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A novel high-resolution interference spectrometer
Optics and ¸asers in Engineering 29 (1998) 413—422 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Northern Ireland 0143—8166/98/$19.00 PII: S0143–8166(97)00109–7
A Novel High-resolution Interference Spectrometer T. L. Helga, T. H. Barnesa & T. G. Haskellb a Department of Physics, The University of Auckland, Private Bag 92019, Auckland, New Zealand b Industrial Research Ltd, P.O. Box 31-310, Lower Hutt, New Zealand (Received 20 August 1997; accepted 28 November 1997)
ABS¹RAC¹ A novel precision wavemeter is presented with a resolution of better than 0)01 nm. A Sagnac interferometer with two diffraction gratings forms the basis of the instrument. ºsing spatial heterodyning techniques and a CCD camera/ frame grabber data acquisition system allows fast computer control and power spectrum analysis. ¹he mode structure and mode hopping characteristics of a typical laser diode were examined as a function of diode injection current. ( 1998 Elsevier Science ¸td. All rights reserved.
1 INTRODUCTION Spectroscopic instruments are available in many forms, operating with a variety of principles and purposes. We wished to develop an instrument for characterisation of laser diodes and mode hop detection. Therefore, two spectroscope varieties of interest here are Fourier Transform Spectrometers and Monochromators.1 Fourier Transform Spectrometry2,3 (FTS) is a well-established field in interferometry. Traditional methods of FTS involve moving mirrors in a basic Michelson interferometer. The resulting interferogram recorded by the detector is a function of the interferometer path difference and the frequency of the light source. That frequency is recovered by Fourier transform techniques. This indirect method is particularly useful for low-light measurements as all the available light is used. In the past, this advantage was offset by timeconsuming computer calculations. With more modern computers this is no longer so limiting. Monochromators are extremely common spectrometers that incorporate a dispersive element. They are inexpensive, easy to use and calibrate. However, only one frequency can be examined at a time. This limits the speed at which a spectrum could be obtained with such an instrument. 413
414
T. L. Helg et al.
It is possible to combine the advantages in these instruments with heterodyning4 techniques and the stability of a Sagnac common path interferometer to give an inexpensive easy to construct wavemeter for measuring the power spectrum of lasers.
2 INSTRUMENT OPERATING PRINCIPLE The basic aim of this experiment was to design and build a wavemeter to examine narrow-band light sources. A resolution of 0)01 nm was required with the ability to cope with low intensity light sources with fast-data acquisition, and stable operation. The basic design of a diffraction grating5 interferometer6 was chosen for efficient use of light and for incorporating heterodyning techniques. Stable operation requirements suggested a Sagnac design for the interferometer with a charge-coupled device (CCD) camera as the sensor for fast data acquisition. Figure 1 shows a wavemeter with a diffraction grating (DG) as the dispersive element. The angle at which a beam is refracted from the surface is a function of the incident angle and the light beam frequency. The diffraction grating can be positioned so that at some reference frequency the first-order refracted beams of the clockwise and anticlockwise incident beams will exit the interferometer in parallel. The beams will interfere constructively at the output sensor to form zero fringes. If light of a different frequency is then examined, the beams will exit the interferometer at an angle to each other causing a fringe pattern to form. The number of fringes will indicate how far
Fig. 1. Single grating Sagnac interferometer.
High-resolution interference spectrometer
415
Fig. 2. Asymmetric configuration of the double diffraction grating Sagnac interferometer.
from the reference frequency the test source is. This spatial heterodyning technique allows us to select the resolution of our instrument by using an appropriate line spacing in the diffraction grating. However, while this simple design demonstrates our technique in principle, in practice, the diffraction grating does not sit at a 45° angle causing one beam to be compressed and the other to be expanded. By inserting a second diffraction grating into the interferometer this cylindrical shearing can be corrected. Operation of this configuration, shown in Fig. 2, is similar to before except we now have twice the angular deviation of the beam and hence potentially twice the resolution. It is important to note that the gratings must be in these asymmetric positions to ensure that the beams will be at an angle with each other not just to the instrument optic axis.
3 THEORETICAL DEVELOPMENT The grating equation can be expressed as follows, sin b!sin a"n
j d
(1)
where the angles are labelled so that b'a. We wish to know the change in a as a function of wavelength cf. Fig. 3. a is a constant, as j changes b will 2 1 1 change, giving a corresponding alteration in b . This means that the change in 2 a is a function of the angular change in b due to the dispersion at diffraction 2 2
416
T. L. Helg et al.
Fig. 3. Clockwise beam path near the diffraction gratings.
grating DG1 and the dispersion at diffraction grating DG2 This is expressed in eqn (2). La La *a" 2 *b # 2 *j 2 Lj Lb 2 Now, for DG1, by differentiating the grating equation w.r.t. j gives,
(2)
Lb 1 1 cos b " 1 d Lj *j *b + 1 d cos b 1 From the geometry it is obvious that *b "!*b 2 1 !*j " d cos b 1 We now need to know La /Lb . By differentiating eqn (1) w.r.t. b we obtain 2 2 2 La cos b ! 2 cos a "0 2 2 Lb 2 La cos b 2" 2 Lb cos a 2 2
High-resolution interference spectrometer
417
Fig. 4. Output fringes with corresponding interferometer beam wavefronts.
Similarly, for DG2, by differentiating eqn (1) w.r.t. j we get La !1 2" Lj d cos a 2 Substituting in eqn (2) gives !*j !cos b *j 2 # *a " 2 d cos a cos a d cos b 2 2 1 We make the approximation that cos b +cos b Ncos a +cos a which 1 2 2 1 results in !2*j *a" d cos a Arguing similarly for the anticlockwise beam theta, the angle between the wavefronts is 4*j h" d cos a From this the number of fringes seen at the output can be calculated cf. Fig. 4. nj"hD 4*jD n" jd cos a The resolution, dj, of the instrument is defined as the change in wavelength required to give a change in fringe number, n, of one. dj cos a dj" 4D
418
T. L. Helg et al.
The free spectral range is a function of the number of elements, N, in the measuring sensor array and the nyquist criterion: N FSR" dj 2 Nj d cos a " 8D Using a CCD camera as the sensor array combined with a frame grabber gives N"512. With a beam width of 25 mm, a 600 line/mm diffraction grating, and a wavelength of 633 nm the instrument resolution is 0)009 nm with a free spectral range of 2)36 nm. This is just within our stated objectives.
4 EXPERIMENTAL IMPLEMENTATION The instrument in Fig. 2 was assembled on a light table with no vibration stabilisation. The two diffraction gratings used were recycled from an old pair of monochromators. The blaze angles were different as one was designed for the visible spectrum and the other for ultraviolet. This means that the grating efficiencies at infrared wavelengths were not the same. However, since both beams diffract off both diffraction gratings then they will be of equal intensity. This is wasteful in terms of light but graphically demonstrates the insensitivity of this interferometer design to differences in the diffraction gratings. The maximum aperture size is limited by the components used. In this case the limiting factor was the 30 mm cube beamsplitter. An infrared laser diode was selected as the test narrow band source. The laser diode was placed at the focal point of the input lens to produce plane waves. The previous calculations have assumed that all 25 mm of the beam width is imaged onto the CCD camera. The active area of the camera is 6]8 mm. The single output lens images the fringes down to this size. However, this imposes a spherical wave front shape onto the plane waves. Since this is applied equally to both beams the interference pattern is representative of only the angular displacement between the wave fronts. However, a magnification factor, m, must be included in the equations if, for example, to avoid component edge effects, less of the fringe pattern is imaged onto the semiconductor sensor. dj cos a dj" 4Dm
High-resolution interference spectrometer
419
The angular displacement of the beams also causes a lateral shear between the beams when they are recombined at the output. This shear is a function of how far the beam has travelled and the degree of angular displacement, and therefore, the amount of shear is a function of frequency. The output lens can be used not only to resize the image but also to nullify this shear. That is, there exists a plane in the output where the lateral shear is zero. Calculating this point is not straightforward as the clockwise and anticlockwise beams travel different distances to the imaging lens. For coherent light sources producing plane waves this shear does not change the output fringe profile and can be largely ignored. However, if the wavefronts are not quite plane, the fringe profile will be altered. For example, if the light source is not well collimated, shearing of the now spherical wavefronts will cause linear fringes to appear at the interferometer output. The linear fringes due to the angular beam displacement will be indistinguishable from those due to the lateral shear. This additional source of error must be considered when calibrating the instrument. In our experiments we rely on the careful positioning of the diode at the input lens focus to give near-plane waves. The amount of shear present is also small as the angular beam displacement is very small.
Fig. 5. The wavelength change as a function of laser diode output power is clearly shown.
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T. L. Helg et al.
5 CHARACTERISATION OF A LASER DIODE The output from a laser diode was first examined with a monochromator cf. Fig. 5. The laser frequency was measured as a function of diode injection current and hence laser diode output power. Note that the laser diode frequency is a function of temperature as well as injection current. The diode was used without temperature stabilisation and therefore this graph is more representative than quantitative. The monochromator is able to resolve the central laser frequency but, of course, the mode structure is not revealed. Figure 6 shows the Fast Fourier Transform (FFT) of the data obtained with the double-diffraction grating instrument. The data was recorded from the CCD camera with a frame grabber controlled by the computer. A single line of the 512]512 pixel array is transferred to the hard drive for later analysis. Real-time display of data is also possible. The output power of the diode was then altered from approximately 0—5 mW in 100 steps. This was achieved by changing the diode injection current via a 0—5 V output signal from an analogue to digital board also controlled by the computer. Spatial frequency
Fig. 6.
High-resolution interference spectrometer
421
is plotted along the x-axis and laser power along the y-axis. The intensity of light at a given frequency is represented as a grey scale from 0 to 1 in 256 steps, high intensity being white. To compensate for the general low output intensity at low power each line of data has been separately normalised. As a consequence, background noise is much more apparent in the lower-power region. We can clearly see the multi-mode structure in the low-power region. As the power rises above the halfway point single-mode operation of the laser commences. A large-mode hop can be seen in this single-mode section. These phenomena are well-known laser characteristics. It is encouraging to see them resolved by the interferometer. The apparent blurring and bifurcation of the modes at low power is very interesting. This is most probably a result of the laser modes jumping about in frequency on a time scale that is much faster than the CCD camera frame acquisition time. This is not seen in the higherpower region as the laser operation is much more stable at these injection current levels. As a gross check on the calibration of the instrument the mode spacing measured by the interferometer was compared to the typical spacing given in the laser diode specifications. This was given as being between 0)3 and 0)4 nm. On average, our measured mode spacing was 0)33 nm. This was very encouraging as it confirmed in a small way our assumptions that the input waves were plane and that the lateral shear was not causing major errors.
6 CONCLUSION By incorporating FTS techniques with Heterodyning and a Sagnac common path interferometer we were able to achieve our goal of building a wavemeter with a resolution of better than 0)01 nm. This was achieved with inexpensive or recycled components. Stand out features of this design are the absence of any moving parts, the insensitivity to differences in the diffraction grating specifications, and the stability afforded by the common path design against vibration during measurement. Computer control enabled fast data acquisition with on screen conversion to the frequency domain. This resulted in the quick easy characterisation of a laser diode distinguishing domains of multimode and single-mode operation while locating mode hopping points in the power spectrum as a function of diode injection current.
REFERENCES 1. Bousquet, P., Spectroscopy and its Instrumentation. Adam Hilger, London, 1971.
422
T. L. Helg et al.
2. Barnes, T. H., Photodiode array Fourier transform spectrometer with improved dynamic range. Appl. Opt., 24(22) (1985) 3702—6. 3. Mertz, L., ¹ransformations in Optics. Wiley, London, 1965. 4. Barnes, T. H., Eiju, T. & Matsuda, K., Heterodyned photodiode array Fourier transform spectrometer. Appl. Opt., 25(12) (1986) 1864—6. 5. Hutley, M. C., Diffraction Gratings. Academic Press, London, 1982. 6. Connes, P., Spectrometre interferentiel a` selection par l’Amplitude de modulation, J. Phys. Radium, 19 (1958) 215—22.
A Novel High-resolution Interference Spectrometer T. L. Helga, T. H. Barnesa & T. G. Haskellb a Department of Physics, The University of Auckland, Private Bag 92019, Auckland, New Zealand b Industrial Research Ltd, P.O. Box 31-310, Lower Hutt, New Zealand (Received 20 August 1997; accepted 28 November 1997)
ABS¹RAC¹ A novel precision wavemeter is presented with a resolution of better than 0)01 nm. A Sagnac interferometer with two diffraction gratings forms the basis of the instrument. ºsing spatial heterodyning techniques and a CCD camera/ frame grabber data acquisition system allows fast computer control and power spectrum analysis. ¹he mode structure and mode hopping characteristics of a typical laser diode were examined as a function of diode injection current. ( 1998 Elsevier Science ¸td. All rights reserved.
1 INTRODUCTION Spectroscopic instruments are available in many forms, operating with a variety of principles and purposes. We wished to develop an instrument for characterisation of laser diodes and mode hop detection. Therefore, two spectroscope varieties of interest here are Fourier Transform Spectrometers and Monochromators.1 Fourier Transform Spectrometry2,3 (FTS) is a well-established field in interferometry. Traditional methods of FTS involve moving mirrors in a basic Michelson interferometer. The resulting interferogram recorded by the detector is a function of the interferometer path difference and the frequency of the light source. That frequency is recovered by Fourier transform techniques. This indirect method is particularly useful for low-light measurements as all the available light is used. In the past, this advantage was offset by timeconsuming computer calculations. With more modern computers this is no longer so limiting. Monochromators are extremely common spectrometers that incorporate a dispersive element. They are inexpensive, easy to use and calibrate. However, only one frequency can be examined at a time. This limits the speed at which a spectrum could be obtained with such an instrument. 413
414
T. L. Helg et al.
It is possible to combine the advantages in these instruments with heterodyning4 techniques and the stability of a Sagnac common path interferometer to give an inexpensive easy to construct wavemeter for measuring the power spectrum of lasers.
2 INSTRUMENT OPERATING PRINCIPLE The basic aim of this experiment was to design and build a wavemeter to examine narrow-band light sources. A resolution of 0)01 nm was required with the ability to cope with low intensity light sources with fast-data acquisition, and stable operation. The basic design of a diffraction grating5 interferometer6 was chosen for efficient use of light and for incorporating heterodyning techniques. Stable operation requirements suggested a Sagnac design for the interferometer with a charge-coupled device (CCD) camera as the sensor for fast data acquisition. Figure 1 shows a wavemeter with a diffraction grating (DG) as the dispersive element. The angle at which a beam is refracted from the surface is a function of the incident angle and the light beam frequency. The diffraction grating can be positioned so that at some reference frequency the first-order refracted beams of the clockwise and anticlockwise incident beams will exit the interferometer in parallel. The beams will interfere constructively at the output sensor to form zero fringes. If light of a different frequency is then examined, the beams will exit the interferometer at an angle to each other causing a fringe pattern to form. The number of fringes will indicate how far
Fig. 1. Single grating Sagnac interferometer.
High-resolution interference spectrometer
415
Fig. 2. Asymmetric configuration of the double diffraction grating Sagnac interferometer.
from the reference frequency the test source is. This spatial heterodyning technique allows us to select the resolution of our instrument by using an appropriate line spacing in the diffraction grating. However, while this simple design demonstrates our technique in principle, in practice, the diffraction grating does not sit at a 45° angle causing one beam to be compressed and the other to be expanded. By inserting a second diffraction grating into the interferometer this cylindrical shearing can be corrected. Operation of this configuration, shown in Fig. 2, is similar to before except we now have twice the angular deviation of the beam and hence potentially twice the resolution. It is important to note that the gratings must be in these asymmetric positions to ensure that the beams will be at an angle with each other not just to the instrument optic axis.
3 THEORETICAL DEVELOPMENT The grating equation can be expressed as follows, sin b!sin a"n
j d
(1)
where the angles are labelled so that b'a. We wish to know the change in a as a function of wavelength cf. Fig. 3. a is a constant, as j changes b will 2 1 1 change, giving a corresponding alteration in b . This means that the change in 2 a is a function of the angular change in b due to the dispersion at diffraction 2 2
416
T. L. Helg et al.
Fig. 3. Clockwise beam path near the diffraction gratings.
grating DG1 and the dispersion at diffraction grating DG2 This is expressed in eqn (2). La La *a" 2 *b # 2 *j 2 Lj Lb 2 Now, for DG1, by differentiating the grating equation w.r.t. j gives,
(2)
Lb 1 1 cos b " 1 d Lj *j *b + 1 d cos b 1 From the geometry it is obvious that *b "!*b 2 1 !*j " d cos b 1 We now need to know La /Lb . By differentiating eqn (1) w.r.t. b we obtain 2 2 2 La cos b ! 2 cos a "0 2 2 Lb 2 La cos b 2" 2 Lb cos a 2 2
High-resolution interference spectrometer
417
Fig. 4. Output fringes with corresponding interferometer beam wavefronts.
Similarly, for DG2, by differentiating eqn (1) w.r.t. j we get La !1 2" Lj d cos a 2 Substituting in eqn (2) gives !*j !cos b *j 2 # *a " 2 d cos a cos a d cos b 2 2 1 We make the approximation that cos b +cos b Ncos a +cos a which 1 2 2 1 results in !2*j *a" d cos a Arguing similarly for the anticlockwise beam theta, the angle between the wavefronts is 4*j h" d cos a From this the number of fringes seen at the output can be calculated cf. Fig. 4. nj"hD 4*jD n" jd cos a The resolution, dj, of the instrument is defined as the change in wavelength required to give a change in fringe number, n, of one. dj cos a dj" 4D
418
T. L. Helg et al.
The free spectral range is a function of the number of elements, N, in the measuring sensor array and the nyquist criterion: N FSR" dj 2 Nj d cos a " 8D Using a CCD camera as the sensor array combined with a frame grabber gives N"512. With a beam width of 25 mm, a 600 line/mm diffraction grating, and a wavelength of 633 nm the instrument resolution is 0)009 nm with a free spectral range of 2)36 nm. This is just within our stated objectives.
4 EXPERIMENTAL IMPLEMENTATION The instrument in Fig. 2 was assembled on a light table with no vibration stabilisation. The two diffraction gratings used were recycled from an old pair of monochromators. The blaze angles were different as one was designed for the visible spectrum and the other for ultraviolet. This means that the grating efficiencies at infrared wavelengths were not the same. However, since both beams diffract off both diffraction gratings then they will be of equal intensity. This is wasteful in terms of light but graphically demonstrates the insensitivity of this interferometer design to differences in the diffraction gratings. The maximum aperture size is limited by the components used. In this case the limiting factor was the 30 mm cube beamsplitter. An infrared laser diode was selected as the test narrow band source. The laser diode was placed at the focal point of the input lens to produce plane waves. The previous calculations have assumed that all 25 mm of the beam width is imaged onto the CCD camera. The active area of the camera is 6]8 mm. The single output lens images the fringes down to this size. However, this imposes a spherical wave front shape onto the plane waves. Since this is applied equally to both beams the interference pattern is representative of only the angular displacement between the wave fronts. However, a magnification factor, m, must be included in the equations if, for example, to avoid component edge effects, less of the fringe pattern is imaged onto the semiconductor sensor. dj cos a dj" 4Dm
High-resolution interference spectrometer
419
The angular displacement of the beams also causes a lateral shear between the beams when they are recombined at the output. This shear is a function of how far the beam has travelled and the degree of angular displacement, and therefore, the amount of shear is a function of frequency. The output lens can be used not only to resize the image but also to nullify this shear. That is, there exists a plane in the output where the lateral shear is zero. Calculating this point is not straightforward as the clockwise and anticlockwise beams travel different distances to the imaging lens. For coherent light sources producing plane waves this shear does not change the output fringe profile and can be largely ignored. However, if the wavefronts are not quite plane, the fringe profile will be altered. For example, if the light source is not well collimated, shearing of the now spherical wavefronts will cause linear fringes to appear at the interferometer output. The linear fringes due to the angular beam displacement will be indistinguishable from those due to the lateral shear. This additional source of error must be considered when calibrating the instrument. In our experiments we rely on the careful positioning of the diode at the input lens focus to give near-plane waves. The amount of shear present is also small as the angular beam displacement is very small.
Fig. 5. The wavelength change as a function of laser diode output power is clearly shown.
420
T. L. Helg et al.
5 CHARACTERISATION OF A LASER DIODE The output from a laser diode was first examined with a monochromator cf. Fig. 5. The laser frequency was measured as a function of diode injection current and hence laser diode output power. Note that the laser diode frequency is a function of temperature as well as injection current. The diode was used without temperature stabilisation and therefore this graph is more representative than quantitative. The monochromator is able to resolve the central laser frequency but, of course, the mode structure is not revealed. Figure 6 shows the Fast Fourier Transform (FFT) of the data obtained with the double-diffraction grating instrument. The data was recorded from the CCD camera with a frame grabber controlled by the computer. A single line of the 512]512 pixel array is transferred to the hard drive for later analysis. Real-time display of data is also possible. The output power of the diode was then altered from approximately 0—5 mW in 100 steps. This was achieved by changing the diode injection current via a 0—5 V output signal from an analogue to digital board also controlled by the computer. Spatial frequency
Fig. 6.
High-resolution interference spectrometer
421
is plotted along the x-axis and laser power along the y-axis. The intensity of light at a given frequency is represented as a grey scale from 0 to 1 in 256 steps, high intensity being white. To compensate for the general low output intensity at low power each line of data has been separately normalised. As a consequence, background noise is much more apparent in the lower-power region. We can clearly see the multi-mode structure in the low-power region. As the power rises above the halfway point single-mode operation of the laser commences. A large-mode hop can be seen in this single-mode section. These phenomena are well-known laser characteristics. It is encouraging to see them resolved by the interferometer. The apparent blurring and bifurcation of the modes at low power is very interesting. This is most probably a result of the laser modes jumping about in frequency on a time scale that is much faster than the CCD camera frame acquisition time. This is not seen in the higherpower region as the laser operation is much more stable at these injection current levels. As a gross check on the calibration of the instrument the mode spacing measured by the interferometer was compared to the typical spacing given in the laser diode specifications. This was given as being between 0)3 and 0)4 nm. On average, our measured mode spacing was 0)33 nm. This was very encouraging as it confirmed in a small way our assumptions that the input waves were plane and that the lateral shear was not causing major errors.
6 CONCLUSION By incorporating FTS techniques with Heterodyning and a Sagnac common path interferometer we were able to achieve our goal of building a wavemeter with a resolution of better than 0)01 nm. This was achieved with inexpensive or recycled components. Stand out features of this design are the absence of any moving parts, the insensitivity to differences in the diffraction grating specifications, and the stability afforded by the common path design against vibration during measurement. Computer control enabled fast data acquisition with on screen conversion to the frequency domain. This resulted in the quick easy characterisation of a laser diode distinguishing domains of multimode and single-mode operation while locating mode hopping points in the power spectrum as a function of diode injection current.
REFERENCES 1. Bousquet, P., Spectroscopy and its Instrumentation. Adam Hilger, London, 1971.
422
T. L. Helg et al.
2. Barnes, T. H., Photodiode array Fourier transform spectrometer with improved dynamic range. Appl. Opt., 24(22) (1985) 3702—6. 3. Mertz, L., ¹ransformations in Optics. Wiley, London, 1965. 4. Barnes, T. H., Eiju, T. & Matsuda, K., Heterodyned photodiode array Fourier transform spectrometer. Appl. Opt., 25(12) (1986) 1864—6. 5. Hutley, M. C., Diffraction Gratings. Academic Press, London, 1982. 6. Connes, P., Spectrometre interferentiel a` selection par l’Amplitude de modulation, J. Phys. Radium, 19 (1958) 215—22.