1. Field of the Invention
The present invention generally relates to a technique being utilized in developing/adjusting an ultrashort light pulse laser which produces a light pulse whose time interval is shorter than one picosecond. More specifically, the present inventions directed to a technique capable of measuring wavelength dispersion of such a laser cavity.
2. Description of Prior Art
Currently, great development has been made in producing such a light pulse whose time interval is shorter than one picosecond. As a result, it could be recognized that when the light pulses having short time intervals are generated or transmitted, either the wavelength dispersion characteristics of the optical components employed to generate/transmit such light pulses, or the wavelength dispersion characteristics of the optical path consisting of the assembly of these optical components could largely give influences to the shapes of the light pulses.
When such a short duration light pulse passes through, for instance, an optical path whose wavelength dispersion characteristic is rapidly changing, a waveform deforming phenomenon happens to occur. When such an optical component is employed whose wavelength dispersion characteristic is rapidly changed, it is essentially difficult to generate such a light pulse having a short time interval. In particular, as to the optical components employed in the cavity for the ultrashort light pulse laser, since a large number of waveform deformations can be accumulated while the light pulse circulates within the cavity, the wavelength dispersion characteristic of this cavity must be controlled with a high precision. Under such circumstances, the wavelength dispersion characteristic of the laser cavity must be measured with a high precision.
As one possible method for measuring wavelength dispersion of a laser cavity, it is conceivable such a method for measuring wavelength dispersion of an individual optical component employed in the laser cavity with a high precision, and then for summing each of the measured wavelength dispersion to estimate the wavelength dispersion of this laser cavity. As the conventional wavelength dispersion measuring method for such an individual optical element, for instance, Japanese Patent Laying-open No. 2-134543 (Patent Application No. 63-287566) discloses such dispersion measuring method and measuring apparatus that the element under measurement is inserted into one of the arms of the white-light Michelson interferometer, the interference waveform produced by varying the delay time difference are stored, and then the waveform dispersion of this element under measurement is obtained by Fourier-transforming the stored interference waveform to acquire the phase information in the frequency domain, and based on this phase information the wavelength dispersion of the element is calculated. As to the conventional measuring method for the wavelength dispersion of the waveguide type element, for example, Japanese Patent Laying-open No. 3-216530 (Patent Application No. 2-11813) opens such waveguide dispersion measuring method and measuring apparatus that the identical optical coupling system is provided in both arms of the white-light Michelson interferometer, and the wavelength dispersion of the optical coupling system is canceled through which the light is coupled into and out of the waveguide.
However, there are some optical components employed in the laser cavity, the wavelength dispersion characteristic of which greatly depends upon the light incident direction or position to these components For example, "Optics Letter volume 9, pages 150 to 152, in 1984" describes that when the light is incident on such a pair of prism that two pieces of equilateral triangular prism whose apex angles are formed in such a manner that the incoming/outgoing angles of the light form the Brewster angles, are arranged whose bottom edges are located in parallel to each other, so that an anomalous dispersion characteristic is produced in which the group delay time is increased with respect to the wavelength. At this time, the produced dispersion amount greatly depends upon the optical path length over which the light passes through the glass within the prism, namely depends upon the incoming/outgoing positions of the light to the prism. Since in fact, it cannot be expected that the incident condition when the wavelength dispersion of the respective elements is measured is completely equal to that when this element is actually used in the laser cavity, an estimation of this wavelength dispersion of the laser cavity with the respective elements practically becomes ambiguous. Moreover, there are other problems in view of the workloads and time losses that the above-explained measurement should be carried out for the laser cavity which contains at least three elements.
On the other hand, another technique for measuring the wavelength dispersion of the laser cavity thereof (particularly, will be referred to "cavity dispersion" in the specification) has been proposed. This conventional measuring technique will now be briefly described.
FIG. 1 schematically shows the cavity wavelength dispersion measuring method according to the first prior art. This first cavity dispersion measuring method is disclosed in "Optics Letter volume 17, pages 514 to 516, in 1992" as the cavity wavelength dispersion measuring method which has been utilized in measuring of the wavelength dispersion for the titanium sapphire laser cavity.
In FIG. 1, a laser cavity 11 whose wavelength dispersion is to be measured comprises a laser medium 12, a wavelength selecting element 13, a total reflecting endmirror 14 and an output coupling mirror 15. The pulsed oscillation is established by exciting the laser medium 12 by a continuous exciting apparatus 16. It should be noted that as this continuous exciting apparatus 16, there are utilized a continuous wave laser light source, a continuous wave flash lamp, or a continuous current injecting source. The oscillation wavelength ".lambda." of this laser cavity under measurement is controlled by the wavelength selecting element 13 employed therein.
The laser light output from the laser cavity under measurement is incident upon a photodetector 18 forming an output light pulse train 17 from the output coupling mirror 15. The output light pulse train 17 incident on this photodetector 18 is converted into the electric pulse train. Then, this electric pulse train is supplied to an frequency counter 19 so that the pulse repetition frequency f(.lambda.) of this electric pulse train is measured. This measurement is repeatedly carried out while the oscillating wavelength ".lambda." is sequentially varied by the wavelength selecting element, whereby the pulse repetition frequency f (.lambda.) for the respective wavelength is obtained.
Here, the repetition frequency f(.lambda.) is expressed by employing the optical length "T" of the laser cavity 11 under measurement as well as derivative of the cavity optical length by the wavelength as follows: ##EQU1## In this formula (1), symbol "c" denotes the light velocity in vacuum. The group delay time ".tau..sub.d " of the laser cavity is expressed by the below-mentioned formula containing the derivative of the cavity optical length by the wavelength: ##EQU2##
When this formula (2) is substituted for another formula containing the repetition frequency, the following formula is obtained: ##EQU3##
The dispersion characteristic of the cavity corresponds to changes the group delay time .tau..sub.d regarding to the wavelength (.lambda.) for the laser cavity. The above-described formula (3) represents the basic formula which expresses the principle to measure the cavity dispersion characteristic according to this conventional measuring method.
In FIG. 2, there is schematically shown another method for measuring cavity wavelength dispersion according to the second prior art. This measuring method is disclosed in "Summaries of Papers presented at the Conference on Lasers and Electro-Optics, May 2-7, 1993, pages 570 to 573".
In accordance with this second measuring method, a laser cavity 21 under measurement is excited below the oscillation threshold value. At this time, fluorescent light (namely, amplified spontaneous emission light) emitted from the laser cavity 21 under measurement is used for the wavelength dispersion measurement. This fluorescent light may be made parallel light beams by using the optical means for increasing the parallelism of the light beams, e.g., the optical fiber, if required.
In this measuring apparatus, the Michelson interferometer comprises a cube beam splitter 22, a fixed mirror 23 and a scanning mirror 24. The light beam emitted from the laser cavity 21 under measurement is divided into the first and second light beams by the cube beam splitter 22. In this case to increase parallelism of the light beam emitted from the laser cavity 21, a single mode optical fiber 28 and coupling lenses 29 and 30 provided on both ends of this optical fiber 28 are employed between this laser cavity 21 and the beam splitter. The first deviled light beam is propagated toward the fixed mirror 23 to be reflected thereon, and then the reflected first light beam is returned (via the first light path) to the cube beam splitter 22. On the other hand, the second divided light beam is propagated toward the scanning mirror 24 to be reflected thereon, and then the reflected second light beam is returned (via the second light path) to the cube beam splitter 22. Thereafter, both the first and second light beams returned to the cube beam splitter 22 are superimposed with each other, thereby producing the interference light. This interference light is incident upon a photodetector 25. The photodetector 25 converts intensity of this interference light into the corresponding voltage value to measure the power of the interference light.
Under this condition, the position of the scanning mirror 24 is moved along the second optical path in one direction in a vicinity where the relative difference L.sub.1 between the first optical path and the second optical path becomes N times of the cavity length of the laser cavity under measurement, N being any integer other than zero. Then, the output voltage values of the photodetector 25 are sequentially stored into a waveform memory 26 every time the relative difference L.sub.1 between the optical path lengths is varied by a predetermined step. Thus, the data stored in the waveform memory 26 are Fourier-transformed by a computer 27 to obtain the phase information. Based on this phase information in the frequency domain, the wavelength dispersion characteristic of the laser cavity 21 under measurement can be obtained.
In general, a change suffered by the electric field while light having an angular frequency ".omega." is traveled around a cavity is expressed by a complex number t(.omega.) called as a transfer function of this cavity. The absolute value of this cavity transfer function responds to a change in intensity of an electric field, and a phase of this cavity transfer function represents a change in phases of the electric field.
In a vicinity where the measurement is carried out and the optical path length becomes N times of the cavity length of the laser cavity under measurement (N being any integer other than zero), the voltage value derived from the photodetector 25 and stored in the waveform memory 26 is expressed by S.sub.N (.tau.) as a function of the delay time ".tau." defined by dividing the relative optical path length difference by the light velocity. In case that the phase imbalance between both arms in the measuring interferometer constructed of the cube beam splitter 22, the fixed mirror 23, and the scanning mirror 24, is negligible, the Fourier-transformed signal S.sub.N (.tau.) is expressed by the following formula (4): EQU F[S.sub.N (.tau.)]=t.sup.N (.omega.)U(.omega.) (4)
In this formula (4), where symbol "F" denotes the Fourier transformation, and symbol "U(.omega.)" denotes optical spectrum.
The optical spectrum is always the positive real number. As a consequence, the phase as the complex number of the formula (4) always reflects only the phase of t(.omega.), namely the change .phi.(.omega.) in the phase, which is suffered by the electric field while the light is traveled inside the cavity. In other words, it is expressed by the following formula (5): EQU arg(F[S.sub.N (.tau.)])=N.phi.(.omega.) (5)
Here, based upon the obtained phase change .phi.(.omega.), the cavity group delay time ".tau..sub.d " may be calculated in accordance with the following formula (6): EQU .tau..sub.d (.omega.)=d.phi.(.omega.)/d.omega. (6)
As a consequence, the above-described formula (5) corresponds to the basic formula which expresses the principle to measure the cavity dispersion characteristic according to the second conventional measuring method.
As the method for measuring difference with a the optical path lengths with a high precision, the measuring method using a monochromatic laser light source 31 with linearly polarized light as the reference light source. In FIG. 2, the laser light beam emitted from the monochromatic laser light source 31 is reflected on a reflecting mirror 32 toward the cube beam splitter 22, and is divided into the first and second light beams by the cube beam splitter 22. The first divided light beam is propagated toward the fixed mirror 23 to be reflected thereon, and then the reflected first light beam is returned to the cube beam splitter 22. On the other hand, the second divided light beam is propagated toward the scanning mirror 24. This second divided light beam passes a 1/8 wave plate 33 placed between the cube beam splitter 22 and the scanning mirror 24, and then is reflected by the scanning mirror 24, and thereafter passes through the 1/8 wave plate 33 to the reverse direction. As a result of this twice propagation by the laser light beam, an equivalent effect may be achieved in which the laser light beam has passed through the 1/4 wave plate, so that the linearly polarized light is converted into the circularly polarized light.
The linearly polarized light emitted from the monochromatic laser light source 31 is incident upon the Michelson interferometer. A He--Ne laser whose oscillation waveform is 632.8 nm is used as the monochromatic laser light source 31. The laser light derived from this monochromatic laser light source 31 is linearly polarized light having such a polarization plane inclined at 45 degrees with respect to the paper plane of FIG. 2. This linearly polarized light is divided by the cube beam splitter 22. One divided beam of this linearly polarized light beam is reflected by the fixed mirror 23, and then is returned to the cube beam splitter 22. The other divided beam of this linearly polarized light beam is reflected by the scanning mirror 24, and converted into the circularly polarized light beam, as previously explained, and thereafter returned to the cube beam splitter 22. Thus, two light beams which have returned to the cube beam splitter 22 are superimposed with each other, and the superimposed light beam forms the interference light. The interference light having the wave length of 632.8 nm from the Michelson interferometer is incident upon a polarizing beam splitter 35 via a reflecting mirror 34 to be separated into both a polarization component located perpendicular to the paper plane of FIG. 2 and a polarization component parallel to this paper plane. The light intensity of the respective polarization components is converted into a voltage value by the respective photodetectors 36 and 37. These two interference voltage signals have phases mutually different from each other by 90 degrees, and are input into a trigger signal generator 38. From the trigger signal generator 38, a voltage pulse is generated as the trigger signal in response to the two voltage signals every time the difference L in the optical path lengths is varied by a half of the waved length of 632.8 nm, namely 316.4 nm. In response to this trigger signal, the waveform memory 26 sequentially stores therein the output voltage values of the photodetector 25 when this voltage pulse (trigger signal) is produced. A series of voltage signals sequentially stored in the waveform memory 26, namely the interference signals are read by the computer 27 to be processed by the Fourier transformation.
However, the above-explained conventional cavity dispersion measuring methods bear the below-mentioned problems:
As the first problem of the first conventional dispersion measuring method, there is such a problem that the laser cavity under measurement is excited by the continuous exciting apparatus, under which the pulsed oscillation must be established. Such a requirement is not always satisfied by the various sorts of laser apparatuses.
As the method for realizing the pulsed oscillation in the laser, at least three pulse oscillation modes may be conceived, i.e., the forced mode-locking, the hybrid mode-locking, and the passive mode-locking. In both the forced mode-locking and the hybrid mode-locking, either the modulation signal or the excitation pulse is externally applied whose time interval is equal to the round-trip time of the laser cavity. In this case, the repetition period of the produced pulsed oscillation is always, the precisely, equal to the period of signal which is externally applied, and does not depend upon the oscillation wavelength. As a result, with regard to either the forced mode-lock type laser cavity, or the hybrid mode-lock type laser cavity, the dispersion measurement cannot be carried out with the conventional cavity dispersion measuring method.
As the second problem of the first conventional measuring method, the laser cavity under measurement must employ the wavelength selecting element for controlling the oscillation wavelength.
In general, the laser oscillation occurs at a constant wavelength determined by such a combination between the wavelength-dependent gain for the laser medium, and the wavelength dependent loss in the cavity. The dispersion characteristic of the cavity under measurement is the amount involving the wavelength derivative of the repetition frequency. Accordingly, the measurement should be necessarily carried out for the repetition frequencies under at least two different lasing wavelengths. Therefore, the lasing wavelengths must be forcedly changed by employing the wavelength selecting element within the cavity.
As is known in the art, the wavelength dependent gain is varied by such operating conditions as the excitation intensity, or the temperature in a certain sort of laser medium, for instance, a semiconductor. It might be conceived that the lasing wavelength is varied by changing these conditions. However, since such a change in the operating condition of the laser medium would inevitably cause a change in the dispersion characteristic of this laser medium, it is not allowable to change the operating condition thereof. This is because the cavity dispersion characteristic under constant operating condition is the subject of the measurement. As a consequence, the wavelength selecting element must be provided within the laser cavity under measurement. Moreover, for the purpose of this measurement, it is required to employ such a wavelength selecting element having a negligible change in the dispersion characteristic of this element accompanying the wavelength selection operation.
Hence, since the wavelength selecting element employed in the cavity will more or less induce an expansion of the width of the generated pulse in the ultrashort pulse laser, such a wavelength selecting element is not often utilized. In this case, it is inconvenient to temporarily install such a wavelength selecting element in order only to perform the measurement of the cavity dispersion. Moreover, to obtain dispersion of the original cavity under such a normal state without the wavelength selecting element, the dispersion characteristic of this wavelength selecting element must be measured using the dispersion measuring method for the individual elements. In addition, for example, in individual case of the monolithic mode-lock type semiconductor laser, it is inherently impossible to additionally employ such a wavelength selecting element within a cavity after this laser has been manufactured.
The above-explained first and second problems of the conventional dispersion measuring methods restrict the subject to be measured. In addition to this subject limitation, the response time of the photodetector employed in the first conventional measuring method must be sufficiently fast compared the round-trip time of the cavity. This requirement may be easily satisfied with the commercially available PIN photodetector when the length of the laser cavity is long, e.g., 1.5 m, namely the round-trip time of the cavity is in the order of 10 nanoseconds. Actually, the dispersion measurement is carried out on such a long cavity laser as described in the above-mentioned publications. However, in case of such a short cavity laser as a semiconductor laser having a cavity length of approximately 300 micrometers, the round-trip time of the cavity is rather short, e.g., approximately 7 picoseconds. Here, there is no commercially available photodetector capable of responding to the above short round-trip time of the cavity. As a result, the dispersion measurement could not be carried out by the first conventional method with respect to such a short cavity laser. A similar highspeed response characteristic is required to the frequency counter placed after the photodetector. As a result, the dispersion measurement for the short cavity laser is practically difficult by the first conventional dispersion measuring method.
As a consequence, the first conventional dispersion measuring method strictly requires the following two conditions as to the laser cavities to be measured:
(1) The pulse oscillation is established under the continuous excitation. PA1 (2) The oscillation wavelength of the laser is controlled by such a wavelength selecting element having a very small variation in the dispersion characteristic thereof.
Accordingly, only limited sort of laser cavities can be measured. Moreover, since both the photodetector and the frequency counter under use must be sufficiently responding to the round-trip time of the cavity, it is practically difficult to measure the cavity dispersion characteristic of a short cavity laser. These problems of the first conventional measuring method are in principle solved by the second conventional measuring method. That is, the laser cavity under measurement is excited under the oscillation threshold value and no laser oscillation occurs in this second conventional dispersion measuring method, so that the above-described problems such as limitations in the oscillation mode and selectivities of the oscillation wavelength can be solved.
Furthermore, in the second conventional measuring method, the interferometer is utilized, and then the time axis can be produced with a high precision based on the relative difference in the optical path lengths between the two arms of this interferometer, namely the difference in the delay times. The measuring precision of the optical path length difference reaches 1 micrometer even in a simple measuring system, and several nm when the interferometric ranging method is utilized. This length precision corresponds to 3 to 0.02 femtoseconds with respect to the precision of the delay time difference. Equivalent time resolution may be determined by this delay time precision. There is completely no relationship between this time resolution and the response time of the photodetector used for receiving the light emitted from the interferometer. As a result, however short cavities are employed, the dispersion characteristics thereof could be measured. Therefore, above limitation caused by the response time of the photodetector and the electronic circuit can also be solved with the second conventional measuring method.
However, the second conventional measuring method owes to an assumption that the optical length of the laser cavity under measurement is kept constant. When the optical length of the laser cavity under measurement would be varied during the dispersion measurement, even if the relative difference in the optical path lengths of the measuring interferometer has been calibrated with a high precision, the result indicated in the above formula (4) could not be obtained after the detected interference signal is Fourier-transformed. This is because the relative difference in the optical path lengths concerning the formula (4) is defined relative to the optical path length of the laser cavity under measurement. As a consequence, the variation in the optical lengths of the laser cavity under measurement is equal to errors in the relative optical path length difference.
Assume now that the light velocity is "c", and the interference signal is acquired every an interval "c.DELTA..tau." of the relative optical path length difference of the interferometer. At this time, the results of the Fourier transformation are decomposed into the Fourier components from ".omega.=0" to ".omega.=.pi./.DELTA..tau." in accordance with the well known sampling theorem. The upper end .omega..sub.NYQ of this angular frequency expressed in the components corresponds to the well known Nyquist frequency expressed as the angular frequency. This upper end .omega..sub.NYQ must be selected to be larger than the light angular frequency .omega..sub.L =2.pi.C/.lambda..sub.L corresponding to the short wavelength end .lambda..sub.L of the fluorescent light emitted from the laser cavity under measurement. That is to say, .omega..sub.NYQ &gt;.lambda..sub.L. This requirement is provided so as to prevent aliasing accompanying the Fourier transformation of the discrete data. This aliasing is that, when the original signal contains the high-frequency components over the Nyquist frequency, the high-frequency components is folded over the low-frequency components under the Nyquist frequency. Regarding the interval c.DELTA.T of the optical path length difference, this condition is converted into the following condition of the formula (7) is derived: EQU C.DELTA..tau.&lt;.lambda..sub.L /2 (7)
As understood from this formula (7), when the short waveform edge of the fluorescent light emitted form the laser cavity under measurement is, for instance, 800 nm, the interference signal must be measured with a step of the optical path length difference shorter than at least 400 nm. To achieve such a fine step, it is necessarily required to calibrate the relative difference in the optical path lengths with a precision of at least several nm.
As previously described, since the variation in the optical lengths of the laser cavity under measurement is equivalent to the variation in the relative optical path lengths, this variation in the optical lengths of the laser cavity under 24 measurement must be maintained at most approximately several tens nm.
For instance, as to a semiconductor having an cavity lengths of approximately 300 micrometers, the optical length of the laser cavity is about 2 mm, and then variations of 150 nm occur in the optical length in connection with a temperature change of 1 degree Centigrade in this semiconductor laser. As a consequence, in order that this variation in the optical lengths is suppressed to the allowable 1 value of the second conventional measuring method, the temperature control with the order of 0.1 degree must be carried out. Such a temperature control may be readily achieved using the recent temperature control technique, so that dispersion of the semiconductor laser cavity having the element length of 300 micrometers is actually measured using the second conventional measuring method.
Here, the allowable width of the temperature variation is inversely proportional to the optical length of the cavity. As a consequence, even in the same semiconductor lasers, in case of such a semiconductor laser as a monolithic mode-lock semiconductor laser having the typical cavity length of 3 mm, the required temperature control becomes on the order of 0.01 degree. To achieve such a high precision temperature control, high-cost temperature controlling apparatuses are required. Consequently, the cavity dispersion of the monolithic mode-lock semiconductor laser cannot be readily measured with this measuring method.
These semiconductor lasers are solid-state devices, and the variations in the cavity optical lengths of these monolithic lasers are rather small. In the typical laser cavity built by surrounding a laser medium with optical components such as mirrors, light is propagated in air in more than half of an optical path inside this cavity. Here, an air flow cannot be avoided by which the variation in the cavity optical lengths is induced. The mechanism for holding such optical components as the mirrors is ceaselessly vibrating because of the ambient vibrations. As a result, these vibrations are propagated to the respective components employed in the cavity , and therefore the optical length of the cavity will be changed. The experimental variation value in the cavity optical lengths of the usual laser cavities is on the order of 500 nm, which does not depend upon the lengths of the cavities. This implies that the major portion of the variations in the cavity optical lengths is induced by the vibrations of the mirrors located at the outer peripheral of the laser cavity. This variation in the cavity optical lengths exceeds the allowable value for the second conventional measuring method. As a result, the usual laser cavities cannot be measured with the second conventional measuring method.
As described above, the second conventional measuring method requires such a condition that the variation in the optical lengths of the laser cavity under measurement should be very small. Therefore, the laser cavity to which the second conventional measuring method is applicable is practically limited to, a semiconductor laser cavity having a short cavity length.
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