DESCRIPTION

TECHNICAL FIELD

The present invention relates to a method of observing optical devices made, by way of example and not limitation, in integrated optical technology.

STATE OF THE ART.

The term "observation" of an optical device means in the present description the tuning, monitoring, testing or controlling of the device under consideration.

In relation to tuning and testing of frequency-selective optical devices, solutions of known art are based on the measurement of the spectral response of the device which is compared with a reference spectral mask.

An example of testing an optical device, of a reconfigurable type, is described in document US-A-6892021. That document describes an optical gain equalizing filter having a waveguide multiplexer (Waveguide Grating Router) equipped with Mach-

Zehnder type adjustable optical attenuators, each associated with a relative wavelength of the optical channels employed.

Document US-A-6512414 describes a control system that detects and adjusts the characteristic frequency of a filter that is tuned using a pulse signal or a stepped signal and then stores the tuning result on a memory for future reuse.

Document US-A-2009121802 describes a microwave filter system based on measuring the spectral response of the device to a step signal.

Document WO2015/197920 describes a method for determining spectral calibration data of a Fabry-Perot interferometer. Document EP0378267 describes a device for measuring the cut-off wavelength of an interference filter in a television display tube.

JP-S63-182541 relates to the measurement of characteristics, such as optical losses or optical power splitting ratio, of an optical multiplier/demultiplier.

SUMMARY OF THE INVENTION

The Applicant has noticed that the optical device observation techniques of the known art present excessive complexity, both in computational terms and in relation to their structural implementation.

The present invention addresses the problem of providing an alternative optical device observing system to the known ones, which has not particularly computationally onerous modes of operation and is not significantly complex from a structural point of view, while at the same time ensuring due efficiency, accuracy, and reduced observing time.

According to a first aspect, the present invention is directed to an optical system as described by claim 1 and preferred embodiments thereof as defined by claims 2-14.

It is also an object of the present invention to method of observing an optical system as defined by claim 15.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is hereinafter described in detail, by way of illustration and not limitation, with reference to the accompanying drawings, in which:

- Figure 1 shows an example of a first form of implementation of an optical system including an optical reference device and a device to be observed;

- Figure 2 shows illustratively the spectra of an optical radiation on two complementary outputs, band-clear and band-pass, of said optical devices; - Figure 3 shows schematically an optical device with more than two output ports employable in said optical system;

- Figure 4(a) shows the intensity response as a function of wavelength of an optical device not yet tuned, and Figure 4(b) shows the intensity response as a function of wavelength of a tuned or reference device;

- Figure 5 shows the power trend on two output ports of the optical device to be observed of Figure 4a during the tuning process;

- Figure 6 shows schematically, as an example of a device, a coupled resonant ring filter that can be used in said optical system;

- Figure 7 shows the intensity of wavelength responses observed experimentally on two output ports, bandpass (solid line) and band-elimination (dot stretch line) of the filter in Figure 6;

- Figure 8 shows the wavelength-dependent intensity responses obtained experimentally and related to a reference filter (dashed lines) and the controlled optical device (solid lines);

- Figures 9-12 show the power spectral densities output to an optical detector of the optical system of Fig. 1 in different possible configurations and also show graphs describing the trend of a signal sent to a controller of said system;

- Figure 13 refers to the device in Fig. 6: Figure 13(a) relates to a situation in which the bandpass gate is subject to random perturbations; Figure 13(b) shows the mean square error of the wavelength response of the device with respect to a desired response and the power output from the same device for different cases of perturbation, shown in

Figure 13(a). DETAILED DESCRIPTION

In this description, similar or identical elements or components will be referred to in the figures with the same identifying symbol.

Figure 1 schematically shows an example of a first form of implementation of an optical system 100 comprising: an optical radiation source 1 (BBS), an optical reference device 2 (H _R ), an optical device to be observed 3 (H _C ), and an optical detector

4 (DTC). In addition, according to the first described form of implementation, the optical system 100 includes a controller 5 (CNT) of the optical device to be observed 3.

In particular, the optical system 100 is such that it operates with electromagnetic radiation at wavelengths between, preferably, 300 nm and 5000 nm, between 1250 nm and 1750 nm.

For example, optical system 100 is a system that operates in the fields of optical telecommunications, optical interconnection, optical signal and image processing, and sensing.

Optical system 100 is suitable for observation of optical device 3. As already reported, for the purposes of the present invention, observation means at least one of the following operations performed on optical device 3: tuning, monitoring, testing, and control of the considered device.

In tuning one operates so that the optical device 3 assumes a predetermined state of operation. In particular, such tuning can be carried out at a calibration step following the production of the device itself. The term monitoring refers to the set of operations aimed at maintaining the required functional characteristics of the optical device 3 in the face of external perturbations (e.g., changes in temperature, optical, electrical, acoustic interference, etc.) and/or aging phenomena.

Monitoring involves observing the state of the optical device 3 during its operation to detect deviations from the required functional characteristics. Testing is the verification of the functional characteristics of the optical device 3 to validate and/ or rank its performance against specifications.

According to the implementation form of Figure 1, the optical device to be observed 3 is a reconfigurable device and the optical system 100 is such that it tunes and/ or controls the optical device 3. For the purpose of monitoring and testing, the optical device 3 is not neccessary reconfigurable.

Referring to Figure 1, the optical device to be observed 3 (hereafter optical device 3 for the sake of brevity) is equipped with at least one first input port IN _C for an input optical radiation and one or two output ports.

Optical device 3 is of the selective type in wavelength and that is, it is such that it distributes to the two output ports portions of the input optical radiation present at the first input port IN _C Note that the two output ports may not be physically distinct from the input port, as is the case in reflective devices in which one output port physically coincides with the input port but the radiation propagates in the opposite direction.

According to another version, one of the two output ports may not be reachable from the outside (so it is as if it were not present), as is the case, for example, in devices that introduce wavelength-selective losses in which the internally dissipated optical power represents the optical output of the port that is not reachable from the outside. A form of realization in which the device to be observed 3 has more than two output ports will also be described later.

Specifically, the optical device 3 depicted in Figure 1 has a first bandpass port

O _PC to which input radiation belonging to a given wavelength band B _P is sent and a first band-stop port O _EC to which input radiation belonging to an additional wavelength band B _E other than the band B _p is sent

Figure 2 shows example trends of the spectrum of optical radiation on the first band-stop port O _EC and the output band-pass port O _PC . In this example, as appears from Figure 2, the first band-stop port O _EC the first band-pass port O _PC appear complementary.

For example, the optical device 3 is a band-pass or band-stop filter that can be used as an interleaver, multiplexer/demultiplexer, OADM (Optical Add and Drop

Multiplexer) tunable or reconfigurable (TOADM, RO ADM), switch (WSS, Wavelength

Selective Switch), router, dispersion compensator. Other possible optical devices with similar functionality to optical device 3 are: single or multiple Mach-Zehnder interferometer circuits, circuits based on ring resonators or combination of the two,

Arrayed Waveguide Gratings (AWG), Wavelength Locker, tunable devices based on

Bragg Gratings.

Note that the terms " band-stop port" and "band-pass port," usually employed for particular one-input, two-output devices can also be adopted for the types of optical devices listed above, as recognized by the expert in the field.

Optical device 3 provides for the possibility of changing its operating point by means of external control signals. Optical device 3 can assume different wavelength responses (or, equivalently, frequency responses) that depend on the value of a plurality of N state variables that are controlled by N control signals S ₁ ,

..., S _N provided by controller 5.

Specifically, optical device 3 includes an number N _A of actuators (not shown) controllable by control signals S ₁ , ..., S _N . Note that the number of actuators N _A can be equal to or greater than the number N of the control signals. The actuators N _A can be both phase and amplitude actuators. Possible physical implementations are, for example, thermo-optic, electro-optic, acousto-optic, piezo-electric, electro-absorptive, electromechanical, or all-optical actuators (whether or not based on nonlinear optical effects). Particularly, transmission from the first input port IN _c to the first band-pass port O _PC is described by the corresponding wavelength response H _PC,i (λ) (where subscript i refers to a generic i-th state), and transmission from the first input port IN _C to the first band-stop port O _EC is described by a corresponding wavelength response

H _EC,i (λ).

Considering the typology of the optical device 3, the two wavelength responses H _PC,i (λ) and H _EC,i (λ) are complementary, namely, ideally:

| H _PC,i (λ) | ² = 1- | H _EC,i (λ) | ² (1)

The selectivity of the optical device 3 implies that in at least one spectral range

B _p = |λ1-λ2 | (where the wavelengths λi, λ2 delimit the operating band of optical device

3), the transmission | H _PC,i (λ) | ² » | H _EC,i (λ) | ² . The symbol » is intended to mean that H _PC,i (λ) e H _EC,i (λ) differ in square modulus (intensity response) by at least 10 dB or equivalently:

| H _PC,i (λ)| ² / | H _EC,i (λ) | ² > 10 (2) in the band B _p . Note that the more this ratio decreases, the better are the performance of the optical system 100 described here.

The tuning performed by the 100 optical system is such that either the wavelength response H _PC,i (λ) or the response H _EC,i (λ) equals a target response (i.e., a desired response) respectively.

Optical radiation source 1 is a broadband source having, in particular, a wavelength band Bs that includes (equal to or greater than) the wavelength band B _p in which the optical device 3 operates.

As an example, the source of optical radiation 1 may be the ASE (Amplified

Spontaneous Emission) noise of an Erbium Amplifier (EDFA) or that emitted by a super-luminescent diode.

Reference optical device 2 (hereafter, for brevity, reference device) is an optical device that exhibits spectral behavior corresponding to that desired for optical device

3. More specifically, reference optical device 2 exhibits a wavelength response close to or equal to the target response for the optical device 3, namely, according to the example: where subscripts R and C refer to the reference device 2 and the device to be observed 3, and subscripts P and E refer to the band-pass and band-stop outputs, respectively.

The reference device 2 may be implemented by a device of the same type (i.e., same structure and same technology) as optical device 3, or it may be a device different from optical device 3. In any case, the spectral density at the band-pass or band-stop output port of reference device 2 represent the reference for tuning, monitoring, testing, and controlling of optical device 3. Reference device 2 then acts as a spectral shaper of the radiation emitted by source 1.

With reference to the example described, the reference device 2 includes a second input port IN _R and at least a second bandpass port O _PR . The device may also include a second band-stop port O _ER . Similar to the device to be observed 3, for the reference device 2 one of the output ports may not be physically distinct from the input port or may not be reachable from the outside.

Particularly, the transmission from the second input port IN _R to the second band- pass port O _PR is described by its wavelength response H _PR (λ). In contrast, the transmission from the input port IN _R to the second band-stop port O _ER is described by its wavelength response H _ER (λ). Note that even for reference device 2, the wavelength responses H _PR (λ) and H _ER (λ) are complementary.

According to the example of Figure 1, one output of the radiation source 1 is coupled to the second input port IN _R of the reference device 2. In addition, the second bandpass port O _PR of the reference device 2 is coupled to the first input port IN _C of the optical device 3. The first band-stop port O _EC of optical device 3 is coupled to an input port of the optical detector 4.

Optical detector 4 is such that it converts the optical radiation coming out of the first band-stop port O _EC into an electrical signal S _E representative of the power of that exiting optical radiation. The optical detector 4 is, for example, a photodiode.

Controller 5 is configured to the control optical device 3 by means of control signals S ₁ -S _N so so that it assumes wavelength responses as similar as possible to those of the reference device 2, relative to the same outputs. Controller 5 can be realized, for example, by a microcontroller, a CPU (Central

Processing Unit), an FPGA (Field Programmable Gate Array) or a DSP (Digital Signal

Processor), programmed according to the control methodology described below.

The following describes an example of the operation of the optical systemlOO, as depicted in Figure 1.

Radiation source 1 emits an optical signal I _S (λ) having a power spectral density

(PSD) equal to S _S (λ): S _S (λ)= | I _S (λ) | ² (3)

This optical signal I _S (λ) is supplied to the second input port IN _R of the reference device 2, which returns a first output signal OS _R (λ) to the second band-pass port O _PR , given by the following relationship OS _R (λ) = H _PR (λ) I _S (λ) (4)

The first output signal OS _R (λ) is then supplied to the first input port IN _C of the optical device 3 which returns a second output signal OSPG(λ) present at the first band- pass port O _PC of optical device 3 and expressed by the following relation:

OS _PC,i (λ) = H _PC,i (λ) OS _R (λ) = H _PC,i (λ) H _PR (λ) I _S (λ) (5) where subscript i denotes the i-th state of device 3. It follows that a first power spectral density S _PC,i (λ) of the second output signal OS _PC,i (λ) from relation (5) is expressed by the following relation:

S _PC,i (λ)= | OS _PC,i (λ) | ² = | H _PC,i (λ) | ² | H _PR (λ) | ² | I _S (λ) | ² (6)

For the reference device 2, the wavelength response H _PR (λ) is equal to the target response: defined above. Also, note that when the optical device to be observed 3 achieves the desired behavior (state M), its wavelength response H _PC,M (λ) is also equal to and the relation (6) takes the following form: where S _S (λ) is the power spectral density of the input signal I _S (λ).

Relationship (7) shows that when the behavior of the optical device to be observed 3 equals that of the reference device 2, the first power spectral density

S _PC,M (λ) takes on a maximum value.

We refer to the second band-stop port O _EC of the optical device 3 that provides a third output signal OS _EC (λ), produced in response to the first output signal OS _R (λ).

Such a third OS _EC (λ) output signal can be expressed as:

OS _EC,i (λ) = H _EC,i (λ) OS _R (λ)= H _EC,i (λ) H _PR (λ) I _S (λ) (8)

Considering relation (8), a second power spectral density S _EC,i (λ) of the third output signal OS _EC,i (λ) hi the generic i-th state is expressed by the following relation: S _EC,i (λ) = I OS _EC,i (λ) | ² | H _EC,i (λ) | ² | H _PR (λ) | ² | I _S (λ) | ² (9)

Due to the complementarity of the output ports of reference device 2, we have that | H _EC,i (λ) | ² = 1- | H _PC 4(λ) | ² (i.e., equation (1)). Furthermore, the wavelength response H _PR (λ) of the reference device 2 is equal to the target response H _PR (λ) =

As mentioned above, when the optical device 3 achieves the desired behavior

(state M), its wavelength response H _EC,M (λ) is also equal to

Therefore, relation (9) can be rewritten as below: Relationship (10) shows how, when the behavior of the optical device 3 equals that of reference device 2, the second power spectral density S _EC,M (λ) takes on a minimum value.

The third output signal OS _EC,i (λ) (of relation 8) is received at the input port of optical detector 4 which returns an electrical signal S _E (of voltage or current) proportional to the optical power P _EC,i of that third output signal OS _EC,i (λ).

The optical power P _EC,i is equivalent to the integral over one band (B _R ) of optical detector 4 of the second power spectral density S _EC,i (λ) expressed by the relation (9):

The electrical signal S _E is supplied to the controller 5, which operates according to a control law based on minimization of optical power P _EC,i so as to achieve the condition of relation (10).

Note that in this case, an output port (O _PR ) of reference device 2 complementary to the output port (O _PC ) of optical device 3 connected to the optical detector 4 was used for control purposes.

In more detail, the controller 5 acts on the actuators of optical device 3 in such a way as to vary its state variables θ ₁ , θ _N minimizing the optical power P _EC,i represented by the electrical signal S _E and thus bringing the wavelength response

H _EC,i (λ) take on the trend of the response

The controller 5 changes the operating point of the actuators and operates the search for an optimal set of state variables according to a minimization technique such as, for example: the least square mean error (LSME) technique, the gradient technique, a genetic algorithm. In the case of tuning, the process begins by bringing all the N _A actuators to a predefined initial operating point (e.g., all off or at defined values: i = 1)) and present in the controller memory 5. At this point the optical device to be observed 3 has wavelength response H _EC,i (λ). The operating point of the actuators is then changed by an amount much smaller than their dynamics, and the wavelength response at the O _EC port becomes H _EC,2 (λ).

If an error function (represented by power P _EC ) is reduced, then the direction in which the operating point is moving is correct otherwise we have moved away from the target. Controller 5 generates a new set of control signals S ₁ -S _N to be sent to the actuators, and a further iteration is performed. At each iteration, the wavelength response is changed until H _EC,i (λ) takes on the trend which minimizes the residual error. Under these conditions, the value of 'i' reached represents the desired state M.

In an alternative version to that in Figure 1, optical detector 4 is connected to the first band-pass port O _PC of the device 3 and then receives the second output signal

OS _PC (λ) present at the first band-pass port O _PC , in response to the signal coming out of the first band-pass port O _PR of the reference device 2. In this version, the non- complementary ports (both bandpass ports) of the optical device 3 (O _PC ) and the reference device 2 (O _PR ) were used.

In such a case, controller 5 acts to maximize the optical power associated with the first power spectral density S _PC,i (λ) expressed by relation (6) and thus bring itself into the situation indicated by relation (7). The control or tuning process carried out by controller 5 in the case of output power maximization is similar to that described above for the case of output power minimization (relations (9) and (10)).

The above description for optical devices having one input port and two output ports can also be extended to devices with more than one input port and with more than two output ports. Figure 3 schematically shows an optical device to be observed

3 having P input ports (IN ₁ -IN _P ) and Q output ports (O ₁ -O _Q ). A similar schematization applies to the reference device 2.

In this case each output port is connected to a related optical detector 4, which in turn is connected to the controller 5. In an alternative realization some of the output ports can be combined and connected to the same detector, as known to the expert in the field.

The wavelength response relative to the input and output ports employed for reference device 2 is H _R (λ). The wavelength response assumed by the reference device

2 and corresponding to the target wavelength response for optical device 3 is: H _R (λ) =

The wavelength response from the input port p to the output port q for optical device 3 is: H _C,pq (λ). If H _C,pq (λ) represents the wavelength response to the bandpass port (and consequently H _C,ps (λ), for each s#q, are wavelength responses to the band- stop ports), regarding selectivity, condition (2) can esse rewritten as

| H _C,pq (λ) | ² / | H _C,ps (λ) | ² > 10 (con s/q) (12)

In a first case, consider that the reference device 2 is of the same type as the optical device 3. Consider the power spectral density at an output port of the optical device 3 of a similar type (band-pass or band-stop) to the output port employed for the reference device 2. In that case, the power spectral density from the input port p of the reference device 2 to the output port q of the device to be observed 3 (analogous to expression (6)) is dependent on the product

This product takes the maximum value when and that is:

Therefore, relation (13) shows the quantity to be maximized by controller 5 to approach the condition of relation (14).

According to another situation, consider that the reference device 2 is of a complementary type to the optical device to be observed 3. By "complementary" we mean the function with s/q, given by the sum of the frequency responses on all other output ports. Considering lossless devices: while in the presence of leakage

Consider also the power spectral density at an output port of optical device 3 of a complementary type to the output port employed for reference device 2. In that case, the power spectral density at the output port q of optical device 3 (analogous to expression (10)) is product dependent

This product takes the minimum value when and that is: is minimal.

Thus, expression (17) shows the quantity to be minimized by controller 5 in a similar way as described above. Thus, under the assumption of relation (12) regarding selectivity, using the p-th port as input, the controller 5 operates in the following alternative ways A) and B):

A) It maximizes the power output from the q-th port

B) It minimizes the summation of the power output from ports other than the q-th port

In the implementation form of Figure 1, source 1 is connected to reference device 2, which is cascaded with optical device to be observed 3. According to an alternative implementation form, the positions of the two optical devices can be reversed and thus provide that source 1 is connected to the optical device to be observed 3, which is cascaded with reference device 2 that has an output port connected to optical detector 4.

In that case the same power spectral density relations (6) and (9) remain valid, as do the control modes operated by controller 5, described above.

In addition, regarding the possible modes of connection between the ports of optical device 3 and reference device 2, solutions other than those described above can also be provided.

For example, it is possible that optical device to be observed 3 and reference device 2 are connected to each other so that the optical output signal provided to optical detector 4 depends on the cascade of wavelength responses relative to the respective band-pass ports: H _PR (λ) and H _PC (λ). In this case, control 5 operates to maximize the optical power of the signal received at the detector itself.

In addition, it is possible that optical device 3 and reference device 2 are connected to each other so that the optical output signal provided to optical detector 4 depends on the cascade of wavelength responses relative to the respective band-pass ports: H _ER (λ) e H _EC (λ). In this case, the controller 5 operates to minimize the optical power of the signal received at optical detector 4.

In the case of devices with more than one input port and more than two output ports, controller 5 operates as indicated in (A) and (B) above.

The following table summarizes the error function optimization strategy performed by controller 5 described above depending on the type of connection between the ports.

Note that the optical system 100 (for example, in its various forms of implementation described above) can be used not only for tuning and control purposes but also for testing or monitoring pinposes. Testing or monitoring can also be done for an optical device 3 type that cannot be reconfigured or tuned.

It should also be noted that reference device 2 may have only one output port (of the band-stop or band-pass type).

In testing or monitoring cases, the controller 5 acting on the actuators of the optical device 3 is replaced by a processing device that still operates by analyzing the optical power of the signal received at the optical detector 4 and from this obtains information about the deviation of the behavior of the optical device 3 from the behavior of the reference device 2

The following describes results obtained experimentally or obtained by numerical simulations related to the operation of the optical system 100.

Figure 4 refers to an example of tuning a generic filter with one input and two outputs, one band-clear and one band-pass, by the approach described with reference to Figure 1. The spectral response of the two outputs is both H _PC (λ) and H _EC (λ).

Figure 4(a) shows the intensity of the H _EC,i (λ) and H _PC,i (λ) spectral response of a generic optical device 3 that has not yet been tuned, and Figure 4(b) shows the intensity response of the reference device 2 to which it must tend after tuning e

Assume that the output H _PR (H _ER ) of the device 2 is used. When the device to be observed 3 is not tuned, the output power measured by detector 4 is worth P _PC,1 (P _EC,1 ) and corresponds to the first measured value. By successively changing the set iteratively as described above, the output power increases (decreases) to a maximum (minimum) equal to to which corresponds the best-tuned filter to be observed 3, with spectral responses at its output ports. The performance of P _PC,i (P _EC,i ) at the ports O _PC and O _EC in the two cases is depicted in Figure 5.

The validity of the present invention is also supported by experimental results. For example, the described technique has been tested for a fourth-order filter 3 having coupled resonant rings 6 made in silicon photonics technology, shown in figure 6. Such a filter 3 has two input ports (Inc and Add) and two output ports. Upon entering with a signal into the port In _C one of the two outputs is band-stop (Through) and the other is band-passing (Drop).

The device in Figure 6 is equipped with four thermo-optical actuators 7 on each individual resonant structure 6. The filter 3 designed to have a minus 3dB bandwidth above 40 GHz (measured at the Drop gate) and an average rejection of 17 dB (over 20 GHz around the center frequency).

The filter of Figure 6 used in the experiment is made with integrated silicon waveguides. However, other propagating materials such as semiconductors (InP, InGaAs, SiC), LiNbO, dielectrics (SiO2:Ge, SiON, SiOC, SiN, SiOF, ITO, BaTiO) and polymers (acrylates, polymides, polycarbonates, alkenes) can be used. Other physical implementations besides integrated optics are also possible, such as free-space optics or micro-optics.

The squared modulus of the wavelength responses observed at both output ports ( | H _drop | ² e | H _through | ² ) is shown in Figure 7 when the filter 3 is tuned to best effect This response is obtained by resorting to the scheme shown in Figure 1 with a reference device 2, placed downstream of a broadband ASE source, nominally equal to test filter 3, with a bandwidth of about 40 GHz, just as per the filter specification in figure 6.

Figure 8 refers to an experiment performed with an optical system similar to that in Figure 1, employing a reference device 2 nominally identical to the optical device of Test 3 to be tuned or tested.

In this case, the output O _PR (i.e., the Drop port) was connected to the input IN _C of the optical device under Test 3. Applying the described tuning technique results in the device under Test 3 assuming a wavelength response (observed in both outputs O _PC and O _EC ) very similar to that of Reference 2. In other words, the device to be tuned 3 turns out to be a faithful replica of reference filter 2.

Therefore, using a nominally identical version as reference filter 2, the technique described above can be employed to calibrate the device to be tuned 3 and find a working point that puts it in the same condition as the reference device. Figure 8 shows the experimental result of this first application: the dashed curves are for reference filter 2, while the solid curves are for tuned optical device 3.

The, is the wavelength response observed at the Drop port of reference filter 2 and is the wavelength response observed at the Through port of Test filter 3 (at the end of the tuning procedure), it turns out that the power spectral density output from the series of the two devices is (assuming that a broadband, flat-spectrum source is used): and then detector 4 (downstream of the system, placed at the Through port of optical device 3) reads a power P _out equal to where BR is the band of optical detector 4.

As already noted, in the case where the filter to be tuned 3 is the perfect replica of reference 2 such a power value is the minimum possible. Otherwise the power P _out,thr is an indication of how different the two devices are from a wavelength response point of view.

Shown in Figures 9-11, as an example, are the output power spectral densities when the spectral response of the reference device 2 is not centered at the same frequency as that of the device to be observed 3 (the continuous curve represents the optimal case H _C (λ) = H _R (λ), i.e., the two frequency responses are centered at exactly the same frequency). Also depicted are graphs describing the trend of the detected power (P _out ), and thus of the electrical signal S _E as a function of the frequency mismatch between the spectral response of the reference and that of the device to be tuned.

Figure 9 considered the case where the relevant band-pass port is used for both the optical device under Test 3 and the reference device 2.

Figure 10 considered the case where the band-stop port is used for both the optical device under Test 3 and the reference device 2.

Figure 11 considered the case where the band-stop port is used for the optical device under Test 3 and the band-pass port is used for the reference device 2.

Figures 9-11 were generated, simulating the frequency response of a filter consisting of a single ring resonator.

Figure 12 considered the case where the band-pass port was used for the optical device to be observed 3 and the band-stop port for the reference device 2, considering a filter under Test 3 with coupled fourth-order resonators, such as that shown in Fig. 6.

With reference to the same device in Fig. 6, also shown in Fig. 13(a) is the situation in which the band-pass port of the filter to be observed 3 is subject to random perturbations. The solid line in this case indicates the band-stop port of the reference filter 2. In Fig. 13(b), we also show the power of the optical signal P _out,thr collected at the output and the mean square error (MSE) calculated as between the frequency response of the reference device 2 (H _drop (λ)) and that of the filter to be tuned 3 in the target state both considered at the bandpass port From the latter figure, a strong correlation between output power P _out,thr and the MSE quantity can be observed. Thus minimizing the output power P _out,thr is equivalent to minimizing the mean square error MSE between the frequency response of the reference filter 2 and that of the filter to be tuned 3 in the target state.

Advantages

As appears from the preceding description, the optical system 100 and the method described allow tuning, monitoring, testing, or control operations of an optical device to be carried out in an extremely simpler and quicker way than is done according to the known art In fact, the method of the present solution makes it possible to avoid measuring the entire spectrum of the observed optical device.

The described methodology also has time advantages in that the measurement of optical power and subsequent processing is much faster than that based on spectrum measurement

LEGEND

- optical system 100

- optical radiation source 1

-reference device 2

- optical device to be observed 3

- optical detector 4

- controller 5

- resonant rings 6

- thermo-optical actuators 7

- control signals S ₁ -S _N

- first input port IN _C

- first band-pass port O _PC

- first band-stop port O _EC

- second input port IN _R

- second band-pass port O _PR

- second band-stop port O _ER

- first output signal O _SR

- second output signal OS _PC

- third output signal O _SEC

- electrical signal S _E

- input ports (IN ₁ -IN _P )

- output ports (O ₁ -O _Q )