods, the boundary conditions across the interface between the capillary walls and the surrounding cladding are such that the pressure is continuous
The pressure on the boundary of the holes is determined using the empirical equation-of-state of liquid ethanol [
In general, the average birefringence of the core as well as the sensitivity of the birefringence to temperature is dependent on the several factors mentioned in the preceding section. Referencing Figure
Conventional fiber with a secondary set of mutually orthogonal capillary tubes filled with liquid ethanol.
In an effort to limit the parameter space, we fix the core and cladding diameter to 25
Practical parameters for Magnetic Quasi-Phase matching in a fiber.
Name | Expression | Description |
---|---|---|
0.0001 (m) | Fiber Radius | |
1346.15 (K) | Fiber Melting Temperature | |
73e9 (Pa) | Young's Modulus of Fiber | |
2.28e-006 (1/K) | Thermal Expansion Coefficient of solid rods | |
5e-007 (1/K) | Thermal Expansion Coefficient of Cladding | |
0.17 | Poison's Ratio of Fiber | |
1.25e-005 (m) | Core Radius | |
3.22e-012 (1/Pa) | Stress-Optic Coefficient at 1064 nm |
As described in the proceeding sections the parameters
Wall Pressure versus operating temperature of capillary tubes filled with liquid ethanol.
Near room temperature, the wall pressure can be “tuned” from approximately 30–160 MPa, resulting in a range of stresses applied in the orthogonal directions relative to the standard borosilicate rods. Figure
Practical parameters for Magnetic Quasi-Phase matching in a fiber.
Name | Expression | Description |
---|---|---|
0.0001 (m) | Fiber Radius | |
3.46e-005 (m) | Center-to-center distance of solid rods | |
4.78e-005 (m) | Center-to-center distance of solid rods | |
8.2e-006 (m) | Solid rod radius | |
2.9e-006 (m) | Liquid rod radius | |
1.25e-005 (m) | Core Radius |
Example of birefringence of a fiber with both liquid and solid stress rods. The liquid capillary tubes and solid stress rods are shown aligned with the vertical and horizontal axes respectively.
Another important feature of Figure
After considering a significant portion of the parameter space, the fiber described by the parameters in Table
Average Core Birefringence versus Operating Temperatures.
Normalized change in birefringence with respect to temperature versus operating temperature.
Notice that in the normal operating regime (20–40
Figure
Beat length versus operating temperature for various ethanol loading temperatures.
A tunable, temperature insensitive, birefringent fiber was theoretically designed by investigating the use of a secondary set of mutually orthogonal liquid-filled capillaries in conjunction with traditional borosilicate stress rods. Although this paper is concerned with using this technique to construct a fiber with a nominal beat length of 1.75 cm, a similar analysis could be done aiming at designs spanning a range of beat lengths. This paper has demonstrated that, by using a secondary set of capillaries filled with liquid ethanol, two of the practical limitations facing an all-fiber isolator using magnetic quasi-phase matching can be overcome: tunability is enabled to a selected wavelength within a range of
The authors would like to thank Iyad Dajani for useful discussions. This research was supported in part by the High-Energy Laser Joint Technology Office.