Wavelength Locker

Abstract

Conventionally, wavelength locking and monitoring has been achieved used various components, including calibrated etalon filters, gratings, and arrays of color filters, which offer fairly bulky solutions that require complicated controls. An improved on-chip wavelength monitor comprises: a combination comb filter comprising a plurality of comb filters, each for receiving a test beams, and each comb filter including a substantially different FSR, e.g. 10.times. to 20.times. the next closest FSR. A controller dithers a phase tuning section of each comb filter to generate a maximum or minimum output in a corresponding photodetector indicative of the wavelength of the test signal.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of and claims priority to U.S. patent application Ser. No. 15/855,242, filed Dec. 27, 2017, now allowed, which is hereby incorporated by reference herein in its entirety.

TECHNICAL FIELD

[0002] The present invention relates to a wavelength locker, and in particular to an integrated wavelength monitor and locker for use with photonic integrated circuits.

BACKGROUND

[0003] Accurately determining the absolute wavelength of a single mode laser signal has many potential applications in many fields, including spectroscopy, communication system, and wavelength tunable lasers. Conventionally, wavelength locking and monitoring has been achieved used various components, including calibrated etalon filters, gratings, and arrays of color filters. Unfortunately, all of the conventional systems offer fairly bulky solutions that require complicated controls and assembly. Furthermore, some of these devices reflect a significant amount of light back to the light source that can potentially disturb laser sources, which further necessitates the use of bulky isolators. Conventional wavelength lockers and monitors that provide fine resolutions, e.g. 1 GHz or 10 pm of accuracy, typically require large footprints.

[0004] An object of the present invention is to overcome the shortcomings of the prior art by providing an integrated wavelength locker with low reflectivity and high resolution.

SUMMARY OF THE INVENTION

[0005] Accordingly, the present invention relates to a wavelength monitor and measurement system comprising:

[0006] a splitter for splitting a test signal into a plurality of test beams;

[0007] a combination comb filter comprising a plurality of comb filters, each for receiving a respective one of the test beams, each comb filter including a different FSR;

[0008] at least one photodetector for measuring output from each comb filter;

[0009] a phase tuning section for each comb filter for tuning a resonance of each of the plurality of comb filters; and

[0010] a controller for controlling the phase tuning section of each comb filter to generate a maximum or minimum output in the corresponding photodetector indicative of the wavelength of the test signal.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The invention will be described in greater detail with reference to the accompanying drawings which represent preferred embodiments thereof, wherein:

[0012] FIG. 1 is an schematic diagram of a wavelength locker/monitor in accordance with an embodiment of the present invention;

[0013] FIG. 2 is a plot of the response vs wavelength of the combined comb filter device of FIG. 1;

[0014] FIG. 3 is a schematic diagram of an embodiment of a comb filter of the device of FIG. 1;

[0015] FIG. 4 is a schematic diagram of an embodiment of a comb filter of the device of FIG. 1;

[0016] FIG. 5A a plot of the response vs wavelength of the device of FIG. 3 for various phase shifts;

[0017] FIG. 5B a plot of the response vs wavelength of the device of FIG. 4 for various phase shifts.

DETAILED DESCRIPTION

[0018] While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives and equivalents, as will be appreciated by those of skill in the art.

[0019] An embodiment of the present invention, relates to a novel compact on-chip wavelength locker (WLL) 1 based on integrated components to determine absolute wavelength of incoming light from a laser source 2 with minimum back reflection, high accuracy and stable temperature performance. The purpose of the WLL 1 is specifically to monitor and identify, with great accuracy, the wavelength of an incoming laser signal 7. One possible use for the WLL system 1 is to enable the laser source 2 to be tuned by control system 3 to a very precise wavelength, since now there is a means of seeing the current wavelength of the laser 2. The WLL 1 would be most suitable for different classes of tunable lasers 2, including integrated InP based photonic integrated circuits, hybrid III/V, and Silicon Photonic devices.

[0020] With reference to FIG. 1, the WLL 1 may use integrated components on a device layer of an independent photonic integrated circuit (PIC), an existing PIC including the laser source 2 or an independent PIC connected to a separate chip including the laser source 2. The WLL 1 may comprise a tunable, periodic, high-fineness, combination comb filter 5 in wavelength space, which may include a plurality of separate comb filters 4.sub.1 to 4.sub.n, each with a different free spectral range (FSR). A tap 6 may be used to tap off a small portion, e.g. less than 5%, typically 1% to 5%, of the light 7 from the laser source 2 forming a test signal 7' to be fed to the WLL 1. A splitter 8 divides the test signal 7' into individual test beams 7''.sub.1 to 7''.sub.n, each for transmission to a respective one of the comb filters 4.sub.1 to 4.sub.n.

[0021] During operation, the control system 3 tunes each comb filter 4.sub.1 to 4.sub.n by dithering a phase shifter, and locking each individual test beam 7''.sub.1 to 7''.sub.n to a high fineness peak or a null point of the respective comb filter 4.sub.1 to 4.sub.n. Once the comb filter 4.sub.1 to 4.sub.n is locked, the value of a pre-calibrated electrical signal used to tune the comb filters 4.sub.1 to 4.sub.n is used by the controller 3 to determine the absolute wavelength of the test signal 7'.

[0022] To lock each comb filter 4.sub.1 to 4.sub.n, the control system 3 tunes the phase of each comb filter 4.sub.1 to 4.sub.n using control signals 9.sub.1 to 9.sub.n to maximize or minimize a current generated in a corresponding photodetector 11.sub.1 to 11.sub.n depending on whether a null point or a peak point of the comb filter 4.sub.1 to 4.sub.n is found, i.e. maximum transmission or minimum transmission of light through the comb filter 4.sub.1 to 4.sub.n.

[0023] In the example plot illustrated in FIG. 2, three comb filters are utilized, i.e. a first comb filter 4.sub.1 with a first fine FSR1, e.g. 10 GHz to 40 GHz, ideally 20 GHz, an second comb filter 4.sub.2 with a second intermediate FSR2, e.g. 100 GHz to 800 GHz, ideally 400 GHz, and a third comb filter 4.sub.3 with a third coarse FSR3, e.g. 2000 GHz to 16000 GHz, ideally 8000 GHz. Additional comb filters with additional intermediate FSR's may be used. For this example, the WLL 1 is tuned whereby all of the combs align at a null point to the incoming light wavelength. Accordingly, the wavelength range of the comb filter 5 is defined as the FSR of the coarsest comb FSR3.

[0024] Based on this method and depending on the accuracy of electronics, wavelength accuracy as small as a fraction of the smallest FSR may be achieved. The fraction is as many phase levels as the electronics can detect within each a range. Hence each phase section needs to be tuned for a full 2.pi.. Obviously electronics with lower phase noise will be able to detect finer phases. For instance, it is possible to achieve wavelength accuracy at least 10 to 30 times, preferably 20 times, finer than the FSR, e.g. achieving 18.degree. phase accuracy.

[0025] In order to maximize the wavelength range of WLL 1, the illustrated embodiment uses multiple filters, e.g. 4.sub.1 to 4.sub.3, with different values of FSRs, e.g. FSR1, FSR2 and FSR3, respectively. The finest filter 4.sub.1 detects as many wavelength values within one FSR as phase levels, e.g. 20 times in the example mentioned above. The second filter 4.sub.2 may consequently have an FSR that is equal to or larger than fine filter 4.sub.1 by as much as the detectable phase levels. For the quoted example, the second FSR2 may be 10 to 30 times, preferably 20 times, larger than the fine FSR1, resulting in a detection wavelength range as large as 400 times the wavelength resolution. This scheme may be repeated as many time as possible with as many comb filters 4.sub.1 to 4.sub.n as possible to cover the wavelength range of interest. The final WL range will be the FSR FSRn of the coarsest comb filter 4.sub.n.

[0026] The controller 3 may actuate and control the combined comb filter 5 continuously throughout the life of the device, i.e. analog control, utilizing some form of feedback loop. Alternatively, the controller 3 may actuate and control the combined filter 5 whenever a wavelength enquiry is made, e.g. according to a predetermined timing protocol, such as upon start up, and/or at predetermined time periods

[0027] During use, the controller 3 may actuate and control all of the filters 4.sub.1 to 4.sub.n simultaneously. For example, each filter will determine the wavelength of the test beam 7'.sub.1-7'.sub.n within the filters given accuracy and resolution. Then based on phase bias (electrical) readings of each filter 4.sub.1 to 4.sub.n, the controller 3 calculates the precise wavelength of the test signal 7'. Alternatively, the controller 3 may tune the coarsest filter 4.sub.n, e.g. FSR3, first to determine the wavelength of the test beam 7'.sub.n within a first broad range, e.g. 400 GHz for an FSR3 of 8000 GHz and 20 phase levels. Then, knowing the first broad range, the controller 3 many tune one or more intermediate filters 4.sub.2 to determine the wavelength of the test beam 7'2 within a second intermediate range within the first broad range, e.g. 20 GHz for an FSR2 of 400 GHz and 20 phase levels. Finally, knowing the intermediate range, the controller 3, tunes the finest filter 4.sub.1 to determine the wavelength of the test beam 7'.sub.1 to within a fine range within the intermediate range, e.g. 1 GHz for an FSR3 of 20 GHz and 20 phase levels.

[0028] The on-chip comb filters 4.sub.1 to 4.sub.n may be implemented using, inter alia, unbalanced Mach-Zehnders (MZ) filter 30 (FIG. 3), and/or coiled racetrack resonators 51 (FIG. 4).

[0029] With reference to FIG. 3, a MZ filter 30, comprised of a first arm 31 and a second arm 32, with an arm length imbalance, e.g. the longer arm may be 10%-90%, 20%-80%, 30%-50% longer or any suitable imbalance, and a small loss imbalance, may provide high fineness combs 4.sub.1 to 4.sub.n. The wavelength of the test signals 7''.sub.1 to 7''.sub.n may be determined at the null or max points of the MZ filter 30. The phase of the MZ filter 30 may be tuned by the control system 3 by including a phase tuning section 33, e.g. a thermal phase tuner, on either of the arms 31 and 32. In an illustrated example, an FSR of 16 GHz is provided, and 16 distinct phase levels may be identified within each FSR. Hence a wavelength resolution of 1 GHz is achieved.

[0030] In order to actively balance the losses between each of the first and second arms 31 and 32, a variable optical attenuator 35 may be provide in one or both of the first and second arms 31 and 32. In order to more passively balance losses between each of the first and second arms, due to components found in either of the first and second arms 31 and 32, a balancing element may be provided in each arm 31 and 32 of the MZ filter 30. For example, a balancing element 34 may be provided on the first arm 31 for tuning the loss of arm 31 by including similar components, e.g. transitions between different waveguide materials, that are found in the second arm 32. Moreover, a second variable optical attenuator (VOA) 36 may be provided on the first arm 32 to balance the losses caused by the first VOA 34 in the first arm 31. The test signal 7''.sub.n enters the input port 37 from the splitter 8, and exits the output port 38 to the corresponding photodetector 11.sub.n.

[0031] The MZ filter 30 may be constructed to have minimum thermal cross talk between the phase tuning section 33 and the rest of the MZ waveguides 31 and 32. Accordingly, the first and second arms 31 and 32 may each include a coiled section, disposed as far away, e.g. >500 .mu.m, from any heat source, e.g. the phase tuning section 33, as possible, to minimize the thermal gradient across each arm. The biggest advantage of MZ filters 30 is that they are not reflective by nature and hence no isolator will be needed for the integrated tunable laser 2. The type of waveguide, e.g. shape and/or material, on each arm may be constructed to reduce temperature sensitivity of the filter response and device back reflection. In order to have smaller temperature sensitivity, waveguides with different properties and/or types may be used for the first and second arms 31 and 32 in the same MZ filter 30 that further boosts the sensitivity.

[0032] The following equation (1) may be used to calculate the FSR of each MZ filter 30, and the following equation (2) may be used to calculate the temperature sensitivity .DELTA..lamda./.DELTA.T, i.e. change in wavelength per change in temperature for the MZ filter 30, wherein n.sub.g is the group index, n.sub.1 and n.sub.2 are the index of refraction for the first and second arms 31 and 32, respectively, and L.sub.1 and L.sub.2 are the lengths of the first and second arms 31 and 32, respectively.

FSR = .lamda. 2 n g 1 L 1 - n g 2 L 2 ( 1 ) .DELTA..lamda. .DELTA. T = .differential. n 1 .differential. T L 1 - .differential. n 2 .differential. T L 2 n g 1 L 1 - n g 2 L 2 ( 2 ) ##EQU00001##

[0033] Accordingly, to minimize the temperature sensitivity, the numerator of equation (2) should be minimized, whereby the change in index with temperature.times.the length of the first arm 31 should be substantially equal to the change in index with temperature.times.the length of the second arm 32. There are several different ways in which to balance this equation, including but not limited to, fabricating the first and second arms 31 and 32 out of different materials, e.g. Silicon (Si) and Silicon Nitride (SiN). The shape, i.e. cross-section, of the first and second arms 31 and 32 may also be different to provide a different change in index with temperature, and therefore minimal temperature sensitivity. For example: one of the first and second arms 31 and 31 may comprise a rectangular or ridge cross-section with first height and width dimensions, while the other arm may comprise a rectangular or ridge cross-section with at least one of second different height and a second different width. In another example the cross-section of the first and second arms 31 and 32 may have different shapes, e.g. one of the first and second arms 31 and 32 may include a rectangular cross section (strip), while the other includes a ridge or rib waveguide cross-section, comprising a stepped or inverted T structure, with a slab portion and a ridge portion. In another possible embodiment, the light in one of the first and second arms 31 and 32 may be rotated from the usual mode, e.g. TE, to the orthogonal mode, e.g. TM, using a first polarization rotator 39a at the beginning of the first arm, and then rotated back to the original polarization, e.g. TE, by a second polarization rotator 39b, at the end of the first arm 31 Different modes may be used because the derivative of n.sub.eff with respect to temperature is significantly different for the TM mode as compared to the TE mode.

[0034] In an example embodiment, a first comb filter 4.sub.1 comprises an FSR.sub.1 of 16 GHz at 1545 nm, and a length L.sub.1 of a first TE0 waveguide 31 of 27.137 mm and a length L.sub.2 of a second TM0 waveguide 32 of 38.103 mm. A second comb filter 4.sub.2 comprises an FSR.sub.2 of 160 GHz at 1545 nm, and a length L.sub.1 of a first TE0 waveguide 31 of 2.7137 mm and a length L.sub.2 of a second TM0 waveguide 32 of 3.8103 mm. The plot below of d.lamda./dT in .mu.m/K vs Wavelength in .mu.m illustrates that a typical MZ filter 30 with similar first and second waveguides 31 and 32 has a consistently large change in wavelength per change in temperature, whereas a thermally balanced MZ filter 30 has a much smaller temperature sensitivity, especially in the C-band (1.53 .mu.m-1.565 .mu.m), hence it requires looser temperature control.

[0035] Alternatively, or in combination with the aforementioned thermally balanced waveguides, in order to more accurately compensate for thermal effects on the MZ filter 30, a plurality of temperature sensors 41, e.g. two to four, ideally three, may be used to map the temperature of the WLL 1. In order to make interpolation within the sensors 41 more accurate, the heat source, e.g. phase section 33, is placed outside of the area defined by the sensors 41, e.g. three sensors 41 define a triangle, four sensors 41 define a quadrilateral. Each temperature sensor 41 may comprise two diodes, each with a different length in order to make differential detection and achieve higher reading accuracy. Further accuracy is achieved by using four-point-detection scheme on each diode. From the temperature readings of the plurality of sensors 41, a temperature profile of the MZ filter 30 may be determined by the control system 3. Based on the temperature profile, the control system 3 may then compensate for the thermal effects by adjusting the peaks of the comb filters 4.sub.1 to 4.sub.n, i.e. the ultimate wavelength reading of the test signals 7''.sub.1 to 7''.sub.n.

[0036] With reference to FIG. 4, a ring resonator 51 may also be used to achieve the high fineness spectral response required for the comb filters 4.sub.1 to 4.sub.n in the WLL 1. Conventional ring or multi-ring resonators may be used, but the illustrated embodiment includes a coiled racetrack resonator 51, to minimize area and thermal effects. The coiled racetrack resonator 51 includes an input waveguide 52 with an input port 53 and a through port 54. At least one closed loop waveguide 56 is coupled to the input waveguide 52. An output waveguide 57 is coupled to an opposite side of the loop waveguide 56, and includes drop port 58, which is optically coupled to one of the photodetectors 11.sub.1 to 11.sub.n. When light of the resonant wavelength is passed through the loop waveguide 56 from the input waveguide 52, it builds up in intensity over multiple round-trips due to constructive interference and is output to the output waveguide 57, which serves as a detector waveguide. Because only a select few wavelengths will be at resonance within the loop waveguide 56, the optical ring resonator 51 functions as a filter.

[0037] For resonance to take place in the ring resonator 51, the following resonant condition must be satisfied:

.lamda..sub.m=2.pi.r n.sub.eff/m

[0038] Wherein r is the radius of the ring resonator and n.sub.eff is the effective index of refraction of the waveguide material making up the ring resonator 51.

[0039] Where .lamda..sub.m is the resonant wavelength, and m is the mode number of the ring resonator 51. Accordingly, in order for light to interfere constructively inside the ring resonator 51, the circumference of the closed loop 56 must be an integer multiple of the wavelength of the light. As such, the mode number must be a positive integer for resonance to take place. As a result, when the incident light contains multiple wavelengths, only the resonant wavelengths will be able to pass through the ring resonator 51 fully. As a result, when the wavelength of the test beam 7n'' matches the resonant wavelength of the ring resonator 51, a maximum transmission measurement will be detected by the photodetector 11n, whereby the value of a pre-calibrated electrical signal used to tune the ring resonator 51 is used by the controller 3 to determine the absolute wavelength of the test signal 7''.sub.n.

[0040] Similar to the MZ filter 20 above, the ring resonator 51 includes at least one phase tuning section 61, e.g. thermo-optic or electro-optic, within the closed loop 56 to enable the aforementioned tunability. The phase tuning section 61 also should include waveguides with low back reflection and small thermal coefficient. The ring resonator 51 may also be comprised of waveguides 52, 56 and 57 that result in minimal thermal effects. For example: if combination of positive and negative thermal coefficient waveguides are used. One advantage of the ring resonator devices 51 over the MZ filter 20 based devices is that the resonator device 51 may be accessed both via the through port 54 and the drop port 58, which provides different signal amplitudes at high fineness section. For example, providing the photodetector 11.sub.n or an additional photodetector optically coupled to the through port 54 may provide an indication of when light from the test signal 7''.sub.n at the resonant wavelength of the ring resonator 51 is minimized or null at the through port 54, and therefore fully passed to the drop port 58. Accordingly, the through port 54 may provide an alternative location for the photodetector 11.sub.n or a secondary location for an additional photodetector providing a secondary or confirmation measurement that the ring resonator 51 is locked to the wavelength of the laser signal 7.

[0041] As mentioned above with reference to the MZ filter 20, the ring resonator device 51 may also be temperature sensitive. Despite constructing the waveguides 52, 56 and 57, of materials to minimize thermal effects, the absolute wavelength of the high fineness point may slightly change with temperature, resulting in reading error. Accordingly, as with the MZ filter 20, a few on-chip temperature sensing devices 62 may be used around each ring resonator 51 to closely monitor and control its temperature. The polygon formed by temperature sensing devices 62 should contain no heat sources to allow for thermal interpolation anywhere inside such shape. Each temperature sensor 62 may comprise two diodes, each with a different length in order to make differential detection and achieve higher reading accuracy. Further accuracy is achieved by using four-point-detection scheme on each diode. From the temperature readings of the plurality of sensors 62, a temperature profile of the ring resonator filter 51 may be determined by the control system 3. Based on the temperature profile, the control system 3 may then compensate for the thermal effects by adjusting the peaks of the comb filters 4.sub.1 to 4.sub.n, i.e. the ultimate wavelength reading of the test signals 7''.sub.1 to 7''.sub.n.

[0042] Each filter device, e.g. MZ filter 30 or ring resonator 51, requires calibration to define the precise location of comb filter lines depending on the measured temperatures, as well as the applied current to the phase tuning section 33 or 61. This calibration data is used to calculate the absolute wavelength based on the phase shifter bias and temperature for which the filter, e.g. MZ filter 30 or ring resonator 51, is locked to the test signal 7''.sub.1 to 7''.sub.n.

[0043] FIG. 5A is an example of a fine comb filter response for different phase shifts based on the MZ filter 40, and FIG. 5B is an example of a fine comb filter response for different phase shifts based on the coiled racetrack resonator 51. As the phase tuning section 33 or 61 is adjusted by the controller 3, the null point (or peak point) of the response shifts. The control system 3 determines the wavelength of the test signal 7', and may lock the WLL 1 to either peak or null points on both designs. The control system 3 may then send laser control signals back to the laser source 2 to provide adjustments to the wavelength, i.e. control the wavelength of the tunable laser 2.

[0044] The foregoing description of one or more embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.

Claims

1. An apparatus, comprising a laser source to generate a laser signal and a wavelength monitor, wherein the wavelength monitor comprises: a tap for tapping a portion of the laser signal from the laser source to form a test signal; a splitter for splitting the test signal into a plurality of test beams; a combination comb filter comprising a plurality of comb filters, each one of the plurality of comb filters connected to receive a respective one of the test beams, each comb filter having a different FSR; a plurality of photodetectors, each one of the photodetectors configured for measuring light output from a respective one of the plurality of comb filters; a plurality of phase tuning sections, each of the plurality of phase tuning sections for tuning a corresponding one of the comb filters; and a controller to control the plurality of phase tuning sections to determine a wavelength of the test signal by generating a maximum output or a minimum output in some of the plurality of photodetectors, and configured to tune the laser source based on the determined wavelength of the test signal.

2. The apparatus according to claim 1, wherein the controller is configured to determine the wavelength of the test signal based on values of pre-calibration values of electrical signals for controlling the some of the phase tuning sections to tune corresponding ones of the plurality of comb filters.

3. The apparatus according to claim 2, wherein the controller is configured to dither the some of the plurality of phase tuning sections such that some of the test beams are locked to a peak or a null point of the corresponding ones of the plurality of comb filters.

4. The apparatus according to claim 1, wherein the plurality of comb filters comprises at least a first of the comb filters and a second of the comb filters; and wherein the FSR of the second of the comb filters is at least 10 times larger than the FSR of the first of the comb filters.

5. The apparatus according to claim 4, wherein the plurality of comb filters further comprises a third of the comb filters; wherein the FSR of the third of the comb filters is at least 10 times larger than the FSR of the second of the comb filters.

6. The apparatus according to claim 5, wherein the FSR of the first of the comb filters is between 10 GHz to 40 GHz; wherein the FSR of the second of the comb filters is between 100 GHz to 800 GHz; and wherein the FSR of the third of the comb filters is between 2000 GHz to 16000 GHz.

7. The wavelength monitor according to claim 5, wherein each of the plurality of phase tuning sections are configured to provide wavelength accuracy of at least 10 to 30 times finer than the first FSR, the second FSR and the third FSR.

8. The apparatus according to claim 1, wherein each one of the plurality of comb filters comprises a ring resonator.

9. The apparatus according to claim 8, wherein at least one of the ring resonators comprises waveguides with positive and negative thermal coefficients on each side thereof to minimize temperature sensitivity between each side.

10. The apparatus according to claim 8, wherein each ring resonator comprises a drop port and a through port; and wherein one of the plurality of photodetectors is coupled to each drop port.

11. The apparatus according to claim 1, wherein each of the plurality of comb filters comprises a Mach-Zehnder filter.

12. The apparatus according to claim 11, wherein at least one of the Mach-Zehnder filters comprises a first arm and a second arm; and wherein the first arm includes a first polarization rotator for rotating a polarization of light in the first arm, and a second polarization rotator for rotating back the polarization of light in the first arm.

13. The apparatus according to claim 12, wherein the first arm comprises Silicon and the second arm comprises Silicon Nitride.

14. The apparatus according to claim 12, wherein the first arm comprises a strip waveguide, and the second arm comprises a rib waveguide.

15. The apparatus according to claim 12, wherein the first arm includes a width that is different than a width of the second arm.

16. The apparatus according to claim 1, further comprising a temperature sensor; wherein the temperature sensor comprises at least three temperature sensors; and wherein a heat source is placed outside an area defined by the at least three sensors.

17. The apparatus according to claim 16, wherein each of the at least three temperature sensors comprises two diodes with different lengths.

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