Abstract:
A variable optical attenuator, or VOA, for attenuating an optical signal between two photonic components by changing an alignment of a light beam with an output photonic component in at least two dimensions. A first configuration of the invented VOA has an actuator and two optical fibers. The actuator moves one optical fiber to form a light beam trajectory on the remaining optical fiber, wherein the shape of the trajectory has at least two separate dimensional components. A second configuration of the invented VOA includes a mirror that the actuator moves within at least two degrees of freedom and thereby forms a two-dimensional trajectory of the reflected light beam on a photonic component. A third embodiment includes a mirror, a mirror actuator and a dual fiber collimator having a lens and two optical fibers. The VOA may be partially or wholly integrated on a substrate and/or incorporated as a MEMS-based device.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to methods and devices for attenuating an optical signal. The present invention more particularly relates to methods and devices for variably attenuating an optical signal within an optical network or a micro-electro-mechanical system (MEMS).  
         BACKGROUND OF THE INVENTION  
         [0002]    In the modem optical network there are many places where there are requirements to attenuate the optical power of a signal. The prior art includes methods and devices that enable transmission and attenuation of a light beam from an input wave guide and to an output wave guide by aiming and mis-aiming the light beam in a direct transmission from the input wave guide and into the output wave guide. The prior art additionally includes devices that employ a mirror to reflect the light beam from an input wave guide, such as an optical fiber, and into an output wave guide, where the output wave guide may also be an optical fiber. These prior art techniques, however, exhibit highly non-linear relationships between an actuator control signal and a resulting attenuation, as measured in decibels, of a transmission of the light beam, wherein the sensitivity of the effected attenuation is often undesirably high in response to small variations in the control signal.  
           [0003]    A long felt need therefore exists to provide a method and device for variably attenuating an optical signal in a more linear relationship between the actuator control signal and the resulting optical signal attenuation, where the attenuation is measured in decibels. Additionally, a MEMS based variable optical attenuator that provides a finer and more precise control over the optical attenuation of the optical signal would satisfy certain needs of optical systems architects and improve the performance of an optical communications network.  
         OBJECTS OF THE INVENTION  
         [0004]    It is an object of the present invention to provide a method of variable optical attenuation with improved performance.  
           [0005]    It is an object of certain preferred embodiments of the present invention to provide a variable optical attenuator, or VOA, having improved characteristics.  
           [0006]    It is an alternate object of certain preferred embodiments of the present invention to provide a VOA that attenuates an optical signal with improved linearity.  
           [0007]    It is a still alternate object of certain preferred embodiments of the present invention to provide a VOA that attenuates an optical signal with improved resolution.  
           [0008]    It is another object of certain preferred embodiments of the present invention to provide a VOA that attenuates an optical signal with improved accuracy.  
           [0009]    It is yet another object of certain preferred embodiments of the present invention to provide a VOA that attenuates an optical signal with decreased power requirements.  
         SUMMARY OF THE INVENTION  
         [0010]    The invention is a variable optical attenuator and method of use thereof for attenuating an optical signal by directing the transmission of a light beam into a photonic component along a trajectory, where the trajectory lies on a receiving face of the photonic component and has geometric components in at least two dimensions. The method of the preferred embodiment of the present invention comprises the generation of a non-linear trajectory of a light beam on an output photonic component by directing the light beam in two dimensions between an input photonic component and the output photonic component. The non-linear trajectory is formed by changing the direction of the light beam and thereby changing an alignment of the light beam with regard to the receiving face of the output photonic component.  
           [0011]    The method of the present invention linearizes the optical-loss-versus-actuation curve for the invented VOA, in which attenuation of an optical signal is based on a misalignment of the light beam from, for example, as transmitted from the receiving face  14  of the first optical fiber to the receiving face of the second optical fiber.  
           [0012]    Prior art VOA&#39;s based on this misalignment method generate variable optical losses by moving a spot of the light beam along the trajectory therefore upon the receiving face of the photonic component. The spot is the intersection, or strike, of the light beam on the receiving face. The spot includes a center point (peak power density point) of the light beam. In the prior art attenuation is achieved by locating strike and the center point away from a center of the core of an output optical fiber along a linear trajectory, i.e. within a straight line. The disadvantage of the prior art is that the loss versus position of the image is a highly non-linear (approximately quadratic) relationship due to the wave guide properties of single mode fibers. This means that at higher attenuation settings, the actual attenuation is highly sensitive to the spot position which puts severe constraints on the control of the spot position.  
           [0013]    The method of the present invention comprises the steps of moving the light beam to locate the spot on the face of the receiving fiber along a two-dimensional trajectory, instead of along a straight line. The two-dimensional trajectory can be designed such that the overall loss-versus-trajectory-position is linearized significantly compared to the quadratic relation when moving along a straight line, reducing the sensitivity to position uncertainty.  
           [0014]    A trajectory path of the light beam is established on a receiving face of the photonic component by dynamically altering the direction of the light beam in at least two dimensions. A trajectory path is created in certain preferred embodiments of the method of the present invention wherein the relationship between the distance traveled by the light beam within the trajectory and the resulting attenuation, as expressed in decibels, is more linear as compared with the prior art.  
           [0015]    A trajectory path of the light beam can alternately or additionally be chosen as to improve the linearity between a control signal and a resulting attenuation, as expressed in decibels, as the control signal is varied. The method of the present invention is not limited to actuators that act on a photonic component in linear or near relationships between the control signal and a variable force, load or other output of the attenuator directed to a photonic component, such as an optical fiber or a mirror.  
           [0016]    A photonic component as defined herein includes mirrors, prisms, wave guides, optical fibers, lenses, collimators, and other suitable photonic and optical devices and elements known in the art. A wave guide as defined herein includes optical fibers, planar wave guides, and other suitable channels for optical signal and light energy transmission known in the art.  
           [0017]    A first preferred embodiment of the present invention includes an input wave guide, an output wave guide and an actuator. The actuator is operatively coupled, in alternate preferred embodiments, to either the input wave guide or the output wave guide, or both. The light beam travels from the input wave guide and towards the output wave guide. The actuator moves one or more wave guides to which it is operatively coupled within at least two degrees of freedom, or in two dimensions, to form a trajectory of the light beam having geometric components of at least two dimensions. The at least two-dimensional trajectory enables the attenuation, as expressed in decibels, of the transmission of the light beam with an increased linearity, over the prior art, in relation to a control or driving signal supplied to the actuator. The control signal is, or comprises, in various preferred embodiments of the present invention, an electrical current, a voltage, power, or other suitable control signal parameters, qualities or content known in the art. Certain alternate preferred embodiments include optical fibers as input and/or output wave guides.  
           [0018]    A second preferred embodiment of the present invention includes an input wave guide, an output wave guide, a mirror, a mirror actuator and an output collimator. The output collimator may be or comprise an optical lens, a spherical lens, an aspherical lens, a ball lens, a GRIN lens, a C-lens, a lens system, or another suitable collimating element known in the art. The output collimator is positioned between the mirror and the output wave guide. The light beam travels from the input wave guide to the mirror and is reflected from the mirror and focused through the output collimator and into the output wave guide. The mirror may be a substantially flat mirror or another suitable mirror known in the art. The position of the mirror determines the variable optical attenuation of the light beam transmission from the input wave guide to the output wave guide. The mirror actuator is operatively coupled to the mirror. The mirror actuator moves the mirror within at least two degrees of freedom, or in two dimensions, to form a trajectory of the light beam wherein the trajectory has geometric components of at least two dimensions. The at least two-dimensional trajectory enables the attenuation of the light beam transmission with an increased linearity, over the prior art, in relation to a driving signal supplied to the actuator. The second preferred embodiment may include optical fibers as wave guides. The second preferred embodiment may optionally include an input collimator. The input collimator is positioned between the input wave guide and the mirror. The light beam travels from the input wave guide to the mirror via the input collimator, and is reflected from the mirror and toward the output wave guide via the output collimator.  
           [0019]    A third preferred embodiment of the present invention includes a mirror, a mirror actuator, and a dual optical fiber collimator having a lens and an input optical fiber and an output optical fiber. The dual fiber collimator lens may be or comprise one or more collimating elements or focusing elements, such as an optical lens, a spherical lens, an aspherical lens, a ball lens, a GRIN lens, a C-lens, a lens system, or another suitable collimating element known in the art. The dual fiber collimator lens is positioned relative to the mirror and the input and output optical fibers to collimate the light beam as the light beam travels toward the mirror and to focus the light beam as the light beam travels from the mirror. The light beam travels from the input optical fiber to the mirror via the input collimator component, and is reflected from the mirror and toward the output optical fiber via the output collimator component. The mirror actuator moves the mirror within at least two degrees of freedom, or in two dimensions, to form a trajectory of the light beam wherein the trajectory has geometric components of at least two dimensions. The at least two-dimensional trajectory enables the attenuation of the light beam transmission with an increased linearity, over the prior art, in relation to a driving signal supplied to the actuator.  
           [0020]    Other objects, features, and advantages of the present invention will be apparent from the accompanying drawings and from the detailed description which follows below. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]    The present invention is illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like references indicate similar elements, and in which:  
         [0022]    [0022]FIG. 1 is a schematic of a first preferred embodiment of the present invention that generates a prior art linear-radial trajectory, a circular trajectory and a spiral trajectory of FIGS. 7A and 8, as well as ellipse trajectory, an oval trajectory and other suitable non-linear trajectories known in the art, by moving one of two optical fibers while transmitting the light beam from one optical fiber to another optical fiber.  
         [0023]    [0023]FIG. 2A is an illustration of prior art implementation of two optical fibers in close proximity and having a prior art linear trajectory.  
         [0024]    [0024]FIG. 2B is an illustration of the first preferred embodiment of FIG. 1 in close proximity and without the optional collimators and having a circular, two dimensional trajectory.  
         [0025]    [0025]FIG. 3 is an illustration of an alternate second preferred embodiment of the present invention that generates the prior art linear-radial trajectory, a circular trajectory and a spiral trajectory, as well as an ellipse trajectory and an oval trajectory and other suitable two dimensional trajectories, by actuating a mirror that reflects the light beam from one optical fiber to another optical fiber.  
         [0026]    [0026]FIG. 4 is an illustration of a still alternate third preferred embodiment of the present invention having a mirror, two optical fibers and a lens.  
         [0027]    [0027]FIG. 5 is a schematic of a MEMS mirror VOA designed and implemented according to the method of the present invention.  
         [0028]    [0028]FIG. 6A illustrates the prior art linear trajectory of FIG. 2A.  
         [0029]    [0029]FIG. 6B graphs the optical loss versus the light beam spot position of the prior art trajectory of FIG. 2A.  
         [0030]    [0030]FIG. 7A illustrates the circular trajectory of FIGS. 1A and 2B.  
         [0031]    [0031]FIG. 7B graphs the optical loss versus the light beam spot position of the prior art trajectory of FIG. 2A.  
         [0032]    [0032]FIG. 8 charts the attenuation position sensitivity versus attenuation setpoint of the prior art trajectory of FIG. 2A and the circular trajectory of FIG. 2B.  
         [0033]    [0033]FIG. 9A illustrates three curved, spiraled trajectories.  
         [0034]    [0034]FIG. 9B graphs the optical loss versus the light beam spot position of the prior art linear trajectory of FIG. 2A and the three trajectories of FIG. 9B.  
         [0035]    [0035]FIG. 10 charts the attenuation position sensitivity versus attenuation setpoint of the prior art trajectory of FIG. 2A and the trajectories of FIG. 9A. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0036]    While the description above provides a full and complete disclosure of the preferred embodiments of the present invention, various modifications, alternate constructions, and equivalents will be obvious to those with skill in the art. Thus the scope of the present invention is limited solely by the appended claims.  
         [0037]    Referring now generally to the Figures and particularly to FIG. 1, a preferred embodiment of the present invention, or invented VOA  2 , includes a first optical fiber  4  operatively coupled with an actuator  6 . The actuator  6  moves the first optical fiber  4  while a light beam  8  travels either (1) from the first optical fiber  4  to a second optical fiber  10 , or (2) from the second optical fiber  10  to the first optical fiber  4 . The actuator  6  moves the first optical fiber within two linear degrees of freedom, or in two dimensions, namely via linear motion along an X axis and via linear motion along a Y axis. The X axis and the Y axis are substantially mutually orthogonal to each other and to a Z vector, where the Z vector is the direction of travel of the light beam  8  after the light beam  8  has exited an optical fiber  4 ,  10 . The two dimensional movement range of the actuator  6  thus enables the invented VOA  2  to cause the light beam  8  to enter an optical fiber  4 ,  10  at points within a two dimensional, circular trajectory  12 , as further discussed below. The change of direction of the light beam  8  causes a change of alignment of the light beam  8  with respect to the receiving optical fiber  4 ,  10 . The circular trajectory  12  is formed on a receiving face  14  of the optical fiber  4 ,  10  that is receiving the light beam  8  after the light beam has exited the other optical fiber  4 ,  10 . The first optical fiber  4  and the second optical fiber  10  may either or both have optional collimators  15 . The optional collimator  15  collimates the light beam  8  as the light beam  8  enters the optical fiber  4 ,  10  and focuses the light beam  8  after the light beam  8  exits the optical fiber  4 ,  10 . The invented VOA  2  may further comprise a secondary actuator  16  that is operatively coupled with the second optical fiber  10  and moves the second optical fiber  10  in order to facilitate the formation of the trajectory  12  and a direction of the light beam  8  at a particular point of the trajectory  12 . Additionally and optionally, the actuator  6  and the secondary actuator  16  may be comprised as operatively coupled actuators or as a single actuator that actuates and cause both optical fibers  4 ,  10  to move in relation to the other optical fiber, and within at least two degrees of freedom, or in two dimensions, . The invented VOA  2  can form trajectories shaped as circles, ellipses, ovals, spirals, straight lines, and other suitable nonlinear trajectories known in the art.  
         [0038]    The actuator  6  and the secondary actuator  16  of the invented VOA  2  may be or comprise, in various alternate preferred embodiments of the present invention, an actuator selected from the group consisting of an electro-mechanical actuator, an electro-static actuator, a piezo-electric actuator, a thermo-mechanical actuator, an electromagnetic actuator, and a polymer actuator. Where the actuator  6  or the secondary actuator  16  comprises a polymer actuator, the actuator  6  or the secondary actuator  16  may be or comprise an actuator selected from the group consisting of an electro-active polymer actuator, an optical-active polymer, a chemically active polymer actuator, a magneto-active polymer actuator, an acousto-active polymer actuator and a thermally active polymer actuator.  
         [0039]    Either or both of the optional collimators  15  of the invented VOA  2  may be or comprise, in various alternate preferred embodiments of the present invention, a lens selected from the group consisting of an optical lens, an optical lens, a spherical lens, an aspherical lens, a ball lens, a GRIN lens, a C-lens, and a lens system, or another suitable lens known in the art. In various alternate preferred embodiments of the preset invention the actuator  6  and/or the optional collimator(s)  15  of the invented VOA  2  may be integrated on a substrate or comprised within a MEMS-based device.  
         [0040]    Referring now generally to the Figures and particularly to FIGS. 1 and 2A, the invented VOA  2  of FIG. 1 is shown in a VOA configuration  17  wherein the optional collimators  15  are not included. The light beam  8  has an optical axis  8 A that is aimed by the VOA configuration  17  within a linear-radial prior art trajectory  18 . The prior art linear trajectory  18  is shown by way of comparison with the method of the present invention. A plurality of light beam spots  17 A, or strike circles  17 A, are each particular positions of the light beam  8  that occur as the light beam  8  strikes the receiving face  14  while the light beam optical axis  8 A moves within the prior art trajectory  18  while striking the receiving face  14 . The immediate strike circle  17 B is caused by the present striking of the light beam  8  onto the receiving face  14 . The light beam  8  additionally strikes the core  17 C of the optical fiber  4  to achieve minimum attenuation. The prior art trajectory  18  includes a wave guide center point  18 A and a wave guide peripheral point  18 B as end points of the linear trajectory  18 . The optical axis  8 A is striking the wave guide peripheral point  18 B. The wave guide center point  18 A is located at the axial center of the wave guide  4 .  
         [0041]    Referring now generally to the Figures and particularly to FIGS. 1 and 2B, the circular trajectory  12  includes the wave guide center point  18 A and the periphery point  18 B. The light beam optical axis  8 A remains within the circular trajectory  12  as the light beam is moved within at least two dimensions to form the circular trajectory  12 . A plurality of strike circles  17 A are each particular positions of the light beam  8  that occur as the light beam  8  strikes the receiving face  14  while the light beam optical axis  8 A moves within the circular trajectory  12  and while striking the receiving face  14 . The immediate strike circle  17 B is caused by the present striking of the light beam  8  onto the receiving face  14 . The optical axis  8 A is shown to be striking the receiving face  14  at a point  12 A of the circular trajectory  12 .  
         [0042]    Referring now generally to the Figures and particularly to FIG. 3, an alternate preferred embodiment of the present invention, or mirror VOA  20 , includes an input optical fiber  21  having an input optical axis A, an optional input collimator  22 , a mirror  24 , a mirror actuator  26 , an optional output focusing element  28  and an output optical fiber  30  having an output optical axis B. The light beam  8  exits the input optical fiber  21  along the input optical axis A, is then collimated by the input collimator  22  and strikes the mirror  24 . The position of the mirror  24  determines a direction of travel of a reflected light beam  32  that is formed by the reflection of the light beam  8  from the mirror  24 . The reflected light beam  32  generally travels towards the optional output focusing element  28 . The mirror actuator  26  is operatively coupled to the mirror  24  and moves the mirror  24  within two degrees of rotational freedom of motion. The mirror  24  is rotatable by the mirror actuator  26  about both the X axis and the Y axis. The X axis and the Y axis are mutually orthogonal to each other and to the Z vector, where the Z vector is the direction of travel of the light beam  8  after the light beam  8  has exited the input optical fiber  21 , i.e. parallel to optical axis A. The reflected light beam  32  is focused by the optional output focusing element  28  and travels via the optional output focusing element  28  into the receiving face  14  of the output optical fiber  30 . The actuation of the mirror  24  by the mirror actuator  26  within two degrees of rotational freedom of motion enables the formation of a two dimensional trajectory  12  on the receiving face  14  of the output optical fiber. The mirror VOA  20  can form trajectories shaped as circles, ellipses, ovals, spirals and straight lines.  
         [0043]    The mirror actuator  26  of the mirror VOA  20  may be or comprise, in various alternate preferred embodiments of the present invention, an actuator selected from the group consisting of an electro-mechanical actuator, an electro-static actuator, a piezo-electric actuator, a thermo-mechanical actuator, an electromagnetic actuator, and a polymer actuator. Where the mirror actuator  26  comprises a polymer actuator, the mirror actuator  26  may be or comprise an actuator selected from the group consisting of an electro-active polymer actuator, an optical-active polymer, a chemically active polymer actuator, a magneto-active polymer actuator, an acousto-active polymer actuator and a thermally active polymer actuator.  
         [0044]    Either or both the optional input collimator  22  and the output focusing element  28  of the mirror VOA  20  may be or comprise, in various alternate preferred embodiments of the present invention, a lens selected from the group consisting of an optical lens, a spherical lens, an aspherical lens, a ball lens, a GRIN lens, a C-lens, a lens system, or another suitable lens known in the art. In various alternate preferred embodiments of the preset invention the mirror  24  and the mirror actuator  26 , and/or the optional input collimator  22  an optional output focusing element  28 , of the mirror VOA  20  may be integrated on a substrate or comprised within a MEMS-based device. The substrate used with an integrated mirror VOA  20  or a MEMS mirror VOA  20  may be a semiconductor material, such as silicon, or gallium arsenide, or another suitable substrate material known in the art. The substrate comprised within an integrated invented VOA  2  or a MEMS invented VOA  2  may be a single, or two, or a plurality of substrates in combination. The substrate comprises a semiconductor material, such as silicon, or gallium arsenide, or another suitable substrate material known in the art.  
         [0045]    Referring now generally to the Figures and particularly to FIG. 4, a second mirror configuration VOA  33  includes an input optical fiber  21  having an input optical axis A, a lens  34 , a mirror  24 , a mirror actuator  26 , and an output optical fiber  30  having an output optical axis B. The light beam  8  exits the input optical fiber  21  along the input optical axis A, is then collimated by the lens  34  and strikes the mirror  24 . The position of the mirror  24  determines a direction of travel of the reflected light beam  32  that is formed by the reflection of the light beam  8  from the mirror  24 . The reflected light beam  32  generally travels towards the lens  34 . The mirror actuator  26  is operatively coupled to the mirror  24  and moves the mirror  24  within two degrees of rotational freedom of motion. The mirror  24  is rotatable by the mirror actuator  26  about both the X axis and the Y axis. The X axis and the Y axis are mutually orthogonal to each other and to the Z vector, where the Z vector is the direction of travel of the light beam  8  after the light beam  8  has exited the input optical fiber  21 , i.e. parallel to optical axis A. Axis A′ is parallel to axis A and vector Z and is presented to highlight the parallelism of axis A and vector Z. The reflected light beam  32  is focused by lens  34  and travels into the receiving face  14  of the output optical fiber  30 . The actuation of the mirror  24  by the mirror actuator  26  within two degrees of rotational freedom of motion enables the formation of a two dimensional trajectory  12  on the receiving face  14  of the output optical fiber.  
         [0046]    Referring now generally to the Figures and particularly to FIG. 5, a MEMS mirror VOA  36  is a MEMS-based device designed and implemented according to the method of the present invention. The MEMS mirror VOA  36  includes an input optical fiber  21 , the lens  34 , the mirror  24 , an electrostatic mirror actuator  37 , and the output optical fiber  30 . The mirror  24 , the electrostatic mirror actuator  37  and the suspension system  38  are coupled with each other and a substrate  40 . The electrostatic mirror actuator  37  actuates the mirror  24  in at least two dimensions and the suspension system  38  provides a restoring force to return the mirror to an initial position when the mirror is actuated out of the initial position.  
         [0047]    The substrate  40  may be a single, or two, or a plurality of substrates in combination. The substrate  40  comprises a semiconductor material, such as silicon, or gallium arsenide, or another suitable substrate material known in the art. The MEMS mirror VOA  36  is comprised as a MEMS-based device  42  within a package  44 .  
         [0048]    Referring now generally to the Figures and particularly to FIGS. 2A, 2B,  6 A and  6 B, the method of the present invention linearizes the optical-loss-versus-actuation curve for the invented VOA  2 , in which attenuation of an optical signal is based on a misalignment of the light beam  8 , as one example, as transmitted from the second optical fiber  10 , or input fiber  10 , to the receiving face  14  of the first optical fiber  4 , or output fiber  4 . FIG. 6A shows the prior art VOA linear trajectory  18  and FIG. 6B graphs the corresponding optical loss versus light beam optical axis  8 A position along the prior art linear trajectory  18 .  
         [0049]    Prior art VOA&#39;s based on this misalignment method generate variable optical losses by moving the optical axis  8 A (containing the peak power density points) of the light beam  8 , as the light beam  8  strikes the receiving face  14 , away from the center  18 A, of the output fiber  4  in a linear fashion, i.e. along a straight line. The disadvantage of prior art is that the optical loss versus position of the light beam  8  is a highly non-linear (approximately quadratic) relationship due to the wave guide properties of single mode fibers. This means that at higher attenuation settings, the actual attenuation is highly sensitive to the light beam  8  position on face  14  which puts severe constraints on the control of the light beam  8  position.  
         [0050]    The method of the present invention comprises the steps of moving the light beam  8  within a two-dimensional trajectory on the face  14  of the input fiber instead of along a straight line trajectory  18 . The two-dimensional trajectory can be designed such that the overall loss-versus-trajectory-position is linearized significantly compared to the quadratic relation when moving along a straight line, whereby the method of the present invention reduces the sensitivity of optical attenuation to light beam  8  position uncertainty.  
         [0051]    The function of the invented VOA  2  is, in one implementation, to transmit light beams  8  of an optical signal from the input fiber  10  to the output fiber  4  with controllable and variable attenuation of the optical power of the transmitted signal. Optical attenuation is achieved with the invented VOA  2  by mis-aiming the optical axis  8 A of the light beam  8  away from the center  18 A of the output fiber  4 . In the example described, the amount of mis-aiming is determined by the at least two dimensional movement of the output fiber  4  by the actuator  6  and optionally by movement of the input fiber  10  by the optional actuator  16 . In mirror VOA  20  of FIG. 3, the mirror actuator  26  causes the desired misalignment of the reflected light beam  32  by moving the mirror  24  in at least two dimensions. As a result of controlled mis-positioned of the light beam spot  17 A,  17 B &amp;  17 C, the optical losses, when expressed in decibels, are in good approximation proportional to the square of the distance of the striking of the light beam optical axis  8 A on the face  14  of the output fiber  4  from the center  18 A of the core  17 C of the output fiber  4 .  
         [0052]    The variable mis-positioning of the optical axis  8 A of the light beam  8 ,  32  in prior art VOA&#39;s follows a straight trajectory  18  on the receiving face  14  of the output fiber  4  as shown in FIG. 6A. Because the prior art trajectory  18  is straight, the distance from the center of the light beam  8  to the center  18 A of the fiber core  17 C equals the position on the trajectory. Therefore, the corresponding loss-versus-trajectory-position is quadratic, as shown in FIG. 6B, where the relationship between the attenuation of the light beam  8 , as expressed in decibels, versus the trajectory position, i.e. ΔX, as expressed in microns is shown as curve  18 ′.  
         [0053]    The prior art straight-line trajectory  18  will therefore exhibit a highly non-uniform sensitivity of the attenuation to position inaccuracy on the trajectory with the largest sensitivity at the high end of the attenuation range.  
         [0054]    The highly non-linear attenuation vs. trajectory position of FIG. 6A can be linearized by implementing two dimensional, or 2D, mis-positioning of the light beam  8  on the face  14  of the output fiber  4  rather than the prior art one dimensional, or 1D, mis-positioning. A 2D trajectory can be realized, in various suitable configurations and in accordance with the method of the present invention, by the use of 2D beam directing actuators  6 ,  16 ,  26 ,  37  and mirrors  24 .  
         [0055]    Referring now generally to the Figures and particularly to FIGS. 7A, 7B,  8 ,  9 A and  9 B, two alternate embodiments of the method of the present invention include linearizing 2D trajectories in a half-circle trajectory  12 , and alternately, in an optimized spiral shape trajectory  46 . Implementing a half-circle trajectory  12  starting in the center  18 A of the fiber core  17 C and ending at the peripheral point  18 B of desired maximum attenuation, equal to the end-point of the straight line trajectory  18  shown in FIGS. 2A and 6A, the same attenuation range can be covered with an improved linearity profile, as is illustrated in FIGS. 7A and 7B. FIG. 7A illustrates a 2D, half-circle trajectory  12  of the optical axis  8 A on the receiving face  14  of the output fiber  4 . FIG. 7B presents a corresponding optical loss versus image position along the half-circle trajectory  12 , where the relationship formed by the trajectory  12  between the attenuation of the light beam  8 , as expressed in decibels, versus the trajectory position, i.e. ΔX, as expressed in microns is shown as curve  12 ′. The dotted line  18 ′ of FIG. 7B is the relationship of attenuation versus trajectory position of the straight line trajectory  18 , as per FIG. 6B.  
         [0056]    By calculating the change in attenuation per micron travel along the trajectories  12  and  18 , i.e. the derivative of the attenuation curves, we can compare the positional sensitivity and the linearity of the attenuation for the straight line trajectory  18  and the half-circle trajectory  12 , as is shown in FIG. 8. FIG. 8 graphs the sensitivity to positional uncertainty along half-circular trajectory  12 , and compares sensitivities of the straight line trajectory  18 , as per the dotted line  18 ″, and of the half-circle trajectory  12 , as shown by the solid line  12 ″.  
         [0057]    Referring to the comparison shown in FIG. 8, it is clear that the half-circle trajectory  12  shows much reduced positional sensitivity for higher attenuation settings. There is a benefit in performance for the half-circle case as the maximum adjusted positional sensitivity is reduced by 50% for a 30 dB attenuation range.  
         [0058]    Referring now generally to the Figures, and particularly to FIGS. 9A and 9B, the half-circle trajectory  12  is presented herein as an illustrative example rather than as an optimized application. The trajectory  46  of FIG. 9A is theoretically calculated to be the most optimal trajectory for minimum sensitivity of the attenuation along the trajectory. FIG. 9A displays samples of calculated curved or spiral trajectories  46 ,  47 ,  48 , where the spiral trajectories  46 ,  47  and  48  are formed on the receiving face  14  of the output fiber  4 . The spiral trajectories  46 ,  47  and  48  are formed to investigate for a trajectory having an optimized linearity of attenuation versus trajectory position. FIG. 9B presents corresponding attenuation versus trajectory position graphs of  46 ′,  47 ′ and  48 ′ as respectively caused by the spiral trajectories  46 ,  47 , and  48 . The results of the optimization show that there is a continuum of these spiral shaped trajectories  46 ,  47 , and  48  that satisfy a linear attenuation versus trajectory position requirement for a large portion of the required attenuation range. As the given examples of spiral trajectories  46 ,  47  and  48  illustrate, there is a solution for any amount of total circulating angle, even beyond 360° to multiple circulations.  
         [0059]    Making a similar comparison of the position sensitivity as we did between the half-circular trajectory  12  and straight line trajectory  18  as described above, FIG. 10 shows the results for the linearity optimized trajectories  46 ,  47  and  48  of FIG. 9A as curves  46 ″,  47 ″ and  48 ″. FIG. 10 graphs the attenuation sensitivity to positional uncertainty along trajectory  46 ,  47 ,  48  paths, and comparison between straight line trajectory  18 , as per dotted line  18 ″, and spiral trajectories  46 ,  47  &amp;  48 , as shown with corresponding solid lines  46 ″,  47 ″ and  48 ″. FIG. 10 shows that as soon as the trajectory position moves into the linearized portion, i.e. the spiraled portion, there is a substantial benefit to the achievable attenuation accuracy.  
         [0060]    The invention has been described in conjunction with the preferred embodiments. Although the present invention has been described with reference to specific exemplary embodiments, it will be evident that various modifications and changes may be made to these embodiments without departing from the broader spirit and scope of the invention as set forth in the claims. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense.