CN109031516A - A kind of large mode field Double Cladding Ytterbium Doped Fiber - Google Patents
A kind of large mode field Double Cladding Ytterbium Doped Fiber Download PDFInfo
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- CN109031516A CN109031516A CN201810755373.8A CN201810755373A CN109031516A CN 109031516 A CN109031516 A CN 109031516A CN 201810755373 A CN201810755373 A CN 201810755373A CN 109031516 A CN109031516 A CN 109031516A
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/02—Optical fibres with cladding with or without a coating
- G02B6/036—Optical fibres with cladding with or without a coating core or cladding comprising multiple layers
- G02B6/03616—Optical fibres characterised both by the number of different refractive index layers around the central core segment, i.e. around the innermost high index core layer, and their relative refractive index difference
- G02B6/03622—Optical fibres characterised both by the number of different refractive index layers around the central core segment, i.e. around the innermost high index core layer, and their relative refractive index difference having 2 layers only
- G02B6/03633—Optical fibres characterised both by the number of different refractive index layers around the central core segment, i.e. around the innermost high index core layer, and their relative refractive index difference having 2 layers only arranged - -
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/02—Optical fibres with cladding with or without a coating
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Abstract
The invention discloses a kind of large mode field Double Cladding Ytterbium Doped Fibers, including fibre core, successively surround the quartzy inner cladding, low-refraction surrounding layer and external coating of core periphery from inside to outside, quartzy inner cladding is equipped with index dip region close to the medial surface of fibre core, contain ytterbium in fibre core, along the diametrical direction of fibre core, the concentration of ytterbium is in that class is trapezoidal or the parabola shaped distribution of class, the diameter of ytterbium doped region are less than or equal to core diameter from inside to outside.The present invention, in the case where not changing mechanical fiber optic performance, not increasing fiber manufacturing cost and difficulty, improve the index distribution and dopant profiles of optical fiber, the two collective effect can keep foundational model field area, it is designed in conjunction with triangle and the fibre core complex refractive index of step shape, the balance between basic mode effective core area and basic mode extraction efficiency is adjusted by changing complex morphological, Light Energy is concentrated to core centre, therefore the extraction efficiency of basic mode can be improved, the laser output of high light beam quality is obtained, beam quality is improved.
Description
Technical field
The present invention relates to technical field of optical fiber, and in particular to a kind of large mode field Double Cladding Ytterbium Doped Fiber.
Background technique
If doped with the optical fiber of rare earth element, in pump light injection fibre appropriate, the outer layer of rare earth element in fibre core
Electrons absorb the energy of photon and transit to higher energy level.When the number of particles in excitation state inverts, pass through
The signal light of fibre core will cause stimulated radiation and be amplified.In optical fiber laser, cavity resonator structure forms excited radiation light
The laser generation output of high light beam quality, high power density.Different fiber optic materials systems combine it is different rare earth doped,
The light of various wavelength can be radiated under the excitation of the light of respective wavelength, and ultraviolet to infrared spectral region can be covered.Optical fiber
Laser is substantially distinguished from traditional solid state laser with its excellent beam quality, in material retrofit, military affairs, detection
There is apparent application advantage in equal fields.
Ytterbium (Yb) silica fibre is mixed as a kind of rare earth doped fiber, can absorb the pump light near 915nm or 975nm
To realize the laser output near 1064nm.Since ytterbium is not susceptible to concentration quenching, it can be achieved that higher doping concentration, and it swashs
Hair state service life, quantum efficiency are higher, energy conversion efficiency with higher, therefore mix ytterbium silica fibre and be commonly used for manufacturing Gao Gong
The optical fiber laser of rate.
In order to improve pumping efficiency, high-capacity optical fiber laser is using cladding pumping technique, i.e., very using double clad
To the Yb dosed optical fiber of triple clad, inhibit covering spiral by coupling pump light to inner cladding, and using non-circular inner cladding structure
Light and increasing light pass through the probability of fibre core, to increase fibre core to the absorbability of pump light.In high-power operation, ytterbium is mixed
The fibre core of optical fiber has very high energy density, this will lead to thermal damage and nonlinear effect, seriously affects the property of optical fiber laser
Energy.In order to reduce fibre core energy density, reduce nonlinear effect, Yb dosed optical fiber can be designed to big core diameter, large mode field structure, and
Guarantee high light beam quality, the small divergence angle of optical fiber laser, it is necessary to assure optical fiber is single mode or quasi- single-mode output, such ability
Make have sufficiently high energy density on far field, ensures the application effect of optical fiber laser.Step shape or quasi- step shape refractive index are set
The big core diameter yb-doped double-clad fiber of the large mode field of meter can all accommodate few mould transmission, and foundational model field intensity is usually Gaussian Profile, and
High-order mode intensity distribution can expand light radiation angle and reduce beam quality close to core area edge.Therefore biggish core diameter and
Mould field makes the single-mode output for keeping optical fiber become a problem, to inhibit the oscillation of higher order mode, realizes that the standard of optical fiber is single
Mould operating, mainly there is following three methods:
1. most direct method be reduce fibre core numerical aperture (NA), but too low numerical aperture can dramatically increase it is curved
Song is lost and is unfavorable for the application of optical fiber, and the numerical aperture of Yb dosed optical fiber can be down to 0.05, by material system at present
Limitation is difficult have the space for reducing NA again in the case where higher-doped concentration.
2. the loss of high-order mode can be increased by fibre-optical bending or around ring, achieve the effect that filter out high-order mode, but for big
For the high power Yb dosed optical fiber of the low numerical aperture of diameter, the bending loss difference between basic mode and high-order mode is smaller, and big function
When rate filters mould, the energy of leakage will damage the normal work of fibre coating and then influence optical fiber.
3. a certain section of drawing of optical fiber is bored, high-order mode can be leaked when light beam passes through light cone to realize quasi- single mode operation, but
It is to draw easily to damage at cone since core diameter becomes smaller, energy leakage is big at high power.
4. the theoretically preferable large mode field area Yb-doped optical fiber of chirality coupling fibre core (CCC) optical fiber and photonic crystal fiber
Embodiment, the single mode transport that CCC optical fiber dissipates higher order mode by the spiral side core around fibre core to realize fibre core, photon
Crystal optical fibre then limits the transmission mode of optical fiber by the specific arrangement of stomata in covering, but the manufacture work of both optical fiber
Skill is more complicated, and manufacturing cost is very high, is mainly seen in laboratory report at present, and wouldn't be suitble to large-scale commercial applications application.
It can be seen that current ytterbium silica fibre of mixing is difficult to realize the standard of optical fiber in big core diameter, large mode field structure basis
Single mode operating.
Summary of the invention
The technical problem to be solved by the present invention is to current ytterbium silica fibre presence of mixing to be difficult in big core diameter, large mode field knot
The problem of quasi- single mode operating of optical fiber is realized on the basis of structure.
In order to solve the above-mentioned technical problem, it is mixed the technical scheme adopted by the invention is that providing a kind of large mode field double clad
Ytterbium optical fiber including fibre core, successively surrounds the quartzy inner cladding of the core periphery, low-refraction surrounding layer and outer from inside to outside
Coating, the quartz inner cladding are equipped with index dip region close to the medial surface of the fibre core, and the quartz inner cladding is cut
Face shape is octagon, contains ytterbium in the fibre core, and along the diametrical direction of the fibre core, the concentration of ytterbium is in class ladder from inside to outside
Shape or the parabola shaped distribution of class, the diameter of ytterbium doped region are less than or equal to core diameter, packet in the fibre core and the quartz
The index distribution of layer meets following relational expression:
Wherein a is fiber core radius, and b is to have to stablize refractive index n in fibre core1Region radius, h be index dip area
The outer peripheral radius in domain, j are the spacing on the opposite both sides of quartzy inner cladding, and meet h < 1.4a, 0.5a < b < a, 0.5 (n1+
n4) < n2< n1, n4-0.5(n1-n4) < n3< n4。
Variable r is the distance relative to core centre, n1For fibre core in diameter b with the refractive index of inner region, n2For fibre core
Outer peripheral refractive index, n3For the refractive index in index dip region, n4It is removed except index dip region for quartzy inner cladding
Region refractive index.
In another preferred embodiment, the concentration of ytterbium is in class trapezoidal profile on core diameter direction, and ytterbium is dense
Degree distribution meets following relational expression:
Wherein p is that the center of fibre core has highest ytterbium concentration cmaxRegion radius, q be ytterbium doped region radius, a
For fiber core radius, and meet q≤a, slope s meets 0≤s≤cmax/ (q-p), variable r are the distance relative to core centre,
cmaxFor the ytterbium concentration of core centre.
In another preferred embodiment, the concentration of ytterbium is in the parabola shaped concentration distribution of class on core diameter direction,
And the concentration distribution of ytterbium meets following relational expression:
Wherein cmaxFor the highest ytterbium concentration of core centre, k is the radius of ytterbium doped region, and a is fiber core radius, and meets k
≤ a, coefficient t meet 0≤t≤cmax/k2, variable r is the distance relative to core centre.
In another preferred embodiment, the value range of the diameter 2a of the fibre core is 10 microns~200 microns.
In another preferred embodiment, the value range of j is 125 microns~650 microns.
In another preferred embodiment, the spacing on the opposite both sides of the quartzy inner cladding and the core diameter
Ratio j/a be greater than or equal to 3.
In another preferred embodiment, the numerical aperture NA of the fibre core and the quartzy inner cladding14Range be
0.05~0.09, i.e.,
In another preferred embodiment, the numerical aperture of the quartzy inner cladding and the low-refraction surrounding layer
NA45More than or equal to 0.46, i.e.,Wherein n5For the refractive index of the low-refraction surrounding layer.
In another preferred embodiment, the fibre core using quartz substrate ytterbium aluminium be co-doped with material, ytterbium aluminium phosphorus is co-doped with
Material or ytterbium aluminium phosphorus fluorine are co-doped with material, and wherein the range of the maximum concentration of ytterbium is 200ppm~4000ppm.
In another preferred embodiment, beam quality factor M2Less than or equal to 1.5.
The present invention is under same fiber core refractive index distribution situation compared with existing optical fiber, and ytterbium is more distributed
In core centre, and as the increase of radial direction distance gradually decreases ytterbium content until not mixing in fibre core outermost certain thickness
Ytterbium, in this way, the distribution shape of ytterbium can be preferably be overlapped with the envelope of basic mode central part, ytterbium after pump light excites,
The basic mode that intensity focuses primarily upon core centre can preferentially be amplified, and intensity focuses primarily upon the acquisition of the higher order mode on the outside of fibre core
Gain it is less, start in terms of the core design of optical fiber itself, do not change mechanical fiber optic performance, do not increase fiber manufacturing at
Originally and in the case where difficulty, the index distribution and dopant profiles of optical fiber are improved, the two collective effect can keep basic mode mould
Scene product.On this basis, it designs in conjunction with triangle and the fibre core complex refractive index of step shape, is adjusted by changing complex morphological
The balance between basic mode effective core area and basic mode extraction efficiency is saved, while ensureing foundational model field area, by Light Energy
It is concentrated to core centre, therefore the extraction efficiency of basic mode can be improved, obtained the laser output of high light beam quality, improve light beam matter
Amount.
Detailed description of the invention
Fig. 1 is schematic cross-section of the invention and its refractive index profile schematic diagram；
Fig. 2 is the class trapezoidal profile figure of the ytterbium doping concentration of fibre core of the invention；
Fig. 3 is the parabola shaped distribution map of class of the ytterbium doping concentration of fibre core of the invention.
Specific embodiment
The present invention provides a kind of large mode field Double Cladding Ytterbium Doped Fibers, start in terms of the core design of optical fiber itself,
In the case where not changing mechanical fiber optic performance, not increasing fiber manufacturing cost and difficulty, improves the index distribution of optical fiber and mix
Miscellaneous distribution, the two collective effect can keep foundational model field area.On this basis, in conjunction with the fibre core of triangle and step shape
Complex refractive index design is adjusted flat between basic mode effective core area and basic mode extraction efficiency by changing complex morphological
Weighing apparatus while ensureing foundational model field area, Light Energy is concentrated to core centre, therefore the extraction efficiency of basic mode can be improved,
The laser output of high light beam quality is obtained, beam quality is improved.Combined with specific embodiments below with Figure of description to this hair
It is bright to be described in detail.
As shown in Figure 1, a kind of large mode field Double Cladding Ytterbium Doped Fiber provided by the invention, including fibre core 1, from inside to outside successively
Surround the quartzy inner cladding 2, low-refraction surrounding layer 3 and external coating 4 of 1 periphery of fibre core, quartzy inner cladding 2 is close to fibre core 1
Medial surface is equipped with index dip region, and the cross sectional shape of quartzy inner cladding 2 is octagon, contains ytterbium in fibre core 1, along fibre core
1 diametrical direction, the concentration of ytterbium are in that class is trapezoidal or the parabola shaped distribution of class, the diameter of ytterbium doped region are less than or wait from inside to outside
In 1 diameter of fibre core, the index distribution of fibre core 1 and quartzy inner cladding 2 meets following relational expression:
Wherein a is 1 radius of fibre core, and b is to have to stablize refractive index n in fibre core 11Region radius, h is index dip
The radius of region outer edge, j are the spacing on the opposite both sides of quartzy inner cladding 2, and meet h < 1.4a, 0.5a < b < a, 0.5
(n1+n4) < n2< n1, n4-0.5(n1-n4) < n3< n4。
Variable r is the distance relative to 1 center of fibre core, n1For fibre core 1 in diameter b with the refractive index of inner region, n2For fibre core
1 outer peripheral refractive index, n3For the refractive index in index dip region, n4Index dip region is removed for quartzy inner cladding 2
Except region refractive index.
Wherein various ways setting can be used in the concentration of ytterbium, uses the following two kinds mode in present patent application:
One, class trapezoidal profile
As shown in Fig. 2, the concentration of ytterbium is in class trapezoidal profile in 1 diametrical direction of fibre core, and the concentration distribution of ytterbium meets such as
Lower relational expression:
Wherein p is that the center of fibre core has highest ytterbium concentration cmaxRegion radius, q be ytterbium doped region radius, a
For fiber core radius, and meet q≤a, slope s meets 0≤s≤cmax/ (q-p), variable r are the distance relative to core centre,
cmaxFor the ytterbium concentration of core centre.
Two, the parabola shaped concentration distribution of class
As shown in figure 3, the concentration of ytterbium is in the parabola shaped concentration distribution of class in 1 diametrical direction of fibre core, and the concentration of ytterbium is divided
Cloth meets following relational expression:
Wherein cmaxFor the highest ytterbium concentration of core centre, k is the radius of ytterbium doped region, and a is fiber core radius, and meets k
≤ a, coefficient t meet 0≤t≤cmax/k2, variable r is the distance relative to core centre.
Preferably, the value range of the diameter 2a of fibre core 1 is 10 microns~200 microns.
Preferably, the value range of j is 125 microns~650 microns.
The spacing on the opposite both sides of quartzy inner cladding 2 and ratio (the i.e. cored ratio) j/a of 1 diameter of fibre core are greater than or equal to 3.
The numerical aperture NA of fibre core 1 and quartzy inner cladding 215Range be 0.05~0.09, i.e.,
The numerical aperture NA of quartzy inner cladding 2 and low-refraction surrounding layer 345More than or equal to 0.46, i.e.,
Wherein n5For the refractive index of low-refraction surrounding layer 3.
Fibre core 1 is co-doped with material using the ytterbium aluminium of quartz substrate, ytterbium aluminium phosphorus is co-doped with material or ytterbium aluminium phosphorus fluorine is co-doped with material, wherein
The range of the maximum concentration of ytterbium is 200ppm~4000ppm.
It is below the several embodiments and comparative example of present patent application, in order to compare, comparative example is used and set without special
The conventional scheme of meter.Embodiment and comparative example all use identical geometric dimension design, and 1 diameter of fibre core is 30.0 μm of (a=
15.0 μm), edge-to-edge's distance 2j of quartzy inner cladding 2 is 250 μm, the numerical aperture NA of fibre core 114It is 0.06, and use
Low-refraction surrounding layer 3 and external coating 4 are all the same, and the difference is that the index profile design and doping concentration of fibre core 1
Distribution design.
The 915nm pumping source that 300W is all made of when testing optical fiber is pumped into tested optical fiber, the long 7.5m of tested optical fiber, coil diameter
25cm in its measurement of output end and analyzes its beam quality after the oscillation amplification of the grating at tested optical fiber both ends.
Embodiment one
The ytterbium doping concentration of fibre core 1 is class trapezoidal profile, and the doped region radius q of ytterbium is 11.9 μm, and the doping of highest ytterbium is dense
The radius p for spending region is 5.8 μm, highest ytterbium doping concentration CmaxFor 1200ppm, the outermost ytterbium concentration of doped region is
400ppm, therefore fibre core 1 is using triangle and the design of the complex refractive index of step shape, the Laser Measuring for the use of wavelength being 632.8nm
The refractive index obtained is n1=1.45891, n2=1.45840, n3=1.45719, n4=1.45762, and refractive index is n1Region
B=9.0 μm of radius, h=17.0 μm of index dip area outer diameter, measure its export mode field diameter be 20.7 μm, light beam matter
Measure factor M2=1.32.
Embodiment two
1 ytterbium doping concentration of fibre core is the parabola shaped distribution of class, and doped region radius k is 12.0 μm, highest ytterbium doping concentration
CmaxFor 1200ppm, the outermost ytterbium concentration of doped region is 480ppm, t=5ppm μm of coefficient-2, the refractive index of fibre core 1 sets
Meter is the same as example 1, and measuring it and exporting mode field diameter is 21.0 μm, beam quality factor M2=1.41.
Comparative example one
Fibre core 1 uniformly mixes ytterbium, and concentration 1100ppm, 1 refractive index design and implementation example 1 of fibre core is identical, measures it and exports mould
Field diameter is 20.8 μm, beam quality factor M2=1.83.
Comparative example two
It is simple step shape, i.e. n that fibre core 1, which uniformly mixes ytterbium, concentration 1100ppm, and index distribution,1=n2=
1.45891 n3=n4=1.45762, measuring it and exporting mode field diameter is 22.7 μm, beam quality factor M2=2.19.
It can be seen that being lower than two comparative examples, M using two embodiment beam quality factors of the invention2=2.19 phases
Than possessing more preferably output beam quality in comparative example.The beam quality factor M of optical fiber made from present patent application2It is less than or waits
In 1.5.
The present invention, which can be used improved chemical vapor deposition (MCVD) method and manufacture it, mixes ytterbium fibre core, as above in order to realize
Two kinds of ytterbium concentration distributions need to carry out more times depositions of different parameters, and the deposition number of plies is at least 10 layers, and the deposition number of plies is recommended to be greater than
30 layers.The parabola shaped concentration distribution of class only needs successively linearly to reduce ytterbium doping concentration, and collapsing is can be realized after solid bar, therefore
It is more easily performed in technique.The doping process that the distribution of class trapezoidal concentration then needs square root curve incremental, implements complex.
The present invention is under same fiber core refractive index distribution situation compared with existing optical fiber, and ytterbium is more distributed
In core centre, and as the increase of radial direction distance gradually decreases ytterbium content until not mixing in fibre core outermost certain thickness
Ytterbium, in this way, the distribution shape of ytterbium can be preferably be overlapped with the envelope of basic mode central part, ytterbium after pump light excites,
The basic mode that intensity focuses primarily upon core centre can preferentially be amplified, and intensity focuses primarily upon the acquisition of the higher order mode on the outside of fibre core
Gain it is less, start in terms of the core design of optical fiber itself, do not change mechanical fiber optic performance, do not increase fiber manufacturing at
Originally and in the case where difficulty, the index distribution and dopant profiles of optical fiber are improved, the two collective effect can keep basic mode mould
Scene product.On this basis, it designs in conjunction with triangle and the fibre core complex refractive index of step shape, is adjusted by changing complex morphological
The balance between basic mode effective core area and basic mode extraction efficiency is saved, while ensureing foundational model field area, by Light Energy
It is concentrated to core centre, therefore the extraction efficiency of basic mode can be improved, obtained the laser output of high light beam quality, improve light beam matter
Amount.
The present invention is not limited to above-mentioned preferred forms, and anyone should learn that the knots made under the inspiration of the present invention
Structure variation, the technical schemes that are same or similar to the present invention are fallen within the scope of protection of the present invention.
Claims (10)
1. a kind of large mode field Double Cladding Ytterbium Doped Fiber, which is characterized in that including fibre core, successively surround the fibre core from inside to outside
Quartzy inner cladding, low-refraction surrounding layer and the external coating of periphery, the quartz inner cladding are set close to the medial surface of the fibre core
There is index dip region, the cross sectional shape of the quartz inner cladding is octagon, contains ytterbium in the fibre core, along the fibre
The diametrical direction of core, the concentration of ytterbium are in that class is trapezoidal or the parabola shaped distribution of class from inside to outside, the diameter of ytterbium doped region be less than or
Equal to core diameter, the index distribution of the fibre core and the quartzy inner cladding meets following relational expression:
Wherein a is fiber core radius, and b is to have to stablize refractive index n in fibre core1Region radius, h be index dip region outside
The radius at edge, j are the spacing on the opposite both sides of quartzy inner cladding, and meet h < 1.4a, 0.5a < b < a, 0.5 (n1+n4) <
n2< n1, n4-0.5(n1-n4) < n3< n4。
Variable r is the distance relative to core centre, n1For fibre core in diameter b with the refractive index of inner region, n2For the outside of fibre core
The refractive index of edge, n3For the refractive index in index dip region, n4The area except index dip region is removed for quartzy inner cladding
The refractive index in domain.
2. a kind of large mode field Double Cladding Ytterbium Doped Fiber as described in claim 1, which is characterized in that the concentration of ytterbium is in core diameter
It is in class trapezoidal profile on direction, and the concentration distribution of ytterbium meets following relational expression:
Wherein p is that the center of fibre core has highest ytterbium concentration cmaxRegion radius, q be ytterbium doped region radius, a be fibre
Core radius, and meet q≤a, slope s meets 0≤s≤cmax/ (q-p), variable r are the distance relative to core centre, cmaxFor
The ytterbium concentration of core centre.
3. a kind of large mode field Double Cladding Ytterbium Doped Fiber as described in claim 1, which is characterized in that the concentration of ytterbium is in core diameter
It is in the parabola shaped concentration distribution of class on direction, and the concentration distribution of ytterbium meets following relational expression:
Wherein cmaxFor the highest ytterbium concentration of core centre, k is the radius of ytterbium doped region, and a is fiber core radius, and meets k≤a,
Coefficient t meets 0≤t≤cmax/k2, variable r is the distance relative to core centre.
4. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that the fibre core
The value range of diameter 2a be 10 microns~200 microns.
5. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that the value model of j
Enclose is 125 microns~650 microns.
6. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that the quartz
The spacing on the opposite both sides of inner cladding and the ratio j/a of the core diameter are greater than or equal to 3.
7. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that the fibre core
With the numerical aperture NA of the quartzy inner cladding15Range be 0.05~0.09, i.e.,
8. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that the quartz
The numerical aperture NA of inner cladding and the low-refraction surrounding layer45More than or equal to 0.46, i.e.,Wherein n5
For the refractive index of the low-refraction surrounding layer.
9. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that the fibre core
Material is co-doped with using the ytterbium aluminium of quartz substrate, ytterbium aluminium phosphorus is co-doped with material or ytterbium aluminium phosphorus fluorine is co-doped with material, the wherein maximum concentration of ytterbium
Range be 200ppm~4000ppm.
10. a kind of large mode field Double Cladding Ytterbium Doped Fiber as claimed in any one of claims 1 to 3, which is characterized in that beam quality
Factor M2Less than or equal to 1.5.
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