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Direct measurement of the spectral width of a transform-limited ruby laser giant pulse
Volume 1, number
5
OPTICS COMMUNICATIONS
DIRECT OF
MEASUREMENT
A TRANSFORM-LIMITED
OF THE RUBY
November/December
SPECTRAL LASER
1969
WIDTH
GIANT
PULSE
D. J. BRADLEY, C. J. MITCHELL and M. S. PETTY The Queen’s
Department of Pure and Applied Physics, University of Belfast, Belfast BT7 INN, Northern Ireland Received
4 October
1969
A spherical Fabry-Perot etalon was employed to record the spectral width of a single, (longitudinal and transverse), mode Q-switched ruby laser. The spectral width of 11.4 f 2.6 MHz corresponds, within experimental error, to the Fourier transform limit set by the pulse duration (“- 50 nsec).
The characteristics of the defocussed spherical Fabry-Perot etalon (FPS) for both continuous [l] and pulsed [2] inputs have previously been described. The instrument employed for the present work consisted of two high-quality plates of optical grade fused silica, the radius of curvature of the 1 inch diameter reflecting surfaces being 20 cm. The adjustable invar steel spacer was set so that the pole separation of the plates was about 300 jun less than their radius of curvature. This gave a dispersion characteristic which was quadratic at the centre of the field of view, with an annular region of linear dispersion at about one and a half orders from the centre. Details of the construction of the instrument and the dispersion formulae have been given elsewhere [l]. The reflecting surfaces on the plates were ll-layer dielectrics desig@ to have a maximum reflectivity at about 6 600 A, giving a reflectivity of about 0.99 at the wavelenaths of both the ruby (6 943 b) and helium-neon (6 328 Ai) lasers. The ruby laser system employed [3] consisted of a plane parallel 4 inch by 3/8 inch diameter ruby rod, pumped with a helical flashtube. A three-plate resonant reflector provided longitudinal mode selection [4], and the second laser mirror had dielectric coatings of 100 per cent nominal reflectivity. Transverse mode selection was achieved with an angular filter [5], inside the laser cavity, consisting of a unit magnification telescope with a 350 nm aperture at the common focus of the two 30 cm focal length lenses. This aperture diameter correponded to four times the Gaussian beam waist for a single filament of the ruby. A second aperture, a few
millimetres in diameter, placed close to the ruby, ensured that oniy one filament contributed to the laser action. The lenses and ruby faces were anti-reflection coated with a single layer of magnesium fluoride. Passive Q-switching was achieved by means of a cell of high optical quality of optical thickness 2 cm, containing a solution of cryptocyanine in methanol. The laser output was monitored by means of an EM1 D404 photodiode and a Tektronix type 519 oscilloscope. Typical peak powers for pulses from this system were 0.1 MW. The FPS interference patterns, consisting of sets of concentric rings localised between the etalon plates, were recorded on Kodak 2479 RAR film which has extended red sensitivity. The fringes employed for spectral width measurement were those occurring as near as possible to the centre of the fringe pattern, consistent with a satisfactory (nearly linear) dispersion characteristic [ 11. For these fringes distortion arising from the annular wedge etalon effect [6, l] is at a minimum. The photographic interferograms were scanned on a double beam recording microdensitometer to determine the spectral half-intensity width of the profiles. It was necessary to determine both the intensity response of the emulsion and the width of the instrumental profile. Numerical computations indicate [2] that the recorded profile is close to the convolution of the pulse spectral profile and the instrumental profile for time-integrated interferograms, even when the transit time of the etalon is not negligibly small in comparison to the rate of temporal intensity variation of the input laser pulse. 245
Volume
1, number
5
OPTICS COMMUNICATIONS
High-intensity reciprocity failure [7] in the photographic emulsion requires calibration of the intensity response characteristic with the giant pulse laser light itself. Pre-calibrated neutral density filters are not necessarily quantitatively reliable, and for conditions of highly coherent illumination by very short pulses, the following method was adopted to obtain the emulsion intensity response curve for giant pulse laser illumination. The FPS was removed and replaced by a neutral density step wedge in the object plane of the camera lens, where the fringes are localised. Although nominal values of the step wedge density increments were known, these values were not assumed in the calibration. The density of each step was regarded merely as an arbitrary constant. The step wedge was then photographed in the light of the Q-switched laser. (A slight beam divergence was introduced to give a reasonably uniform field of illumination.) The intensity of the illuminating pulse was monitored with a photodiode and oscilloscope by means of a beam splitter. Two more photographs of the wedge were taken, the illumination in each case being varied by means of a uniform (arbitrary) neutral density filter situated in front of the monitoring beam splitter. Microdensitometer traces of the photographs of the wedge, recorded on a linear density scale, then yielded one set of three points on the density against log intensity curve, for the edges of each step on the wedge. The ordinates of all the points, and the horizontal spacing between the members of each set of three points, being known, the absolute values of the abscissae were readily adjusted to yield a smooth characteristic curve for the emulsion under pulsed conditions (fig. 2). The accuracy of the method was limited by the repeatability of the spatial characteristics of the laser beam. The interferometer instrumental profile, which is a function of fringe radius [l], was determined by microdensitometry of the interferogram produced by a stabilised helium-neon gas laser (Spectra Physics type 119), of linewidth < 5 MHz. Since the interferometer plate reflectivities at the ruby and gas laser wavelengths were made very nearly equal, the correction to the gas laser fringe profile for the small difference was practically independent of the exact shape of the actual instrumental profile [a]. Fig. 1 shows a microdensitometer trace of a fringe of a ruby laser interferogram. To within the resolution limit of the FPS, this represents a single longitudinal and transverse mode of the oscillator. The asymmetry in the wings of the profile, accentuated here by the linear density 246
November/December
FREQUENCY
1969
[MHz)
Fig. 1. Microdensitometer trace of interferogram fringe produced by single-mode Q-switched ruby laser.
scale, is of instrumental origin, arising from the wedge angle between the spherical aberration wavefronts [l]. This behaviour is predicted by numerical wavefront tracing on a computer [l]. The recorded half-intensity width of the fringe determined from the emulsion calibration curve, is 15 f 2 MHz. For this value of the fringe radius, the instrumental profile of the
RELATIVE
LOG
INTENSITY
OF
LASER
PULSE
Fig. 2. Film response calibration under pulsed conditions. (Vertical error bars represent estimated probable error in density due to spatial intensity variations. Horizontal errors represent uncertainty in oscilloscope trace height measurements.)
Volume
1, number
5
OPTICS COMMUNICATIONS
FPS has a half-intensity width of 6 f 1 MHz. Deconvolving the instrumental profile from the recorded width by means of the curves given by Chabbal [8] yields a half-intensity spectral width of 11.4 f 2.6 MHz for the laser pulse. The main source of error in the result is the lack of exact reproducibility of the laser beam during calibration of the emulsion. The 519 oscilloscope trace for this pulse shows a smooth, almost time-symmetric envelope of 50 f 3 nsec half-intensity duration, the Fourier transform width of which is 8.8 f 0.4 MHz. This result is in agreement, within experimental error, with the measured value of 11.4 f 2.6 MHz. The profile of fig. 1 thus represents the minimum spectral width obtainable for a pulse of this duration. However, it is interesting to note that a maximum frequency shift [9], or chirping, of = 6 MHz could be concealed within the experimental uncertainty of our spectral width measurement.
November/December
1969
REFERENCES [l] D. J. Bradley and C. J. Mitchell, Phil. Trans. Roy. Sot. A263 (1968) 209. [2] D. J. Bradley, A. W. McCullough and C. J. Mitchell, Ont. Acta. to be published. [3] D: J. Bradley, A.W. McCullough and C. J. Mitchell, IEEE J. Quantum Electron. &E-4 (1968) 366. [4] D.A.Kleiman and P.D.Kisliuk, Bell. System Tech. J. 41 (1962) 453. [5] V.Evtuhov and J.K.Neeland, in: Lasers, Vol. I, ed. A.K.Levine (E.Arnold and Co., London, 1966). [6] J.Brossel, Proc‘. Phys. Sot. 59 (1947) 224. [i’] J. F.Hamilton, in: The theory of the photographic process, 3rd edition, eds. C.E.K.Mees and T.H. James (Macmillan, London, New York, 1966) p. 132. [8] R. Chabbal, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 24 (1953) 138. [9] D. J. Bradley, M. S.Engwell, A. W.McCullough, G. Magyar and M. C . Richardson, Phil. Trans. Roy. Sot. A 263 (1968) 225.
247
5
OPTICS COMMUNICATIONS
DIRECT OF
MEASUREMENT
A TRANSFORM-LIMITED
OF THE RUBY
November/December
SPECTRAL LASER
1969
WIDTH
GIANT
PULSE
D. J. BRADLEY, C. J. MITCHELL and M. S. PETTY The Queen’s
Department of Pure and Applied Physics, University of Belfast, Belfast BT7 INN, Northern Ireland Received
4 October
1969
A spherical Fabry-Perot etalon was employed to record the spectral width of a single, (longitudinal and transverse), mode Q-switched ruby laser. The spectral width of 11.4 f 2.6 MHz corresponds, within experimental error, to the Fourier transform limit set by the pulse duration (“- 50 nsec).
The characteristics of the defocussed spherical Fabry-Perot etalon (FPS) for both continuous [l] and pulsed [2] inputs have previously been described. The instrument employed for the present work consisted of two high-quality plates of optical grade fused silica, the radius of curvature of the 1 inch diameter reflecting surfaces being 20 cm. The adjustable invar steel spacer was set so that the pole separation of the plates was about 300 jun less than their radius of curvature. This gave a dispersion characteristic which was quadratic at the centre of the field of view, with an annular region of linear dispersion at about one and a half orders from the centre. Details of the construction of the instrument and the dispersion formulae have been given elsewhere [l]. The reflecting surfaces on the plates were ll-layer dielectrics desig@ to have a maximum reflectivity at about 6 600 A, giving a reflectivity of about 0.99 at the wavelenaths of both the ruby (6 943 b) and helium-neon (6 328 Ai) lasers. The ruby laser system employed [3] consisted of a plane parallel 4 inch by 3/8 inch diameter ruby rod, pumped with a helical flashtube. A three-plate resonant reflector provided longitudinal mode selection [4], and the second laser mirror had dielectric coatings of 100 per cent nominal reflectivity. Transverse mode selection was achieved with an angular filter [5], inside the laser cavity, consisting of a unit magnification telescope with a 350 nm aperture at the common focus of the two 30 cm focal length lenses. This aperture diameter correponded to four times the Gaussian beam waist for a single filament of the ruby. A second aperture, a few
millimetres in diameter, placed close to the ruby, ensured that oniy one filament contributed to the laser action. The lenses and ruby faces were anti-reflection coated with a single layer of magnesium fluoride. Passive Q-switching was achieved by means of a cell of high optical quality of optical thickness 2 cm, containing a solution of cryptocyanine in methanol. The laser output was monitored by means of an EM1 D404 photodiode and a Tektronix type 519 oscilloscope. Typical peak powers for pulses from this system were 0.1 MW. The FPS interference patterns, consisting of sets of concentric rings localised between the etalon plates, were recorded on Kodak 2479 RAR film which has extended red sensitivity. The fringes employed for spectral width measurement were those occurring as near as possible to the centre of the fringe pattern, consistent with a satisfactory (nearly linear) dispersion characteristic [ 11. For these fringes distortion arising from the annular wedge etalon effect [6, l] is at a minimum. The photographic interferograms were scanned on a double beam recording microdensitometer to determine the spectral half-intensity width of the profiles. It was necessary to determine both the intensity response of the emulsion and the width of the instrumental profile. Numerical computations indicate [2] that the recorded profile is close to the convolution of the pulse spectral profile and the instrumental profile for time-integrated interferograms, even when the transit time of the etalon is not negligibly small in comparison to the rate of temporal intensity variation of the input laser pulse. 245
Volume
1, number
5
OPTICS COMMUNICATIONS
High-intensity reciprocity failure [7] in the photographic emulsion requires calibration of the intensity response characteristic with the giant pulse laser light itself. Pre-calibrated neutral density filters are not necessarily quantitatively reliable, and for conditions of highly coherent illumination by very short pulses, the following method was adopted to obtain the emulsion intensity response curve for giant pulse laser illumination. The FPS was removed and replaced by a neutral density step wedge in the object plane of the camera lens, where the fringes are localised. Although nominal values of the step wedge density increments were known, these values were not assumed in the calibration. The density of each step was regarded merely as an arbitrary constant. The step wedge was then photographed in the light of the Q-switched laser. (A slight beam divergence was introduced to give a reasonably uniform field of illumination.) The intensity of the illuminating pulse was monitored with a photodiode and oscilloscope by means of a beam splitter. Two more photographs of the wedge were taken, the illumination in each case being varied by means of a uniform (arbitrary) neutral density filter situated in front of the monitoring beam splitter. Microdensitometer traces of the photographs of the wedge, recorded on a linear density scale, then yielded one set of three points on the density against log intensity curve, for the edges of each step on the wedge. The ordinates of all the points, and the horizontal spacing between the members of each set of three points, being known, the absolute values of the abscissae were readily adjusted to yield a smooth characteristic curve for the emulsion under pulsed conditions (fig. 2). The accuracy of the method was limited by the repeatability of the spatial characteristics of the laser beam. The interferometer instrumental profile, which is a function of fringe radius [l], was determined by microdensitometry of the interferogram produced by a stabilised helium-neon gas laser (Spectra Physics type 119), of linewidth < 5 MHz. Since the interferometer plate reflectivities at the ruby and gas laser wavelengths were made very nearly equal, the correction to the gas laser fringe profile for the small difference was practically independent of the exact shape of the actual instrumental profile [a]. Fig. 1 shows a microdensitometer trace of a fringe of a ruby laser interferogram. To within the resolution limit of the FPS, this represents a single longitudinal and transverse mode of the oscillator. The asymmetry in the wings of the profile, accentuated here by the linear density 246
November/December
FREQUENCY
1969
[MHz)
Fig. 1. Microdensitometer trace of interferogram fringe produced by single-mode Q-switched ruby laser.
scale, is of instrumental origin, arising from the wedge angle between the spherical aberration wavefronts [l]. This behaviour is predicted by numerical wavefront tracing on a computer [l]. The recorded half-intensity width of the fringe determined from the emulsion calibration curve, is 15 f 2 MHz. For this value of the fringe radius, the instrumental profile of the
RELATIVE
LOG
INTENSITY
OF
LASER
PULSE
Fig. 2. Film response calibration under pulsed conditions. (Vertical error bars represent estimated probable error in density due to spatial intensity variations. Horizontal errors represent uncertainty in oscilloscope trace height measurements.)
Volume
1, number
5
OPTICS COMMUNICATIONS
FPS has a half-intensity width of 6 f 1 MHz. Deconvolving the instrumental profile from the recorded width by means of the curves given by Chabbal [8] yields a half-intensity spectral width of 11.4 f 2.6 MHz for the laser pulse. The main source of error in the result is the lack of exact reproducibility of the laser beam during calibration of the emulsion. The 519 oscilloscope trace for this pulse shows a smooth, almost time-symmetric envelope of 50 f 3 nsec half-intensity duration, the Fourier transform width of which is 8.8 f 0.4 MHz. This result is in agreement, within experimental error, with the measured value of 11.4 f 2.6 MHz. The profile of fig. 1 thus represents the minimum spectral width obtainable for a pulse of this duration. However, it is interesting to note that a maximum frequency shift [9], or chirping, of = 6 MHz could be concealed within the experimental uncertainty of our spectral width measurement.
November/December
1969
REFERENCES [l] D. J. Bradley and C. J. Mitchell, Phil. Trans. Roy. Sot. A263 (1968) 209. [2] D. J. Bradley, A. W. McCullough and C. J. Mitchell, Ont. Acta. to be published. [3] D: J. Bradley, A.W. McCullough and C. J. Mitchell, IEEE J. Quantum Electron. &E-4 (1968) 366. [4] D.A.Kleiman and P.D.Kisliuk, Bell. System Tech. J. 41 (1962) 453. [5] V.Evtuhov and J.K.Neeland, in: Lasers, Vol. I, ed. A.K.Levine (E.Arnold and Co., London, 1966). [6] J.Brossel, Proc‘. Phys. Sot. 59 (1947) 224. [i’] J. F.Hamilton, in: The theory of the photographic process, 3rd edition, eds. C.E.K.Mees and T.H. James (Macmillan, London, New York, 1966) p. 132. [8] R. Chabbal, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 24 (1953) 138. [9] D. J. Bradley, M. S.Engwell, A. W.McCullough, G. Magyar and M. C . Richardson, Phil. Trans. Roy. Sot. A 263 (1968) 225.
247