Optical filter wavelength tuning using raised cosine control signals

Abstract

The invention relates to optical filter wavelength tuning using raised cosine control signals. The raised cosine waveform is used as a drive signal input to an optical device (e.g., a tunable optical filter) that exhibits a non-linear time domain response. The raised cosine waveform (current or voltage) exhibits significantly fewer high-frequency components than conventional drive signals, thus reducing oscillatory movement of the device when it is stabilized to a target position. In particular examples of MEMS tilt mirrors for tuning non-linear optical filters, raised cosine drive signals allow the tilt mirrors to quickly stabilize to new positions and avoid long-term oscillatory motion known to limit the responsivity of prior art tunable optical filters.

Description

Technical Field

[0001] A control system is disclosed herein for providing wavelength tuning and locking of a tunable optical filter to an input signal applied thereto. background

[0003] Many optical filters today are configured to provide the ability to adjust (tune) the wavelengths allowed to pass through the filter element. In addition to being able to tune the optical filter to select a specific wavelength value, another desirable feature is to maintain the stability of the selected wavelength. That is, any type of drift or shift of the selected wavelength over time needs to be avoided. Tunable optical filters can include a feedback loop that monitors the output and adjusts the filter parameters to provide a lock on the output wavelength.

[0004] While many different arrangements can be used to provide tuning and locking functions for optical filters, one common arrangement is based on the use of a micro-electromechanical system (MEMS) tilt mirror. In a MEMS tilt mirror arrangement, an electrical control signal (current or voltage) is applied to the tilt mirror structure in a manner that adjusts the angular position of the mirror to change the specific wavelength of the output signal. A known problem with conventional MEMS tilt mirrors is that the time domain response of the mirror element to the applied control signal is non-linear. That is, the movement of the mirror itself exhibits underdamped oscillations for a period of time, after which it settles to the desired "new" tilt angle relative to the incoming optical signal.

[0005] This nonlinear oscillatory response inevitably limits the speed at which wavelength tuning can be performed, which is particularly problematic when using a tunable optical filter as part of a tune-and-hold device. The nonlinear response also affects the ability of the feedback control to lock the optical filter to a selected wavelength. The control loop typically uses a dither signal (the dither is typically a step change or a sinusoidal change) added to the tilt mirror control signal, where multiple measurements are required over time to achieve locking. The nonlinear time response of the MEMS tilt mirror affects how large and how fast these multiple measurements can be performed, which in turn affects the efficiency of the locking process. In fact, the nonlinear response time of the MEMS tilt mirror to the applied control signal limits the speed and / or stability that can be achieved in both tuning and locking of the optical wavelength selective filter.

[0006] In addition to specific embodiments of tunable optical filters, there are other optical devices that exhibit undesirable nonlinear responses to applied control (stimulus) input signals. Therefore, in general, it is desirable to find a solution that minimizes fluctuations in the nonlinear response of an optical device to certain input stimuli.

[0007] Overview of the Disclosure

[0008] Problems associated with the nonlinear response of certain devices (e.g., MEMS tilted mirrors used in tunable optical filters) are proposed to be addressed by utilizing a drive signal that minimizes fluctuations in the response of the device. In particular, it is proposed to utilize a raised cosine waveform as a drive signal input to the nonlinear device, rather than utilizing a step function drive signal (or perhaps a ramp-based drive signal) of the prior art. Raised cosine waveforms (current or voltage) exhibit significantly fewer high frequency components than conventional drive signals, thereby reducing oscillatory movement of the device. In the specific example of a MEMS tilted mirror for tuning a nonlinear optical filter, the raised cosine drive signal allows the tilted mirror to quickly settle to a new position and avoid prolonged oscillatory motions that are known to limit the responsivity of the prior art.

[0009] In an example embodiment, a raised cosine signal is used as a drive signal to adjust the position of the MEMS tilt mirror from an initial position (associated with a previously selected wavelength value) to an updated position (associated with a newly selected wavelength value). The rise time of the raised cosine waveform can be selected to achieve optimal performance for a given filter response, or as required by a particular application. The tunable optical filter itself has a second harmonic transfer function, where the damping coefficient ζ is associated with the rise time of the raised cosine. The range of values ​​can be, for example, from 0.01 to 1.00, where a trade-off is made between the stability of the mirror position and the length of time required for the mirror to reach the final position.

[0010] Another example embodiment involves locking a tunable optical filter to an input optical signal operating at a nominal wavelength, using application of a raised cosine signal to sweep across a wavelength range ± nominal to account for signal wavelength drift or filter wavelength shift (or both). An optimal filter wavelength that achieves maximum output signal power is then identified, and another raised cosine drive signal is used to adjust the filter wavelength to the optimal value.

[0011] One example may take the form of a tunable filter for filtering out a selected optical signal from a plurality of (unique) signals, each having its own wavelength defined within a wavelength division multiplexing grid. The tunable filter may be tuned and locked to the selected optical signal of interest using the previously described electrical drive signal having a raised cosine waveform, the tuning and locking to the selected optical signal occurring in a relatively short period of time (relative to the prior art), and the filter itself having minimal resonance.

[0012] Another embodiment may include a tunable optical filter including a nonlinear filter assembly and a control source. The nonlinear filter assembly is responsive to a multi-wavelength input optical signal and an electrical drive signal, the electrical drive signal being used to tune an output wavelength of the tunable optical filter from an initial wavelength value to a selected target wavelength value. The nonlinear filter assembly exhibits an oscillatory response to the electrical drive signal. The control source is used to provide a raised cosine signal as an input to the nonlinear filter assembly, the raised cosine signal exhibiting a defined rise time associated with a degree of minimizing the oscillatory response of the nonlinear filter assembly.

[0013] More generally, example embodiments may take the form of a switchable optical device comprising an optical component and an associated control source. The optical component is configured to control a switching function between one or more input signals and one or more output signals according to an applied electrical control signal. The optical component exhibits a nonlinear response to the applied electrical control signal. The control source is used to provide a raised cosine signal as an electrical control signal input to the optical component, the raised cosine signal exhibiting a defined rise time associated with minimizing fluctuations in the nonlinear response of the component.

[0014] Other and further aspects and embodiments of the disclosed arrangements may become apparent during the course of the following discussion and by reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Now referring to the accompanying drawings,

[0017] Figure 1 A typical application of a tunable optical filter is shown;

[0018] Figure 2 Another possible application of the same filter is shown;

[0019] Figure 3 is a simplified diagram of a MEMS tilt mirror controlled via an applied electrical drive signal (here a voltage signal);

[0020] Figure 4 is a graph of two types of electrical drive signals for operating a tunable optical filter, one signal (I) having a unit step response waveform and the other signal (II) exhibiting a raised cosine waveform for use in accordance with the present disclosure;

[0021] Figure 5 Contains tunable optical filters for Figure 4 The corresponding curve diagrams of the second-order responses of the two driving signal waveforms shown;

[0022] Figure 6 yes Figure 5an enlarged view of a portion of a graph of better illustrating the minimum oscillation present in the response to a raised cosine drive signal;

[0023] Figure 7 A set of graphs showing selected raised cosine drive signals that can be used to control a tunable optical filter, each drive signal exhibiting a different rise time;

[0024] Figure 8 is with Figure 7 A set of second-order responses associated with this set of raised cosine driving signals;

[0025] Fig. 9 The settling time of a second-order filter (which is defined here as the time taken to reach within ±1% of the target value) is plotted against the time period of the raised cosine;

[0026] Fig.10 is a flow chart of an example set of steps that may be used to perform a tuning and locking process of an optical filter in response to a raised cosine drive signal used to control the filter;

[0027] Fig.11 Is to use Fig.10 Graphs of experimental measurements of raised cosine drive signal and corresponding optical power through a tunable optical filter (which is based on a MEMS tilting mirror) in accordance with the tuning and locking described in the process;

[0028] Fig.12 yes Fig.11 an enlarged view of the initial 20 ms of the graph of to better illustrate the voltage scale associated with the initial drive signal used to tune the filter; and

[0029] Fig.13 shows the use of parabolic fitting to scan from Fig.12 data and is used to identify the optimal drive voltage to achieve maximum optical power of the filtered signal. Detailed Description

[0031] Figure 1 A two-port tunable optical filter 10 is shown, which can be used as an in-line filter in a variety of different optical systems. The optical filter 10 includes a wavelength tunable element 12 arranged to receive a propagating optical signal (which may be a multi-wavelength signal). The wavelength tunable element 12 is configured to allow only a selected wavelength portion of the multi-wavelength signal (which is shown here as having a wavelength λ) to pass through the optical filter. aAn optical tap 14 is positioned at the output of the tunable element 12 and is used to direct a small portion (e.g., no more than 10%, and typically closer to 1%) of the filtered output signal to a photodetector 16. The photodetector 16 converts the optical power of the tapped signal into an electrical equivalent (E), which is applied as an input to a processing module 18, which is used to analyze the properties of the output signal. In particular, the processing module 18 determines whether the tunable element 12 is properly aligned to direct the selected wavelength (e.g., λ a ) into the output signal path, or whether adjustment is required. The control between the processing module 18 and the tunable element 12 is shown as an electrical drive signal D, which the module 18 applies to the tunable element 12 to adjust the position of the tunable element 12 as required to ensure that the appropriate selected wavelength appears at the output.

[0032] Figure 2 A terminated optical filter 20 is shown which may be suitable for use in a tunable optical receiver. In this configuration, the filtered output from the wavelength tuning element 22 is applied directly as input to a photodetector 24, where a converted measure of the output power is applied as input to a processing module 26 for a similar type of wavelength adjustment control. The same measure may also include information, such as digital data, which is not used for the wavelength control function, but as part of the monitoring of the optical receiver itself.

[0033] As discussed above, many techniques for providing wavelength tunability of elements 12, 22 exhibit non-linear responses in the time domain, with one such technique being based on the use of micro-electromechanical systems (MEMS) to control the angular position of mirrors used to redirect incoming light beams.

[0034] Figure 3 is a simplified diagram of a MEMS tilting mirror element 30 that can be used to adjust a selected output wavelength from a multi-wavelength input. The element 30 is shown to include a mirrored component 32 that is typically suspended between a pair of torsion bars 36 within a housing 34. An electrical drive signal is applied to a substrate supporting the mirrored component 32 in a manner that produces a torque on the torsion bars 36 and rotates the mirrored component 32. The magnitude of the drive signal is directly related to the torque and the resulting angular movement of the mirrored component 32. Figure 3 Also shown in FIG. 1 is the variation of the tilt angle controlled by the applied drive signal (exaggerated for explanation purposes).

[0035] The time domain response of a tunable optical filter based on a nonlinear component (e.g., a MEMS tilting mirror 30) can be described as a highly underdamped second-order oscillator with the following transfer function:

[0036]

[0037] where ζ is the damping factor (the smaller the value of ζ, the higher the resonant peak of the oscillator). More generally, in addition to tunable optical filters with similar second-order nonlinear responses, there are various types of devices that can benefit from using drive (control / stimulus) signals that minimize fluctuations in the generated output signal.

[0038] As will be described in detail below, utilizing a drive signal having a raised cosine waveform can significantly reduce the amplitude of the fluctuations produced due to the resonant frequency of the device because the number of higher frequencies present in the drive signal is reduced when compared to conventional waveforms used in the prior art.

[0039] Figure 4 A graph containing a prior art step function drive signal (curve A) and a graph of an example raised cosine drive signal (curve B) which is used as a drive signal input to a nonlinear optical device, such as a tunable optical filter (or, perhaps, a switchable optical device) in accordance with the principles of the present disclosure. The graphs show the (time-varying) drive signal applied to the filter (normalized on a y-axis scale from 0 to 1). The prior art step function drive signal is theoretically depicted as having an instantaneous shift between an initial drive value and a final (target) drive value (i.e., as in Figure 4 Such temporal transients are known to contain many high frequency components which, unfortunately, can excite the resonances of the filter and lead to an oscillatory response.

[0040] Figure 5 Curve A in FIG. 1 shows this oscillatory response of the prior art step function in terms of the deviation of the response of the example tunable optical filter from the target value. The deviation is depicted by the angular movement (fluctuation) of the filter over time. It should be understood that Figure 5 The curves are generated from modeling results rather than experimental results. The filter in this example is modeled as an oscillator with a 1kHz resonance and a damping factor ζ of 0.01.

[0041] Based on this understanding of the oscillatory nature of the response of the prior art step function drive signal, it is shown that the improvement found by using a raised cosine drive signal ( Figure 4 and Figure 5In accordance with the principles of the present disclosure, using a raised cosine waveform for the filter's drive signal means that there is now a perceptible transition (rise time) between the initial value and the final (target) value of the drive signal. Figure 4 In the specific illustration of curve B of , a 5 ms rise time is shown as the interval required for the raised cosine drive signal to reach its target value. The raised cosine waveform contains little high frequency content, so the filter response rarely behaves in an oscillatory manner before settling to the desired angular position. In fact, as Figure 5 The response shown in curve B looks essentially flat.

[0042] Figure 6 Shows Figure 5 1 is an enlarged view of curves A and B in FIG. 1 (expanding the y-axis scale by two orders of magnitude). This enlargement is sufficient to show the very slight oscillation experienced in response to the raised cosine drive signal in curve B. It is believed that this minimal oscillatory behavior will be insignificant for most applications.

[0043] Use as Figure 4 The raised cosine shown with a 5 ms rise time is only an example; it is contemplated that other rise times may be used as appropriate for various applications. In general, a raised cosine drive signal with a faster rise time (e.g., 1 ms faster than 5 ms) may exhibit some instability in the device response before settling, but is still a significant improvement over the prior art. A slower rise time (e.g., 10 ms slower than 5 ms) improves the stability of the response, but at the expense of a longer period of time for the device to reach its target position. Figure 7 The graphs contain the following three different examples of the rise time of the raised cosine drive signal: 1 ms, 2.5 ms and 5 ms. For comparison purposes, a prior art step function drive signal is also shown again.

[0044] Figure 8 Contains Figure 5 curves similar to those of Figure 7 The deviation of the response signal from the target response obtained for a set of three raised cosine drive signals is shown in FIG. 1 under similar circumstances as described above (ie, for a filter with a resonant frequency of 1 kHz and ζ of 0.01). Figure 8 As shown in the nonlinear device response data of FIG. 1 , a raised cosine drive signal with a 2.5 ms rise time is less susceptible to fluctuations than a prior art step function. The faster rise time of 1 ms results in a somewhat oscillatory response, but again settles into place within a reasonable period of time, in this case in about 3 ms-4 ms (i.e., 3-4 times the resonant period of the oscillator). Note that Figure 8The time scale used in Figure 5 The time scale is shorter (2ms intervals compared to 5ms intervals) to better illustrate the change in response rate based on the rise time of the raised cosine drive signal.

[0045] In summary, it has been found that the use of a raised cosine waveform in a drive signal for controlling the response of a nonlinear component (e.g., the wavelength tuning response of a tunable optical filter using a MEMS tilted mirror arrangement) allows for better control of the response of the device. In the example of a tunable optical filter, it was found that the use of a raised cosine drive signal increased the stability of the system during the tuning process compared to a prior art step function drive signal (similar improvements were also found relative to other types of prior art drive signals, such as ramp drive signals).

[0046] Fig. 9 is a graph showing the relationship between the rise time of a raised cosine drive signal (plotted along the x-axis) and the time it takes for the second order response to settle (plotted along the y-axis). In this case, the rise time is defined as a sine half period (in ms), and the stability of the device's (filter's) response is defined as the time required to reach within ±1% of the target value. It should be understood that this ±1% value is only an example, and in general, improvements in stability are more typically demonstrated by a significant reduction in oscillatory movement (e.g., values ​​such as ±10%, ±15%, ±20% are other examples of significant reductions in oscillatory movement).

[0047] like Fig. 9 The specific data shown shows that the optimal half period of the raised cosine (in terms of the shortest time to achieve stability) is shown to be about 2.5ms. It is found that for shorter rise time values, the second order resonance of the device limits the settling time, and for longer rise time values, the drive signal limits the settling time. For reference, the settling time of the step drive function is represented by the horizontal line, indicating that a raised cosine with a half period of less than 5ms will achieve stability faster than a step function. The optimal raised cosine achieves stability about twice as fast as the step function.

[0048] As mentioned above, the same principles can be applied when one wishes to "lock" a tunable optical filter to provide a signal that is fixed at a defined target wavelength λ. T The output signal is Fig.10 A generalized process according to the principles of the present disclosure for providing a wavelength tunable optical filter at a selected (target) output wavelength λ using a raised cosine drive signal is summarized in the flowchart of T The best lock at Fig.11 An example of an experiment applying these steps is shown in the graph of .

[0049] like Fig.10The steps outlined in begin by performing an initial tuning of the optical filter so that the optical filter operates close to the target wavelength λ T For example, this tuning can be used to change the passband of an optical filter from a first initial wavelength (e.g., λ i ) is adjusted to the target wavelength λ T Once the filter is positioned in this way, a scanning process can be used to find the peak power level (indicative of the target wavelength λ T ) and a specific drive signal associated with the peak power.

[0050] Specific reference Fig.10 , the initial proximity tuning is shown as step 100, which is an instruction for using a raised cosine drive signal to adjust the position of the filter (e.g., the angle of the tilted mirror in the MEMS arrangement) from an initial value associated with a previous setting to a value believed to be at the target wavelength λ T The value on the “near side” of .

[0051] An example of step 100 is given by Fig.11 The first 20ms of the example shown are represented. For clarity, Fig.12 The initial 20ms is Fig.11 The timeline is enlarged, and the y-axis drive signal voltage range is changed from Fig.11 The values ​​of 5.95e4 to 5.97e4 (au) are extended to the range 0-8e4 au. Fig.11 and Fig.12 , shows the application of a raised cosine "tuning" drive signal with a 10 ms rise time (i.e., requiring 10 ms to reach the close "near side" position), followed by a dwell time at that drive signal value. The dwell time is used to allow the filter (mirror) to settle to this new position. Fig.12 In the example shown, a dwell interval of 10 ms was found to be sufficient to stabilize the filter position to within an example value of ±1% of the final position. Fig.11 and Fig.12 Also shown in FIG. 5 is the response signal showing the oscillatory movement of the tilt mirror during changes in its position, and in particular the stabilization of the response towards the end of the dwell period.

[0052] Return to Fig.10 Once the initial tuning step is completed, the locking process continues to perform the scanning step (such as Fig.10 Specifically, the scanning step uses a raised cosine "scanning" drive signal to control the movement of the filter (e.g., a tilted reflector) to include the selected target wavelength λ TThe scan is performed over a defined wavelength interval Δλ of . The scan is performed in the presence of an applied light signal, with an associated photodetector used to measure the output power as the scan proceeds. By maintaining a correlation between the drive signal value (voltage or current) and the power level, the "optimal" drive signal is defined as the value associated with the maximum output power.

[0053] Along Fig.11 The timeline of FIG. 1 further depicts an example of the scanning process (in this example along the time span between 20 ms and 40 ms). Fig.12 The scanning process is performed using a raised cosine drive signal with much smaller voltage changes, as compared to the relatively large amplitude changes required to move the filter from one wavelength setting to another through a large angular change, as shown in FIG. Fig.11 The smaller drive signal range used for scanning is based on the assumption that the output power near the peak changes relatively slightly and is therefore very sensitive to changes in the drive signal. Fig.11 In the particular example shown, the sweep begins with a drive signal at the level found in the initial tuning step, after which a raised cosine signal with a rise time of the order of about 20 ms is used to move the filter through the wavelength interval Δλ. As the drive signal increases, a photodetector included with the filter is used to measure the associated optical output power at a set number of sample positions within the wavelength interval Δλ.

[0054] Return to reference Fig.10 The next step in the locking process (step 120) is to evaluate the collected power data to determine the drive signal associated with the highest power recorded. The filter element (e.g., tilted mirror) position associated with this particular drive signal value is then defined as the target wavelength λ T The "optimal" drive signal.

[0055] Fig.13 is a graph of optical power data collected during the scan as a function of drive signal value, and is an example of a method for performing step 120. The optimal drive signal value can be derived by analyzing the graph, in this case by using a parabola fit (as shown). In general, the number of samples used during the scan is a factor in determining which type of fit and / or approximation should be used to obtain the optimal drive signal value. For illustration purposes, Fig.13 Indicates the driving signal D T is associated with the maximum output power. Therefore, the drive signal D T is determined for the target wavelength λ T "Locked" is the best driving signal.

[0056] Return to Fig.10 The last step 130 in the locking process is to move the filter to a wavelength corresponding to the target wavelength λ T The raised cosine drive signal is again used to make this final adjustment in the position of the filter according to the disclosed principles. This final movement is also Fig.11 , where this value is achieved using a (negative) rise time (or "fall time") of 10 ms (from 40 ms to 50 ms).

[0057] It should be understood that the specific examples of raised cosine rise times and filter characteristics included above are only examples specified for the purpose of understanding the principles presented. In a larger sense, the present disclosure is intended to recognize that the use of a raised cosine waveform for a drive signal applied to a tunable nonlinear optical filter solves the instability problem associated with the high frequency component of a conventional drive signal (step function or ramp). The raised cosine drive signal has the lowest possible frequency component that can drive the filter to a target position while avoiding the oscillatory nature of the filter response associated with the prior art drive signal. When compared to the prior art, the use of raised cosine tuning and locking to control a tunable optical filter results in reduced oscillations and faster settling times. That is, the use of a raised cosine waveform in the drive signal minimizes the total time to tune and lock the optical filter to a target output wavelength while minimizing the instability caused by the nonlinear time domain response of the filter.

[0058] In addition, in one or more embodiments illustrating various aspects of the present disclosure, the described features, structures or characteristics of the wavelength tunable optical filter may be combined in any suitable manner. Those skilled in the relevant art will recognize that the principles of the present disclosure may be implemented without one or more specific details, or may be implemented using other methods, components, etc. Therefore, although the foregoing examples are considered to be illustrative of the disclosed principles, it is obvious to those skilled in the art that a large number of modifications may be made to the form, usage and implementation details without exercising creative ability and without departing from the principles and concepts presented in the present disclosure. Therefore, the subject matter of the present disclosure is not intended to be limited except as set forth in the claims.

Claims

1. A tunable optical filter, comprising: a nonlinear optical filter assembly exhibiting a nonlinear time domain response, the optical filter assembly being responsive to a multi-wavelength input optical signal and an electrical drive signal, the electrical drive signal being used to tune an output wavelength of the tunable optical filter from an initial wavelength value to a selected target wavelength value, the nonlinear optical filter assembly exhibiting an oscillatory response to the electrical drive signal; as well as A control source is used to provide a raised cosine signal as an electrical drive signal input to the nonlinear optical filter component, the raised cosine signal exhibiting a defined rise time, the defined rise time being associated with a degree of minimizing the oscillatory response of the nonlinear optical filter component.

2. The tunable optical filter according to claim 1, wherein: The nonlinear optical filter assembly includes a component exhibiting an underdamped second order oscillatory response, the underdamped second order oscillatory response being approximated by a transfer function defined as follows: Here, ζ is defined as the damping factor of the transfer function and is expressed as a value less than unity.

3. The tunable optical filter according to claim 2, wherein: The nonlinear optical filter assembly includes a MEMS tilting mirror.

4. The tunable optical filter according to claim 1, wherein: The rise time of the raised cosine signal is selected to reduce oscillations to a defined percentage of a selected target wavelength value during a defined stabilization time period that is less than a stabilization time period associated with a step function waveform drive signal.

5. A switchable optical device comprising: an optical component for controlling a switching function between one or more input signals and one or more output signals in accordance with an applied electrical control signal, the optical component exhibiting a non-linear response to the applied electrical control signal; as well as A control source is provided for providing a raised cosine signal as an electrical control signal input to the optical component, the raised cosine signal exhibiting a defined rise time associated with minimizing fluctuations in a nonlinear response of the optical component.

6. The switchable optical device according to claim 5, wherein: The optical component exhibits an underdamped second-order oscillatory response that is approximated by the transfer function defined below: Here, ζ is defined as the damping factor of the transfer function and is expressed as a value less than unity.

7. The switchable optical device according to claim 6, wherein: The optical assembly includes a MEMS tilting mirror.

8. The switchable optical device according to claim 6, wherein: The rise time of the raised cosine signal is selected to reduce the ripple to a value less than a defined percentage of a target during a defined stabilization time period that is less than a stabilization time period associated with the step function waveform drive signal.

9. A method for wavelength tuning an optical filter, comprising: determining the nonlinear response of optical wavelength filtering elements for wavelength tuning; selecting a target wavelength to be used as an output wavelength of the optical filter; determining a target electrical drive signal associated with a selected target wavelength based on a nonlinear response of the optical wavelength filtering element; as well as A raised cosine drive signal is applied to the optical wavelength filtering element to tune the wavelength of the optical filter from an initial value to the selected target wavelength.

10. The method according to claim 9, wherein: The rise time of the raised cosine drive signal is selected to achieve the target wavelength, and the oscillation is less than a defined percentage of the target in the output signal.

11. The method according to claim 9, wherein: The optical wavelength filtering element comprises a MEMS tuned mirror and the determined nonlinear response takes the form of a highly underdamped second order oscillation.

12. A method of maintaining a selected output wavelength of a tunable optical filter, comprising: determining the nonlinear response of optical wavelength filtering elements for wavelength tuning; selecting a target wavelength to be used as an output wavelength of the optical filter; applying a first raised cosine drive signal to the optical wavelength filtering element for tuning the wavelength of the optical filter from an initial value to a value close to a selected target wavelength; applying a second raised cosine drive signal to the optical wavelength filtering element for scanning the optical output wavelength over a wavelength band including the target wavelength, and recording the optical output power at the identified wavelength within the wavelength band; determining a final raised cosine drive signal associated with the recorded maximum output power; as well as A third raised cosine drive signal is applied to the optical wavelength filtering element to tune the optical filter to a maximum output power value.

13. The method according to claim 12, wherein: The steps to determine the final raised cosine drive signal include: Plot the output power as a function of the drive signal value; applying an approximation curve to the plotted output power; and finding the maximum value of the approximation curve; and The maximum value is defined as the optimum drive signal for maintaining the optical filter at the selected target wavelength.

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