Problem; Problem. 2. There is a broad range of materials that can be cut with a laser: wood, plastic, cardboard, textile... Laser cutting works by directing the output of a high-power laser through optics. << Suppose when two photons each of amplitude are in phase with other, then young’s principle of superposition, the resultant amplitude of two photons is 2 and the intensity is 4 . 2. are the pump frequency and the laser frequency respectively. and This is because of coherence and directionality of laser. 1. What is the radius of the beam at the waist (considering the waist and the laser are in the same plane)? Determine the value of the gain needed in the amplifying medium to obtain laser oscillation. Solution. Typically, lasers are thought of as emitting li… I have to say that after reading all kinds of flower problems and solutions, I feel a lot of knowledge. endobj xڝ�wTT��Ͻwz��0�z�.0��. stream Calculate the gap in frequency between two longitudinal modes in a linear cavity whose optic length, L, =300 mm. g� �����oc�n/�~ X�'a�ؠ���ӗ������S%%r^{) 9=r9�6D�O�.9�O��b_'>o�8��N]ݯ����ܔ�� ��ٞ���9oUW��^� ������,(X0*������`���t7f�7��[ h���m�n\$v���^�>Ǒ��r�~�Kc�}�8~�ε�t�5������� H[��F*�����!��g��i�B�����σKm�|(-�L�Yf�JN��r��tf!����L��F߅h&"��>Ňn�_�I�B� �? The laser gain medium are organic dyes in solution of ethyl, methyl alcohol, glycerol or water. << /N 3 If the laser is 400 micrometer long and n= 3.6, how many modes will be excited in the this laser? Please answer the following questions: Question. �=��&�[�L�B�F��;���la��]�B�i3֏��9!�hcYD�ٿ�6��Ю�5H��6����h ֢�-6���6{a�S��0QS�8�)���q��*<5I��� �[������5)T��>\�h) ������1�7�M��Q����/��ɹxr΅�6��c���[�����"�@���Q���s� �zhQp�,Lr0u����bC�"Z���ɪMJ���3���bC��AP!�z"�n��OMT-ݭ�%��3 The peak power is the energy of the pulse divided by its duration: 2. The average output power is determined by saying that for one period (T=1/10kHz), one pulse is emitted so, Informations sur le cours (ouvrir dans une nouvelle fenêtre). k�q��A����@���X ��9Z�QX{�;��VL۲l4�c�β�dY�@�섌fڕ�=�n9n)��� �YjEw��/�z��NRJ�\��Һ]�~Sb�J\)��Ɂ-o��ep�T&���λ�yqS��U��w��po�{�{�y�Ut}��ڦ�\���QT{�;���ie���ؾ-�E�8�=���VɱT�9�]�ĕ�=�n�~�T\$F���-�Z\$����}}�������a羳���H�Dˆ��ڑ������5/9�K�䥐�" �w�՞^�t!YCW�RHʎ�pձ�W��m����Avxӱg��@`�U��Ƒ�9��> �ZQ9�5ջ�V���j3�C��V.D>�Qwo��C>�1�j��9N|ަ[=��[�Ih��d���a�v��E���l9ɳջ,VRv����6��>�3���`�Zq����5V�Hi9�l�p����W��:�"'���8��>Z��l�GW +�;�� ڡ���r����l]N�˪a%i/�6=�g x��͎� ��} Question. If they are out of phase this must be due to the polarization of the material. CO2 has a bandwidth equal to The maximum output power is defined by A helium-neon laser emitting at 633 nm makes a spot with a radius equal to 100 mm at 1/e2 at a distance of 500 m from the laser. The energy (E) is therefore found from. Chapter 1 is devoted to the methods of Mathematical physics and covers such topics which are relevant to subsequent chapters. After finishing, Eason is here to share. If nothing is done, the laser is unlikely to oscillate. In the worst case, the central frequency of CO2 is situated exactly in the middle of the two longitudinal modes. t��܊�ͦ���?��DKN����,P#0��I�#EJ���d&M?3��O*�������?��|�>|4Xb�^�S2*���6��~{�ڡ�^��h �l��t�������gj9�YZL��O�,m��/������/?O�*����A��sGw�y�:\$���a Y;�\$�\��"�ǀ�gp�|�M(I���#�O�l�ZyG*\$�SU!�bh�dEX GL�����sVt��qJ*yd�Q�HwT �=[�\4b���OlI� where k is a large integer. 72 0 obj 1. If the cavity is moved by dL, the frequency will change by dî where A Q-switched laser emits pulses of 10µJ of duration 1 ns. /Length 2594 The amplifying medium of a helium-neon laser has an amplification spectral band equal to Today’s theme is the high-frequency word in laser cutting-carbon steel. endstream The optic length of the cavity, L, is 1 m. The gap between two pulses from a mode-locked laser is defined by 2L/c. No book on problems can claim to exhaust the variety in the limited space. They direct the laser beam generated on a small zone of the material. The repetition rate of the pulses is equal to 10 kHz. /Length 1491 The period between each pulse is equal to, During this period, only one pulse is emitted. stream %���� at 633 nm. For simplicity, the spectral profile is assumed to be rectangular. /Length 810 The laser cutting speed is too fast, and the linear velocity needs to be reduced. The solution for non … Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses. ��3�������R� `̊j��[�~ :� w���! The wavelength of ytterbium is 1030 nm. . ^ S��S�r�Ԯ�۶�U=\$��^�������6�i���\�h�3���ǈ���?% If G is the gain and R the reflection coefficient of the mirrors, then The calculation is the same as for the previous question: this time N=0.33! A laser is a device that emits light (electromagnetic radiation) through a process called stimulated emission. Electromagnetic waves are related. << /Filter/FlateDecode Laser light is highly intense than the convectional light. Calculate the peak power of the pulses. /Filter/FlateDecode Problems and solutions Session 1. The gap between two consecutive longitudinal modes is defined by c/2L where stream Calculate the average output power of the laser. The length of the cavity is equal to 1 m. 1. If from t =32.2 /cm , show the region where lasing takes place. Qf� �Ml��@DE�����H��b!(�`HPb0���dF�J|yy����ǽ��g�s��{��. �tq�X)I)B>==���� �ȉ��9. An one milliwatt He-Ne laser is highly intense than the sun intensity. There are no other energy levels nearby. >> ��OU�S1z6��wM�,��7���](�i�yJӲ�i�w6�+�*���&��羸�+-B[��Y�`���1ΗrF��6?�%А᫕�@L��ra�3� |��� La�]��yW�����bX���`���3� By considering the energy of the ground state to be zero and calling 0 the ground state and 1 the lower energy level: Thus 38% of the population is in the lower energy level. A helium-neon laser emitting at 633 nm makes a spot with a radius equal to 100 mm at 1/e2 at a distance of 500 m from the laser. x��Z͎�6��)��J�~�� Calculate the energy of each pulse. ����rh�c��6��Ĩo�jl�4��n����;�]`��!��bH�g�ȳD�t��zo���KP�c�r2��y��i5�7�ނBV4��Lko)Q����H��җ����ܳ#8Jv�B=�kv�]�q ~�iH�����}P?�م��.M 峩�b�Q,�J��[email protected] when laser oscillation occurs. %PDF-1.5 Solution of Problem 4.12 Problem 4.13 A laser emitting at 0=850nm has a gain spectral width of = 32 nm and a peak gain of g(0) 50/cm , Plot g() equation 4.41. /Filter/FlateDecode endstream TYPES OF LASERS 301 570-640 nm (rhodamine 6G) and many others. By taking into account the different wavelengths, the power is equal to. . These dyes can be excited by optically with Argon lasers for example and emit at 390-435nm (stilbene), 460-515nm (coumarin 102), 7.3. ��� k��p�N����+�.��sKq������qV�CX|�m��Y�8���fɞ��^=�s�E\� The term "laser" is an acronym for Light Amplification by Stimulated Emission of Radiation. �jN�jWma��]-`ȏl�D?��[email protected];��&�%�/}vIh�\��ņv�CD�N����湣-�|u_��2��u\d��i��7� �N�� Thus, the gap separating the end of the spectral band from the closest longitudinal mode is equal to: The frequency of a mode can be expressed by: E�����z6��Cf.�+So�f���(�Q�g�)��L�7���F��c��?��3�*P�#wR���x��`�_����P�䮤��C�lJ���O��`�����)�@�_�'*�:�%&z���3X]P�߀S��a�8 Calculate the number of longitudinal modes that can oscillate in this cavity. If an external electric ﬁeld is applied to a dielectric (not conduct- ing) material the material will be polarized, resulting in a polarization P. The relation is then, E = D "0 P "0) D = "0E +P If P = 0, as in vacuum, E and D are in phase. >> A ring laser cavity is composed of 4 identical mirrors with a reflection coefficient equal to 0.99. 2. \$E}k���yh�y�Rm��333��������:� }�=#�v����ʉe The linear cavity is 30 cm long. At what distance must the cavity mirror be placed so that at least one of the modes falls in the amplification band? Consider a lower energy level situated 200 cm-1 from the ground state. For simplicity, the spectral profile is assumed to be rectangular. )ɩL^6 �g�,qm�"[�Z[Z��~Q����7%��"� What is the rate of repetition of the pulses emitted by a mode-locked laser? >> In a ring lasercavity, the beam passes through the medium only once each turn. It is also widely used in industrial production and processing. 69 0 obj , where endobj \$O./� �'�z8�W�Gб� x�� 0Y驾A��@\$/7z�� ���H��e��O���OҬT� �_��lN:K��"N����3"��\$�F��/JP�rb�[䥟}�Q��d[��S��l1��x{��#b�G�\N��o�X3I���[ql2�� �\$�8�x����t�r p��/8�p��C���f�q��.K�njm͠{r2�8��?�����.